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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 1278089, 68767]*) (*NotebookOutlinePosition[ 1279318, 68808]*) (* CellTagsIndexPosition[ 1279149, 68800]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Calculation of spatial distributions of emission in CH4-Ar mixtures.\ \>", "Subtitle"], Cell["\<\ This version has been converted from cross sections to reaction coefficients \ for describing the electron behavior. The critical approximation used here is that the electron transport and \ ionization coefficients are independent of the CH4/Ar ratio for E/n > 500 Td. \ See Figs. 2 and 3 of de Urquijo et al, J. Phys. D 32, 1646 (1999).\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Setup notebook enviroment ", "SmallText", PageWidth->Infinity], Cell[BoxData[ \(\(a = 1;\)\)], "Input"], Cell[BoxData[ \(\(\(ClearAll["\"];\)\(\ \)\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(\(\(Remove["\"];\)\(\ \)\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(\(startclock\ = \ SessionTime[];\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(\(Off[General::spell];\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(\(Off[General::spell1];\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(Needs["\"]\)], "Input", PageWidth->Infinity, Evaluatable->True] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SetDirectory["\"]\)], "Input"], Cell[BoxData[ \("c:\\allprojects\\methane"\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(now\ = \ StringForm["\<``/``/`` ``:``:``\>", \(Date[]\)[\([2]\)], \ \(Date[]\)[\([3]\)], \(Date[]\)[\([1]\)], \(Date[]\)[\([4]\)], \ \(Date[]\)[\([5]\)], \(Date[]\)[\([6]\)]]\)], "Input"], Cell[BoxData[ InterpretationBox["\<\"\\!\\(5\\)/\\!\\(14\\)/\\!\\(2001\\) \ \\!\\(21\\):\\!\\(56\\):\\!\\(5\\)\"\>", StringForm[ "``/``/`` ``:``:``", 5, 14, 2001, 21, 56, 5], Editable->False]], "Output"] }, Open ]], Cell["\<\ Symbols for species and data types used in coefficients: 1 - CH+, 2 - CH2+, 3 - CH3+, 4 - CH4+, 5 - CH5+, 6 - Ar+, 7 - ArH+, 8 - H+, 9 - fast CH, 0 - C2H5+, o - neutrals other than fast CH F - fast CH3 c - CH4, a - Ar, e - electron, I - total ionization q - cross section, a - spatial reaction coefficient, m - metastable, w - drift energy, u - total energy\ \>", "SmallText", PageWidth->Infinity, Evaluatable->False, ShowSpecialCharacters->False], Cell[BoxData[ \(\(\(\ \)\(plotColors\ = \ {\[IndentingNewLine]{Hue[0.0], Thickness[0.007], Dashing[{}]}, \[IndentingNewLine]{Hue[0.1], Thickness[0.007], Dashing[{}]}, \[IndentingNewLine]{Hue[0.3], Thickness[0.007], Dashing[{}]}, \[IndentingNewLine]{Hue[0.5], Thickness[0.007], Dashing[{}]}, \[IndentingNewLine]{Hue[0.7], Thickness[0.007], Dashing[{}]}, \[IndentingNewLine]{Hue[0.8], Thickness[0.007], Dashing[{}]}, \[IndentingNewLine]{Thickness[0.007], Dashing[{}]}, \[IndentingNewLine]{Hue[0.0], Thickness[0.007], Dashing[{0.05, 0.05}]}, \[IndentingNewLine]{Hue[0.1], Thickness[0.007], Dashing[{0.05, 0.05}]}, {Hue[0.3], Thickness[0.007], Dashing[{0.05, 0.05}]}, \[IndentingNewLine]{Hue[0.5], Thickness[0.007], Dashing[{0.05, 0.05}]}, \[IndentingNewLine]{Hue[0.7], Thickness[0.007], Dashing[{0.05, 0.05}]}, \[IndentingNewLine]{Hue[0.8], Thickness[0.007], Dashing[{0.05, 0.05}]}, \[IndentingNewLine]{Thickness[0.007], Dashing[{0.02, 0.02}]}};\)\)\)], "Input"], Cell[CellGroupData[{ Cell["Input cross sections and spatial reaction coefficients", "Section"], Cell["In this model we negelect heavy particle ionization.", "SmallText"], Cell["\<\ The red equation means that the cross section is just a guess.\ \>", "Subsubtitle", FontColor->RGBColor[1, 0, 0]], Cell["\<\ The magenta equation means that the cross section is from experiment for at \ least part of the energy range.\ \>", "Subsubtitle", FontColor->RGBColor[1, 0, 1], Background->None] }, Open ]], Cell["Adjustable model parameters", "Subsection", Background->RGBColor[0, 1, 1]], Cell[TextData[{ "Scale factors for heavy particle collisions. Note that at high f the \ program works properly only when", StyleBox[" fa4c8o = 0 or k -> 0.", FontColor->RGBColor[1, 0, 0]] }], "Text"], Cell["\<\ Model using momentum balance. This model leads to lower ion energies.\ \>", "Text"], Cell[BoxData[{\(falphai\ = \ 1. ; faec1o = 1. ; faec2o = \ 1. ; faec3o = 1. ; faec4o = 1. ; faea6o = 1. ;\), "\[IndentingNewLine]", RowBox[{\(fl1cn\ = \ 1. ; fa1c0o = 1. ; fa1c3o = 1. ; fa1c49 = 1. ; fa1c4p = 1. ;\), " ", \( (*CH + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl2cn\ = \ 1. ; fa2c0o = 1. ; fa2c1o = 1. ; fa2c4p = 1. ; \ \ fa2c94\ = \ 1;\), \( (*CH2 + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl3cn\ = \ 1. ; fa3c0o\ = \ 1. ; fa3c4F = 1. ; fa3c1o = 1. ; fa3c4p = 1. ; \ fa3c94\ = \ 1;\), \( (*CH3 + \(-CH4\)\ data*) \)}], "\n", StyleBox[\(\(fl4cn\ = \ 1. ; fa4c4o = 1. ; fa4c5o = 1. ; fa4c3o = 1.0;\)\(\ \)\( (*CH4 + \(-CH4\)\ data*) \)\), FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", StyleBox[\(\(fa4c1o\ = \ 1. ; \ fa4c8o\ = \ 1. ; \ fa4a8o = \ 1. ; a4c0o = 0;\)\(\ \ \)\( (*CH4 + \(-CH4\)\ data*) \)\), FontColor->RGBColor[1, 0, 0]], "\n", RowBox[{\(fl5cn\ = \ 1. ; fa5c3o = 0.1; fa5c4o = 0.1\ ;\), " ", \( \ (*CH5 + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl6cn\ = \ 1. ; fa6c3o\ = 1. ; fa6c2o\ = 1. ;\), " ", \( (*Ar \ + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl7cn\ = \ 1. ; fa7c3o\ = \ 1. ; \ fa7c5o\ = \ 1. ;\), " ", \( (*ArH + \ \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl8cn\ = \ 1. ; fa8c8p = 1. ;\), " \ ", \( (*H + \(+CH4\)\ data*) \)}], "\n", RowBox[{\(fl9cn\ = \ 1. ; fa9coc\ = \ 1. ; fa9cpc\ = 1. ;\), " ", \( (*fast\ CH \ + CH4\ data*) \)}], "\n", \(fl0cn\ = \ 1. ; fa0c5o\ = \ 0; fa0c1o = 0; fa0c3o = 0; fa0c4o = 0; fa0c8o = 0;\), "\[IndentingNewLine]", RowBox[{" ", \(a0c0c = 0;\), " ", \( (*C2H5 + \(-CH4\)\ data*) \)}], "\ \[IndentingNewLine]", RowBox[{\(faFcoc\ = \ 1. ; \ faFc9c\ = \ 1. ; \ faFcpc\ = \ 1. ;\), " ", \( (*fast\ CH3\ + CH4*) \)}], "\n", \(faea6o = 1. ;\), "\[IndentingNewLine]", RowBox[{\(fl1an\ = \ 1. ; fa1a59\ = \ 1. ; fa1a6p\ = \ 1. ; fa1a69 = 1;\), " ", \( (*CH + \(-Ar\)\ data*) \)}], "\n", RowBox[{\(fl2an\ = \ 1. ;\), " \ ", \( (*CH2 + \(-Ar\)\ data*) \)}], "\n", RowBox[{\(fl3an\ = \ 1. ; fa3a6F\ = \ 1. ; fa3a1o = 1. ; fa3a6p = 1. ; \ fa3a96\ = 1;\), " ", \( (*CH3 + \(-Ar\)\ data*) \)}], "\n", RowBox[{\(fl4an\ = \ 1. ; fa4a6o\ = \ 1. ; fa4a7o = 1. ;\), " ", \( (*CH4 + \ \(-Ar\)\ data*) \)}], "\n", RowBox[{\(fl5an\ = \ 1. ; \ fa5a3a\ = \ 1;\), " \ ", \( (*CH5 + \(-Ar\)\ data*) \)}], "\n", RowBox[{\(fl6an\ = \ 1. ; fa6a6a = 4. ;\), " \ ", \( (*Ar + \(+Ar\)\ data*) \)}], "\n", RowBox[{\(fl7an\ = \ 1. ; fa7a6a = 1. ; fa7a8a = 1. ;\), " ", \( \ (*ArH + \(+Ar\)\ data*) \)}], "\n", RowBox[{\(fl8an\ = \ 1. ; fa8a6o\ = \ 1. ;\), " \ ", \( (*H + \(+Ar\)\ data*) \)}], "\[IndentingNewLine]", RowBox[{\(fl9an\ = \ 1. ; fa9aoa = 1. ; fa9apa = 1;\), " ", \( \ (*fast\ CH - Ar\ data*) \)}], "\n", RowBox[{\(fl0an\ = \ 1. ; a0a1o\ = 10^\(-30\); \ a0a3o = 0; \ a0a4o = 0; a0a6o = 0; \ a0a7o = 0; a0a8o = 0;\), \( (*C2H5 + \(-Ar\)\ data*) \)}], "\[IndentingNewLine]", RowBox[{\(faFaoa\ = \ 1. ; \ faFa9a\ = \ 1. ; \ faFapa\ = \ 1. ;\), " ", \( (*fast\ CH3\ + Ar*) \)}], "\n", \(balance\ := \ "\";\)}], "Input"], Cell["\<\ Model using energy balance. This model leads to higher energies.\ \>", "Text"], Cell[BoxData[{\(falphai = 1. ; faec1o = 1. ; faec2o = \ 1. ; faec3o = 1. ; faec4o = 1. ; faea6o = 1. ;\), "\[IndentingNewLine]", RowBox[{\(fl1cn\ = \ 13. *16. /\((13. + 16. )\)^2; fa1c0o = 1. ; fa1c3o = 1. ; fa1c49 = 1. ; fa1c4p = 1. ;\), " ", \( (*CH + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl2cn\ = \ 14. *16. /\((14. + 16. )\)^2; fa2c0o = 1. ;\), " \ ", \( (*CH2 + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl3cn\ = \ 15. *16. /\((15. + 16. )\)^2; fa3c0o\ = \ 1. ; fa3c4F = 1. ; fa3c1o = 1. ; fa3c4p = 1. ; \ \ fa3c94\ = \ 1;\), " \ ", \( (*CH3 \ + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl4cn\ = \ 1. ; fa4c4o = 1. ; fa4c5o = 1. ; fa4c3o = 1.0;\), " ", \( (*CH4 + \ \(-CH4\)\ data*) \)}], "\[IndentingNewLine]", RowBox[{\(fa4c1o\ = \ 1. ; \ fa4c8o\ = \ 1. ; \ fa4a8o = \ 1. ; a4c0o = 0;\), StyleBox[" ", FontColor->GrayLevel[0]], \( (*CH4 + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl5cn\ = \ 17. *16. /\((17. + 16. )\)^2; fa5c3o = 0.001; fa5c4o = 0.001;\), " ", \( \ (*CH5 + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl6cn\ = \ 40. *16. /\((40. + 16. )\)^2; fa6c3o\ = 1. ; \ fa6c2o\ = 1. ;\), " ", \( (*Ar + \ \(-CH4\)\ data*) \)}], "\n", RowBox[{\(fl7cn\ = \ 41. *16. /\((41. + 16. )\)^2; \ fa7c3o\ = \ 1. ; \ fa7c5o\ = \ 1. ;\), " ", \( (*ArH + \(-CH4\)\ \ data*) \)}], "\n", RowBox[{\(fl8cn\ = \ 1. *16. /\((1. + 16. )\)^2; fa8c8p = 1. ;\), " \ ", \( (*H + \(+CH4\)\ data*) \)}], "\n", RowBox[{\(fl9cn\ = \ 13. *16. /\((13. + 16. )\)^2; fa9coc\ = \ 1. ; fa9cpc\ = 1. ;\), " ", \( (*fast\ CH \ + \ \(-CH4\)\ data*) \)}], "\n", \(fl0cn\ = \ 29. *16. /\((29. + 16. )\)^2; fa0c5o\ = \ 0; fa0c1o = 0; fa0c3o = 0; fa0c4o = 0; fa0c8o = 0;\), "\[IndentingNewLine]", RowBox[{" ", \(a0c0c = 0;\), " ", \( (*C2H5 + \(-CH4\)\ data*) \)}], "\n", RowBox[{\(faFcoc\ = \ 1. ; \ faFc9c\ = \ 1. ; \ faFcpc\ = \ 1. ;\), " \ ", \( (*fast\ CH3\ + CH4*) \)}], "\n", \(faea6o = 1. ;\), "\[IndentingNewLine]", RowBox[{\(fl1an\ = \ 13. *40. /\((13. + 40. )\)^2; fa1a59\ = \ 1. ; fa1a6p\ = \ 1. ; fa1a69 = 1;\), " ", \( (*CH + \(-Ar\)\ data*) \)}], "\n", RowBox[{\(fl2an\ = \ 14. *40. /\((14. + 40. )\)^2;\), " \ ", \( (*CH2 + \(-Ar\)\ data*) \)}], \ "\n", RowBox[{\(fl3an\ = \ 15. *40. /\((15. + 40. )\)^2; fa3a6F\ = \ 1. ; fa3a1o = 1. ; fa3a6p = 1. ; \ fa3a96\ = 1;\), " ", \( (*CH3 + \(-Ar\)\ data*) \)}], "\n", RowBox[{\(fl4an\ = \ 16. *40. /\((16. + 40. )\)^2; fa4a6o\ = \ 1. ; fa4a7o = 1. ;\), " ", \( (*CH4 + \ \(-Ar\)\ data*) \)}], "\n", RowBox[{\(fl5an\ = \ 17. *40. /\((17. + 40. )\)^2; \ fa5a3a\ = \ 1;\), " \ ", \( (*CH5 + \(-Ar\)\ data*) \)}], "\n", RowBox[{\(fl6an\ = \ 40. *40. /\((40. + 40. )\)^2; fa6a6a = 4. ;\), " \ ", \( (*Ar + \(+Ar\)\ data*) \)}], "\n", RowBox[{\(fl7an\ = \ 41. *40. /\((41. + 40. )\)^2; fa7a6a = 1. ; fa7a8a = 1. ;\), " ", \( (*ArH \ + \(+Ar\)\ data*) \)}], "\n", RowBox[{\(fl8an\ = \ 1. *40. /\((1. + 40. )\)^2; fa8a6o\ = \ 1. ;\), " \ ", \( (*H + \(+Ar\)\ data*) \)}], "\[IndentingNewLine]", RowBox[{\(fl9an\ = \ 13. *40. /\((13. + 40. )\)^2; fa9aoa = 1. ; fa9apa = 1;\), " ", \( \ (*fast\ CH - Ar\ data*) \)}], "\n", RowBox[{\(fl0an\ = \ 29. *40. /\((29. + 40. )\)^2; a0a1o\ = 10^\(-30\); \ a0a3o = 0; \ \ \ \ \ a0a4o = 0; a0a6o = 0; \ a0a7o = 0; a0a8o = 0;\), " ", \( (*C2H5 + \(-Ar\)\ data*) \)}], "\[IndentingNewLine]", RowBox[{\(faFaoa\ = \ 1. ; \ faFa9a\ = \ 1. ; \ faFapa\ = \ 1. ;\), " \ ", \( (*fast\ CH3\ + Ar*) \)}], "\n", \(balance\ = \ "\";\)}], "Input"], Cell["\<\ The following value of fa6c3o = 0.01 reduced the CHA excitation by ~ 20% for \ 35% CH4 (case 14), but did not straighten the spatial varaition.\ \>", "Text"], Cell[BoxData[ \(\(fa6c3o\ = \ 0.01;\)\)], "Input", Evaluatable->False], Cell["\<\ The following value of fa9apa = 0.01 reduced the CHA excitation by ~ 0.01 for \ 35% CH4 (case 14), but did not straighten the spatial varaition. It \ essentially left only excitation by CH+. On the other hand, setting fa9cpc = \ 0.01 had little effect.\ \>", "Text"], Cell[BoxData[ \(\(fa9apa\ = \ 0.01;\)\)], "Input", Evaluatable->False], Cell["\<\ Setting fa3a96 = 0.01 or fa3c94 = 0.01 for 35% CH4 (case 14) had little \ effect. This means that the direct conversion of CH3+ to fast CH is not \ important in the present model. Setting fa3a1o = 0.01 or fa3c1o = 0.01 had \ little effect. Setting fa1a69 = 0.01 or 0.001 reduced the CHA emission via \ j9 by a factor of ~ 0.3, while fa1c49 = 0.01 had little effect. Setting \ fa1a6p = 0.01 reduced the CHAj1 signal as expected. The combination of \ fa1a69 = 0.001, fa3a96=0.01, and fa3c94=0.01 reduces the CHAj9 emission to \ essentially zero as expected.\ \>", "Text"], Cell[BoxData[ \(fa1a69\ = \ 0.001; fa3a96 = 0.01; fa3c94 = 0.01;\)], "Input", Evaluatable->False], Cell["The key scale factors are expected to be the following:", "Text"], Cell[BoxData[ \(fa1a69\ = \ 0.001; fa1c49\ = \ 0.001; fa3a96 = 0.001; fa3c94 = 0.001; fa1a6p\ = \ 0.001; fa1c4p\ = \ 0.001; fa6c3o\ = \ 0.001; fa9apa\ = \ 0.001;\)], "Input", Evaluatable->False], Cell["\<\ With our initial choice of cross sections fa1c4p and fa1c49 were much too \ small to be important. We have raised the initial cross sections for a1c49 \ and a1c4p by 1E5.\ \>", "Text"], Cell["\<\ Via e -> CH3+ -> CH -> CHA with Ar collisions dominant, but no ionization of \ Ar. Gives very small CHA at cathode\ \>", "Text"], Cell[BoxData[ \(fa1a69\ = \ 0.001; fa1c49\ = \ 0.001; fa3a96 = 1. ; fa3c94 = 0.001; fa1a6p\ = \ 0.001; fa3c1o\ = \ 0.001; fa3a1o\ = \ 0.001; fa1c4p\ = \ 0.001; fa6c3o\ = \ 0.001; fa9apa\ = \ 1. ; fa9cpc\ = 0.001;\)], "Input", Evaluatable->False], Cell["\<\ Via e -> CH3+ -> CH -> CHA with Ar collisions dominant and ionization of Ar. \ Gives small CHA at cathode\ \>", "Text"], Cell[BoxData[ \(fa1a69\ = \ 0.001; fa1c49\ = \ 0.001; fa3a96 = 1. ; fa3c94 = 0.001; fa3c1o\ = \ 0.001; fa3a1o\ = \ 0.001; fa1a6p\ = \ 0.001; fa1c4p\ = \ 0.001; fa6c3o\ = \ 1. ; fa9apa\ = \ 1. ; fa9cpc\ = 0.001;\)], "Input", Evaluatable->False], Cell["\<\ Via e -> CH3+ -> CH -> CHA with CH4 collisions dominant. Gives extremely \ small CHA at cathode\ \>", "Text"], Cell[BoxData[ \(fa1a69\ = \ 0.001; fa1c49\ = \ 0.001; fa3a96 = 0.001; fa3c94 = 1. ; fa1a6p\ = \ 0.001; fa3c1o\ = \ 0.001; fa3a1o\ = \ 0.001; fa1c4p\ = \ 0.001; fa6c3o\ = \ 0.001; fa9apa\ = \ 0.001; fa9cpc\ = \ 1. ;\)], "Input", Evaluatable->False], Cell["\<\ Via e -> Ar+ -> CH3+ -> CH -> CHA and e -> CH3+ -> CH -> CHA. Gives ~ 40% of \ observed CHA at cathode\ \>", "Text"], Cell[BoxData[ \(fa1a69\ = \ 0.001; fa1c49\ = \ 0.001; fa3a96 = 1. ; fa3c94 = 1. ; fa3c1o\ = \ 0.001; fa3a1o\ = \ 0.001; fa1a6p\ = \ 1. ; fa1c4p\ = \ 0.001; fa6c3o\ = \ 1. ; fa9apa\ = \ 1. ; fa9cpc\ = \ 1. ;\)], "Input"], Cell["\<\ Redo all of above without CH3+ -> CH+. Mistakenly done with CH3+ -> CH+.\ \>", "Subsubtitle"], Cell["\<\ Via e -> Ar+ -> CH3+ -> CH+ -> CH -> CHA and e -> CH3+ -> CH+ -> CH -> CHA. \ Gives ~ 30% of observed CHA at cathode\ \>", "Text"], Cell[BoxData[ \(fa1a69\ = \ 1. ; fa1c49\ = \ 1. ; fa3a96 = 0.001; fa3c94 = 0.001; fa3c1o\ = \ 1. ; fa3a1o\ = \ 1. ; fa1a6p\ = \ 1. ; fa1c4p\ = \ 0.001; fa6c3o\ = \ 1. ; fa9apa\ = \ 1. ; fa9cpc\ = \ 1. ;\)], "Input", Evaluatable->False], Cell["\<\ Via e -> Ar+ -> CH3+ -> CH+ -> CH -> CHA, e -> CH3+ -> CH+ -> CH -> CHA, e -> \ Ar+ -> CH3+ -> CH -> CHA and e -> CH3+ -> CH -> CHA.. Gives ~ 60% of \ observed CHA at cathode, but very poor shape. Here the spatial distribution \ fo the heavy particle emission show that the usable ion flux decreases before \ it gets to the cathode. Apparently this is caused by a1c4p converting CH+ to \ CH4+.\ \>", "Text", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(fa1a69\ = \ 1. ; fa1c49\ = \ 1. ; fa3a96 = 1. ; fa3c94 = 1. ; fa3c1o\ = \ 1. ; fa3a1o\ = \ 1. ; fa1a6p\ = \ 1. ; fa1c4p\ = \ 1. ; fa6c3o\ = \ 1. ; fa9apa\ = \ 1. ; fa9cpc\ = \ 1. ;\)], "Input", Evaluatable->False], Cell["\<\ Via e -> Ar+ -> CH3+ -> CH+ -> CH -> CHA, e -> CH3+ -> CH+ -> CH -> CHA, e -> \ Ar+ -> CH3+ -> CH -> CHA, e -> CH3+ -> CH -> CHA, and e -> CH3+ -> CH+ -> \ CHA. Returns a1c49 to initial low values. The heavy particle component gives \ ~ 60% of observed CHA at cathode and has a shape given by 1- exp(alphai*x). \ This shape appears to require that the CHA excitation is proportional to the \ total ion flux and that the usable ion flux is not being depleted.\ \>", "Text", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(fa1a69\ = \ 1. ; fa1c49\ = \ 0.00001; fa3a96 = 1. ; fa3c94 = 1. ; fa3c1o\ = \ 1. ; fa3a1o\ = \ 1. ; fa1a6p\ = \ 1. ; fa1c4p\ = \ 1. ; fa6c3o\ = \ 1. ; fa9apa\ = \ 1. ; fa9cpc\ = \ 1. ;\)], "Input", Evaluatable->False], Cell["\<\ Via e -> Ar+ -> CH3+ -> CH+ -> CH -> CHA, e -> CH3+ -> CH+ -> CH -> CHA, e -> \ Ar+ -> CH3+ -> CH -> CHA and e -> CH3+ -> CH -> CHA.. Returns a1c4p to \ initial values. Gives ~ 60% of observed CHA at cathode and good shape. Using \ the electron scaling factors shows that the initial formation of CH2+ and \ CH4+ contributes little to our model of excitation of CHA. The production of \ CH+ by electrons initiates about half of the calculated CHA excitation, even \ though only 3% of the ionizatin goes by that route. The production of CH3+ \ by electrons initiates ~ 10% of the calculated CHA excitation in the 35% CH4 \ mixture, although it must be larger for the high CH4 fractions. The \ production of Ar+ by electrons initiates about 40% of the CHA excitation in \ the 35% CH4 mixture, although it must be larger for the low CH4 fractions.\ \>", "Text"], Cell[BoxData[ \(faec1o\ = \ 1. ; faec2o\ = \ 1. ; faec3o\ = 1. ; faec4o\ = \ 1. ; faea6o\ = \ 1. ; falphai = 1. ; fa1a69\ = \ 1. ; fa1c49\ = \ 1. ; fa3a96 = 1. ; fa3c94 = 1. ; fa3c1o\ = \ 1. ; fa3a1o\ = \ 1. ; fa1a6p\ = \ 1. ; fa1c4p\ = \ 0.00001; fa6c3o\ = \ 1. ; fa9apa\ = \ 1. ; fa9cpc\ = \ 1. ;\)], "Input", Evaluatable->False], Cell["\<\ One way to increase the CHA production would seem to be to make better use of \ the CH3+ production. One should also be able to improve the shape by \ increasing a3c1o or a3a1o. This turns out to be the case when fa3c1o is set \ to ~ 10000 and/or fa3a1o ~ 10000. However, these values are too large so we \ reduce them. The following gives the right magnitude of the cathode peak \ versus CH4 concentration, but a peak that occurs at too low a CH4. Here the \ values of fa3c1o was reduced relative to fa3a1o in an unsuccessful attempt to \ lower the initial slope of the cathode signal versus fractional CH4. We need \ to try a different step in the chain.\ \>", "Text"], Cell[BoxData[ \(faec1o\ = \ 1. ; faec2o\ = \ 1. ; faec3o\ = 1. ; faec4o\ = \ 1. ; faea6o\ = \ 1. ; falphai = 1. ; fa1a69\ = \ 1. ; fa1c49\ = \ 1. ; fa3a96 = 1. ; fa3c94 = 1. ; fa3c1o\ = \ 1. ; fa3a1o\ = \ 3000. ; fa1a6p\ = \ 1. ; fa1c4p\ = \ 0.00001; fa6c3o\ = \ 1. ; fa9apa\ = \ 1. ; fa9cpc\ = \ 1. ;\)], "Input", Evaluatable->False], Cell[TextData[ButtonBox["Go to emission for test case", ButtonData:>"Emission for test case", ButtonStyle->"Hyperlink"]], "SmallText"], Cell["", "Text", CellTags->"Scale factors"], Cell[TextData[ButtonBox["Tabulated fluxes", ButtonData:>"Tabulated fluxes", ButtonStyle->"Hyperlink"]], "Text"], Cell["\<\ We now try to use fa1c49 and fa1a69 to lower the slope of signal versus \ fractional CH4. Lowering fa1a69 lowered the magnitude but did not shift the \ peak. Lowering fa1c49 did not change the magnitude or shift the peak much. \ Lowering fa1c49 and fa1a69 by 0.001 and raising fa1a6p lowers the magnitude \ some, gives a broad maximum, and counteracts the undesirable quardratic \ dependence on fractional Ar. I do not like raising fa1a6p because it \ conflicts with Ottinger and means CH+ emission is important. The following \ values give a kind of fit, but the negative curvature of the spatial \ dependence is larger than seems correct.\ \>", "Text"], Cell[BoxData[ \(faec1o\ = \ 1. ; faec2o\ = \ 1. ; faec3o\ = 1. ; faec4o\ = \ 1. ; faea6o\ = \ 1. ; falphai = 1. ; fa1a69\ = \ 0.7; fa1c49\ = \ 0.01; fa3a96 = 1. ; fa3c94 = 1. ; fa3c1o\ = \ 1. ; fa3a1o\ = \ 3000. ; fa1a6p\ = \ 3. ; fa1c4p\ = \ 0.00001; fa6c3o\ = \ 1. ; fa9apa\ = \ 1. ; fa9cpc\ = \ 1. ;\)], "Input"], Cell["\<\ We now try to use fa3c96 and fa3a1o to improve the shape at small [Ar]. \ These reduce the CHA magnitude. \ \>", "Text"], Cell[BoxData[ \(faec1o\ = \ 1. ; faec2o\ = \ 1. ; faec3o\ = 1. ; faec4o\ = \ 1. ; faea6o\ = \ 1. ; falphai = 1. ; fa1a69\ = \ 0.7; fa1c49\ = \ 0.01; fa3a96 = 0.001; fa3c94 = 10. ; fa3c1o\ = \ 1. ; fa3a1o\ = \ 1500. ; fa1a6p\ = \ 3. ; fa1c4p\ = \ 0.00001; fa6c3o\ = \ 1. ; fa9apa\ = \ 1. ; fa9cpc\ = \ 1. ;\)], "Input"], Cell[CellGroupData[{ Cell["electron + CH4 data and electron + Ar", "Section", PageWidth->Infinity, Evaluatable->False, ShowSpecialCharacters->False], Cell["\<\ Here we take advantage of the experimental observation that for E/n >= 500 Td \ the electron drift velocity and ionization coefficients are independent of \ the ratio of CH4 to Ar in the mixture. Because these properties are \ independent of mixture at fixed E/n, we assume that the excitation \ coefficients for Halpha and the C->X band are independent of mixture at fixed \ E/n.\ \>", "Subsubtitle"], Cell["\<\ e + CH4 -> ionization Here we use the formula given by Davies et al (1989) for E/n > 500 Td. We \ have not include the mixture fraction f here because this relation also \ applies approximately to ionization of Ar in the mixtures. See de Uqurijo et \ al (1998).\ \>", "SmallText"], Cell[BoxData[ \(\(alphai\ := \ n*falphai*\((2.51*10^\(-20\)*Exp[\(-624\)/eontd] + 7. *10^\(-20\)*Exp[\(-3500\)/eontd])\);\)\)], "Input", CellFrame->False, FontColor->RGBColor[1, 0, 1], Background->None], Cell["The ionization by the CH4 and by Ar are:", "SmallText"], Cell[BoxData[ \(\(aecie\ = \ f*alphai;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell[BoxData[ \(\(aeaie\ = \ \((1 - f)\)*alphai;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ The division among various ion fragments is assumed to be given by\ \>", "SmallText"], Cell[BoxData[ \(\(aec1o\ = \ 0.03*f*faec1o\ *alphai;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell[BoxData[ \(\(aec2o\ = \ 0.17*f*faec2o*alphai;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell[BoxData[ \(\(aec3o\ = \ 0.4*f*faec3o*alphai;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell[BoxData[ \(\(aec4o\ = \ 0.4*f*faec4o*alphai;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell[BoxData[ \(\(aea6o\ = \ \((1 - f)\)*faea6o*alphai;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ e + CH4 -> 432 nm excitation. This is a fit to Zoran's experiment in pure \ CH4 using the shape from the solution to the Boltzmann calculation.\ \>", "SmallText"], Cell[BoxData[ \(\(aecp432\ := \ f*n*\ \((6. *10^\(-22\)* Exp[\(-665. \)/eontd]/\((1 + \((eontd/3000. )\)^0.8)\) + 9. *10^\(-22\)* Exp[\(-1500\)/ eontd]/\((1 + \((eontd/ 3000. )\)^0.8)\))\);\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ e + CH4 -> Halpha excitation. This is a fit to Zoran's experiment in pure \ CH4 using the shape from the solution to the Boltzmann calculation.\ \>", "SmallText"], Cell[BoxData[ \(\(aecp656\ := \ f*n*5.5*10^\(-22\)* Exp[\(-1900. \)/eontd]/\((1 + \((eontd/8200. )\)^5)\);\)\)], "Input",\ FontColor->RGBColor[1, 0, 1]], Cell["\<\ Plot these coefficients in units of 10^-20 m^2 or 10^-16 cm^2. We note that \ the column depth for most of our data is that for 4 cm and 100 mTorr, i.e., \ 1.3*10^20 m^2, so that a process with a coefficient of 10^-20 m^2 has a near \ unit probability of occurrence in the passage an electron across the tube. \ \ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{aecie, aecp432, aecp656}, {eontd, 10. , 10000. }, \ PlotRange\ -> \ \ {{10. , 10000. }, {10^\(-4\), 10. }}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 %%ImageSize: 432 266.991 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.333333 0.333333 0.494427 0.123607 [ 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.57402 L .83574 .57426 L .83665 .57448 L .83751 .5747 L .83843 .57492 L .83931 .57514 L .84015 .57534 L .84103 .57556 L .84188 .57576 L .84278 .57598 L .84364 .57618 L .84446 .57638 L .84533 .57659 L .84616 .57678 L .84696 .57697 L .8478 .57717 L .84861 .57736 L .84946 .57755 L .85028 .57774 L .85106 .57792 L .85188 .57811 L .85267 .5783 L .85351 .57849 L .85431 .57867 L .85508 .57884 L .85589 .57902 L .85666 .5792 L .85741 .57936 L .85819 .57954 L .85895 .5797 L .85974 .57988 L .8605 .58005 L .86123 .58021 L .86201 .58038 L .86275 .58054 L .86353 .58071 L .86428 .58087 L .865 .58102 L .86576 .58118 L .86649 .58134 L .86718 .58149 L .86792 .58164 L .86863 .58179 L Mistroke .86937 .58195 L .87009 .5821 L .87078 .58224 L .8715 .58239 L .8722 .58253 L .87286 .58267 L .87357 .58282 L .87425 .58295 L .87496 .5831 L .87565 .58324 L .8763 .58337 L .877 .58351 L .87766 .58364 L .87837 .58378 L .87904 .58392 L .87969 .58405 L .88038 .58418 L .88103 .58431 L .88166 .58443 L .88233 .58456 L .88297 .58469 L .88364 .58482 L .88429 .58494 L .88491 .58506 L .88557 .58519 L .8862 .58531 L .8868 .58542 L .88744 .58555 L .88805 .58566 L .8887 .58578 L .88932 .5859 L .88992 .58601 L .89055 .58613 L .89116 .58624 L .8918 .58636 L .89241 .58647 L .893 .58658 L .89363 .5867 L .89422 .5868 L .8948 .58691 L .8954 .58702 L .89599 .58712 L .8966 .58724 L .89719 .58734 L .89776 .58744 L .89836 .58755 L .89894 .58765 L .89955 .58776 L .90013 .58786 L .90069 .58796 L Mistroke .90128 .58807 L .90185 .58816 L .9024 .58826 L .90298 .58836 L .90353 .58846 L .90412 .58856 L .90468 .58865 L .90522 .58875 L .90579 .58884 L .90634 .58894 L .90687 .58903 L .90743 .58912 L .90796 .58921 L .90853 .58931 L .90907 .5894 L .90959 .58948 L .91014 .58958 L .91067 .58966 L .91123 .58976 L .91177 .58984 L .91229 .58993 L .91283 .59002 L .91336 .5901 L .91386 .59019 L .9144 .59027 L .91491 .59036 L .91545 .59044 L .91597 .59053 L .91647 .59061 L .917 .59069 L .9175 .59077 L .91804 .59086 L .91855 .59094 L .91905 .59102 L .91957 .5911 L .92007 .59118 L .92056 .59125 L .92107 .59133 L .92156 .59141 L .92208 .59149 L .92257 .59157 L .92305 .59164 L .92356 .59172 L .92405 .59179 L .92451 .59186 L .92501 .59194 L .92548 .59201 L .92598 .59209 L .92647 .59216 L .92693 .59223 L Mistroke .92742 .5923 L .92789 .59237 L .92839 .59245 L .92887 .59252 L .92933 .59259 L .92981 .59266 L .93028 .59273 L .93073 .59279 L .9312 .59286 L .93166 .59293 L .93214 .593 L .93261 .59307 L .93305 .59313 L .93352 .5932 L .93398 .59327 L .93441 .59333 L .93487 .5934 L .93531 .59346 L .93578 .59353 L .93623 .59359 L .93666 .59365 L .93712 .59372 L .93756 .59378 L .93803 .59384 L .93847 .59391 L .9389 .59397 L .93936 .59403 L .93979 .59409 L .94021 .59415 L .94066 .59421 L .94108 .59427 L .94153 .59433 L .94197 .59439 L .94238 .59445 L .94283 .59451 L .94325 .59457 L .9437 .59463 L .94413 .59469 L .94454 .59474 L .94498 .5948 L .9454 .59486 L .94581 .59491 L .94624 .59497 L .94665 .59502 L .94709 .59508 L .9475 .59514 L .94791 .59519 L .94833 .59525 L .94874 .5953 L .94914 .59535 L Mistroke .94955 .59541 L .94995 .59546 L .95038 .59552 L .95078 .59557 L .95117 .59562 L .95159 .59567 L .95199 .59572 L .95241 .59578 L .95282 .59583 L .9532 .59588 L .95362 .59593 L .95401 .59598 L .95439 .59603 L .9548 .59608 L .95518 .59613 L .95559 .59618 L .95599 .59623 L .95637 .59628 L .95677 .59633 L .95715 .59638 L .95756 .59643 L .95795 .59648 L .95833 .59653 L .95873 .59658 L .95911 .59662 L .95948 .59667 L .95987 .59672 L .96025 .59676 L .96065 .59681 L .96103 .59686 L .9614 .5969 L .96178 .59695 L .96216 .597 L .96252 .59704 L .9629 .59709 L .96326 .59713 L .96365 .59718 L .96402 .59722 L .96438 .59726 L .96476 .59731 L .96512 .59735 L .96551 .5974 L .96588 .59744 L .96624 .59748 L .96661 .59753 L .96698 .59757 L .96732 .59761 L .96769 .59765 L .96805 .5977 L .96842 .59774 L Mistroke .96879 .59778 L .96913 .59782 L .9695 .59787 L .96985 .59791 L .97019 .59795 L .97055 .59799 L .9709 .59803 L .97127 .59807 L .97162 .59811 L .97196 .59815 L .97232 .59819 L .97266 .59823 L .97303 .59827 L .97338 .59831 L .97371 .59835 L .97407 .59839 L .97442 .59843 L .97475 .59846 L .9751 .5985 L .97543 .59854 L .97579 .59858 L .97613 .59862 L .97646 .59865 L .97681 .59869 L .97715 .59873 L .9775 .59877 L .97784 .59881 L .97817 .59884 L .97852 .59888 L .97885 .59892 L .97918 .59895 L .97952 .59899 L .97984 .59902 L .98019 .59906 L .98052 .5991 L .98084 .59913 L .98118 .59917 L .98151 .5992 L .98182 .59924 L .98216 .59927 L .98248 .59931 L .98282 .59934 L .98314 .59938 L .98346 .59941 L .98379 .59945 L .98411 .59948 L .98444 .59951 L .98477 .59955 L .98508 .59958 L .98541 .59962 L Mistroke .98573 .59965 L .98604 .59968 L .98636 .59972 L .98667 .59975 L .987 .59978 L .98732 .59981 L .98763 .59985 L .98795 .59988 L .98826 .59991 L .98856 .59994 L .98888 .59997 L .98918 .60001 L .9895 .60004 L .98981 .60007 L .99011 .6001 L .99043 .60013 L .99073 .60016 L .99106 .6002 L .99137 .60023 L .99166 .60026 L .99198 .60029 L .99228 .60032 L .99257 .60035 L .99288 .60038 L .99318 .60041 L .9935 .60044 L .9938 .60047 L .99409 .6005 L .9944 .60053 L .9947 .60056 L .99501 .60059 L .99531 .60062 L .9956 .60065 L .99591 .60068 L .99621 .60071 L .99649 .60074 L .9968 .60076 L .99709 .60079 L .99739 .60082 L .99769 .60085 L .99797 .60088 L .99828 .60091 L .99857 .60094 L .99885 .60096 L .99914 .60099 L .99942 .60102 L .99973 .60105 L 1 .60107 L Mfstroke 1 .6 0 r .341 0 m .34868 .01865 L .37331 .06846 L .39362 .10361 L .41078 .12976 L .42706 .15195 L .44117 .16936 L .4548 .18478 L .46682 .19734 L .47751 .20779 L .48808 .21749 L .49757 .22572 L .50703 .23349 L .51558 .24017 L .52336 .24599 L .53121 .25159 L .53838 .25651 L .54495 .26085 L .55164 .2651 L .5578 .26887 L .56407 .27257 L .56986 .27588 L .57523 .27883 L .58072 .28177 L .58582 .2844 L .59056 .28678 L .59545 .28915 L .6 .2913 L .60468 .29344 L .60906 .29539 L .61314 .29715 L .61737 .29892 L .62132 .30053 L .62541 .30215 L .62924 .30363 L .63283 .30497 L .63656 .30633 L .64006 .30757 L .64335 .30871 L .64677 .30986 L .64999 .31092 L .65333 .31199 L .65648 .31297 L .65945 .31387 L .66254 .31478 L .66545 .31562 L .66849 .31647 L .67135 .31726 L .67406 .31798 L .67688 .31871 L Mistroke .67954 .31939 L .68206 .32001 L .6847 .32065 L .68719 .32124 L .68979 .32184 L .69225 .32239 L .69458 .3229 L .69702 .32342 L .69933 .3239 L .70152 .32435 L .70381 .3248 L .70598 .32522 L .70826 .32565 L .71041 .32605 L .71246 .32642 L .71461 .32679 L .71664 .32714 L .71877 .3275 L .7208 .32783 L .72272 .32813 L .72474 .32845 L .72666 .32874 L .72848 .329 L .73039 .32928 L .73221 .32953 L .73411 .32979 L .73593 .33003 L .73765 .33026 L .73946 .33048 L .74118 .3307 L .74282 .33089 L .74454 .33109 L .74618 .33128 L .74791 .33147 L .74955 .33165 L .75111 .33181 L .75275 .33198 L .75431 .33213 L .75596 .33229 L .75752 .33244 L .75901 .33257 L .76058 .33271 L .76208 .33284 L .7635 .33295 L .765 .33308 L .76643 .33319 L .76794 .3333 L .76937 .3334 L .77074 .3335 L .77218 .3336 L Mistroke .77355 .33369 L .77499 .33378 L .77637 .33387 L .77769 .33395 L .77907 .33402 L .78039 .3341 L .78165 .33416 L .78298 .33423 L .78425 .33429 L .78558 .33436 L .78686 .33441 L .78807 .33447 L .78936 .33452 L .79058 .33457 L .79175 .33461 L .79298 .33465 L .79416 .33469 L .7954 .33473 L .79658 .33477 L .79771 .3348 L .79891 .33483 L .80005 .33486 L .80125 .33489 L .8024 .33491 L .80349 .33494 L .80465 .33496 L .80576 .33498 L .80681 .33499 L .80793 .33501 L .80899 .33502 L .81012 .33503 L .81119 .33504 L .81222 .33505 L .8133 .33506 L .81434 .33506 L .8149 .33506 L .81543 .33507 L .81569 .33507 L .81596 .33507 L .81621 .33507 L .81644 .33507 L .81668 .33507 L .81682 .33507 L .81688 .33507 L .81695 .33507 L .817 .33507 L .81707 .33507 L .81709 .33507 L .81712 .33507 L .81715 .33507 L Mistroke .81717 .33507 L .81721 .33507 L .81722 .33507 L .81724 .33507 L .81727 .33507 L .8173 .33507 L .81733 .33507 L .81736 .33507 L .81739 .33507 L .81742 .33507 L .81748 .33507 L .81754 .33507 L .81767 .33507 L .81779 .33507 L .81791 .33507 L .81816 .33507 L .81844 .33507 L .81894 .33507 L .81948 .33506 L .82043 .33506 L .82144 .33506 L .82241 .33505 L .82343 .33504 L .82441 .33503 L .82534 .33502 L .82633 .33501 L .82727 .335 L .82826 .33499 L .82922 .33497 L .83013 .33496 L .83109 .33494 L .83201 .33492 L .83289 .33491 L .83382 .33489 L .83471 .33487 L .83565 .33484 L .83655 .33482 L .83742 .3348 L .83833 .33478 L .8392 .33475 L .84012 .33472 L .841 .3347 L .84184 .33467 L .84273 .33464 L .84359 .33461 L .8444 .33459 L .84526 .33456 L .84609 .33453 L .84696 .33449 L .8478 .33446 L Mistroke .8486 .33443 L .84945 .3344 L .85026 .33436 L .85103 .33433 L .85185 .33429 L .85263 .33426 L .85346 .33422 L .85426 .33419 L .85502 .33415 L .85583 .33411 L .8566 .33407 L .85741 .33403 L .85819 .33399 L .85894 .33396 L .85973 .33392 L .86049 .33388 L .86121 .33384 L .86198 .33379 L .86271 .33375 L .86349 .33371 L .86423 .33367 L .86495 .33363 L .8657 .33358 L .86642 .33354 L .86711 .3335 L .86785 .33345 L .86855 .33341 L .86929 .33336 L .87 .33332 L .87068 .33327 L .8714 .33322 L .87209 .33318 L .87282 .33313 L .87353 .33308 L .8742 .33304 L .87491 .33299 L .87559 .33294 L .87624 .33289 L .87693 .33285 L .87759 .3328 L .87829 .33275 L .87896 .3327 L .8796 .33265 L .88028 .3326 L .88093 .33255 L .88162 .3325 L .88229 .33245 L .88292 .3324 L .88359 .33235 L .88423 .3323 L Mistroke .88485 .33225 L .8855 .33219 L .88613 .33214 L .88679 .33209 L .88742 .33204 L .88803 .33199 L .88868 .33193 L .88929 .33188 L .88989 .33183 L .89051 .33178 L .89111 .33173 L .89175 .33167 L .89236 .33162 L .89294 .33157 L .89356 .33151 L .89416 .33146 L .89479 .33141 L .89539 .33135 L .89597 .3313 L .89658 .33124 L .89717 .33119 L .89773 .33114 L .89832 .33108 L .89889 .33103 L .8995 .33097 L .90008 .33092 L .90064 .33087 L .90123 .33081 L .90179 .33075 L .90239 .3307 L .90296 .33064 L .90351 .33059 L .9041 .33053 L .90465 .33048 L .90519 .33042 L .90576 .33037 L .9063 .33031 L .90688 .33025 L .90743 .3302 L .90796 .33014 L .90853 .33009 L .90907 .33003 L .90958 .32998 L .91013 .32992 L .91066 .32986 L .91121 .32981 L .91175 .32975 L .91226 .3297 L .9128 .32964 L .91332 .32958 L Mistroke .91387 .32952 L .9144 .32947 L .91491 .32941 L .91545 .32935 L .91596 .3293 L .91646 .32924 L .91698 .32919 L .91749 .32913 L .91802 .32907 L .91853 .32901 L .91902 .32896 L .91954 .3289 L .92004 .32884 L .92052 .32879 L .92102 .32873 L .92151 .32868 L .92203 .32862 L .92252 .32856 L .92299 .32851 L .9235 .32845 L .92398 .32839 L .92449 .32833 L .92498 .32828 L .92545 .32822 L .92595 .32816 L .92643 .3281 L .92689 .32805 L .92738 .32799 L .92784 .32794 L .92834 .32788 L .92881 .32782 L .92927 .32776 L .92975 .32771 L .93022 .32765 L .93071 .32759 L .93118 .32753 L .93163 .32748 L .93211 .32742 L .93257 .32736 L .93301 .32731 L .93348 .32725 L .93393 .32719 L .93441 .32713 L .93487 .32708 L .93531 .32702 L .93577 .32696 L .93622 .32691 L .93665 .32685 L .9371 .32679 L .93754 .32674 L Mistroke .938 .32668 L .93844 .32662 L .93887 .32657 L .93932 .32651 L .93975 .32645 L .94021 .32639 L .94065 .32634 L .94107 .32628 L .94152 .32622 L .94195 .32617 L .94237 .32611 L .94281 .32605 L .94323 .326 L .94367 .32594 L .9441 .32588 L .94451 .32583 L .94495 .32577 L .94536 .32571 L .94581 .32565 L .94623 .3256 L .94664 .32554 L .94707 .32548 L .94749 .32543 L .94789 .32537 L .94831 .32532 L .94872 .32526 L .94915 .3252 L .94956 .32514 L .94996 .32509 L .95038 .32503 L .95079 .32498 L .95117 .32492 L .95159 .32487 L .95198 .32481 L .9524 .32475 L .9528 .3247 L .95319 .32464 L .9536 .32458 L .95399 .32453 L .95441 .32447 L .95481 .32441 L .95519 .32436 L .9556 .3243 L .95599 .32425 L .95637 .32419 L .95676 .32414 L .95715 .32408 L .95755 .32402 L .95794 .32397 L .95832 .32391 L Mistroke .95871 .32386 L .95909 .3238 L .95946 .32375 L .95985 .32369 L .96022 .32364 L .96061 .32358 L .96099 .32353 L .96136 .32347 L .96174 .32342 L .96211 .32336 L .96251 .32331 L .96288 .32325 L .96325 .3232 L .96363 .32314 L .964 .32308 L .96436 .32303 L .96473 .32298 L .96509 .32292 L .96548 .32287 L .96584 .32281 L .9662 .32276 L .96657 .3227 L .96693 .32265 L .96731 .32259 L .96768 .32254 L .96803 .32248 L .96841 .32243 L .96877 .32237 L .96911 .32232 L .96947 .32226 L .96983 .32221 L .9702 .32215 L .97056 .3221 L .9709 .32205 L .97126 .32199 L .97161 .32194 L .97195 .32189 L .9723 .32183 L .97265 .32178 L .97301 .32172 L .97336 .32167 L .97369 .32162 L .97405 .32156 L .97439 .32151 L .97475 .32145 L .9751 .3214 L .97543 .32135 L .97579 .32129 L .97613 .32124 L .97645 .32119 L Mistroke .9768 .32113 L .97713 .32108 L .97748 .32102 L .97782 .32097 L .97815 .32092 L .9785 .32087 L .97883 .32081 L .97915 .32076 L .97948 .32071 L .97981 .32066 L .98015 .3206 L .98049 .32055 L .9808 .3205 L .98114 .32044 L .98146 .32039 L .98181 .32034 L .98214 .32028 L .98246 .32023 L .98279 .32018 L .98312 .32013 L .98343 .32008 L .98376 .32002 L .98407 .31997 L .98441 .31992 L .98473 .31987 L .98504 .31982 L .98537 .31976 L .98569 .31971 L .98602 .31966 L .98634 .3196 L .98665 .31955 L .98698 .3195 L .9873 .31945 L .9876 .3194 L .98792 .31935 L .98823 .31929 L .98856 .31924 L .98887 .31919 L .98917 .31914 L .98949 .31909 L .9898 .31903 L .9901 .31899 L .99041 .31893 L .99071 .31888 L .99103 .31883 L .99134 .31878 L .99164 .31873 L .99195 .31868 L .99225 .31863 L .99257 .31857 L Mistroke .99288 .31852 L .99317 .31847 L .99349 .31842 L .99379 .31837 L .99408 .31832 L .99438 .31827 L .99468 .31822 L .99499 .31817 L .99529 .31812 L .99558 .31807 L .99588 .31802 L .99618 .31797 L .99649 .31791 L .99679 .31786 L .99708 .31781 L .99738 .31776 L .99768 .31771 L .99796 .31766 L .99826 .31761 L .99855 .31756 L .99885 .31751 L .99915 .31746 L .99943 .31741 L .99973 .31736 L 1 .31731 L Mfstroke .2 1 0 r .49299 0 m .49757 .01074 L .50703 .03147 L .51558 .0491 L .52336 .06426 L .53121 .07874 L .53838 .0913 L .54495 .10229 L .55164 .11296 L .5578 .12236 L 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.25973 L .9992 .25935 L .99948 .25899 L .99978 .25861 L 1 .25833 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{432, 266.938}, ImageCacheValid->False] }, Open ]], Cell["\<\ In the following cross sections we need the effective elastic and inelastic \ momentum transfer cross sections, because previous work indicated that the \ momentum balance gives better results for heavy particles than does the \ energy balance. In several cases the reaction cross sections at low energies \ are measured to be essentially equal to the Langevin cross section. Generally \ a significant fraction of the total reaction cross section is found to be \ highly anisotropic, i.e., very differnent than expected for the classical \ Langevin scattering. It is not clear whether the theorems relating the \ maximum elastic and inelastic cross sections apply here. Updated 3/7/01\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["CH+ - CH4 data", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ CH+ +CH4 momentum loss. Because we are using the momentum balance rather than the energy balance, the \ usual 2mM/(m+M)^2 factor is replaced by 2 in the loss function and we should \ use just the elastic plus inelastic (nonreactive) part of the Langevin cross \ section. It is not clear whether the theorems relating the maximum elastic \ and inelastic cross sections apply here.\ \>", "SmallText"], Cell["l1cn:=n*f*2.*w1[z]*fl1cn*3.38*10^-19./w1[z]^.5;", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell[" Note that w1[z], etc. are lab energies.", "Subsubtitle"], Cell["\<\ CH+ + CH4 -> C2H3+ + H2 From Smith and Adams, Int'l. J. Mass Spectrom. and Ion Phys. 23, 123 (1977) \ the thermal rate coefficient is essentially equal to the Langevin value. The \ question then is how rapidly does the rate coefficient drop at high energies. \ From Huntress, Laudenslager, and Pinnizzotto (1974) this rate coefficient \ falls off by a factor of two at about 2 eV (CM) or 4 eV (LAB). This is a \ considerably lower energy than found for CH4+ + CH4 by Peko et al (1998). We \ have raised this energy in an attempt to fit de Urquijo et al (1998)\ \>", "SmallText"], Cell["\<\ a1c0o:=fa1c0o*n*f*1.*3.38*10^-19./w1[z]^.5/(1+(w1[z]/8)^4); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH+ + CH4 -> CH3+ + CH2", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{a\ == \ chp\ + \ ch4, \ ch3\ == \ ch3p\ + \ e\ + 9.8, ch\ == \ chp\ + \ e\ + \ 11.14, \ ch4\ == \ ch3\ + \ h\ + 103.4/23.07, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {h, ch, ch3, chp, ch4, e}]\)], "Input"], Cell[BoxData[ \(\(-1.192622453402688`\) + 1.`\ ch2 + 1.`\ ch3p == a\)], "Output"] }, Open ]], Cell["\<\ According to Smith and Adams (1977) the probability of this process is \ negligible at thermal energies. According to Fig. 1 of Peko et al (1998) the \ reaction CH3+ + H -> CH3 + H+ requires 5.4 - 1.6 = 3.8 eV, so that the IP of \ CH3 is 13.6 - 3.8 = 9.8 e V. According to Partridge and Bauschlicher (1995) \ CH4 -> CH3 + 2H requires 103.4 and CH2 -> CH + H requires 100. from somewhere \ I got the IP(CH) = 11.14. Putting these together in the following set of \ equations, we find CH+ + CH4 -> CH3+ + CH2 is exothermic by about 1 eV. We \ therefore make this process small at all energies.\ \>", "SmallText"], Cell["\<\ a1c3o:=fa1c3o*n*f*1.*10^-25*(UnitStep[w1[z]-3.8]*(1-3.8/w1[z])/w1[z]^.5/(1+w1[\ z]/1.)^4+1.*10^-30) \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell[CellGroupData[{ Cell[BoxData[ \(a1c3o\ /. \ {w1[z]\ -> \ 4.0, n -> 10^20/f}\)], "Input"], Cell[BoxData[ \(4.000000000000003`*^-10\)], "Output"] }, Open ]], Cell["CH+ + CH4 -> fCH + CH4+ ", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{ch\ == \ chp\ + \ e\ + \ 11.14, \ ch4\ == \ ch4p\ + \ e\ + \ 12.61}, {e}]\)], "Input"], Cell[BoxData[ \(\(\(1.4699999999999989`\)\(\[InvisibleSpace]\)\) + 1.`\ ch + 1.`\ ch4p - 1.`\ chp == ch4\)], "Output"] }, Open ]], Cell["\<\ According to Smith and Adams (1977) the probability of this process is \ negligible at thermal energies. It has a threshold of 1.47 in CM and 2.66 eV \ LAB. !! This process could be important. !!\ \>", "SmallText"], Cell["\<\ a1c49 := n*f*(fa1c49*(UnitStep[w1[z]-2.66]* 1.0*10^-20*(w1[z]-2.66)/(w1[z]+50.)/(1+w1[z]/1000.)*100.*1.05/44.)+1.*10^-30);\ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH+ + CH4 -> CH4+ + CH According to Smith and Adams (1977) the probability of charge transfer is \ negligible at thermal energies. The threshold for this process is 12.615- \ 10.6 = 2.1 eV (CM) or 3.8 eV (Lab).\ \>", "SmallText"], Cell["a1c4o=0; ", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH+ +CH4 -> CH(A) +CH4+ -> C + H + CH4+ + 432 nm According to Smith and Adams (1977) the probability of charge transfer is \ negligible at thermal energies as it should be because it is exothermic. The \ threshold for this process is 12.615 (CH4)- 10.6 (CH) + 2.87 (CH(A->X) = 5 eV \ (CM) or 9.1 eV (Lab).\ \>", "SmallText"], Cell["\<\ a1c4p := n*f*(fa1c4p*(UnitStep[w1[z]-9.1]* 1.*10^-20*(w1[z]-9.1)/(w1[z]+50.)/(1+w1[z]/50.)*100.*2./25.2)+1.*10^-30);\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH+ + CH4 -> CH5+ + C This seems like a very unlikely reaction.\ \>", "SmallText"], Cell["a1c5o=0; ", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH+ + CH4 -> H+ + ?2 CH2 According to Smith and Adams (1977) the probability of this breakup is \ negligible at thermal energies.\ \>", "SmallText"], Cell["a1c8o=0; ", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ Plot these cross section in units of 10^-20 m^2. We note that the column \ depth for most of our data is that for 4 cm and 100 mTorr, i.e., 1.3*10^20 \ m^2, so that a process with a cross section of 10^-20 m^2 has a near unit \ probability of occurrence in the free fall passage of a CH+ across the \ tube.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{\((\(\(l1cn/2\)/fl1cn\)/w1[z]\ /. \ w1[z]\ -> \ w1z)\), \((a1c0o\ \ /. \ w1[z]\ -> \ w1z)\), \((a1c49\ /. \ w1[z]\ -> \ w1z)\), \((a1c4p\ \ /. \ w1[z]\ -> \ w1z)\), \((a1c3o\ \ /. \ w1[z]\ -> \ w1z)\)}, {w1z, 1, 1000}, \ PlotRange\ -> \ \ {{1, 1000}, {10^\(-3\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 2000, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 %%ImageSize: 432 266.991 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def 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.95066 .38354 L .95076 .38352 L .95086 .38351 L .95096 .38349 L .95106 .38347 L .95117 .38345 L .95127 .38343 L .95137 .38341 L .95147 .38339 L .95157 .38337 L .95167 .38336 L .95177 .38334 L .95187 .38332 L .95198 .3833 L .95208 .38328 L .95217 .38326 L .95228 .38324 L .95237 .38322 L .95248 .38321 L .95258 .38319 L .95268 .38317 L .95278 .38315 L .95288 .38313 L .95298 .38311 L .95308 .38309 L .95318 .38308 L .95328 .38306 L .95338 .38304 L .95348 .38302 L Mistroke .95358 .383 L .95368 .38298 L .95377 .38297 L .95387 .38295 L .95397 .38293 L .95407 .38291 L .95417 .38289 L .95427 .38287 L .95437 .38286 L .95447 .38284 L .95457 .38282 L .95467 .3828 L .95477 .38278 L .95487 .38276 L .95497 .38274 L .95506 .38273 L .95516 .38271 L .95526 .38269 L .95536 .38267 L .95546 .38265 L .95555 .38264 L .95565 .38262 L .95575 .3826 L .95585 .38258 L .95595 .38256 L .95605 .38254 L .95615 .38253 L .95625 .38251 L .95634 .38249 L .95644 .38247 L .95653 .38245 L .95664 .38243 L .95673 .38242 L .95683 .3824 L .95693 .38238 L .95703 .38236 L .95712 .38235 L .95722 .38233 L .95731 .38231 L .95741 .38229 L .95751 .38227 L .9576 .38226 L .9577 .38224 L .9578 .38222 L .9579 .3822 L .958 .38218 L .95809 .38217 L .95819 .38215 L .95828 .38213 L .95838 .38211 L Mistroke .95848 .38209 L .95857 .38208 L .95867 .38206 L .95877 .38204 L .95886 .38202 L .95896 .382 L .95905 .38199 L .95915 .38197 L .95925 .38195 L .95934 .38193 L .95944 .38191 L .95954 .3819 L .95963 .38188 L .95973 .38186 L .95982 .38184 L .95992 .38183 L .96002 .38181 L .96011 .38179 L .96021 .38177 L .9603 .38176 L .96039 .38174 L .96049 .38172 L .96058 .3817 L .96068 .38169 L .96077 .38167 L .96087 .38165 L .96096 .38163 L .96106 .38162 L .96116 .3816 L .96125 .38158 L .96134 .38156 L .96144 .38154 L .96153 .38153 L .96162 .38151 L .96172 .38149 L .96181 .38148 L .96191 .38146 L .962 .38144 L .9621 .38142 L .96219 .3814 L .96228 .38139 L .96237 .38137 L .96247 .38135 L .96256 .38134 L .96266 .38132 L .96275 .3813 L .96284 .38128 L .96294 .38127 L .96303 .38125 L .96313 .38123 L Mistroke .96322 .38121 L .96331 .3812 L .96341 .38118 L .9635 .38116 L .96359 .38115 L .96368 .38113 L .96377 .38111 L .96387 .38109 L .96396 .38108 L .96405 .38106 L .96415 .38104 L .96424 .38103 L .96434 .38101 L .96443 .38099 L .96452 .38097 L .96461 .38096 L .96471 .38094 L .96479 .38092 L .96489 .3809 L .96498 .38089 L .96508 .38087 L .96517 .38085 L .96526 .38084 L .96535 .38082 L .96544 .3808 L .96553 .38079 L .96562 .38077 L .96571 .38075 L .96581 .38073 L .9659 .38072 L .96599 .3807 L .96608 .38068 L .96617 .38067 L .96627 .38065 L .96636 .38063 L .96645 .38062 L .96654 .3806 L .96663 .38058 L .96672 .38057 L .96681 .38055 L .9669 .38053 L .96699 .38051 L .96709 .3805 L .96717 .38048 L .96727 .38046 L .96736 .38045 L .96744 .38043 L .96753 .38041 L .96762 .3804 L .96772 .38038 L Mistroke .96781 .38036 L .96789 .38035 L .96798 .38033 L .96807 .38031 L .96817 .3803 L .96826 .38028 L .96835 .38026 L .96844 .38025 L .96853 .38023 L .96861 .38021 L .9687 .3802 L .96879 .38018 L .96888 .38016 L .96897 .38015 L .96906 .38013 L .96915 .38011 L .96924 .3801 L .96933 .38008 L .96942 .38006 L .96951 .38005 L .9696 .38003 L .96969 .38001 L .96978 .38 L .96987 .37998 L .96996 .37997 L .97005 .37995 L .97014 .37993 L .97022 .37992 L .97032 .3799 L .9704 .37988 L .97049 .37987 L .97058 .37985 L .97066 .37983 L .97076 .37982 L .97084 .3798 L .97093 .37978 L .97102 .37977 L .97111 .37975 L .9712 .37973 L .97129 .37972 L .97137 .3797 L .97146 .37969 L .97155 .37967 L .97164 .37965 L .97172 .37964 L .97181 .37962 L .9719 .3796 L .97199 .37959 L .97207 .37957 L .97216 .37956 L Mistroke .97225 .37954 L .97234 .37952 L .97243 .37951 L .97252 .37949 L .97261 .37947 L .97269 .37946 L .97278 .37944 L .97287 .37943 L .97295 .37941 L .97304 .37939 L .97313 .37938 L .97322 .37936 L .97331 .37934 L .97339 .37933 L .97347 .37931 L .97356 .3793 L .97365 .37928 L .97374 .37926 L .97382 .37925 L .97391 .37923 L .974 .37922 L .97408 .3792 L .97417 .37918 L .97426 .37917 L .97434 .37915 L .97443 .37914 L .97452 .37912 L .9746 .3791 L .97469 .37909 L .97477 .37907 L .97486 .37906 L .97495 .37904 L .97503 .37902 L .97512 .37901 L .9752 .37899 L .97529 .37898 L .97537 .37896 L .97546 .37895 L .97555 .37893 L .97563 .37891 L .97571 .3789 L .9758 .37888 L .97588 .37887 L .97597 .37885 L .97606 .37883 L .97614 .37882 L .97623 .3788 L .97631 .37879 L .9764 .37877 L .97648 .37876 L Mistroke .97657 .37874 L .97665 .37872 L .97674 .37871 L .97682 .37869 L .97691 .37868 L .97699 .37866 L .97708 .37864 L .97717 .37863 L .97725 .37861 L .97734 .3786 L .97742 .37858 L .9775 .37857 L .97759 .37855 L .97767 .37853 L .97776 .37852 L .97784 .3785 L .97792 .37849 L .97801 .37847 L .97809 .37846 L .97817 .37844 L .97826 .37843 L .97834 .37841 L .97843 .37839 L .97851 .37838 L .97859 .37836 L .97868 .37835 L .97876 .37833 L .97885 .37832 L .97893 .3783 L .97901 .37829 L .9791 .37827 L .97918 .37825 L .97926 .37824 L .97935 .37822 L .97943 .37821 L .97952 .37819 L .9796 .37818 L .97968 .37816 L .97977 .37815 L .97985 .37813 L .97994 .37811 L .98002 .3781 L .9801 .37808 L .98019 .37807 L .98027 .37805 L .98035 .37804 L .98043 .37802 L .98051 .37801 L .9806 .37799 L .98068 .37798 L Mistroke .98076 .37796 L .98085 .37795 L .98093 .37793 L .98101 .37792 L .98109 .3779 L .98117 .37789 L .98126 .37787 L .98134 .37785 L .98142 .37784 L .9815 .37782 L .98159 .37781 L .98167 .37779 L .98175 .37778 L .98183 .37776 L .98192 .37775 L .982 .37773 L .98208 .37772 L .98216 .3777 L .98224 .37769 L .98233 .37767 L .98241 .37766 L .98249 .37764 L .98257 .37763 L .98265 .37761 L .98273 .3776 L .98281 .37758 L .98289 .37757 L .98298 .37755 L .98306 .37754 L .98314 .37752 L .98322 .37751 L .9833 .37749 L .98338 .37748 L .98347 .37746 L .98354 .37745 L .98363 .37743 L .98371 .37742 L .98379 .3774 L .98387 .37739 L .98395 .37737 L .98403 .37736 L .98411 .37734 L .98419 .37733 L .98427 .37731 L .98435 .3773 L .98444 .37728 L .98452 .37727 L .9846 .37725 L .98468 .37724 L .98476 .37722 L Mistroke .98484 .37721 L .98492 .37719 L .985 .37718 L .98508 .37716 L .98516 .37715 L .98524 .37713 L .98532 .37712 L .9854 .3771 L .98548 .37709 L .98556 .37707 L .98564 .37706 L .98572 .37704 L .9858 .37703 L .98587 .37701 L .98596 .377 L .98603 .37698 L .98612 .37697 L .9862 .37695 L .98628 .37694 L .98636 .37692 L .98644 .37691 L .98651 .3769 L .98659 .37688 L .98667 .37687 L .98675 .37685 L .98683 .37684 L .98691 .37682 L .98699 .37681 L .98707 .37679 L .98714 .37678 L .98722 .37676 L .9873 .37675 L .98738 .37673 L .98746 .37672 L .98754 .37671 L .98762 .37669 L .9877 .37668 L .98778 .37666 L .98786 .37665 L .98793 .37663 L .98801 .37662 L .98809 .3766 L .98817 .37659 L .98825 .37657 L .98832 .37656 L .9884 .37654 L .98848 .37653 L .98856 .37652 L .98864 .3765 L .98872 .37649 L Mistroke .9888 .37647 L .98888 .37646 L .98895 .37644 L .98903 .37643 L .98911 .37641 L .98919 .3764 L .98926 .37639 L .98934 .37637 L .98942 .37636 L .9895 .37634 L .98958 .37633 L .98966 .37631 L .98973 .3763 L .98981 .37628 L .98989 .37627 L .98996 .37626 L .99004 .37624 L .99012 .37623 L .99019 .37621 L .99027 .3762 L .99035 .37618 L .99043 .37617 L .99051 .37615 L .99058 .37614 L .99066 .37613 L .99074 .37611 L .99081 .3761 L .99089 .37608 L .99097 .37607 L .99105 .37605 L .99112 .37604 L .9912 .37603 L .99128 .37601 L .99135 .376 L .99143 .37598 L .99151 .37597 L .99158 .37596 L .99166 .37594 L .99174 .37593 L .99181 .37591 L .99189 .3759 L .99197 .37588 L .99205 .37587 L .99212 .37586 L .9922 .37584 L .99228 .37583 L .99235 .37581 L .99242 .3758 L .9925 .37579 L .99258 .37577 L Mistroke .99265 .37576 L .99273 .37574 L .9928 .37573 L .99288 .37571 L .99296 .3757 L .99304 .37569 L .99311 .37567 L .99319 .37566 L .99326 .37564 L .99334 .37563 L .99341 .37562 L .99349 .3756 L .99356 .37559 L .99364 .37557 L .99372 .37556 L .99379 .37555 L .99387 .37553 L .99394 .37552 L .99401 .3755 L .99409 .37549 L .99416 .37548 L .99424 .37546 L .99432 .37545 L .99439 .37543 L .99447 .37542 L .99454 .37541 L .99462 .37539 L .99469 .37538 L .99477 .37536 L .99484 .37535 L .99492 .37534 L .99499 .37532 L .99507 .37531 L .99514 .3753 L .99522 .37528 L .99529 .37527 L .99536 .37525 L .99544 .37524 L .99551 .37523 L .99559 .37521 L .99567 .3752 L .99574 .37518 L .99582 .37517 L .99589 .37516 L .99596 .37514 L .99604 .37513 L .99611 .37512 L .99619 .3751 L .99626 .37509 L .99634 .37507 L Mistroke .99641 .37506 L .99649 .37505 L .99656 .37503 L .99663 .37502 L .9967 .37501 L .99678 .37499 L .99685 .37498 L .99692 .37496 L .997 .37495 L .99707 .37494 L .99715 .37492 L .99722 .37491 L .9973 .3749 L .99737 .37488 L .99745 .37487 L .99752 .37486 L .99759 .37484 L .99766 .37483 L .99774 .37481 L .99781 .3748 L .99788 .37479 L .99796 .37477 L .99803 .37476 L .99811 .37475 L .99818 .37473 L .99825 .37472 L .99833 .3747 L .9984 .37469 L .99847 .37468 L .99855 .37466 L .99862 .37465 L .9987 .37464 L .99877 .37462 L .99884 .37461 L .99891 .3746 L .99899 .37458 L .99906 .37457 L .99913 .37456 L .9992 .37454 L .99928 .37453 L .99935 .37452 L .99942 .3745 L .99949 .37449 L .99957 .37448 L .99964 .37446 L .99971 .37445 L .99979 .37443 L .99986 .37442 L .99993 .37441 L 1 .37439 L Mistroke Mfstroke 1 .6 0 r 0 .55979 m .05739 .5491 L .10158 .54075 L .13354 .53452 L .15879 .52932 L .18156 .5242 L .20054 .51938 L .21832 .51413 L .23359 .50875 L .24691 .50317 L .25985 .4967 L .2713 .48994 L .28152 .48294 L .29166 .47502 L .30079 .467 L .30991 .45814 L .31818 .44939 L .32571 .44084 L .33332 .43167 L .34028 .42286 L .34734 .41355 L .35382 .40468 L .3598 .39627 L .36589 .38748 L .37153 .37919 L .37675 .37139 L .38211 .36326 L .38709 .35562 L .3922 .3477 L .39696 .34025 L .40139 .33327 L .40597 .32601 L .41024 .3192 L .41423 .3128 L .41836 .30615 L .42223 .2999 L .42623 .29341 L .42998 .28731 L .4335 .28157 L .43716 .2756 L .44059 .26998 L .44415 .26414 L .44751 .25864 L .45066 .25345 L .45394 .24806 L .45703 .24296 L .45994 .23816 L .46297 .23315 L .46583 .22842 L .46882 .22349 L Mistroke .47163 .21883 L .47429 .21443 L .47707 .20983 L .47969 .20548 L .48242 .20094 L .48501 .19665 L .48746 .19259 L .49002 .18834 L .49244 .18432 L .49473 .18051 L .49713 .17652 L .4994 .17274 L .50178 .16879 L .50404 .16504 L .50617 .16149 L .50841 .15776 L .51053 .15423 L .51255 .15088 L .51466 .14736 L .51666 .14403 L .51877 .14053 L .52076 .1372 L .52265 .13405 L .52464 .13074 L .52653 .12759 L .52851 .12429 L .5304 .12115 L .53218 .11817 L .53406 .11504 L .53585 .11207 L .53755 .10924 L .53933 .10626 L .54103 .10343 L .54282 .10046 L .54451 .09763 L .54613 .09494 L .54783 .09211 L .54944 .08941 L .55098 .08685 L .5526 .08415 L .55414 .08158 L .55576 .07888 L .55731 .0763 L .55878 .07385 L .56032 .07127 L .5618 .06881 L .56335 .06622 L .56483 .06375 L .56624 .0614 L .56772 .05893 L Mistroke .56914 .05657 L .57049 .05432 L .57191 .05195 L .57326 .04969 L .57469 .04731 L .57605 .04504 L .57735 .04288 L .57871 .0406 L .58002 .03842 L .58139 .03613 L .5827 .03394 L .58395 .03186 L .58527 .02966 L .58653 .02756 L .58773 .02556 L .589 .02345 L .5902 .02143 L .59148 .0193 L .5927 .01727 L .59386 .01534 L .59508 .01329 L .59625 .01134 L .59737 .00948 L .59854 .00752 L .59967 .00564 L .60086 .00366 L .60199 .00177 L Mfstroke .60199 .00177 m .60305 0 L s .2 1 0 r .2323 0 m .24622 .01004 L .25891 .01833 L .27015 .02513 L .28121 .03142 L .29113 .03675 L .30006 .04134 L .309 .04576 L .31711 .04962 L .32527 .05338 L .33271 .0567 L .33953 .05967 L .34644 .06261 L .3528 .06524 L .35927 .06786 L .36524 .07023 L .37076 .07238 L .37641 .07454 L .38165 .07651 L .38651 .0783 L .39152 .08012 L .39618 .08179 L .40097 .08347 L .40545 .08503 L .40962 .08646 L .41394 .08791 L .41797 .08926 L .42214 .09063 L .42605 .09189 L .42971 .09307 L .43351 .09427 L .43707 .09539 L .44042 .09642 L .4439 .09748 L .44717 .09847 L .45057 .09949 L .45377 .10044 L .45678 .10132 L .45992 .10223 L .46288 .10308 L .46567 .10387 L .46858 .10469 L .47133 .10546 L .4742 .10625 L .47691 .10698 L .47947 .10768 L .48214 .10839 L .48467 .10906 L .48731 .10976 L .4898 .11041 L Mistroke .49217 .11102 L .49464 .11165 L .49698 .11225 L .4992 .11281 L .50152 .11339 L .50372 .11393 L .50602 .1145 L .50821 .11503 L .51028 .11553 L .51245 .11605 L .51451 .11653 L .51647 .11699 L .51852 .11747 L .52047 .11792 L .52251 .11839 L .52445 .11884 L .52629 .11925 L .52823 .11969 L .53007 .1201 L .532 .12052 L .53383 .12092 L .53558 .1213 L .53741 .1217 L .53915 .12207 L .54081 .12243 L .54255 .12279 L .54421 .12314 L .54595 .1235 L .54761 .12384 L .54918 .12417 L .55084 .12451 L .55242 .12482 L .55408 .12516 L .55566 .12547 L .55717 .12577 L .55875 .12608 L .56026 .12638 L .5617 .12665 L .56322 .12694 L .56466 .12722 L .56618 .12751 L .56763 .12778 L .56901 .12804 L .57046 .12831 L .57184 .12856 L .57316 .1288 L .57456 .12906 L .57588 .1293 L .57728 .12955 L .57861 .12978 L Mistroke .57989 .13001 L .58123 .13024 L .58251 .13047 L .58385 .1307 L .58514 .13092 L .58637 .13113 L .58766 .13135 L .5889 .13156 L .59007 .13176 L .59132 .13197 L .59251 .13216 L .59376 .13237 L .59495 .13256 L .59609 .13275 L .5973 .13294 L .59845 .13313 L .59966 .13332 L .60081 .1335 L .60192 .13368 L .60309 .13386 L .6042 .13403 L .60527 .13419 L .60639 .13437 L .60746 .13453 L .6086 .1347 L .60968 .13486 L .61071 .13502 L .6118 .13518 L .61285 .13533 L .61384 .13548 L .6149 .13563 L .61591 .13578 L .61697 .13593 L .61799 .13608 L .61896 .13621 L .61998 .13636 L .62096 .1365 L .622 .13664 L .62299 .13678 L .62394 .13691 L .62494 .13704 L .62589 .13717 L .62681 .1373 L .62778 .13743 L .6287 .13755 L .62968 .13768 L .63061 .1378 L .63151 .13792 L .63245 .13804 L .63335 .13816 L Mistroke .63422 .13827 L .63513 .13839 L .636 .1385 L .63693 .13861 L .63781 .13872 L .63866 .13883 L .63955 .13894 L .64041 .13905 L .64131 .13916 L .64218 .13926 L .64301 .13936 L .64388 .13947 L .64472 .13957 L .64552 .13966 L .64637 .13976 L .64718 .13986 L .64804 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This graph shows that low energy i.e., < 4 eV (LAB), CH+ ions will undergo \ reaction almost immediately. The principle known reaction is that leading to \ CH5+ and that drops out for CH+ ions at above about 4 eV (LAB). It seems \ unlikely that there are no important processes other than elastic scattering \ for energies above 4 eV. Note that values less than roughly 1e-3 will not \ influence the ion fluxes. Updated 3/7/01\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell["CH2+ - CH4 data", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We originally did not consider CH2+ kinetics, but it is the second most \ important ion at high E/n.\ \>", "Subsubtitle"], Cell["\<\ CH2+ +CH4 momentum loss. Because we are using the momentum balance rather than the energy balance, the \ usual 2mM/(m+M)^2 factor is replaced by 2 in the loss function and we should \ use just the elastic plus inelastic (nonreactive) part of the Langevin cross \ section. It is not clear whether the theorems relating the maximum elastic \ and inelastic cross sections apply here.\ \>", "SmallText"], Cell["l2cn:=n*f*2.*w2[z]*fl2cn*3.53*10^-19./w2[z]^.5;", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH2+ + CH4 -> C2H4+ + H2 From Adams and Smith, Chem. Phys. Lett. 47, 383 (1977) the thermal rate \ coefficient is 70% of essentially the Langevin value. The question then is \ how rapidly does the rate coefficient drop at high energies. According to \ Abramson and Futrell (1966), the products of CH3+ + CH4 change from C2H4+, \ C2H5+, C2H3+, and C2H2+ to C2H3+ and C2H2+ as the LAB energy increases from \ 0.3 to 4.2 eV. For our purposes we lump all these products together.\ \>", "SmallText"], Cell["\<\ a2c0o:=fa2c0o*n*f*3.53*10^-19./w2[z]^.5/(1+(w2[z]/4)^4); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH2+ + CH4 -> C2H5+ + H", "SmallText"], Cell["\<\ From Adams and Smith, Chem. Phys. Lett. 47, 383 (1977) the thermal rate \ coefficient is 30% of essentially the Langevin value. The question then is \ how rapidly does the rate coefficient drop at high energies. For our \ purposes we lump all these products together in the previous reaction.\ \>", "SmallText"], Cell["\<\ Plot these cross section in units of 10^-20 m^2 by choosing n = 10^20 m^-3. \ We note that the column depth for most of our data is that for 4 cm and 100 \ mTorr, i.e., 1.3*10^20 m^2, so that a process with a cross section of 10^-20 \ m^2 has a near unit probability of occurrence in the free fall passage of a \ CH3+ across the tube.\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{\(\(l2cn/2\)/fl2cn\)/w2[z]\ /. \ w2[z]\ -> \ w2z, a2c0o\ \ /. \ w2[z]\ -> \ w2z}, {w2z, 1, 1000}, \ PlotRange\ -> \ \ {{1, 1000}, {10^\(-3\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 %%ImageSize: 432 266.991 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def 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ShowSpecialCharacters->False], Cell["\<\ CH3+ +CH4 -> CH3+ + CH4 Momentum loss in elastic collisions Because we are using the momentum \ balance rather than the energy balance, the usual 2mM/(m+M)^2 factor is \ replaced by 2 in the loss function and we should use just the elastic plus \ inelastic (nonreactive) part of the Langevin cross section.\ \>", "SmallText"], Cell["l3cn:=n*f*2*fl3cn*w3[z]*3.76*10^-19./w3[z]^.5;", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ It should be kept in mind that the elastic scattering will be a small \ fraction of the Langevin cross section when ion-molecule reactions are fast, \ as in the present case. This points to the necessity for adding the reaction \ terms to the energy balance equations.\ \>", "Subsubtitle"], Cell["\<\ CH3+ + CH4 -> C2H5+ + H2. We assume a Langevin cross section at low energies. At high energies we add \ falling cross section similar to that measured by Peko et al (1998) for CH4+ \ + CH4 -> CH5+ +CH3. Several authors state that C2H5+ formation is the \ dominant reaction at low energies. See, for example, Abrhamson and Futrell, \ J. Chem. Phys. 45, 1925 (1966). These authors say that the dominant product \ switches to C2H3+ at 4.2 eV reactant ion energy, but do not give data for \ higher energies. Huntress, J. Chem. Phys. 56, 5111 (1972) shows the rate \ coefficient for C2H5+ formation relative to the thermal (Langevin) value \ decreasing by 1/2 at about 2 eV COM or 3.9 eV LAB and to 10% at 10 eV COM or \ 19.4 LAB.. Smith and Adams, Int'l. J. Mass. Spectrom. and Ion Physics 23, \ 123 (1977) support this picture at low energies. Clow and Futrell (1970) \ give a 50% rleative rate at ~ 2.5 eV CM or 5 eV Lab. We include the \ formation of C2H3+ ions (at a low rate relative to Langevin and energies \ above 1 eV) in the C2H5+ formation.\ \>", "SmallText"], Cell["a3c0o:=n*f*fa3c0o*3.76*10^-19./w3[z]^.5/(1+(w3[z]/5.)^3);", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ Note that at low E/n the desired increase in C2H5+ can also be obtained by \ using the momentum balance model so as to lower the ion energies.\ \>", "Subsubtitle"], Cell["\<\ The remaining processes cannot all be small if we are to use the CH3+ route \ to CH(A->X) at nearly pure CH4. \ \>", "Subsubtitle"], Cell["CH3+ + CH4 -> CH3 + CH4+", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{ch3\ == \ ch3p\ + e\ + \ 9.8, ch4\ == \ ch4p\ + \ e\ + \ 12.61, c\ == \ ch3p + ch4}, {e, ch39, ch4}]\)], "Input"], Cell[BoxData[ \(\(\(2.8099999999999987`\)\(\[InvisibleSpace]\)\) + 1.`\ ch3 + 1.`\ ch4p == c\)], "Output"] }, Open ]], Cell["\<\ Using IP(CH4) = 12.615 and IP(CH3) = 9.8, the threshold energy is 31/16*2.8 = \ 5.42. Derwish et al (1964) claim that 56% of the thermal reaction goes by \ this route and only 44% by C2H5 + H2 reaction. However, this does not make \ sense with a 5.42 eV threshold and we make the process negligible.\ \>", "SmallText"], Cell["\<\ a3c4F := n*f*(fa3c4F*(UnitStep[w3[z]-5.4]* 1.0*10^-25*(w3[z]-5.4)/(w3[z]+50.)/(1+w3[z]/1000.)*100.*1.05/44.)+1.*10^-30);\ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + CH4 -> fast CH + CH4+ +H2", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{ch3\ == \ ch3p\ + e\ + \ 9.8, h2\ == \ 2\ h\ + \ 4.48, c\ == \ ch3p\ + \ ch4, ch4\ == \ ch4p\ + \ e\ + \ 12.61, ch3\ == \ ch2\ + \ h\ + 108.8/23.07, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {h, ch2, ch3, ch4, ch3p, e}]\)], "Input"], Cell[BoxData[ \(\(\(7.3807152145643675`\)\(\[InvisibleSpace]\)\) + 1.`\ ch + 1.`\ ch4p + 1.`\ h2 == c\)], "Output"] }, Open ]], Cell["\<\ A crucial question here is whether the reaction also produces a fast CH + H2. \ According to Smith and Adams (1977) the probability of breakup is negligible \ at thermal energies, as it should be considering the threshold energy \ required of 7.38*31/15 = 15.25.\ \>", "SmallText"], Cell["\<\ a3c94 := n*f*(fa3c94*(UnitStep[w3[z]-15.25]* 1.0*10^-21*(w3[z]-15.25)/(w3[z]+50.)/(1+w3[z]/1000.)*100.*1.05/44.)+1.*10^-30)\ ;\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + CH4 -> CH+ + CH4 +H2 ", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{ch3\ == \ ch3p\ + e\ + \ 9.8, h2\ == \ 2\ h\ + \ 4.48, ch\ == \ chp\ + \ e\ + \ 11.14, \ ch3\ == \ ch2\ + \ h\ + 108.8/23.07, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {h, ch, ch3, e}]\)], "Input"], Cell[BoxData[ \(\(\(5.910715214564369`\)\(\[InvisibleSpace]\)\) + 1.`\ chp + 1.`\ h2 == ch3p\)], "Output"] }, Open ]], Cell["\<\ According to Smith and Adams (1977) the probability of breakup is negligible \ at thermal energies, as it should be considering the threshold energy \ required. This process has a threshold of 5.91 in CM and 10.7 in LAB. We \ guess at a cross section.\ \>", "SmallText"], Cell["\<\ a3c1o := n*f*(fa3c1o*UnitStep[w3[z]-10.7]* 1.*10^-25*(w3[z]-10.7)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./88.3+1.*10^-30);\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH3+ +CH4 -> CH(A) +?CH4+ +H2 According to Smith and Adams (1977) the probability of charge transfer is \ negligible at thermal energies, as it should be considering the threshold \ energy required.\ \>", "SmallText"], Cell["\<\ a3c4p := n*f*(fa3c4p*UnitStep[w3[z]-38.3]* 1.0*10^-25*(w3[z]-38.3)/(w3[z]+50.)/(1+w3[z]/50.)*100.*2./11.7+1.*10^-30);\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH3+ + CH4 -> H+ + 2 CH3 According to Smith and Adams (1977) the probability of breakup is negligible \ at thermal energies. We neglect it at all energies.\ \>", "SmallText"], Cell[BoxData[ \(\(a3c8o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH3+ + CH4 -> CH5+ + CH2 Huntress (1972) does not report this reaction at energies below 10 eV COM. \ We neglect it at all energies.\ \>", "SmallText"], Cell[BoxData[ \(\(a3c5o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH3+ + CH4 -> C2H3+ + 2H2 According to Huntress (1972) the rate coefficient for this reaction is very \ small below 1 eV COM and peaks at 12 % of Langevin at about 6 eV COM. We \ assume that it is included in the C2H5+ process.\ \>", "SmallText"], Cell["\<\ Plot these cross section in units of 10^-20 m^2 by choosing n = 10^20 m^-3. \ We note that the column depth for most of our data is that for 4 cm and 100 \ mTorr, i.e., 1.3*10^20 m^2, so that a process with a cross section of 10^-20 \ m^2 has a near unit probability of occurrence in the free fall passage of a \ CH3+ across the tube.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{\((\(\(l3cn/2\)/fl3cn\)/w3[z]\ /. \ w3[z]\ -> \ w3z)\), \((a3c0o\ /. \ w3[z]\ -> \ w3z)\), \((a3c4F\ \ /. \ w3[z]\ -> \ w3z)\), \((a3c1o\ \ /. \ w3[z]\ -> \ w3z)\), \((a3c4p\ /. \ w3[z]\ -> \ w3z)\), \((a3c94\ \ /. \ w3[z]\ -> \ w3z)\)}, {w3z, 1, 1000}, \ PlotRange\ -> \ \ {{1, 1000}, {10^\(-6\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: 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Mistroke .81225 .09917 L .81335 .09903 L .81441 .0989 L .81541 .09877 L .81648 .09864 L .8175 .09851 L .81847 .09839 L .8195 .09826 L .82048 .09813 L .82152 .098 L .82251 .09787 L .82346 .09775 L .82446 .09762 L .82542 .09749 L .82643 .09736 L .8274 .09723 L .82833 .09711 L .82931 .09698 L .83024 .09685 L .83113 .09673 L .83208 .0966 L .83299 .09648 L .83394 .09635 L .83485 .09622 L .83573 .0961 L .83665 .09598 L .83754 .09585 L .83838 .09573 L .83928 .09561 L .84013 .09549 L .84104 .09536 L .8419 .09524 L .84273 .09512 L .84361 .095 L .84445 .09488 L .84533 .09475 L .84618 .09463 L .84699 .09451 L .84785 .09439 L .84867 .09427 L .84946 .09415 L .85029 .09403 L .85109 .09391 L .85193 .09379 L .85273 .09367 L .85351 .09356 L .85432 .09343 L .8551 .09332 L .85585 .09321 L .85664 .09309 L Mistroke .8574 .09297 L .8582 .09285 L .85897 .09274 L .8597 .09263 L .86048 .09251 L .86123 .09239 L .86201 .09227 L .86277 .09216 L .86349 .09205 L .86426 .09193 L .86499 .09182 L .86569 .09171 L 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Mistroke .96292 .07468 L .96329 .07461 L .96365 .07454 L .96403 .07446 L .96439 .07439 L .96478 .07432 L .96515 .07425 L .96551 .07418 L .96589 .07411 L .96625 .07404 L .9666 .07397 L .96697 .0739 L .96732 .07383 L .9677 .07376 L .96806 .07369 L .96841 .07362 L .96878 .07355 L .96913 .07348 L .9695 .07341 L .96986 .07334 L .97021 .07327 L .97058 .0732 L .97093 .07313 L .97127 .07307 L .97163 .073 L .97197 .07293 L .97234 .07286 L .97269 .07279 L .97303 .07273 L .97339 .07266 L .97373 .07259 L .97406 .07253 L .97441 .07246 L .97475 .07239 L .9751 .07232 L .97545 .07226 L .97578 .07219 L .97613 .07213 L .97646 .07206 L .97682 .07199 L .97716 .07192 L .97749 .07186 L .97784 .07179 L .97817 .07173 L .97849 .07166 L .97883 .0716 L .97916 .07153 L .97951 .07146 L .97984 .0714 L .98016 .07134 L Mistroke .9805 .07127 L .98083 .07121 L .98117 .07114 L .98151 .07107 L .98183 .07101 L .98217 .07094 L .98249 .07088 L .98281 .07082 L .98314 .07075 L .98346 .07069 L .98379 .07062 L .98412 .07056 L 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This plot shows that for 100 mTorr of CH4 and at energies below ~10 eV, CH3+ \ is converted into C2H5+. Updated 3/18/01\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["CH4+ - CH4 data ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Here we need to convert the Peko et al (1998) cross sections for CH4+-CH4 \ collisions from COM energies to LAB energies using w4[z] = 2*releng. \ \>", "Subsubtitle"], Cell["\<\ CH4+ + CH4 elastic scattering = Langvin rate coefficient. The Peko et al experiments cover the energy range from ~ 1 to 200 eV. We \ have no data for higher energies. Momentum loss in elastic collisions Because we are using the momentum \ balance rather than the energy balance, the usual 2mM/(m+M)^2 factor is \ replaced by 2 in the loss function and we should use just the elastic plus \ inelastic (nonreactive) part of the Langevin cross section.\ \>", "SmallText"], Cell["\<\ l4cn :=n*f*fl4cn*2*releng*3.82*10^-19/Abs[releng]^.5 /. releng ->w4[z]/2; \ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ CH4+ +CH4 -> CH4 +CH4+ Peko et al (1998) give the symmetric charge exchange cross section for releng \ < 200 eV. Smith and Kevan (1971) found the charge transfer cross section to \ be smaller than 2.4e-20 m^2 at 50 eV.\ \>", "SmallText"], Cell[BoxData[ \(\(a4c4o := n*f*fa4c4o*10^\(-20\)*\((1.3 + \((releng/ 10)\)^1.5)\)/\((1 + \((releng/40. )\)^3)\)\ /. releng \[Rule] w4[z]/2;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ CH4+ +CH4 -> CH+ +CH3 From Peko et al (1998) this reaction was not observed\ \>", "SmallText"], Cell[BoxData[ \(\(a4c1o = 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ CH4+ +CH4 -> CH5+ +CH3 From Peko et al (1998) this cross section for for this reaction at 3 < releng \ < 200 eV is well below the Langevin value. Other people agree, e.g., \ Giardini-Guidoni and Friedman (1966), but reviews by Anicich (1993) and by \ Kim and Fox (1994) and paper like Henchman et al (1989) claim the Langevin \ value gives the CH5+ formation rate at thermal energhies. Peko et al (1998) \ suggest that the low energy process falls off at energies below 3 eV. We try \ to compromize by adding a low energy Langevin cross section that falls off \ near 0.5 eV to Peko et al (1998).\ \>", "SmallText"], Cell[BoxData[ \(\(a4c5o := n*f*fa4c5o/ Sqrt[releng] \((5.5*10^\(-20\)/\((1 + \((releng/ 10.5)\)^4)\)\ + 3.4*10^\(-19\)/\((1 + \((releng/0.5)\)^4)\))\)\ /. releng \[Rule] w4[z]/2;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell[CellGroupData[{ Cell[BoxData[ \(\((a4c5o\ /. \ {f\ -> 1, \ n\ -> \ 10^20})\)\ /. \ w4[z]\ -> \ 2*{2.5, 5, 10, 20}\)], "Input"], Cell[BoxData[ \({3.50171304750254`, 2.340906478350261`, 0.954283663446603`, 0.0868360265240371`}\)], "Output"] }, Open ]], Cell["\<\ CH4+ +CH4 -> H+ +?CH3 +?CH4 From Peko et al (1998) this cross section for this reaction at 3 < releng < \ 200 eV is\ \>", "SmallText"], Cell[BoxData[ \(a4c8o\ := n*f*\((fa4c8o*10^\(-20\)* UnitStep[releng - 5.4]*\((1 - 5.4/releng)\)^0.7*1.3* releng^0.6/\[IndentingNewLine]\((1 + \((releng/25)\)^1.1)\) + 1. *10^\(-30\))\)\ /. releng \[Rule] w4[z]/2\)], "Input", Evaluatable->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ To try to avoid problems with solving the differential equations, we make the \ substitution for releng.\ \>", "Text"], Cell[BoxData[ \(a4c8o\ := \ n*f*\((fa4c8o*10^\(-20\)* UnitStep[ w4[z] - 10.8]*\((1 - 10.8/w4[z])\)^0.7*1.3*\((w4[z]/ 2)\)^0.6/\[IndentingNewLine]\((1 + \((\(w4[z]/2\)/ 25)\)^1.1)\) + 1. *10^\(-30\))\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["It does not help the k = 0 problem.", "Text"], Cell["CH4+ +CH4 -> CH3+ +CH3 +H2", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{\ c\ == \ ch4p\ + \ ch4, ch4\ == \ ch4p\ + \ e\ + \ 12.61, ch4\ == \ ch3\ + \ h\ + 103.4/23.07, ch3\ == \ ch3p\ + e\ + \ 9.8, h2 == 2\ h\ + \ 4.48}, {ch4, ch4p, h, e}]\)], "Input"], Cell[BoxData[ \(\(\(1.674022540095363`\)\(\[InvisibleSpace]\)\) + 1.`\ ch3 + 1.`\ ch3p + 1.`\ h2 == c\)], "Output"] }, Open ]], Cell["or", "Text"], Cell["CH4+ +CH4 -> CH3+ +CH4 +H", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{\ c\ == \ ch4p\ + \ ch4, ch4\ == \ ch4p\ + \ e\ + \ 12.61, ch4\ == \ ch3\ + \ h\ + 103.4/23.07, ch3\ == \ ch3p\ + e\ + \ 9.8, h2 == 2\ h\ + \ 4.48}, {ch4p, h2, ch3, e}]\)], "Input"], Cell[BoxData[ \(\(\(1.6720112700476832`\)\(\[InvisibleSpace]\)\) + 1.`\ ch3p + 1.`\ ch4 + 1.`\ h == c\)], "Output"] }, Open ]], Cell["\<\ The cross section for this reaction from Peko et al (1998) at releng < 200 eV \ is modified to give a finite slope at threshold. Note that the two preceding \ reactions have the same threshold of 1.67 in CM or (14+14)/14*1.67 = 3.34 \ LAB. This is consistent with Peko et al (1998), but is difficult to \ reconcile with Huntress (1972).\ \>", "SmallText"], Cell["\<\ a4c3o := n*f*(fa4c3o*UnitStep[releng-1.55]*10^-20*(1-1.55/releng)^2/(0.04*\ releng^2/(1+(releng/8.)^3.5)+ 3.5*(releng/50)^2.5/(1+(releng/60)^2.8))+1.*10^-30) /. releng \ ->w4[z]/2;\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH4+ +CH4 -> CH2+ +CH4 +H2", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{\ c\ == \ ch4p\ + \ ch4, ch4p\ == \ ch2p\ + \ h2\ + \ 2.6}, {ch4p}]\)], "Input"], Cell[BoxData[ \(\(\(2.6`\)\(\[InvisibleSpace]\)\) + 1.`\ ch2p + 1.`\ ch4 + 1.`\ h2 == c\)], "Output"] }, Open ]], Cell["\<\ The cross section for this reaction from Huntress, J. Chem. Phys. 56, 5111 \ (1972) shows an increasing relative reaction rate for enLab between 1.5 and \ 10 eV. In view of the expected threshold of 5.2 eV LAB, Huntress must have \ had a poor energy resolution. This enegy balance is based on Fig. 1 of Peko \ et al (1998). Peko et al (1998), Fig. 3 show this process to be very small, \ e.g., < 0.05E-16 for enrel from 3 to 50 eV and then to rise to ~ 0.3E-16 at \ 250 eV. We will neglect it.\ \>", "SmallText"], Cell["a4c2c := 0;", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ Plot these cross section in units of 10^-20 m^2 by choosing n = 10^20 m^-3. \ We note that the column depth for most of our data is that for 4 cm and 100 \ mTorr, i.e., 1.3*10^20 m^2, so that a process with a cross section of 10^-20 \ m^2 has a near unit probability of occurrence in the free fall passage of a \ CH4+ across the tube.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{\(\(l4cn/2\)/fl4cn\)/\((w4[z]/2)\)\ /. \ w4[z]\ -> \ w4z, a4c4o\ \ /. \ w4[z]\ -> \ w4z, a4c5o\ \ /. \ w4[z]\ -> \ w4z, a4c8o\ /. \ w4[z]\ -> \ w4z, \ a4c3o\ /. \ w4[z]\ -> \ w4z}, {w4z, 0.1, 1000}, \ PlotRange\ -> \ \ {{0.1, 1000}, {5. *10^\(-2\), 500}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 2000, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], 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L .96288 .24843 L .96296 .2484 L .96303 .24838 L .96311 .24836 L .96318 .24833 L .96326 .24831 L .96334 .24828 L .96341 .24826 L .96349 .24824 L .96357 .24821 L .96364 .24819 L .96371 .24817 L .96379 .24814 L .96386 .24812 L .96394 .2481 L .96402 .24807 L .96409 .24805 L .96417 .24803 L .96424 .24801 L .96432 .24798 L .9644 .24796 L .96447 .24793 L .96455 .24791 L .96462 .24789 L .9647 .24787 L .96477 .24784 L .96485 .24782 L .96492 .24779 L .965 .24777 L .96507 .24775 L Mistroke .96515 .24773 L .96522 .2477 L .96529 .24768 L .96537 .24766 L .96544 .24763 L .96552 .24761 L .96559 .24759 L .96566 .24757 L .96574 .24754 L .96581 .24752 L .96589 .2475 L .96597 .24747 L .96604 .24745 L .96612 .24743 L .96619 .2474 L .96626 .24738 L .96633 .24736 L .96641 .24734 L .96648 .24731 L .96656 .24729 L .96663 .24727 L .9667 .24724 L .96678 .24722 L .96685 .2472 L .96693 .24718 L .967 .24715 L .96708 .24713 L .96715 .24711 L .96722 .24709 L .96729 .24706 L .96737 .24704 L .96744 .24702 L .96752 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.98048 .24299 L .98054 .24297 L .98061 .24295 L .98068 .24293 L .98074 .24291 L .98081 .24289 L .98087 .24287 L .98093 .24285 L .981 .24283 L .98106 .24281 L .98113 .24279 L .98119 .24277 L .98126 .24275 L .98132 .24273 L .98139 .24271 L .98145 .24269 L .98151 .24267 L .98157 .24265 L .98164 .24263 L .98171 .24261 L .98177 .24259 L .98183 .24257 L .9819 .24255 L .98196 .24253 L .98203 .24251 L .98209 .24249 L .98216 .24247 L .98222 .24245 L .98228 .24243 L .98234 .24241 L Mistroke .98241 .24239 L .98247 .24237 L .98254 .24235 L .9826 .24233 L .98266 .24231 L .98273 .24229 L .98279 .24227 L .98286 .24225 L .98292 .24223 L .98299 .24221 L .98305 .24219 L .98311 .24218 L .98317 .24216 L .98324 .24214 L .9833 .24212 L .98337 .2421 L .98343 .24208 L .98349 .24206 L .98355 .24204 L .98361 .24202 L .98368 .242 L .98374 .24198 L .98381 .24196 L .98387 .24194 L .98393 .24192 L .98399 .2419 L .98406 .24188 L .98412 .24186 L .98418 .24184 L .98425 .24182 L .98431 .2418 L .98437 .24178 L .98443 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.98832 .24057 L .98838 .24055 L .98844 .24053 L .9885 .24051 L .98856 .24049 L Mistroke .98862 .24047 L .98868 .24045 L .98874 .24044 L .9888 .24042 L .98886 .2404 L .98892 .24038 L .98898 .24036 L .98904 .24034 L .9891 .24032 L .98916 .24031 L .98922 .24029 L .98928 .24027 L .98934 .24025 L .9894 .24023 L .98946 .24021 L .98952 .2402 L .98958 .24018 L .98964 .24016 L .9897 .24014 L .98976 .24012 L .98982 .2401 L .98988 .24008 L .98994 .24007 L .98999 .24005 L .99006 .24003 L .99012 .24001 L .99017 .23999 L .99023 .23997 L .99029 .23996 L .99035 .23994 L .99041 .23992 L .99047 .2399 L .99053 .23988 L .99059 .23986 L .99064 .23985 L .9907 .23983 L .99076 .23981 L .99082 .23979 L .99088 .23977 L .99094 .23975 L .991 .23974 L .99106 .23972 L .99112 .2397 L .99118 .23968 L .99123 .23966 L .9913 .23965 L .99135 .23963 L .99141 .23961 L .99147 .23959 L .99153 .23957 L Mistroke .99159 .23955 L .99165 .23954 L .99171 .23952 L .99177 .2395 L .99183 .23948 L .99188 .23946 L .99194 .23945 L .992 .23943 L .99206 .23941 L .99212 .23939 L .99217 .23937 L .99223 .23936 L .99229 .23934 L .99235 .23932 L .99241 .2393 L .99246 .23928 L .99252 .23927 L .99258 .23925 L .99264 .23923 L .9927 .23921 L .99275 .23919 L .99282 .23918 L .99287 .23916 L .99293 .23914 L .99299 .23912 L .99305 .2391 L .9931 .23909 L .99316 .23907 L .99322 .23905 L .99328 .23903 L .99334 .23901 L .99339 .239 L .99345 .23898 L .99351 .23896 L .99357 .23894 L .99363 .23893 L .99368 .23891 L .99374 .23889 L .9938 .23887 L .99385 .23885 L .99391 .23884 L .99397 .23882 L .99403 .2388 L .99409 .23878 L .99414 .23877 L .9942 .23875 L .99426 .23873 L .99431 .23871 L .99437 .2387 L .99443 .23868 L Mistroke .99449 .23866 L .99454 .23864 L .9946 .23862 L .99466 .23861 L .99471 .23859 L .99477 .23857 L .99483 .23855 L .99488 .23854 L .99494 .23852 L .995 .2385 L .99505 .23848 L .99511 .23847 L .99517 .23845 L .99523 .23843 L .99528 .23841 L .99534 .2384 L .9954 .23838 L .99545 .23836 L .99551 .23834 L .99556 .23833 L .99562 .23831 L .99568 .23829 L .99573 .23827 L .99579 .23826 L .99585 .23824 L .9959 .23822 L .99596 .2382 L .99602 .23819 L .99607 .23817 L .99613 .23815 L .99619 .23813 L .99624 .23812 L .9963 .2381 L .99635 .23808 L .99641 .23806 L .99647 .23805 L .99652 .23803 L .99658 .23801 L .99663 .238 L .99669 .23798 L .99675 .23796 L .9968 .23794 L .99686 .23793 L .99692 .23791 L .99697 .23789 L .99703 .23787 L .99708 .23786 L .99714 .23784 L .9972 .23782 L .99725 .23781 L Mistroke .99731 .23779 L .99736 .23777 L .99741 .23775 L .99747 .23774 L .99753 .23772 L .99758 .2377 L .99764 .23769 L .99769 .23767 L .99775 .23765 L .9978 .23763 L .99786 .23762 L .99792 .2376 L .99797 .23758 L .99803 .23757 L .99808 .23755 L .99814 .23753 L .99819 .23751 L .99825 .2375 L .9983 .23748 L .99836 .23746 L .99841 .23745 L .99847 .23743 L .99852 .23741 L .99858 .23739 L .99864 .23738 L .99869 .23736 L .99875 .23734 L .9988 .23733 L .99885 .23731 L .99891 .23729 L .99896 .23728 L .99902 .23726 L .99908 .23724 L .99913 .23722 L .99919 .23721 L .99924 .23719 L .99929 .23717 L .99935 .23716 L .9994 .23714 L .99946 .23712 L .99951 .23711 L .99956 .23709 L .99962 .23707 L .99967 .23706 L .99973 .23704 L .99979 .23702 L .99984 .23701 L .99989 .23699 L .99995 .23697 L 1 .23696 L Mistroke Mfstroke 1 .6 0 r 0 .21864 m .02706 .21865 L .05006 .21866 L .06805 .21867 L .08217 .21868 L .11056 .21871 L .13193 .21874 L .15035 .21877 L .16496 .2188 L .19216 .21888 L .21277 .21897 L .23169 .21907 L .24864 .21919 L .26212 .2193 L .28361 .21954 L .30278 .21981 L .33191 .22039 L .35407 .22101 L .37355 .22173 L .38948 .22247 L .40419 .22331 L .41669 .22415 L .4275 .225 L .43792 .22593 L .4471 .22685 L .45524 .22776 L .46329 .22876 L .47051 .22973 L .4777 .23078 L .4842 .23181 L .4901 .23281 L .49605 .23388 L .50148 .23493 L .50646 .23594 L .51153 .23702 L .51619 .23807 L .52093 .23918 L .52532 .24026 L .52937 .24129 L .53352 .2424 L .53738 .24346 L .54133 .24459 L .54501 .24567 L .54843 .24671 L .55196 .24781 L .55525 .24887 L .55832 .24988 L .5615 .25095 L .56448 .25197 L .56755 .25306 L Mistroke .57043 .25409 L .57314 .25508 L .57594 .25613 L .57857 .25712 L .5813 .25818 L .58387 .25918 L .58628 .26014 L .58879 .26115 L .59115 .26211 L .59338 .26303 L .5957 .26399 L .59788 .26491 L .60016 .26588 L .60231 .2668 L .60434 .26767 L .60645 .26859 L .60845 .26947 L .61034 .2703 L .61232 .27118 L .61419 .27201 L .61614 .27288 L .61798 .27371 L .61973 .27449 L .62156 .27532 L .62329 .2761 L .62511 .27692 L .62682 .2777 L .62845 .27844 L .63015 .27921 L .63177 .27994 L .6333 .28063 L .63491 .28136 L .63644 .28205 L .63803 .28276 L .63955 .28344 L .64099 .28409 L .6425 .28476 L .64394 .28539 L .6453 .28599 L .64673 .28662 L .64809 .28722 L .64952 .28783 L .65088 .28842 L .65217 .28897 L .65353 .28954 L .65482 .29008 L .65617 .29065 L .65746 .29118 L .65869 .29168 L .65998 .2922 L Mistroke .66121 .29269 L .66238 .29315 L .6636 .29363 L .66477 .29408 L .66601 .29455 L .66718 .29499 L .66829 .2954 L .66947 .29583 L .67059 .29623 L .67176 .29665 L .67289 .29704 L .67395 .2974 L .67508 .29778 L .67615 .29813 L .67717 .29846 L .67825 .2988 L .67928 .29912 L .68036 .29945 L .68139 .29975 L .68237 .30004 L .68341 .30033 L .6844 .3006 L .68534 .30086 L .68633 .30112 L .68728 .30136 L .68828 .3016 L .68923 .30183 L .69014 .30204 L .6911 .30226 L .69202 .30245 L .69298 .30266 L .69391 .30284 L .69479 .30301 L .69571 .30318 L .6966 .30334 L .69744 .30348 L .69834 .30363 L .69919 .30376 L .70009 .30389 L .70095 .30401 L .70177 .30411 L .70263 .30422 L .70346 .30431 L .70433 .3044 L .70516 .30448 L .70596 .30455 L .7068 .30462 L .7076 .30468 L .70837 .30473 L .70918 .30477 L Mistroke .70995 .30481 L .71077 .30484 L .71155 .30487 L .7123 .30488 L .71268 .30489 L .71288 .30489 L .71309 .3049 L .71328 .3049 L .71346 .3049 L .71355 .3049 L .71364 .3049 L .71372 .3049 L .71381 .3049 L .71386 .3049 L .71391 .3049 L .71396 .3049 L .71398 .3049 L .714 .3049 L .71401 .3049 L .71403 .3049 L .71405 .3049 L .71407 .3049 L .7141 .3049 L .71412 .3049 L .71414 .3049 L .71416 .3049 L .71419 .3049 L .71424 .3049 L .71428 .3049 L .71439 .3049 L .71449 .3049 L .71458 .3049 L .71476 .3049 L .71496 .3049 L .7153 .30489 L .71571 .30489 L .71608 .30488 L .7168 .30486 L .71756 .30483 L .71828 .3048 L .71897 .30477 L .71971 .30473 L .72041 .30468 L .72114 .30463 L .72185 .30457 L .72253 .30451 L .72324 .30444 L .72393 .30437 L .72465 .30429 L .72534 .3042 L Mistroke .726 .30412 L .7267 .30402 L .72737 .30393 L .72801 .30383 L .72868 .30372 L .72933 .30362 L .73001 .3035 L .73067 .30338 L .73129 .30326 L .73195 .30313 L .73259 .303 L .73319 .30288 L .73383 .30274 L .73445 .3026 L .7351 .30245 L .73572 .3023 L .73631 .30216 L .73694 .302 L .73754 .30184 L .73818 .30167 L .73878 .30151 L .73937 .30134 L .73998 .30117 L .74057 .301 L .74114 .30083 L .74174 .30065 L .74231 .30047 L .74291 .30028 L .74349 .30009 L .74405 .2999 L .74464 .29971 L .7452 .29951 L .74574 .29933 L .74631 .29912 L .74685 .29893 L .74743 .29872 L .74798 .29851 L .74851 .29831 L .74907 .2981 L .74961 .29789 L .75018 .29766 L .75072 .29745 L .75124 .29723 L .7518 .29701 L .75232 .29679 L .75283 .29657 L .75337 .29634 L .75388 .29612 L .75442 .29588 L .75494 .29565 L Mistroke .75544 .29543 L .75597 .29519 L .75648 .29496 L .75701 .29471 L .75752 .29447 L .75801 .29424 L .75853 .29399 L .75903 .29375 L .75951 .29352 L .76002 .29327 L .7605 .29303 L .76101 .29277 L .7615 .29253 L .76198 .29229 L .76247 .29203 L .76295 .29178 L .76341 .29154 L .7639 .29129 L .76436 .29104 L .76485 .29078 L .76532 .29052 L .76578 .29028 L .76626 .29001 L .76672 .28976 L .7672 .28949 L .76767 .28923 L .76811 .28898 L .76859 .28871 L .76904 .28845 L .76947 .2882 L .76994 .28794 L .77038 .28768 L .77084 .28741 L .77129 .28714 L .77172 .28689 L .77218 .28662 L .77261 .28636 L .77307 .28608 L .77352 .28581 L .77394 .28555 L .77439 .28527 L .77482 .28501 L .77524 .28475 L .77568 .28448 L .7761 .28422 L .77654 .28394 L .77697 .28367 L .77738 .28341 L .77781 .28313 L .77823 .28287 L Mistroke .77862 .28261 L .77905 .28234 L .77945 .28207 L .77988 .28179 L .78029 .28152 L .78069 .28126 L .78111 .28099 L .78151 .28072 L .78193 .28044 L .78234 .28017 L .78273 .2799 L .78314 .27962 L .78354 .27936 L .78392 .2791 L .78432 .27882 L .78471 .27856 L .78512 .27828 L .78552 .278 L .78589 .27774 L .78629 .27747 L .78668 .2772 L .78704 .27694 L .78743 .27667 L .78781 .27641 L .78821 .27613 L .78859 .27586 L .78895 .2756 L .78934 .27532 L .78971 .27506 L .7901 .27478 L .79048 .27451 L .79084 .27425 L .79122 .27397 L .79159 .2737 L .79195 .27345 L .79232 .27317 L .79268 .27291 L .79306 .27263 L .79342 .27237 L .79377 .27211 L .79415 .27183 L .7945 .27157 L .79488 .27129 L .79524 .27102 L .79559 .27076 L .79596 .27049 L .79631 .27022 L .79665 .26997 L .79701 .2697 L .79735 .26944 L Mistroke .79772 .26916 L .79807 .2689 L .79841 .26864 L .79876 .26837 L .79911 .26811 L .79944 .26786 L .79978 .26759 L .80012 .26733 L .80047 .26706 L .80081 .2668 L .80114 .26655 L .80149 .26628 L .80182 .26602 L .80217 .26575 L .80251 .26549 L .80283 .26523 L .80318 .26497 L .80351 .26471 L .80382 .26446 L .80416 .2642 L .80448 .26394 L .80482 .26368 L .80515 .26342 L .80547 .26317 L .8058 .2629 L .80612 .26265 L .80646 .26238 L .80679 .26212 L .8071 .26187 L .80743 .26161 L .80775 .26135 L .80806 .26111 L .80838 .26085 L .80869 .2606 L .80902 .26034 L .80934 .26008 L .80964 .25984 L .80996 .25958 L .81027 .25933 L .81057 .25909 L .81089 .25883 L .81119 .25859 L .81151 .25833 L .81182 .25808 L .81211 .25784 L .81243 .25758 L .81273 .25733 L .81304 .25707 L .81335 .25682 L .81365 .25658 L Mistroke .81396 .25633 L .81426 .25608 L .81454 .25585 L .81485 .25559 L .81514 .25535 L .81545 .2551 L .81575 .25485 L .81604 .25462 L .81634 .25436 L .81663 .25412 L .81691 .25389 L .81721 .25365 L .81749 .25341 L .81779 .25316 L .81808 .25292 L .81836 .25268 L .81866 .25244 L .81894 .2522 L .81924 .25195 L .81953 .25171 L .81981 .25148 L .8201 .25123 L .82038 .25099 L .82065 .25077 L .82094 .25052 L .82122 .25029 L .82151 .25004 L .82179 .24981 L .82206 .24958 L .82235 .24934 L .82262 .24911 L .82291 .24886 L .82319 .24862 L .82346 .24839 L .82375 .24815 L .82402 .24792 L .82428 .2477 L .82456 .24746 L .82483 .24723 L .82512 .24699 L .82539 .24676 L .82565 .24653 L .82593 .2463 L .8262 .24607 L .82645 .24585 L .82672 .24562 L .82698 .24539 L .82726 .24516 L .82753 .24493 L .82778 .24471 L Mistroke .82805 .24448 L .82831 .24425 L .82859 .24401 L .82886 .24379 L .82911 .24357 L .82938 .24333 L .82964 .24311 L .82989 .2429 L .83015 .24267 L .83041 .24245 L .83068 .24222 L .83094 .24199 L .83118 .24178 L .83145 .24155 L .8317 .24133 L .83194 .24112 L .8322 .2409 L .83245 .24068 L .83271 .24045 L .83297 .24023 L .83321 .24002 L .83347 .2398 L .83371 .23958 L .83398 .23935 L .83423 .23914 L .83447 .23892 L .83473 .2387 L .83497 .23849 L .83521 .23828 L .83546 .23806 L .8357 .23785 L .83596 .23762 L .8362 .23741 L .83644 .2372 L 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L .98599 .09956 L .98606 .09951 L .98612 .09945 L Mistroke .98618 .09939 L .98624 .09933 L .9863 .09928 L .98637 .09922 L .98643 .09916 L .98649 .09911 L .98655 .09905 L .98661 .09899 L .98667 .09894 L .98673 .09888 L .98679 .09882 L .98686 .09876 L .98692 .09871 L .98698 .09865 L .98704 .09859 L .9871 .09854 L .98716 .09848 L .98722 .09842 L .98728 .09837 L .98735 .09831 L .98741 .09825 L .98747 .0982 L .98753 .09814 L .98759 .09808 L .98765 .09802 L .98771 .09797 L .98777 .09791 L .98783 .09785 L .98789 .0978 L .98795 .09775 L .98801 .09769 L .98807 .09763 L .98813 .09758 L .98819 .09752 L .98825 .09747 L .98831 .09741 L .98837 .09735 L .98844 .09729 L .9885 .09724 L .98856 .09718 L .98862 .09713 L .98868 .09707 L .98874 .09702 L .9888 .09696 L .98886 .0969 L .98892 .09685 L .98898 .09679 L .98904 .09674 L .9891 .09668 L .98916 .09662 L Mistroke .98922 .09657 L .98928 .09651 L .98934 .09646 L .9894 .0964 L .98946 .09634 L .98952 .09629 L .98958 .09623 L .98964 .09618 L .9897 .09612 L .98976 .09606 L .98982 .09601 L .98988 .09595 L .98994 .0959 L .98999 .09585 L .99005 .09579 L .99011 .09574 L .99017 .09568 L .99023 .09562 L .99029 .09557 L .99035 .09551 L .99041 .09546 L .99047 .0954 L .99053 .09535 L .99059 .09529 L .99065 .09524 L .99071 .09518 L .99076 .09513 L .99082 .09507 L .99088 .09502 L .99094 .09496 L .991 .09491 L .99106 .09485 L .99112 .0948 L .99118 .09474 L .99124 .09469 L .9913 .09463 L .99136 .09458 L .99142 .09452 L .99148 .09447 L .99153 .09442 L .99159 .09436 L .99165 .09431 L .99171 .09425 L .99177 .09419 L .99183 .09414 L .99189 .09409 L .99195 .09403 L .992 .09398 L .99206 .09392 L .99212 .09387 L Mistroke .99218 .09382 L .99224 .09376 L .99229 .09371 L .99235 .09365 L .99241 .0936 L .99247 .09354 L .99253 .09349 L .99259 .09344 L .99265 .09338 L .9927 .09333 L .99276 .09328 L .99282 .09322 L .99287 .09317 L .99294 .09311 L .99299 .09306 L .99305 .09301 L .99311 .09295 L .99317 .0929 L .99322 .09285 L .99328 .09279 L .99334 .09274 L .9934 .09268 L .99345 .09263 L .99351 .09258 L .99357 .09252 L .99362 .09247 L .99368 .09242 L .99374 .09236 L .9938 .09231 L .99386 .09225 L .99391 .0922 L .99397 .09215 L .99403 .0921 L .99408 .09204 L .99414 .09199 L .9942 .09194 L .99426 .09188 L .99431 .09183 L .99437 .09178 L .99443 .09172 L .99449 .09167 L .99454 .09162 L .9946 .09156 L .99466 .09151 L .99471 .09146 L .99477 .0914 L .99483 .09135 L .99489 .0913 L .99495 .09124 L .995 .09119 L Mistroke .99506 .09114 L .99511 .09109 L .99517 .09104 L .99523 .09098 L .99528 .09093 L .99534 .09088 L .9954 .09082 L .99545 .09077 L .99551 .09072 L .99557 .09067 L .99562 .09061 L .99568 .09056 L .99574 .09051 L .99579 .09045 L .99585 .0904 L .9959 .09035 L .99596 .0903 L .99602 .09025 L .99608 .09019 L .99613 .09014 L .99619 .09009 L .99624 .09004 L .9963 .08998 L .99636 .08993 L .99642 .08988 L .99647 .08983 L .99653 .08977 L .99658 .08972 L .99664 .08967 L .99669 .08962 L .99675 .08957 L .99681 .08951 L .99686 .08946 L .99692 .08941 L .99698 .08936 L .99703 .0893 L .99708 .08925 L .99714 .0892 L .9972 .08915 L .99725 .0891 L .99731 .08905 L .99736 .089 L .99742 .08894 L .99747 .08889 L .99753 .08884 L .99759 .08879 L .99764 .08874 L .9977 .08868 L .99776 .08863 L .99781 .08858 L Mistroke .99786 .08853 L .99792 .08848 L .99798 .08842 L .99803 .08837 L .99809 .08832 L .99814 .08827 L .9982 .08822 L .99825 .08817 L .99831 .08812 L .99836 .08807 L .99842 .08802 L .99847 .08796 L .99852 .08792 L .99858 .08786 L .99863 .08781 L .99869 .08776 L .99875 .08771 L .9988 .08766 L .99886 .08761 L .99891 .08756 L .99896 .08751 L .99902 .08746 L .99907 .08741 L .99913 .08735 L .99919 .0873 L .99924 .08725 L .99929 .0872 L .99935 .08715 L .99941 .0871 L .99946 .08705 L .99951 .087 L .99957 .08694 L .99962 .08689 L .99968 .08684 L .99973 .08679 L .99979 .08674 L .99984 .08669 L .9999 .08664 L .99995 .08659 L 1 .08654 L Mfstroke .2 1 0 r 0 .54821 m .13193 .50671 L .16518 .4947 L .19216 .48241 L .21407 .46868 L .23113 .45414 L .26212 .41728 L .30375 .35961 L .31982 .3415 L .3328 .32961 L .35491 .31425 L .37368 .30459 L .38911 .29804 L .40343 .29259 L .41563 .28825 L .42726 .28426 L .43739 .28084 L .44632 .27783 L .45507 .27486 L .46289 .27217 L .47061 .26946 L .47757 .26695 L .48387 .2646 L .4902 .26214 L .49596 .25981 L .50122 .25756 L .50656 .25517 L .51146 .25284 L .51644 .25032 L .52102 .24784 L .52526 .2454 L .5296 .24273 L .53361 .24008 L .53734 .23746 L .54117 .23457 L .54474 .23171 L .5484 .22856 L .55182 .22542 L .55501 .22232 L .5583 .21891 L .56138 .21554 L .56456 .21185 L .56754 .20821 L .57033 .20463 L .57322 .20073 L .57594 .19691 L .57848 .19317 L .58113 .18912 L .58362 .18518 L .5862 .18093 L Mistroke .58863 .17679 L .59092 .17278 L .59331 .16847 L .59555 .16431 L .59789 .15986 L .6001 .15556 L .60218 .15141 L .60435 .147 L .6064 .14274 L .60834 .13866 L .61036 .13432 L .61227 .13015 L .61427 .12574 L .61616 .1215 L .61795 .11744 L .61982 .11315 L .62159 .10904 L .62326 .10511 L .62502 .10095 L .62668 .09698 L .62842 .09278 L .63007 .08877 L .63164 .08494 L .63328 .0809 L .63484 .07704 L .63647 .07298 L .63801 .06909 L .63948 .06539 L .64102 .06148 L .64249 .05776 L .64388 .05421 L .64533 .05046 L .64672 .04689 L .64818 .04312 L .64956 .03953 L .65087 .03611 L .65225 .0325 L .65357 .02906 L .65481 .02578 L .65613 .02232 L .65738 .01903 L .65869 .01555 L .65994 .01224 L .66112 .00908 L .66238 .00575 L .66357 .00258 L Mfstroke .66357 .00258 m .66453 0 L s 0 1 1 r .50867 0 m .50874 .00956 L .50888 .02471 L .50902 .03551 L .50932 .05333 L .50964 .06679 L .51021 .08404 L .51082 .09742 L .51148 .10864 L .51274 .12457 L .51387 .1354 L .51637 .15304 L .5186 .16469 L .52097 .17457 L .52549 .18913 L .52968 .19954 L .53355 .20751 L .53753 .21452 L .54123 .22023 L .54502 .22545 L .54856 .22985 L .55186 .23361 L .55526 .2372 L .55843 .24032 L .56171 .24333 L .56478 .24597 L .56765 .24832 L .57062 .25062 L .57341 .25267 L .57602 .25451 L .57874 .25634 L .58129 .25798 L .58394 .25962 L .58643 .26111 L .58877 .26245 L .59121 .26381 L .59351 .26504 L .59568 .26616 L .59794 .2673 L .60007 .26833 L .60229 .26938 L .60438 .27034 L .60636 .27122 L .60843 .27212 L .61038 .27294 L .61242 .27378 L .61435 .27454 L .61617 .27525 L .61808 .27597 L .61988 .27664 L Mistroke .62159 .27725 L .62338 .27788 L .62507 .27846 L .62685 .27906 L .62853 .27961 L .63012 .28011 L .63179 .28063 L .63337 .28112 L .63487 .28156 L .63645 .28202 L .63794 .28245 L .63951 .28289 L .641 .28329 L .64241 .28367 L .6439 .28405 L .64531 .28441 L .64679 .28478 L .64819 .28512 L .64953 .28544 L .65093 .28577 L .65226 .28608 L .65353 .28636 L .65486 .28665 L .65613 .28692 L .65746 .2872 L .65873 .28746 L .65994 .2877 L .6612 .28795 L .66241 .28818 L .66368 .28842 L .66489 .28865 L .66604 .28885 L .66725 .28907 L .6684 .28926 L .6695 .28945 L .67065 .28964 L .67175 .28982 L .67291 .29 L .67402 .29017 L .67507 .29033 L .67617 .29049 L .67723 .29064 L .67824 .29079 L .6793 .29093 L .68031 .29107 L .68137 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L .73033 .29429 L .73049 .29429 L .73063 .29429 L .73079 .29429 L .73087 .29429 L .73095 .29429 L .73099 .29429 L .73103 .29429 L .73106 .29429 L .7311 .29429 L .73112 .29429 L .73114 .29429 L .73116 .29429 L .73118 .29429 L .7312 .29429 L .73121 .29429 L .73123 .29429 L .73125 .29429 L .73127 .29429 L .73129 .29429 L .73134 .29429 L .73138 .29429 L .73142 .29429 L .7315 .29429 L .7316 .29429 L .73177 .29429 L .73192 .29429 L .73223 .29429 L .73256 .29429 L .73321 .29429 L .73383 .29428 L .73449 .29428 L .73512 .29427 L .73572 .29427 L .73636 .29426 L .73697 .29425 L .73756 .29425 L .73817 .29424 L .73877 .29423 L .73939 .29422 L .73999 .2942 L .74056 .29419 L Mistroke .74117 .29418 L .74175 .29417 L .74231 .29415 L .74289 .29414 L .74346 .29412 L .74405 .29411 L .74462 .29409 L .74517 .29408 L .74575 .29406 L .7463 .29404 L .74689 .29402 L .74745 .294 L .74798 .29398 L .74855 .29396 L .7491 .29394 L .74962 .29392 L .75017 .2939 L .7507 .29388 L .75126 .29385 L .75179 .29383 L .75231 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.96064 .25553 L .96072 .25551 L .9608 .25549 L .96088 .25547 L .96095 .25545 L .96103 .25543 L .96111 .25541 L .96119 .25539 L .96126 .25537 L .96134 .25535 L .96142 .25532 L .9615 .2553 L .96157 .25528 L .96165 .25526 L .96173 .25524 L .9618 .25522 L .96188 .2552 L .96196 .25518 L .96204 .25516 L .96211 .25514 L .96219 .25512 L .96227 .2551 L .96234 .25508 L .96242 .25506 L .9625 .25504 L .96257 .25502 L .96265 .255 L .96273 .25498 L .9628 .25496 L .96288 .25494 L .96295 .25492 L .96303 .25489 L .96311 .25487 L .96318 .25485 L .96326 .25483 L .96333 .25481 L .96341 .25479 L .96349 .25477 L .96357 .25475 L .96364 .25473 L .96372 .25471 L .96379 .25469 L .96387 .25467 L Mistroke .96394 .25465 L .96402 .25463 L .9641 .25461 L .96417 .25459 L .96425 .25457 L .96432 .25455 L .9644 .25453 L .96447 .25451 L .96455 .25449 L .96462 .25447 L .9647 .25445 L .96477 .25443 L .96485 .25441 L .96492 .25439 L .965 .25437 L .96508 .25435 L .96515 .25433 L .96523 .25431 L .9653 .25429 L .96537 .25427 L 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.9744 .25183 L .97447 .25181 L .97454 .25179 L .97461 .25177 L .97467 .25175 L Mistroke .97474 .25174 L .97481 .25172 L .97488 .2517 L .97495 .25168 L .97501 .25166 L .97508 .25164 L .97515 .25162 L .97522 .25161 L .97529 .25159 L .97536 .25157 L .97542 .25155 L .97549 .25153 L .97556 .25151 L .97563 .25149 L .9757 .25148 L .97576 .25146 L .97583 .25144 L .9759 .25142 L .97597 .2514 L .97604 .25138 L .9761 .25136 L .97617 .25135 L .97624 .25133 L .97631 .25131 L .97638 .25129 L .97644 .25127 L .97651 .25125 L .97658 .25123 L .97664 .25122 L .97671 .2512 L .97678 .25118 L .97685 .25116 L .97692 .25114 L .97698 .25112 L .97705 .25111 L .97711 .25109 L .97718 .25107 L .97725 .25105 L .97732 .25103 L .97738 .25102 L .97745 .251 L .97751 .25098 L .97758 .25096 L .97765 .25094 L .97772 .25092 L .97779 .25091 L .97785 .25089 L .97792 .25087 L .97798 .25085 L .97805 .25083 L Mistroke .97812 .25081 L .97818 .2508 L .97825 .25078 L .97832 .25076 L .97838 .25074 L .97845 .25073 L .97851 .25071 L 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.99041 .24743 L .99047 .24741 L .99053 .2474 L .99059 .24738 L Mistroke .99065 .24737 L .99071 .24735 L .99077 .24733 L .99083 .24732 L .99089 .2473 L .99095 .24728 L .991 .24727 L .99107 .24725 L .99112 .24723 L .99118 .24722 L .99124 .2472 L .9913 .24719 L .99136 .24717 L .99142 .24715 L .99148 .24714 L .99154 .24712 L .99159 .2471 L .99165 .24709 L .99171 .24707 L .99177 .24706 L .99183 .24704 L .99189 .24702 L .99194 .24701 L .992 .24699 L .99206 .24697 L .99212 .24696 L .99218 .24694 L .99224 .24692 L .9923 .24691 L .99236 .24689 L .99241 .24688 L .99247 .24686 L .99253 .24684 L .99259 .24683 L .99265 .24681 L .9927 .2468 L .99276 .24678 L .99282 .24676 L .99287 .24675 L .99293 .24673 L .99299 .24672 L .99305 .2467 L .99311 .24668 L .99316 .24667 L .99322 .24665 L .99328 .24664 L .99334 .24662 L .9934 .2466 L .99345 .24659 L .99351 .24657 L Mistroke .99357 .24655 L .99363 .24654 L .99368 .24652 L .99374 .24651 L .9938 .24649 L .99386 .24647 L .99391 .24646 L .99397 .24644 L .99403 .24643 L .99409 .24641 L .99415 .24639 L .9942 .24638 L .99426 .24636 L .99432 .24635 L .99437 .24633 L .99443 .24631 L .99449 .2463 L .99455 .24628 L .9946 .24627 L .99466 .24625 L .99472 .24623 L .99477 .24622 L .99483 .2462 L .99489 .24619 L .99494 .24617 L .995 .24616 L .99506 .24614 L .99511 .24612 L .99517 .24611 L .99523 .24609 L .99529 .24608 L .99534 .24606 L .9954 .24605 L .99546 .24603 L .99551 .24601 L .99557 .246 L .99562 .24598 L .99568 .24597 L .99574 .24595 L .99579 .24593 L .99585 .24592 L .99591 .2459 L .99596 .24589 L .99602 .24587 L .99608 .24586 L .99613 .24584 L .99619 .24582 L .99625 .24581 L .9963 .24579 L .99636 .24578 L Mistroke .99641 .24576 L .99647 .24575 L .99653 .24573 L .99658 .24571 L .99664 .2457 L .9967 .24568 L .99675 .24567 L .99681 .24565 L .99686 .24564 L .99692 .24562 L .99698 .24561 L .99703 .24559 L .99709 .24557 L .99714 .24556 L .9972 .24554 L .99726 .24553 L .99731 .24551 L .99737 .2455 L .99742 .24548 L .99748 .24547 L .99753 .24545 L .99759 .24543 L .99765 .24542 L .9977 .2454 L .99775 .24539 L .99781 .24537 L .99787 .24536 L .99792 .24534 L .99798 .24533 L .99803 .24531 L .99809 .2453 L .99814 .24528 L .99819 .24526 L .99825 .24525 L .99831 .24523 L .99836 .24522 L .99842 .2452 L .99847 .24519 L .99853 .24517 L .99858 .24516 L .99864 .24514 L .99869 .24513 L .99875 .24511 L .9988 .24509 L .99886 .24508 L .99891 .24506 L .99897 .24505 L .99902 .24503 L .99908 .24502 L .99913 .245 L Mistroke .99919 .24499 L .99924 .24497 L .9993 .24496 L .99935 .24494 L .99941 .24493 L .99946 .24491 L .99952 .2449 L .99957 .24488 L .99962 .24486 L .99968 .24485 L .99973 .24483 L .99979 .24482 L .99984 .2448 L .99989 .24479 L .99995 .24477 L 1 .24476 L Mfstroke .2 0 1 r .38137 0 m .38182 .00695 L .38387 .03081 L .386 .05058 L .38971 .07711 L .39324 .09613 L .39689 .1116 L .40319 .13139 L .40653 .13938 L .41006 .14638 L .41619 .15585 L .42189 .16227 L .42764 .16696 L .43271 .16991 L .43726 .17179 L .43963 .17252 L .44208 .1731 L .44412 .17348 L .44631 .17377 L .44749 .17389 L .44859 .17397 L .44957 .17402 L .45012 .17404 L .45062 .17405 L .45088 .17406 L .45116 .17406 L .45142 .17407 L .45166 .17407 L .45194 .17407 L .4521 .17407 L .45225 .17407 L .45251 .17406 L .45266 .17406 L .4528 .17406 L .45336 .17405 L .45367 .17404 L .45396 .17403 L .45505 .17398 L .45602 .17392 L .45705 .17384 L .45889 .17366 L .46294 .17309 L .46696 .17234 L .47064 .1715 L .47731 .1697 L .48399 .16762 L .49005 .1656 L .49558 .1637 L .50117 .16179 L .50629 .1601 L Mistroke .51149 .15849 L .51627 .15714 L .52067 .15603 L .52517 .15507 L .52933 .15434 L .5314 .15404 L .53359 .15378 L .53549 .15359 L .53655 .15351 L .53754 .15344 L .53854 .15338 L .53945 .15334 L .54041 .15331 L .54094 .15329 L .54144 .15328 L .54164 .15328 L .54186 .15328 L .54199 .15328 L .5421 .15328 L .54222 .15328 L .54233 .15328 L .54244 .15327 L .54255 .15327 L .54262 .15327 L .54268 .15327 L .54279 .15327 L .54291 .15327 L .54303 .15327 L .54308 .15327 L .54315 .15328 L .54328 .15328 L .5435 .15328 L .5437 .15328 L .54415 .15329 L .54456 .15329 L .54496 .1533 L .54582 .15333 L .54673 .15337 L .54836 .15347 L .55022 .15363 L .55195 .15381 L .55517 .15425 L .5585 .15485 L .5616 .15553 L .56451 .15627 L .56753 .15715 L .57035 .15806 L .57327 .1591 L .57602 .16016 L .57859 .16121 L Mistroke .58127 .16237 L .58378 .16351 L .58614 .16463 L .58861 .16583 L .59092 .16699 L .59333 .16823 L .59561 .16942 L .59775 .17056 L .59998 .17176 L .60209 .1729 L .60429 .1741 L .60636 .17523 L .60832 .17629 L .61037 .17739 L .6123 .17843 L .61413 .1794 L .61605 .1804 L .61786 .18133 L .61975 .18228 L .62154 .18317 L .62324 .18398 L .62501 .18482 L .6267 .18558 L .62846 .18635 L .63013 .18706 L .63171 .1877 L .63337 .18835 L .63494 .18893 L .63643 .18945 L .638 .18997 L .63949 .19044 L .64104 .19089 L .64252 .19129 L .64393 .19164 L .6454 .19197 L .64681 .19226 L .64814 .1925 L .64954 .19273 L .65087 .19291 L .65226 .19307 L .65359 .19319 L .65485 .19328 L .6555 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The small charge transfer \ cross section at high energies worries me. Updated 3/31/01\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["CH5+ - CH4 data ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ CH5+ + CH4 Momentum loss in elastic collisions Because we are using the momentum \ balance rather than the energy balance, the usual 2mM/(m+M)^2 factor does not \ appear in the loss function and we should use just the elastic plus inelastic \ (nonreactive) part of the Langevin cross section. Presumably we need to add a \ fall-off at high energies. Also, the Langevin rate is presumably the total \ collision rate at low energies and the elastic rate coefficient may be much \ smaller.\ \>", "SmallText"], Cell["\<\ l5cn :=n*f*fl5cn*2*w5[z]*3.88*10^-19/w5[z]^.5; \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ Note that the ion mobility data of de Urquijo et al (1997) indicates that a) \ the effective collision frequency is larger than the Langevin value, and b) \ the ion-molecule collision frequency for CH5+ in CH4 begins to drop below \ Langivin at energies of roughly twice thermal.\ \>", "SmallText"], Cell["\<\ CH5+ + CH4 -> CH3+ + CH4 + H2 From Fig. 1 of Peko et al (1998) the energetics are: \ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{\ c\ == \ ch5p\ + \ ch4, ch5p\ == \ ch3p\ + \ h2\ + \ 1.7}, {ch4p, ch5p}]\)], "Input"], Cell[BoxData[ \(\(\(1.7`\)\(\[InvisibleSpace]\)\) + 1.`\ ch3p + 1.`\ ch4 + 1.`\ h2 == c\)], "Output"] }, Open ]], Cell["\<\ According to Field and Munson, J. Am. Chem. Soc. 87, 3289 (1965), the \ reaction rate coefficients for CH5+, C2H4+, C2H5+ and C3F5+ with CH4 are less \ than ~ 1E-12 cm^3/s in a mass spectrometer ion source at pressures up to 1.7 \ Torr, but unspecified energies. According to Glosik et al, J. Chem. Phys. \ 101, 3792 (1994) CH5+ drifting through in He breaks up as if the dissociation \ energy were 1.1 to 1.4 eV rather than the expected 1.8 eV. Also, a column \ density of about 3 torr cm = 1e17 cm^2 or 1e21 m^2 of He is required to reach \ the steady-state dissociation rate at E/n = 100 Td. Because our experiment \ showing interesting heavy particle effects has a column density of only \ 3.8*3.3e15 = 1.25e16 cm^2 or 1.25e20 m^2, the steady-state drift data would \ not apply. The best we can do is assume a threshold of 1.7 eV and guess at \ the dissociation cross section above threshold, where the threshold in the \ LAB frame is 33/16*1.7 = 3.5 eV. Our guess probably overestimates the cross \ section, especially near threshold. We add a fall-off at high energies so as \ to avoid problems with the contribution to the momentum balance caused by the \ derivative term, i.e., the flow of energy along the field direction.\ \>", "SmallText"], Cell[BoxData[ \(a5c3o\ := \ n*f*\((fa5c3o* UnitStep[ w5[z] - 3.5]*3.38*10^\(-19\)*\(\((1 - 3.5/w5[z])\)^\((2)\)/ w5[z]^0.5\)/\((1 + w5[z]/500)\)\ + 1. *10^\(-30\))\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ Here we assume that the C2H9+ complex has too much internal energy to break \ up into things like C2H6+.\ \>", "SmallText"], Cell["CH5+ + CH4 -> CH+ + CH4 + 2 H2 ", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{\ c\ == \ ch5p\ + \ ch4, ch5p\ == \ ch3p\ + \ h2\ + \ 1.7, ch3\ == \ ch3p\ + e\ + \ 9.8, h2\ == \ 2\ h\ + \ 4.48, ch\ == \ chp\ + \ e\ + \ 11.14, \ ch3\ == \ ch2\ + \ h\ + 108.8/23.07, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {ch5p, ch, ch2, ch3, ch3p, h, e}]\)], "Input"], Cell[BoxData[ \(\(\(7.610715214564369`\)\(\[InvisibleSpace]\)\) + 1.`\ ch4 + 1.`\ chp + 2.`\ h2 == c\)], "Output"] }, Open ]], Cell["\<\ We have not found any data for this process. The threshold is \ (17+16)/16*7.61 = 15.7 eV. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a5c1o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH5+ + CH4 -> CH4+ + CH3 + H2", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{\ c\ == \ ch5p\ + \ ch4, ch5p\ == \ ch3p\ + \ h2\ + \ 1.7, ch4\ == \ ch4p\ + \ e\ + \ 12.61, ch3\ == \ ch3p\ + e\ + \ 9.8, ch3\ == \ ch2\ + \ h\ + 108.8/23.07, h2\ == \ 2\ h\ + \ 4.48}, {ch5p, ch2, ch3p, ch4, h, e}]\)], "Input"], Cell[BoxData[ \(\(\(4.509999999999998`\)\(\[InvisibleSpace]\)\) + 1.`\ ch3 + 1.`\ ch4p + 1.`\ h2 == c\)], "Output"] }, Open ]], Cell["\<\ We have not found any data for this charge transfer process, which has a \ threshold at (17+16)/16*4.51 = 9.30 eV. We take the cross section in COM to \ be the same as for CH4+ + CH4 at low energies. We add a fall-off at high \ energies so as to avoid problems with the contribution to the momentum \ balance caused by the derivative term, i.e., the flow of energy along the \ field direction.\ \>", "SmallText"], Cell[BoxData[ \(\(a5c4o\ = \ n*f*fa5c4o*10^\(-20\)*\((1.3 + \((releng/ 10)\)^1.5/\((1 + \((releng/40. )\)^2.5)\))\)/\((1 + releng/500)\)\ /. releng \[Rule] 16/33*w5[z];\)\)], "Input",\ FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH5+ + CH4 -> H+ + 2 CH4 We have not found any data for this process. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a5c8o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH5+ + CH4 -> C2H5+ + 2 H2 We have not found any data for this process. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a5c0o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ fast CH5+ + CH4 -> slow CH5+ + CH4 Antisymmetric charge transfer. 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Langevin collision rate coefficient. Momentum loss in elastic collisions Because we are using the momentum \ balance rather than the energy balance, the usual 2mM/(m+M)^2 factor does not \ appear in the loss function and we should use just the elastic plus inelastic \ (nonreactive) part of the Langevin cross section. Presumably we need to add a \ fall-off at high energies. Also, the Langevin rate is presumably the total \ collision rate at low energies and the elastic rate coefficient may be much \ smaller.\ \>", "SmallText"], Cell["\<\ l0cn :=n*f*fl0cn*2*w0[z]*3.37*10^-19/w0[z]^.5; \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ Note that the ion mobility data of de Urquijo et al (1997) indicates that the \ ion-molecule collision frequency for C2H5+ in CH4 begins to drop below \ Langivin at energies of roughly twice thermal.\ \>", "SmallText"], Cell["\<\ The formation of more complex ions, such as C3H7+, is listed by Anicich \ (1993) as the principal thermal two-body reaction for C2H5+ + CH4 with a rate \ coefficient of 9e-20 m^3/s for a cross section of 2.6e-23/w0[z]^0.5. This \ value is so small we will neglect it.\ \>", "SmallText"], Cell["\<\ de Urquijo et al (1998) see about 8% C3H3+ at E/n = 1 kTd and nz = 1E20 m^2. \ \ \>", "SmallText"] }, Open ]], Cell["We will neglect breakup of C2Hx+ ions", "Text"], Cell[BoxData[ \(\(\(\(a0c5o = 0\) \)\(;\)\(\ \)\(\(a0c1o = 0\) \)\(;\)\(\(a0c3o = 0\) \)\(;\)\(\(a0c4o = 0\) \)\(;\)\(\(a0c8o = 0\) \)\(;\)\(\(a0c0c = 0\) \)\(;\)\(\ \ \ \ \ \ \)\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell[CellGroupData[{ Cell["fast CH + CH4 data", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We assume that the fast CH has the same energy as the CH+ ion. This is based \ on the assumption that the fast CH is produced from CH+ by charge transfer.\ \>", "SmallText"], Cell["fast CH energy (max)", "SmallText"], Cell["w9[z]:=w1[z]; ", "Input", PageWidth->Infinity, Evaluatable->False, ShowSpecialCharacters->False], Cell["\<\ fCH + CH4 -> destruction by cooling. From Allis (1956), p. 408 Eq. (25.2) \ the fractional energy loss in an elastic collision is \ 2Mm/(M+m)^2*[1-cos(theta)]. We assume that, as in viscosity weighted \ scattering, the important angle is 90 deg and that we should use 2Mm/(M+m)^2. \ Unfortunately, we do not know anything about CH-CH4 collisions and have to \ quess at an effective cross section. Our choice is a factor of 3.6 smaller \ than the Langevin cross section for CH+ + CH4. Note that we are effectively \ assuming that every collision results in CH cooling below the energies of \ interest, i.e., effectively the fast CH disappears on collision.\ \>", "SmallText"], Cell["\<\ a9coc:=n*f*fa9coc*1.0*10^-19/w9[z]^0.5/(1+w9[z]/100.); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ fCH + CH4 -> CH(A) + CH4 -> CH + CH4 + 432 nm The threshold COM energy for this process is 1/432E-8/8065 = 2.87 eV and in \ the laboratory 29/16*2.87 = 5.20 eV. Here, again we have to quess at the \ cross section. I have no idea where thie following came from. \ \>", "SmallText"], Cell["\<\ a9cpc :=n*f*(fa9cpc*UnitStep[w9[z]-5.20]*2.5*10^-23*(w9[z]-5.20)/(w9[z]+100.)/\ (1+w9[z]/1000.)*200.*2*1.1/78+1.*10^-30);\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ Plot these cross section in units of 10^-20 m^2 or 10^-16 cm^2. 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This is \ based on the assumption that the fast CH3 is produced from CH3+ by charge \ transfer.\ \>", "SmallText"], Cell["fast CH3 energy (max)", "SmallText"], Cell["wF[z]:=w3[z]; ", "Input", PageWidth->Infinity, Evaluatable->False, ShowSpecialCharacters->False], Cell["\<\ fCH3 + CH4 -> destruction by cooling. From Allis (1956), p. 408 Eq. (25.2) \ the fractional energy loss in an elastic collision is \ 2Mm/(M+m)^2*[1-cos(theta)]. We assume that, as in viscosity weighted \ scattering, the important angle is 90 deg and that we should use 2Mm/(M+m)^2. \ Unfortunately, we do not know anything about CH3-CH4 collisions and have to \ quess at an effective cross section. Our choice is a factor of 3.6 smaller \ than the Langevin cross section for CH3+ + CH4. Note that we are effectively \ assuming that every collision results in CH3 cooling below the energies of \ interest, i.e., effectively the fast CH disappears on collision.\ \>", "SmallText"], Cell["\<\ aFcoc:=n*f*faFcoc*1.0*10^-19/wF[z]^0.5/(1+wF[z]/100.); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell[CellGroupData[{ Cell[BoxData[ \(aFcoc\)], "Input"], Cell[BoxData[ \(\(1.`*^-19\ f\ n\)\/\(\((1 + 0.01`\ wF[z])\)\ wF[z]\^0.5`\)\)], "Output"] }, Open ]], Cell["fCH3 + CH4 -> CH(A) + CH4 + H2 -> CH + CH4 + H2 + 432 nm ", \ "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{a == ch3\ + \ ch4, h2\ == \ 2\ h\ + \ 4.48, ch3\ == \ ch2\ + \ h\ + 108.8/23.07, ch\ == \ cha\ + \ 2.87, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {h, ch, ch2, ch3}]\)], "Input"], Cell[BoxData[ \(\(\(7.440715214564369`\)\(\[InvisibleSpace]\)\) + 1.`\ ch4 + 1.`\ cha + 1.`\ h2 == a\)], "Output"] }, Open ]], Cell["\<\ The threshold COM energy for this process is 1.70 eV and in the laboratory \ 31/16*7.44 = 14.4 eV. 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.99974 .38211 L 1 .38209 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{432, 266.938}, ImageCacheValid->False] }, Open ]], Cell["Ar+ - CH4 data", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[CellGroupData[{ Cell["\<\ Ar+ + CH4 -> CH4 +Ar+ Momentum loss in elastic and inelastic collisions Because we are using the \ momentum balance rather than the energy balance, the usual 2mM/(m+M)^2 factor \ does not appear in the loss function and we should use just the elastic plus \ inelastic (nonreactive) part of the Langevin cross section. Presumably we \ should add a fall-off factor at high energies. We add a fall-off at high \ energies so as to avoid problems with the contribution to the momentum \ balance caused by the derivative term, i.e., the flow of energy along the \ field direction.\ \>", "SmallText"], Cell["l6cn:=n*f*fl6cn*2.*w6[z]*5.06*10^-19/(w6[z]^.5); ", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["Ar+ +CH4\[Rule]CH3+ +Ar +H ", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{c\ == \ arp\ + \ ch4, \ ch3\ == \ ch3p\ + e\ + \ 9.8, ch4\ == \ ch3\ + \ h\ + 103.4/23.07, ar\ == \ arp\ + \ e\ + \ 15.76}, \[IndentingNewLine]{arp, ch4, ch3, e}]\)], "Input"], Cell[BoxData[ \(\(-1.477988729952319`\) + 1.`\ ar + 1.`\ ch3p + 1.`\ h == c\)], "Output"] }, Open ]], Cell["\<\ Cross section based on Tosi et al, Int'l. J. Mass Spectrom. and Ion Processes \ 149/150, 345 (1995). Note that the formation of CH2+ is lower by a factor of \ roughly 6 and we will neglect it. Note that Tosi et al use COM energies so \ that engCOM = 16/(16+40) w6[z]. We add a fall-off at high energies so as to \ avoid problems with the contribution to the momentum balance caused by the \ derivative term, i.e., the flow of energy along the field direction. This \ reaction is exothermic by 1.48 eV in center-of-mass. Note that the \ corresponding reaction with Ar metastables is endothermic. Because the Ar \ metastable should not have kinetic energy they could excite CH(A) , but not \ ionize CH4. We will ignore them.\ \>", "SmallText"], Cell["\<\ Chatham et al, J. Chem. Phys. 79, 1301 (1983) get a rate coefficient for \ charge transfer formation of CH3+ of 1E-15 m^3 for COM energies from 0.03 to \ 2.5 eV, i.e., ion LAB energies from 0.1 to 9 eV. This is very close to the \ theoretical value given above. Jones and Harrison, Int'l. J. Mass \ Spectromertry and Ion Processes 6, 77 (1971) get a 20% lower rate \ coefficient. Gale et al, Int'l. J. Mass Spectromertry and Ion Processes \ 149/150, 529 (1995) get a charge transfer cross section that decreases from \ roughly 5E-20 m^2 at ELAB = 6 eV to 3E-20 at 100 eV. These values are \ roughly 20% of the values from Tosi et al and Chatham et al. We use the Tosi \ et al (1995) cross section up to their maximum at 2.5 eV. At highe energies \ we are guessing.\ \>", "SmallText"], Cell[BoxData[ \(\(a6c3o\ = \ n*f*\(\((fa6c3o*2.0*10^\(-19\)/\((engCOM^ .5)\)*\((1 + \((engCOM/ 0.25)\)^6)\)^0.017)\)/\((1 + \((engCOM/ 25. )\)^6)\)^0.017\)/\((1 + engCOM/3000)\) /. \ engCOM\ -> \ 0.286*w6[z];\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["Ar+ + CH4 -> CH+ + Ar + H2 + H", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{c\ == \ arp\ + \ ch4, ch\ == \ chp\ + \ e\ + \ 11.14, \ ch4\ == \ ch3\ + \ h\ + 103.4/23.07, ar\ == \ arp\ + \ e\ + \ 15.76, ch3\ == \ ch2\ + \ h\ + 108.8/23.07, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {arp, ch4, ch3, ch2, ch, e}]\)], "Input"], Cell[BoxData[ \(\(\(8.912726484612051`\)\(\[InvisibleSpace]\)\) + 1.`\ ar + 1.`\ chp + 3.`\ h == c\)], "Output"] }, Open ]], Cell["\<\ von Koch (1964) and Szabo (1967) do not find any CH+ from this reaction. It \ is exothermic by 8.9 eV in CM and 31.2 in LAB. We will neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a6c1o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["Ar+ + CH4 -> CH2+ + Ar + H2 ", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{c\ == \ arp\ + \ ch4, ar\ == \ arp\ + \ e\ + \ 15.76, ch4p\ == \ ch2p\ + \ h2\ + \ 2.6, ch4\ == \ ch4p\ + \ e\ + \ 12.61}, {arp, ch4, ch4p, e}]\)], "Input"], Cell[BoxData[ \(\(-0.5500000000000003`\) + 1.`\ ar + 1.`\ ch2p + 1.`\ h2 == c\)], "Output"] }, Open ]], Cell["\<\ von Koch (1964) says that ~ 14% of the Ar+ + CH4 products are CH2+ for \ energies from 3 to 900 eV. Szabo (1967) give 20% at 15-20 eV. Jones and \ Harrison (1971) give 17% at energies below 1 eV and summarize earlier datas \ the give nearer 20% at higher energies. Tosi et al (1995) give 17% at \ energies from 0.13 to 2.5 eV. It is exothermic by 0.55 eV in CM.\ \>", "SmallText"], Cell[BoxData[ \(\(a6c2o\ = \ n*f*\(\((fa6c2o*0.17*2.0*10^\(-19\)/\((engCOM^ .5)\)*\((1 + \((engCOM/ 0.25)\)^6)\)^0.017)\)/\((1 + \((engCOM/ 25. )\)^6)\)^0.017\)/\((1 + engCOM/3000)\)\ /. \ engCOM\ -> \ 0.286*w6[z];\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["Ar+ +CH4\[Rule]CH4+ +Ar ", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{c\ == \ arp\ + \ ch4, ch4\ == \ ch4p\ + \ e\ + \ 12.61, ar\ == \ arp\ + \ e\ + \ 15.76}, {arp, ch4, e}]\)], "Input"], Cell[BoxData[ \(\(-3.1500000000000004`\) + 1.`\ ar + 1.`\ ch4p == c\)], "Output"] }, Open ]], Cell["\<\ From Tosi et al, Int'l. J. Mass Spectrom. and Ion Processes 149/150, 345 \ (1995) the formation of CH4+ is small. We will neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a6c4o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ Ar+ + CH4 -> ArH+ +? According to Wyatt et al, J. Chem. Phys. 60, 3702 (1974) the cross section \ for ArH+ formation is about 0.2E-20 m^2 at a COM energy of about 3 eV. We \ therefore neglect it. \ \>", "SmallText"], Cell[BoxData[ \(\(a6c7o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ Ar+ + CH4 -> H+ + Ar + 2 H2 We have no information on this reaction and neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a6c8o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["Ar+ + CH4 -> CH(A) + ArH+ + H2", "SmallText"], Cell["\<\ Using Ar+ + H2 = ArH+ + H - 1.53 eV from Ervin and Armentrout, J. Chem. Phys. \ 83, 166 (1985)\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{\ c == arp\ + ch4, \[IndentingNewLine]arp\ + \ h2 == \ arhp\ + \ h\ - \ 1.53, \ \[IndentingNewLine]h2\ == \ 2*h + 4.48, \[IndentingNewLine]ch4\ == \ ch3\ + \ h\ + 103.4/23.07, \[IndentingNewLine]ch3\ == \ ch2\ + \ h\ + 108.8/23.07, \ \[IndentingNewLine]ch2\ == \ ch\ + \ h\ + \ 100/23.07, \ \[IndentingNewLine]ch\ == \ cha\ + 2.87}, {ch3, ch2, ch, h, arp, ch4}]\)], "Input"], Cell[BoxData[ \(\(\(5.912726484612048`\)\(\[InvisibleSpace]\)\) + 1.`\ arhp + 1.`\ cha + 1.`\ h2 == c\)], "Output"] }, Open ]], Cell["The CM threshold is 5.9*(40+16)/16= 20.6 eV", "Text"], Cell["\<\ Brandt and Ottinger, Phys. Rev. A says that Ar+ + CH4 does not produce \ radiation in the 160 to 300 nm region.\ \>", "SmallText"], Cell["\<\ Ar^meta + CH4 -> ???? We have no information on this reaction\ \>", "SmallText"], Cell["\<\ Plot these cross sections in units of 10^-20 m^2. We note that the column \ depth for most of our data is that for 4 cm and 100 mTorr, i.e., 1.3*10^20 \ m^2, so that a process with a cross section of 10^-20 m^2 has a near unit \ probability of occurrence in the free fall passage of a CH+ across the \ tube.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{\(\(l6cn/2\)/fl6cn\)/w6[z]\ /. \ w6[z]\ -> \ w6z, a6c3o\ /. \ w6[z]\ -> \ w6z, a6c2o\ /. \ w6[z]\ -> \ w6z}, {w6z, 0.1, 1000}, \ PlotRange\ -> \ \ {{0.1, 1000}, {0.1, 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 %%ImageSize: 432 266.991 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 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108.8/23.07, \ \[IndentingNewLine]ch2\ == \ ch\ + \ h\ + \ 100/23.07, \ \[IndentingNewLine]ch\ == \ cha\ + 2.87}, {ch3, ch2, ch}]\)], "Input"], Cell[BoxData[ \(ch4 == \(\(11.922726484612049`\)\(\[InvisibleSpace]\)\) + 1.`\ c && cha == \(\(2.24`\)\(\[InvisibleSpace]\)\) + 1.`\ c - 1.5`\ h2 && h == \(-2.24`\) + 0.5`\ h2\)], "Output"] }, Open ]], Cell["\<\ The CM threshold is 11.9*(40+16)/16= 41.6 eV. We do not know of data for \ this process.\ \>", "Text"], Cell[CellGroupData[{ Cell["ArH+ + CH4 data", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ ArH+ + CH4 -> ArH+ + CH4 - elastic scattering based on Langevin cross \ section and an arbitrary fall-off at high energies. Momentum loss in elastic \ and inelastic collisions Because we are using the momentum balance rather \ than the energy balance, the usual 2mM/(m+M)^2 factor does not appear in the \ loss function and we should use just the elastic plus inelastic (nonreactive) \ part of the Langevin cross section.\ \>", "SmallText"], Cell["\<\ l7cn:=n*f*fl7cn*2.*w7[z]*2.19*10^-19/Abs[w7[z]]^.5/(1+(w7[z]/100.)^2) \ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ ArH+ + CH4 -> CH+ + Ar + 2 H2 We have not found data for this reaction. We will neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a7c1o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["ArH+ + CH4 -> CH3+ + Ar + H2", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{\ c == arhp\ + ch4, \[IndentingNewLine]ch3\ == \ ch3p\ + e\ + \ 9.8, \[IndentingNewLine]arp\ + \ h2 == \ arhp\ + \ h\ - \ 1.53, \ \[IndentingNewLine]ar\ \ == \ arp\ + \ e\ + \ 15.76, \[IndentingNewLine]h2\ == \ 2*h + 4.48, \[IndentingNewLine]ch4\ == \ ch3\ + \ h\ + 103.4/23.07}, \[IndentingNewLine]{ch3, h, arp, arhp, ch4, e}]\)], "Input"], Cell[BoxData[ \(\(\(0.05201127004768402`\)\(\[InvisibleSpace]\)\) + 1.`\ ar + 1.`\ ch3p + 1.`\ h2 == c\)], "Output"] }, Open ]], Cell["\<\ The threshold for this reaction is 0.52 eV in CM and 0.052*(41+16)/16 = 0.185 \ eV in LAB frame. According to Smith and Futrell, Int. J. Mass. Spectrom. 20, \ 43 (1976), the total rate for this reaction coefficient is equal to the \ Langevin value with 40% going to CH5+ and 60% going to CH3+. Unfortunately, \ I cannot find an energy specified.\ \>", "SmallText"], Cell[BoxData[ \(\(a7c3o\ = \ n*f*fl7cn*0.6*2.19*\(10^\(-19\)/ Abs[w7[z]]^ .5\)/\((1 + \((w7[z]/5. )\)^2)\);\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["ArH+ + CH4 -> CH5+ + Ar", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{\ c == arhp\ + ch4, \[IndentingNewLine]ch5p\ == \ ch4\ + hp\ + 228/23.07, \[IndentingNewLine]h\ == \ hp\ + e\ + \ 13.6, \[IndentingNewLine]h2\ == \ 2*h + 4.48, \[IndentingNewLine]arp\ + \ h2 == \ arhp\ + \ h\ - \ 1.53, \ \[IndentingNewLine]ar\ \ == \ arp\ + \ e\ + \ 15.76}, \[IndentingNewLine]{h, arp, arhp, ch4, hp, e}]\)], "Input"], Cell[BoxData[ \(\(-6.0329648894668395`\) + 1.`\ ar + 1.`\ ch5p == c\)], "Output"] }, Open ]], Cell["\<\ This reaction appears to exothermic by a large energy. We base our cross \ section on Smith and Futrell (1976) with an arbitrary fall-off at high \ energies.\ \>", "SmallText"], Cell["\<\ This reaction appears to exothermic by a large energy. We base our cross \ section on Smith and Futrell (1976) with an arbitrary fall-off at high \ energies.\ \>", "SmallText"], Cell[BoxData[ \(\(a7c5o\ = \ \ n*f* fl7cn*0.4*2.19*\(10^\(-19\)/ Abs[w7[z]]^ .5\)/\((1 + \((w7[z]/5. )\)^2)\);\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ ArH+ + CH4 -> CH4+ + Ar + H Smith and Futrell (1976) do not see this reaction at low energies.\ \>", "SmallText"], Cell[BoxData[ \(\(a7c4o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ ArH+ + CH4 -> Ar+ + CH4 + H Smith and Futrell (1976) do not see this reaction at low energies. We have \ not found data for this reaction at high energies and we will neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a7c6o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ ArH+ + CH4 -> H+ + CH4 + Ar Smith and Futrell (1976) do not see this reaction at low energies. We have \ not found data for this reaction at high energies and we will neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a7c8o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ Plot these cross sections in units of 10^-20 m^2. 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Momentum loss in elastic and inelastic \ collisions Because we are using the momentum balance rather than the energy \ balance, the usual 2mM/(m+M)^2 factor does not appear in the loss function \ and we should use just the elastic plus inelastic (nonreactive) part of the \ Langevin cross section. \ \>", "SmallText"], Cell["l8cn:=n*f*fl8cn*2.*w8[z]*1.116*10^-18/Sqrt[w8[z]]; ", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ H+ + CH4 -> CH+ + 2 H2 Chiu et al, J. Chem. Phys. 88, 6814 (1988) find that this product channel is \ too small to measure.\ \>", "SmallText"], Cell[BoxData[ \(\(a8c1o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ H+ + CH4 -> CH3+ + H2 Chiu et al, J. Chem. Phys. 88, 6814 (1988) find that this product channel is \ about 20% of the total. 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Momentum loss in elastic collisions Because we are using the momentum \ balance rather than the energy balance, the usual 2mM/(m+M)^2 factor does not \ appear in the loss function and we should use just the elastic of the \ Langevin cross section plus the nonreactive inelastic part. The fall-off at \ high energies is arbitrary. This cross section is critical in determining \ the role of CH+, because the elastic collisions severely reduce the ion \ energy. Note that this momentum balance model uses a much larger elastic \ loss term than does our 1993 model that multiplies the elastic cross section \ by 2*n*M/(m+M)^2 ~ 0.4 as is appropriate for the energy balance used there.\ \>", "SmallText"], Cell["\<\ l1an:=n*(1-f)*fl1an*2.*w1[z]*2.49*10^-19/w1[z]^.5/(1+w1[z]/50.)\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ CH+ + Ar -> fast CH + Ar+ charge transfer The threshold for this process is 53/40*(15.755-11.14) = \ 6.11 eV. We have not found any data for this process. However, in order for \ excitation of CH(A) to be observed by Ehbrecht et al (1996) the CH+ must be \ neutralized by charge transfer. The following assumes that the total charge \ transfer cross section is larger than charge transfer excitation cross \ section. We guess at how much larger.\ \>", "SmallText"], Cell["\<\ a1a69 := n*(1-f)*fa1a69*(UnitStep[w1[z]-6.11]* 4.0*10^-21*(w1[z]-6.11)/(w1[z]/100.+1.)+1.*10^-30);\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH+ + Ar -> slow CH + Ar+ charge transfer The threshold for this process is 53/40*(15.755-11.14) = \ 6.11 eV. We have not found any data for this process. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a1a6o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH+ + Ar -> ArH+ + C We have not found any data for this process. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a1a7o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH+ + Ar -> H+ +C + Ar We have not found any data for this process. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a1a8o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH+ +Ar -> CH(A) + Ar+ -> CH(X) + Ar+ + 432 nm Ehbrecht, Kowalski, and Ottinger (1996) find a cross section that appears to \ reach 5E-20 m^2 at enrel = 1000 eV and is roughly linear with energy. In \ center-of-mass the treshold for this process is 15.755-11.14+2.89 = 7.5 eV or \ (13+40)/40*7.5 = 9.9 eV LAB.\ \>", "SmallText"], Cell["\<\ a1a6p := n*(1-f)*fa1a6p*(UnitStep[enrel-7.50]*5.0*10^-20*(enrel-7.50)/1000./(\ 1+enrel/10000)+1.*10^-30) /. enrel -> 40/(13.+40.)*w1[z];\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ CH+ +Ar -> CH+(A) + Ar -> CH+(X) + Ar + 422 nm Ehbrecht, Kowalski, and Ottinger (1996) find a cross section that appears to \ reach 5E-19 m^2 at enrel = 1000 eV and is roughly linear with energy. In \ center-of-mass the treshold for this process is 15.755-11.14+2.93 = 7.54\ \>", "SmallText"], Cell["\<\ a1a1p := n*(1-f)*fa1a6p*((UnitStep[enrel-7.54]*5.0*10^-19*(enrel-7.54)/1000./(\ 1+enrel/10000)+ UnitStep[enrel-7.54]*1.0*10^-19*(enrel-7.54)/(enrel+100.)/(1+enrel/\ 100.))+1.*10^-30) /. enrel -> 40./(13.+40.)*w1[z];\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ Plot these cross section in units of 10^-20 m^2 by assuming n = 10^20 m^-3. \ We note that the column depth for most of our data is that for 4 cm and 100 \ mTorr, i.e., 1.3*10^20 m^2, so that a process with a cross section of 10^-20 \ m^2 has a near unit probability of occurrence in the free fall passage of a \ CH+ across the tube.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/\((1 - f)\); \n LogLogPlot[{\(\(l1an/2\)/fl1an\)/w1[z]\ /. \ w1[z]\ -> \ w1z, a1a69\ \ /. \ w1[z]\ -> \ w1z, a1a6p\ \ /. \ w1[z]\ -> \ w1z, 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.93441 .45111 L .93485 .45113 L .93531 .45115 L .93575 .45117 L .93622 .4512 L .93667 .45122 L .9371 .45123 L .93756 .45125 L .938 .45127 L .93846 .45129 L .93891 .45131 L .93934 .45133 L .9398 .45135 L .94023 .45137 L .94065 .45139 L .9411 .45141 L .94152 .45143 L .94197 .45145 L .94241 .45147 L .94282 .45148 L .94327 .4515 L .94369 .45152 L .9441 .45154 L .94453 .45156 L .94494 .45157 L Mistroke .94538 .45159 L .9458 .45161 L .94621 .45163 L .94664 .45164 L .94705 .45166 L .94749 .45168 L .9479 .4517 L .94831 .45171 L .94873 .45173 L .94914 .45175 L .94954 .45177 L .94995 .45178 L .95035 .4518 L .95078 .45182 L .95119 .45183 L .95158 .45185 L .95199 .45187 L .95239 .45188 L .95281 .4519 L .95322 .45191 L .95361 .45193 L .95402 .45195 L .95442 .45196 L .9548 .45198 L .9552 .45199 L .95559 .45201 L .956 .45203 L .95639 .45204 L .95677 .45206 L .95717 .45207 L .95756 .45209 L .95793 .4521 L .95832 .45212 L .9587 .45213 L .9591 .45215 L .95948 .45216 L .95985 .45218 L .96024 .45219 L 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.0447 L .33683 .05568 L .33862 .07123 L .34022 .08178 L .34406 .10029 L .34759 .11268 L .35391 .12926 L .3603 .14193 L .37109 .15828 L .39102 .18013 L .40959 .19553 L .42547 .20659 L .44063 .21594 L .45388 .22342 L .46557 .22959 L .47705 .23533 L .4873 .24025 L .49652 .24451 L .50573 .24864 L .51407 .25228 L .52245 .25585 L .53008 .25904 L .53706 .26191 L .54414 .26477 L .55064 .26736 L .55724 .26996 L .56333 .27232 L .56895 .27449 L .57471 .27668 L .58004 .27869 L .58499 .28054 L .59008 .28244 L .59481 .28418 L .59968 .28597 L .60422 .28762 L .60846 .28916 L .61283 .29074 L .61693 .2922 L .62115 .29371 L .62511 .29512 L .62882 .29643 L .63266 .29778 L .63627 .29905 L .63965 .30023 L .64317 .30146 L .64648 .30261 L Mistroke .64992 .3038 L .65315 .30492 L .6562 .30596 L .65937 .30705 L .66236 .30808 L .66518 .30904 L .66812 .31004 L .67089 .31098 L .67378 .31197 L .67652 .31289 L .6791 .31376 L .68179 .31467 L .68434 .31553 L .687 .31642 L .68952 .31727 L .69191 .31807 L .6944 .3189 L 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.98082 .40827 L .98115 .40837 L .98146 .40846 L .9818 .40856 L .98212 .40865 L .98246 .40875 L .98279 .40885 L Mistroke .9831 .40894 L .98344 .40904 L .98376 .40913 L .98407 .40922 L .98439 .40932 L .98471 .40941 L .98504 .40951 L .98536 .4096 L .98567 .40969 L .98599 .40979 L .98631 .40988 L .98664 .40998 L .98696 .41007 L .98727 .41016 L .98759 .41025 L .9879 .41035 L .98821 .41043 L .98852 .41053 L .98883 .41062 L .98916 .41071 L .98947 .4108 L .98977 .41089 L .99009 .41098 L .99039 .41107 L .99072 .41117 L .99103 .41126 L .99133 .41135 L .99164 .41144 L .99195 .41153 L .99224 .41161 L .99255 .4117 L .99285 .41179 L .99317 .41188 L .99348 .41197 L .99377 .41206 L .99408 .41215 L .99438 .41223 L .99466 .41232 L .99497 .41241 L .99526 .41249 L .99557 .41258 L .99587 .41267 L .99616 .41275 L .99646 .41284 L .99675 .41293 L .99706 .41302 L .99736 .4131 L .99764 .41319 L .99795 .41327 L .99824 .41336 L Mistroke .99852 .41344 L .99882 .41353 L .9991 .41361 L .99941 .4137 L .9997 .41378 L 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The fact that we do not observe the \ CH+(A->X) emission would seem to rule out significant excitation by CH+ + Ar \ -> CH(A) + Ar+ and would be consistent with rapid charge transfer to form \ fast CH(X).\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["CH2+ - Ar data", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ CH2+ momentum loss in Ar. Momentum loss in elastic and inelastic collisions Because we are using the \ momentum balance rather than the energy balance, the usual 2mM/(m+M)^2 factor \ does not appear in the loss function and we should use just the elastic plus \ inelastic (nonreactive) part of the Langevin cross section. Note that this \ momentum balance model uses a much larger elastic loss term than does our \ 1993 model that multiplies the elastic cross section by 2*n*M/(m+M)^2 ~ 0.4 \ as is appropriate for the energy balance used there.\ \>", "SmallText"], Cell["\<\ l2an:=n*(1-f)*fl2an*2.*w2[z]*2.53*10^-19/w2[z]^.5/(1+w2[z]/1000.);\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]] }, Open ]], Cell["\<\ Plot these cross section in units of 10^-20 m^2. 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Momentum loss in elastic and inelastic collisions Because we are using the \ momentum balance rather than the energy balance, the usual 2mM/(m+M)^2 factor \ does not appear in the loss function and we should use just the elastic plus \ inelastic (nonreactive) part of the Langevin cross section. It is not \ clear why we gave this cross section a roll-off at energies above 50 eV. This \ cross section is critical in determining the role of CH+, because the elastic \ collisions severely reduce the ion energy. Note that this momentum balance \ model uses a much larger elastic loss term than does our 1993 model that \ multiplies the elastic cross section by 2*n*M/(m+M)^2 ~ 0.4 as is appropriate \ for the energy balance used there.\ \>", "SmallText"], Cell["\<\ l3an:=n*(1-f)*fl3an*2.*w3[z]*2.53*10^-19/w3[z]^.5/(1+w3[z]/50.);\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH3+ + Ar -> Ar+ +CH3", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{a\ == \ ch3p\ + \ ar, \ ch3\ == \ ch3p\ + e\ + \ 9.8, \ ar\ == \ arp\ + e + 15.755}, {ch3p, ar, e}]\)], "Input"], Cell[BoxData[ \(\(\(5.955`\)\(\[InvisibleSpace]\)\) + 1.`\ arp + 1.`\ ch3 == a\)], "Output"] }, Open ]], Cell["\<\ charge transfer. For some reason we have given this a very small value. \ Here we use IP(CH3) = 9.8 eV and IP(Ar) = 15.755 eV, so that the threshold is \ (15+40)/40*5.955 = 8.18\ \>", "SmallText"], Cell["\<\ a3a6F := n*(1-f)*fa3a6F*(UnitStep[w3[z]-8.18]* 1.0*10^-25*(w3[z]-8.18)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./91.9+1.*10^-30); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + Ar -> CH+ +Ar +H2", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{ch3\ == \ ch3p\ + e\ + \ 9.8, ch\ == \ chp\ + \ e + \ 11.14, \ h2\ == \ 2 h\ + \ 4.48, ch3\ == \ ch2\ + \ h\ + 108.8/23.07, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {h, ch, ch3, ch2, e}]\)], "Input"], Cell[BoxData[ \(\(\(5.910715214564369`\)\(\[InvisibleSpace]\)\) + 1.`\ chp + 1.`\ h2 == ch3p\)], "Output"] }, Open ]], Cell["This has a threshold of 5.91*(15+40)/40 = 8.13", "Text"], Cell["\<\ a3a1o := n*(1-f)*(fa3a1o*UnitStep[w3[z]-8.1]* 1.0*10^-25*(w3[z]-8.1)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./91.7+1.*10^-30);\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + Ar -> fCH +H2 +Ar+", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{ch3\ == \ ch3p\ + \ e + 9.8, ch\ == \ chp\ + \ e + 11.14, \ ar\ == \ arp\ + e + 15.755, h2 == 2\ h\ + 4.48, ch3\ == \ ch2\ + \ h\ + 108.8/23.07, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {h, chp, ch2, ch3, e}]\)], "Input"], Cell[BoxData[ \(\(\(10.525715214564368`\)\(\[InvisibleSpace]\)\) + 1.`\ arp + 1.`\ ch - 1.`\ ch3p + 1.`\ h2 == ar\)], "Output"] }, Open ]], Cell["\<\ A crucial question here is whether the reaction produces a fast CH. We \ assume it does, but have no basis for doing so. The threshold fo this \ reaction is 10.52*(15+40)/40 = 14.47eV\ \>", "SmallText"], Cell["\<\ a3a96 := n*(1-f)*fa3a96*(UnitStep[w3[z]-14.5]* 3.0*10^-21*(w3[z]-14.5)/(w3[z]+100.)/(1+w3[z]/100.)^2*200.*2./85.4+1.*10^-30);\ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ Note that this importanr process will not occur for our typical CH3+ energy \ of 12 eV.\ \>", "Subsubtitle"], Cell["\<\ CH3+ +Ar -> CH(A) +H2 +Ar+ -> CH(X) + Ar + 432 nm Where did this come from? We have made it small. The threshold is (15.755 - \ 5.23+2.87)*(15+40)/40 = 18.42eV\ \>", "SmallText"], Cell["\<\ a3a6p := n*(1-f)*fa3a6p*(UnitStep[w3[z]-18.42]* 1.0*10^-25*(w3[z]-18.42)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./88.9+1.*10^-30);\ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH3+ + Ar -> ArH+ +C + H2 We have not found any data for this process. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a3a7o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH3+ + Ar -> H+ +Ar +C + H2 We have not found any data for this process. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a3a8o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH3+ + Ar -> Ar+ +H +CH2 We have not found any data for this process. We neglect it.\ \>", "SmallText"], Cell["\<\ Plot these cross section in units of 10^-20 m^2. 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.99974 .28817 L 1 .28812 L Mfstroke 0 1 1 r .44575 0 m .44748 .00266 L .45421 .01069 L .46659 .02192 L .47758 .02957 L .48742 .03524 L .49721 .04008 L .50604 .04392 L .51488 .04736 L .52291 .05018 L .53024 .05254 L .53765 .05475 L .54444 .05662 L .55132 .05839 L .55766 .05991 L .5635 .06123 L .56947 .06249 L .575 .0636 L .58012 .06456 L .58538 .06551 L .59027 .06633 L .59529 .06714 L .59997 .06785 L .60433 .06848 L .60883 .0691 L .61304 .06965 L .61737 .07018 L .62144 .07066 L .62524 .07108 L .62918 .07149 L .63287 .07186 L .63634 .07219 L .63994 .07251 L .64332 .0728 L .64683 .07308 L .65013 .07333 L .65324 .07356 L .65648 .07377 L .65953 .07397 L .6624 .07414 L .6654 .0743 L .66822 .07445 L .67117 .07459 L .67395 .07472 L .67658 .07483 L .67932 .07494 L .68191 .07503 L .68462 .07511 L .68718 .07519 L .6896 .07525 L Mistroke .69213 .07531 L .69453 .07536 L .6968 .0754 L .69917 .07544 L .70142 .07547 L .70378 .07549 L .70494 .0755 L .70601 .07551 L .70711 .07552 L .70813 .07552 L 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Instead we are using the \ single beam model.\ \>", "Subsubtitle"], Cell["\<\ CH4+ energy loss to Ar. Momentum loss in elastic and inelastic collisions Because we are using the \ momentum balance rather than the energy balance, the usual 2mM/(m+M)^2 factor \ does not appear in the loss function and we should use just the elastic plus \ inelastic (nonreactive) part of the Langevin cross section.\ \>", "SmallText"], Cell["\<\ l4an:=n*(1-f)*fl4an*2.*w4[z]*2.56*10^-19/Abs[w4[z]]^.5 \ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ CH4+ + Ar -> ArH+ + CH3 The following plots appear to be based on Peko et a (1998).\ \>", "SmallText"], Cell[BoxData[ \(\(a4a7o\ := \ n*\((1 - f)\)* fa4a7o*\((10^\(-20\)*\((UnitStep[w4[z] - 9. ]* Re[\((\((w4[z] - 9. )\)/ 180. )\)^1.3]/\((1 + \((w4[z]/ 93. )\)^6)\) + \[IndentingNewLine]\((w4[z]/ 2000)\)^2/\((1 + \((w4[z]/5000)\)^2)\))\)\ + 1. *10^\(-30\))\);\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH4+ + Ar -> H+ + CH3 + Ar The following plots appear to be based on Peko et a (1998).\ \>", "SmallText"], Cell[BoxData[ \(\(a4a8o\ := \ n*\((1 - f)\)* fa4a8o*\((10^\(-20\)*\((UnitStep[ w4[z] - 5.6]*0.35/\((1 + \((\((w4[z] - 5.6)\)/ 4.5)\)^\(-2\))\) + \ \[IndentingNewLine]UnitStep[ w4[z] - 23. ]*\((\((w4[z] - 23)\)/ 50. )\)^1/\((1 + \((w4[z]/140. )\)^2.2)\))\) + 1. *10^\(-30\))\);\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH4+ + Ar -> CH+ + H3 + Ar We have not found any data for this process. 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Momentum loss in elastic and inelastic collisions Because we are using the \ momentum balance rather than the energy balance, the usual 2mM/(m+M)^2 factor \ does not appear in the loss function and we should use just the elastic plus \ inelastic (nonreactive) part of the Langevin cross section.Probably this \ should have a high enrgy fall-off.\ \>", "SmallText"], Cell["\<\ l5an :=n*(1-f)*fl5an*2*w5[z]*2.58*10^-19/w5[z]^.5; \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ CH5+ + Ar -> CH3+ + Ar + H2 According to Glosik et al, J. Chem. Phys. 101, 3792 (1994) CH5+ drifting \ through in He breaks up as if the dissociation energy were 1.1 to 1.4 eV \ rather than the expected 1.8 eV. Also, a column density of about 3 torr cm = \ 1e17 cm^2 or 1e21 m^2 of He is required to reach the steady-state \ dissociation rate at E/n = 100 Td. Because our experiment showing \ interesting heavy particle effects has a column density of only 3.8*3.3e15 = \ 1.25e16 cm^2 or 1.25e20 m^2, the steady-state drift data would not apply. \ The best we can do is assume a threshold of 1.8 eV and guess at the \ dissociation cross section above threshold, where the threshold oin the LAB \ frame is 57/40*1.8 = 2.56 eV.\ \>", "SmallText"], Cell[BoxData[ \(\(a5a3a\ := \ n*\((1 - f)\)* fa5a3a*\((UnitStep[ w5[z] - 2.56]*2.58*10^\(-19\)*\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \((1 - 2.56/w5[z])\)^2/w5[z]^0.5 + 1. *10^\(-30\))\);\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ CH5+ + Ar -> CH+ + CH4 + Ar We have not found any data for this process. We neglect it. \ \>", "SmallText"], Cell[BoxData[ \(\(a5a1o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH5+ + Ar -> CH3+ + CH2 + Ar We have not found any data for this process. 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Also, the Langevin rate is presumably \ the total collision rate at low energies and the elastic rate coefficient may \ be much smaller.\ \>", "SmallText"], Cell["\<\ l0an :=n*(1-f)*fl0an*2*w0[z]*3.55*10^-19/w0[z]^.5; \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(\(\ \)\(a0a1o\ = 0; \ a0a3o = 0; \ a0a4o = 0; a0a6o = 0; \ a0a7o = 0; a0a8o = 0;\)\)\)], "Input", FontColor->RGBColor[1, 0, 0]] }, Open ]], Cell[CellGroupData[{ Cell["fast CH - Ar data", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ fast CH + Ar -> slow CH + Ar fast CH loss by cooling. Momentum loss in elastic and inelastic collisions \ Because we are using the momentum balance rather than the energy balance, \ the usual 2mM/(m+M)^2 factor does not appear in the loss function and we \ should use just the elastic plus inelastic (nonreactive) part of the Langevin \ cross section. For the cross section we use our empirical fit to the Ar-Ar \ viscosity cross section. Because the energy loss is written as an alpha \ coefficient we do not include w1[z], as in energy loss functions.\ \>", "SmallText"], Cell[BoxData[ \(a9aoa := \ fa9aoa*n*\((1 - f)\)*\((1.85*10^\(-19\)* releng^\((\(-0.15\))\)/\((1 + \((releng/ 9)\)^\((0.7)\) + \ \((releng/ 200)\)^\((1.5)\) + \((releng/ 1000)\)^\((2.5)\))\)^\((0.5)\))\)\ /. \ releng\ -> \ 40/51*w9[z]\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["\<\ fCH +Ar -> CH(A) +Ar -> CH(X) + Ar + 432 nm We have not found cross sections for this process. One possibility is to use \ a cross sections based on that for H + Ar -> H(halpha) + Ar. The threshold \ COM energy for this process is 1/432E-8/8065 = 2.87 eV and in the laboratory \ 52/40*2.87 = 3.73 eV. The magnitude is only a guess.\ \>", "SmallText"], Cell["\<\ a9apa := n*(1-f)*fa9apa*(UnitStep[w9[z]-3.73]*1.4*10^-20/(1+Re[(140/(w9[z]-3.\ 73))^2.5])/ (1+(w9[z]/30)^2)^0.22 + 1.*10^-30) /. w9[z] -> w9[z];\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ I used the following in the 1993 model, but I cannot find any justification \ for it. It has a higher threshold, but a higher slope near threshold.\ \>", "SmallText"], Cell["\<\ a9apa1 := n*(1-f)*fa9apa1*(UnitStep[w9[z]-16.2]* 5.0*10^-22*(w9[z]-16.2)/(w9[z]+100.)/(1+w9[z]/1000.)*200.*2.*1.1/84+1.*10^-30)\ /. w9[z] -> w9[z];\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ Plot these cross section in units of 10^-20 m^2. 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.99969 .16517 L .99999 .16511 L 1 .16511 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{432, 266.938}, ImageCacheValid->False] }, Open ]], Cell["\<\ This plot says that the elastic mfp for a CH molecule is significantly less \ than the electrode separation of the tube and that any excitation produced \ will occur reasonably near the point of CH production. Because we know \ nothing about the enrgy dependence of these excitation cross sections we \ cannot say whether one needs 30 eV or 300 eV for excitation. 03/19/01\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["fast CH3 + Ar data", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We assume that the fast CH3 has the same energy as the CH3+ ion. This is \ based on the assumption that the fast CH3 is produced from CH3+ by charge \ transfer.\ \>", "SmallText"], Cell["fast CH3 energy (max)", "SmallText"], Cell["wF[z]:=w3[z]; ", "Input", PageWidth->Infinity, Evaluatable->False, ShowSpecialCharacters->False], Cell["\<\ fCH3 + Ar -> destruction by cooling. From Allis (1956), p. 408 Eq. (25.2) \ the fractional energy loss in an elastic collision is \ 2Mm/(M+m)^2*[1-cos(theta)]. We assume that, as in viscosity weighted \ scattering, the important angle is 90 deg and that we should use 2Mm/(M+m)^2. \ Unfortunately, we do not know anything about CH3-Ar collisions and have to \ quess at an effective cross section. Our choice is a factor of 3.6 smaller \ than the Langevin cross section for CH3+ + AR. Note that we are effectively \ assuming that every collision results in CH3 cooling below the energies of \ interest, i.e., effectively the fast CH3 disappears on collision.\ \>", "SmallText"], Cell["\<\ aFaoa:=n*f*faFaoa*1.0*10^-19/wF[z]^0.5/(1+wF[z]/100.); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["fCH3 + Ar -> CH + Ar + H2 -> CH + Ar + H2 + 432 nm ", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{a == ch3\ + \ ar, h2\ == \ 2\ h\ + \ 4.48, ch3\ == \ ch2\ + \ h\ + 108.8/23.07, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {h, ch2, ch3}]\)], "Input"], Cell[BoxData[ \(\(\(4.570715214564369`\)\(\[InvisibleSpace]\)\) + 1.`\ ar + 1.`\ ch + 1.`\ h2 == a\)], "Output"] }, Open ]], Cell["\<\ The threshold COM energy for this process is 4.57 eV and in the laboratory \ 55/40*4.57 = 6.3 eV. Here, again we have to guess at the cross section. I \ have no idea where the following came from. \ \>", "SmallText"], Cell["\<\ aFa9a :=n*f*(faFa9a*UnitStep[wF[z]-6.3]*2.5*10^-23*(wF[z]-6.3)/(wF[z]+100.)/ (1+wF[z]/1000.)*200.*2*1.1/78+1.*10^-30);\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["fCH3 + Ar -> CH(A) + Ar + H2 -> CH + Ar + H2 + 432 nm ", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{a == ch3\ + \ ar, h2\ == \ 2\ h\ + \ 4.48, ch3\ == \ ch2\ + \ h\ + 108.8/23.07, ch\ == \ cha\ + \ 2.87, \ ch2\ == \ ch\ + \ h\ + \ 100/23.07}, {h, ch, ch2, ch3}]\)], "Input"], Cell[BoxData[ \(\(\(7.440715214564369`\)\(\[InvisibleSpace]\)\) + 1.`\ ar + 1.`\ cha + 1.`\ h2 == a\)], "Output"] }, Open ]], Cell["\<\ The threshold COM energy for this process is 7.44 eV and in the laboratory \ 55/40*7.44 = 16.4 eV. Here, again we have to guess at the cross section. 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Also, it is customary too express \ the Ar+ energy as kT+ for the exponential fall off of the 1-D energy \ distribution, even though this energy is twice the mean energy.\ \>", "Text"], Cell["\<\ Ar+ + Ar -> Ar+ + Ar momentum loss cross section from Phelps (1994), Eq. (2). At non-thermal \ energies this is twice the charge transfer cross section.\ \>", "SmallText"], Cell[BoxData[ \(\(l6an\ := \ n*\((1 - f)\)*w6[z]* fl6an*1.15*10^\(-18\)/w6[z]^0.1*\((1 + 0.015/w6[z])\);\)\)], "Input",\ FontColor->RGBColor[1, 0, 1]], Cell["\<\ fast Ar+ + Ar -> slow Ar+ + fast Ar charge transfer (backward scattering) from Eqs. 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(1981) give a thermal destruction coefficient for ArH+ in \ Ar of 1.3E-11 cm^3/s or about 2% of Langevin. However, according to Fig. 4 \ of Peko et al (1996), this reaction requires 6.14 eV in the CM frame or 12.43 \ eV in the LAB frame. Therefore the Rakshit and Wranek reaction must be \ something else. Our guess is:\ \>", "SmallText"], Cell[BoxData[ \(\(a7a6a\ = \ \ n*\((1 - f)\)* fa7a6a*\((UnitStep[w7[z] - 12.43]*3.07*10^\(-19\)/ Sqrt[w7[z]]*\((1 - 12.43/w7[z])\)/\((1\ + \ w7[z]/10)\) + 10^\(-30\))\);\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ ArH+ + Ar -> H+ + 2Ar We have not found data for this reaction. 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.95599 .02657 L .95637 .02631 L .95676 .02604 L .95715 .02578 L .95755 .02551 L .95794 .02524 L .95831 .02499 L .95871 .02472 L .95909 .02446 L .95949 .02418 L .95988 .02392 L .96025 .02367 L .96064 .0234 L .96102 .02314 L .96138 .02289 L .96177 .02263 L .96214 .02238 L .96253 .02211 L .96291 .02185 L .96327 .02161 L .96365 .02135 L .96402 .02109 L .96438 .02085 L .96475 .0206 L .96511 .02035 L .96549 .02009 L .96586 .01984 L .96621 .0196 L .96659 .01934 L .96695 .0191 L .96733 .01884 L .96769 .01859 L .96805 .01835 L .96842 .0181 L .96878 .01785 L .96912 .01762 L .96948 .01737 L .96983 .01713 L .97021 .01688 L .97056 .01663 L .9709 .0164 L Mistroke .97127 .01615 L .97162 .01591 L .97195 .01568 L .97231 .01544 L .97265 .01521 L .97301 .01496 L .97336 .01472 L .97369 .0145 L .97405 .01425 L .97439 .01402 L .97475 .01378 L .9751 .01354 L .97543 .01331 L .97578 .01307 L .97612 .01284 L .97645 .01262 L .97679 .01238 L .97713 .01215 L .97748 .01191 L .97782 .01168 L .97814 .01146 L .97849 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.32957 .25258 L .33291 .26548 L .33668 .27675 L .34007 .2848 L .34744 .2979 L .35375 .30592 L .35941 .31142 L .36537 .31593 L .37149 .3195 L .37709 .32202 L .38295 .32401 L .38826 .32536 L .39057 .32582 L .39302 .32623 L .39543 .32657 L .3976 .32682 L .39978 .32702 L .40177 .32716 L .40291 .32722 L .40394 .32726 L .40507 .3273 L .40569 .32732 L .40627 .32733 L .40684 .32734 L .40712 .32734 L .40743 .32735 L .40798 .32735 L .40849 .32735 L .4088 .32735 L .40909 .32735 L .40964 .32735 L .40994 .32734 L .41022 .32734 L .41086 .32733 L .41199 .3273 L .41302 .32727 L .41532 .32716 L .41732 .32704 L .41939 .32688 L .42671 .3261 L .43406 .32499 L Mistroke .44059 .32376 L .45356 .32074 L .46617 .31714 L .47737 .3135 L .48738 .30993 L .49732 .30611 L .50629 .30247 L .51442 .29901 L .5226 .2954 L .53005 .29199 L .53759 .28846 L .54449 .28513 L .55083 .28202 L .55728 .27878 L .56324 .27575 L .56931 .2726 L .57493 .26966 L .58013 .26689 L .58547 .26402 L .59044 .26132 L .59505 .25879 L .59981 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Momentum loss in elastic and \ inelastic collisions Because we are using the momentum balance rather than \ the energy balance, the usual 2mM/(m+M)^2 factor does not appear in the loss \ function and we should use just the elastic plus inelastic (nonreactive) part \ of the Langevin cross section.\ \>", "SmallText"], Cell["\<\ l8an:=n*(1-f)*fl8an*2.*w8[z]*2.19*10^-19/Abs[w8[z]]^.5/(1+(w8[z]/100.)^2) \ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["\<\ H+ + Ar -> H + Ar+ Published data is reviewed by Tawara, Atomic Data and Nuclear Data Tables 22, \ 491 (1978), Graphs I. 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", "SmallText", Evaluatable->False], Cell["\<\ case11 := If[case == 11, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 4.\"; dataname = \"010991-3\"; f = 0.00001; d = 0.04; (*m*) eontd = 2050; (*Td*) p = 100.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case12 := If[case == 12, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 4.\"; dataname = \"010991-7\"; f = 0.03; d = 0.04; (*m*) eontd = 2050; (*Td*) p = 100.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case13 := If[case == 13, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 4.\"; dataname = \"010991-1\"; f = 0.10; d = 0.04; (*m*) eontd = 2050; (*Td*) p = 100.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case14 := If[case == 14, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 4.\"; dataname = \"010991-1\"; f = 0.20; d = 0.04; (*m*) eontd = 2050; (*Td*) p = 100.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case15 := If[case == 15, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 4.\"; dataname = \"010991-9\"; f = 0.35; d = 0.04; (*m*) eontd = 2050; (*Td*) p = 100.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case16 := If[case == 16, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 4.\"; dataname = \"011591-5\"; f = 0.50; d = 0.04; (*m*) eontd = 2050; (*Td*) p =100.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case17 := If[case == 17, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 4.\"; dataname = \"010991-2\"; f = 0.75; d = 0.04; (*m*) eontd = 2050; (*Td*) p = 100.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case18 := If[case == 18, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 4.\"; dataname = \"010991-2\"; f = 0.9999; d = 0.04; (*m*) eontd = 2050; (*Td*) p = 100.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case19 := If[case == 19, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 5.\"; dataname = \"011191-1\"; f = 0.10; d = 0.04; (*m*) eontd = 2050; (*Td*) p = 70.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case20 := If[case == 20, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 5.\"; dataname = \"011191-2\"; f = 0.10; d = 0.04; (*m*) eontd = 2050; (*Td*) p = 50.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["Petrovic and Phelps, Fig. 4 -> cases 21-23. ", "SmallText", Evaluatable->False], Cell["\<\ case21 := If[case == 21, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 3.\"; dataname = \"010791-4\"; f = 0.99999; d = 0.04; (*m*) eontd = 512; (*Td*) p = 300.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case22 := If[case == 22, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 3.\"; dataname = \"010791-1\"; f = 0.9999; d = 0.04; (*m*) eontd = 3070; (*Td*) p = 100.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case23 := If[case == 23, comment := \"% Model of CH(A) emission for Petrovic and Phelps CH4-Ar data Fig. 3.\"; dataname = \"010791-3\"; f = 0.99999; d = 0.04; (*m*) eontd = 30700; (*Td*) p = 35.; (*mTorr*) n = p/1000*3.3*10^(22); (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Ion fluxes for pure CH4 from Figs. 6 to 9 of de Urquijo et al, Gaseous \ Dielectrics, ed by Christophorou and Olthof (Plenum, 1998, New York). \ \>", "SmallText", Evaluatable->False], Cell["\<\ case31 := If[case == 31, comment := \"% Model of relative ion fluxes for de Urquijo et al (1998) data of Fig. \ 6.\"; dataname = \"deUrquijo6\"; f = 0.9999; d = 0.1; (*m*) eontd = 1000; (*Td*) p=30.; (*mTorr*) n = 1.*10^(20)/d; (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case32 := If[case == 32, comment := \"% Model of relative ion fluxes for de Urquijo et al (1998) data of Fig. \ 7.\"; dataname = \"deUrquijo7\"; f = 0.9999; d = 0.1; (*m*) eontd = 2000; (*Td*) p=30.; (*mTorr*) n = 1.*10^(20)/d; (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case33 := If[case == 33, comment := \"% Model of relative ion fluxes for de Urquijo et al (1998) data of Fig. \ 8.\"; dataname = \"deUrquijo8\"; f = 0.9999; d = 0.1; (*m*) eontd = 4000; (*Td*) p=30.; (*mTorr*) n = 1.*10^(20)/d; (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case34 := If[case == 34, comment := \"% Model of relative ion fluxes for de Urquijo et al (1998) data of Fig. \ 9.\"; dataname = \"deUrquijo9\"; f = 0.9999; d = 0.1; (*m*) eontd = 7000; (*Td*) p=30.; (*mTorr*) n = 1.*10^(20)/d; (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Ion fluxes for 50% Ar-50% CH4 from Figs. 10 and 11of de Urquijo et al, \ Gaseous Dielectrics, ed by Christophorou and Olthoff (Plenum, 1998, New \ York). Here we do calculation for 1, 2,4, and 7 kTd, although the published \ experimental data is only for 1 and 7 kTd.\ \>", "SmallText", Evaluatable->False], Cell["\<\ case41 := If[case == 41, comment := \"% Model of relative ion fluxes for de Urquijo et al (1998) data of Fig. 10.\ \"; dataname = \"deUrquijo10\"; f = 0.5; d = 0.1; (*m*) eontd = 1000; (*Td*) p=3.; (*mTorr*) n = 1.*10^(19)/d; (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case42 := If[case == 42, comment := \"% Model of relative ion fluxes for de Urquijo et al (1998) data of Fig. 10.\ \"; dataname = \"deUrquijo10\"; f = 0.5; d = 0.1; (*m*) eontd = 2000; (*Td*) p=3.; (*mTorr*) n = 1.*10^(19)/d; (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case43 := If[case == 43, comment := \"% Model of relative ion fluxes for de Urquijo et al (1998) data of Fig. 10.\ \"; dataname = \"deUrquijo10\"; f = 0.5; d = 0.1; (*m*) eontd = 4000; (*Td*) p=3.; (*mTorr*) n = 1.*10^(19)/d; (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ case44 := If[case == 44, comment := \"% Model of relative ion fluxes for de Urquijo et al (1998) data of Fig. 10.\ \"; dataname = \"deUrquijo10\"; f = 0.5; d = 0.1; (*m*) eontd = 7000; (*Td*) p=3.; (*mTorr*) n = 1.*10^(19)/d; (*m^-3*) ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ The next step uses the case number set at the beginning of the cases to chose \ the set of intial conditions listed immediately below.\ \>", "SmallText"], Cell[BoxData[ \(initialConditions\ := \ Block[{}, case11; case12; case13; case14; case15; case16; case17; case18; case19; case21; case22; case23; case31; case32; case33; case34; case41; case42; case43; case44]\)], "Input"], Cell[BoxData[ \(initialConditions\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(f\)], "Input"], Cell[BoxData[ \(0.35`\)], "Output"], Cell[CellGroupData[{ Cell[BoxData[ \(n\)], "Input"], Cell[BoxData[ \(3.3`*^21\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(d\)], "Input"], Cell[BoxData[ \(0.04`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(eontd\)], "Input"], Cell[BoxData[ \(2050\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ e0=eontd*n*10^-21 (*electric field in V/m*)\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(6765.`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(v0\ = \ \(\(e0\)\(*\)\(d\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\( (*voltage*) \ \)\)\)], "Input"], Cell[BoxData[ \(270.6`\)], "Output"] }, Open ]], Cell["Differential Equations", "Subsection"], Cell["\<\ The direction of integration is from anode to cathode. Assume that the \ electron energy at the anode is \ \>", "SmallText", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ The derivative term on the RHS of the energy equations represents the effects \ of species production and loss on the enegry balance. For example, the \ production of a new ion requires that that ion be accelerated to the beam \ enegy. \ \>", "SmallText"], Cell[BoxData[ \(\(k = 0. ;\)\)], "Input", Background->None], Cell["\<\ Note that according to Phelps et al (1987) we require k = 1 in order to \ include the effects of species loss in the energy balance. We need to look \ at this further, especially for cases of coupled rate and momentum for \ interacting species.\ \>", "Subsubtitle"], Cell["\<\ We use an equilibrium-like model for electrons, i.e., we no longer use the \ electron energy balance. Note that if we follow the procedure of Phelps et \ al, Phys. Rev. 36, 5327 (1987) for deriving the momentum balance, we need to \ include the species changing reactions. This reference discusses the factor \ of 2 multiplying the derivative term in the momentum balance as well as twice \ the full momentum weighting of the elastic and inelastic terms. Note that \ when using the momentum balance the usual 2mM(m+M)^2 does not appear. The \ rationalization for a negative derivative term is that a new ion must be \ brought to the speed of the beam and so reduces the energy of the beam. \ Presumably the reverse logic applied to ion loss, although the argument is \ less intuitive to me. One could say that the ion leaving must first give up \ energy to the beam so that it leaves at zero energy. In the following we \ omit the reaction terms. The derivatives for the differential equations are:\ \ \>", "SmallText"], Cell["\<\ Originally this set of equations was set up omiting the j2[z] and w2[z] \ equations. However, the experiments of de Urquijo et al (1998) show that \ CH2+ becomes the second most important ion at the high E/n of interest to us.\ \ \>", "Subsubtitle"], Cell[BoxData[ \(\(djeodz\ := \ \(-alphai\)*je[z];\)\)], "Input"], Cell[BoxData[ \(\(dj1odz\ := \((\(-a1a6p\) - a1a7o - a1a8o - a1c3o - a1c49 - a1c0o - a1c8o)\)\ j1[z] + \((a3a1o + a3c1o)\)\ j3[ z] + \((a4a1o + a4c1o)\)\ j4[z] + \((a5a1o + a5c1o)\)\ j5[z] + a6c1o\ j6[z] + a7c1o\ j7[z] + \[IndentingNewLine]a8c1o\ j8[ z] + \((a0a1o + a0c1o)\)*j0[z] + aec1o\ je[z];\)\)], "Input"], Cell[BoxData[ \(\(dw1odz\ := \ eontd*n/\((1. *10^21)\) - l1cn - l1an - \ k*dj1odz/j1[z]*w1[z]*2\ ;\)\)], "Input"], Cell["\<\ This next equation needs complete revision to account for CH2+\ \>", "Subsubtitle"], Cell[BoxData[ \(\(dj2odz\ := \((\(-a2c0o\))\)\ j2[z] + \ aec2o\ je[z]\ + \ a6c2o*j6[z];\)\)], "Input"], Cell[BoxData[ \(\(dw2odz\ := \ eontd*n/\((1. *10^21)\) - l2an - l2cn - k*dj2odz/j2[z]*w2[z]*2\ ;\)\)], "Input"], Cell[BoxData[ \(\(dj3odz\ := a1c3o\ j1[ z] + \((\(-a3a1o\) - a3a6p - a3a7o - a3a8o - a3a96 - a3c1o - a3c4F - a3c5o - a3c8o - a3c0o - \[IndentingNewLine]a3c94 - a3a6F)\)\ j3[z] + \((a4a3o + a4c3o)\)\ j4[ z] + \((a5a3a + a5a3o + a5c3o)\)\ j5[ z] + \[IndentingNewLine]a6c3o\ j6[z] + a7c3o\ j7[z] + \ a8c3o\ j8[z] + \((a0a3o + a0c3o)\)*j0[z] + aec3o\ je[z]\ ;\)\)], "Input"], Cell[BoxData[ \(\(dw3odz\ := \ eontd*n/\((1. *10^21)\) - l3an - l3cn - k*dj3odz/j3[z]*w3[z]*2\ ;\)\)], "Input"], Cell[BoxData[ \(dj4odz\ := a1c49\ j1[z] + \((a3c94 + a3c4F)\)\ j3[ z] + \[IndentingNewLine]\((\(-a4a1o\) - a4a3o - a4a6o - a4a7o - a4a8o - a4c1o - a4c3o - a4c5o - a4c8o - a4c0o)\)\ j4[ z]\ + \((a5a4o + a5c4o)\)\ j5[z] + a6c4o\ j6[z] + a7c4o\ j7[z] + a8c4o\ j8[z] + \((a0a4o + a0c4o)\)* j0[z] + \(\(aec4o\)\(\ \)\(je[z]\)\(\ \ \)\)\)], "Input"], Cell[BoxData[ \(\(dw4odz\ := \ eontd*n/\((1. *10^21)\) - l4an\ - \ l4cn\ - a4c4o*w4[z] - k*dj4odz/j4[z]*w4[z]*2\ ;\)\)], "Input"], Cell[BoxData[ \(\(dj5odz\ := \ a3c5o\ j3[z] + a4c5o\ j4[ z] + \((\(-a5a3a\) - a5a1o - a5a3o - a5a4o - a5a6o - a5a7o - a5a8o - a5c1o - a5c3o - a5c4o - a5c8o - a5c0o)\)\ j5[z]\ + a7c5o\ j7[z];\)\)], "Input"], Cell[BoxData[ \(\(dw5odz\ := \ eontd*n/\((1. *10^21)\) - l5an\ - \ l5cn\ - k*dj5odz/j5[z]*w5[z]*2\ ;\)\)], "Input"], Cell[BoxData[ \(\(dj6odz\ := \ a1a6p\ j1[z] + \((a3a96 + a3a6F)\)\ j3[z] + \ Re[a4a6o]\ j4[z] + a5a6o\ j5[ z] + \ \((\(-a6c1o\) - a6c3o - a6c2o - a6c4o - a6c7o)\)\ j6[ z] + \((a7a6a + a7c6o)\)\ j7[z] + a8a6o\ j8[z] + a0a6o*j0[z] + aea6o*je[z];\)\)], "Input"], Cell["\<\ Next we must chose the effective momentum loss function for Ar+ - Ar \ collisions such that it gives the desired ion energy at non-thermal energies, \ i.e., kT+ = eE/nQct. We therefore divide l6an by 2. Because w6[z] = kT+ is \ twice the mean energy, we divide the energy loss caused by particle \ production by 2.\ \>", "Text"], Cell[BoxData[ \(\(dw6odz\ := \ eontd*n/\((1. *10^21)\) - l6an/2 - l6cn - k*dj6odz/j6[z]*w6[z]*2/2\ ;\)\)], "Input"], Cell[BoxData[ \(\(dj7odz\ := a1a7o\ j1[z] + \((a3a7o + a3a6p)\)*\ j3[z] + a4a7o\ j4[z] + a5a7o\ j5[z] + a6c7o\ j6[ z] + \((\(-a7a6a\) - a7a8a - a7c1o - a7c3o - a7c4o - a7c5o - a7c6o - a7c8o)\)\ j7[z] + a0a7o*j0[z];\)\)], "Input"], Cell[BoxData[ \(\(dw7odz\ := \ eontd*n/\((1. *10^21)\)\ - l7an\ - \ l7cn\ - k*dj7odz/j7[z]*w7[z]*2;\)\)], "Input"], Cell[BoxData[ \(\(dj8odz\ := \((a1a8o + a1c8o)\)\ j1[z] + \((a3a8o + a3c8o)\)\ j3[ z] + \((a4a8o + a4c8o)\)\ j4[z] + \((a5a8o + a5c8o)\)\ j5[ z] + \((a7a8a + a7c8o)\)\ j7[ z] + \((\(-a8c1o\) - a8c3o - a8c4o - a8a6o)\)\ j8[ z] + \((a0a8o + a0c8o)\)*j0[z]\ ;\)\)], "Input"], Cell[BoxData[ \(\(dw8odz\ := \ eontd*n/\((1. *10^21)\) - \ l8an - l8cn - k*dj8odz/j8[z]*w8[z]*2\ \ ;\)\)], "Input"], Cell[BoxData[ \(dj9odz\ := \ \((a3c94 + a3a96)\)*j3[z] + \((\ a1c49 + a1a69)\)* j1[z] - \(\((a9cpc + a9coc + a9apa + a9aoa)\)\(*\)\(j9[ z]\)\(\ \)\)\)], "Input"], Cell[BoxData[ \(\(w9[z]\ := \ w1[z];\)\)], "Input"], Cell[BoxData[ \(\(dj0odz\ := a1c0o\ j1[z] + a2c0o\ j2[z] + a3c0o\ j3[z] + a4c0o\ j4[z] + \ a5c0o*j5[ z] + \((\(-a0a1o\) - a0a3o - a0a4o - a0a6o - a0a7o - a0a8o - a0c1o - a0c3o - a0c4o - a0c8o)\)*\ j0[z];\)\)], "Input"], Cell[BoxData[ \(\(dw0odz\ := \ eontd*n/\((1. *10^21)\) - l0an\ - \ l0cn\ - a3c0o*w0[z] - k*dj0odz/j0[z]*w0[z]*2\ ;\)\)], "Input"], Cell[BoxData[ \(\(djFodz\ := \(+\((\(-aFa9a\) - aFapa - aFcoc - aFcpc)\)\)\ jF[ z] + \((a3a6F + a3c4F)\)\ j3[z]\ ;\)\)], "Input"], Cell[BoxData[ \(\(wF[z]\ := \ w3[z];\)\)], "Input"], Cell["Diagnostics", "Subsubsection"], Cell[CellGroupData[{ Cell["\<\ Check on differential equations that makes use of the constant charge \ particle current in the gap, i.e., it assumed that the sum of the derivative \ of the various curents is zero.\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"sumIondjodz", " ", "=", " ", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ "alphai", ",", "aec1o", ",", "aec3o", ",", "aec4o", ",", "aea6o", ",", \( (*e\ - 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Cell["\<\ The only way I have been able to get the energy of Ar+ and CH5+ in pure CH4 \ to stay reasonably close to the limit set by the applied field is to make the \ respective cross sections for collisional loss decrease sufficiently rapidly \ with energy. Is this physically correct? These species are characterized by \ a decreasing ion density with increasing z and one seems to have to limit the \ rate of decrease. Let us look at individual terms in the momentum \ balances.\ \>", "Subsubtitle", Background->None], Cell[BoxData[ \(\(dw5odz\ := \ eontd*n/\((1. *10^21)\) - l5an\ - \ l5cn\ - k*dj5odz/j5[z]*w5[z]*2\ ;\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(Plot[{\ eontd*n/\((1. *10^21)\), Evaluate[l5an\ /. \ solution1], \ Evaluate[\ l5cn\ /. \ solution1], Evaluate[k*dj5odz/j5[z]*w5[z]*2\ \ /. \ solution1]}, {z, 0.0, d}, PlotRange\ -> \ {{0, d}, All}, PlotStyle\ -> \[IndentingNewLine]\ {{Thickness[0.007], Dashing[{0.02, 0.02}]}, {Hue[0.3], Thickness[0.007], Dashing[{}]}, {Hue[0.7], Thickness[0.007], Dashing[{}]}, {Hue[0.8], Thickness[0.007], Dashing[{}]}}, ImageSize\ -> 432, PlotLabel\ -> \ StringForm["\", case]];\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(dj5odz\ := \ a3c5o\ j3[z] + a4c5o\ j4[ z] + \((\(-a5a1o\) - a5a3o - a5a4o - a5a6o - a5a7o - a5a8o - a5c1o - a5c3o - a5c4o - a5c8o - a5c0o)\)\ j5[z]\ + a7c5o\ j7[z];\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(Plot[{\ eontd*n/\((1. *10^21)\), Evaluate[\((\(-a5c1o\) - a5c3o)\)\ w5[z]\ /. \ solution1], Evaluate[\((\(-a5c4o\))\)\ w5[z]\ /. \ solution1], \ Evaluate[\((\(-a5c8o\) - a5c0o)\)\ w5[z]\ \ /. \ solution1], Evaluate[\ \((a3c5o\ j3[z] + a4c5o\ j4[z] + \ a7c5o\ j7[z])\)/j5[z]* w5[z]\ /. \ solution1]}, {z, 0.0, d}, PlotRange\ -> \ {{0, d}, All}, PlotStyle\ -> \[IndentingNewLine]\ {{Thickness[0.007], Dashing[{0.02, 0.02}]}, {Hue[0.3], Thickness[0.007], Dashing[{}]}, {Hue[1. ], Thickness[0.007], Dashing[{}]}, {Hue[0.7], Thickness[0.007], Dashing[{}]}, {Hue[0.8], Thickness[0.007], Dashing[{}]}}, ImageSize\ -> 432, PlotLabel\ -> \ StringForm["\", case]];\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(dw3odz\ := \ eontd*n/\((1. *10^21)\) - l3an - l3cn - k*dj3odz/j3[z]*w3[z]*2\ ;\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(Plot[{\ eontd*n/\((1. *10^21)\), Evaluate[l3an\ /. \ solution1], \ Evaluate[\ l3cn\ /. \ solution1], Evaluate[k*dj3odz/j3[z]*w3[z]*2\ \ /. \ solution1]}, {z, 0.0, d}, PlotRange\ -> \ {{0, d}, {0. , \(+50000\)}}, PlotStyle\ -> \[IndentingNewLine]\ {{Thickness[0.007], Dashing[{0.02, 0.02}]}, {Hue[0.3], Thickness[0.007], Dashing[{}]}, {Hue[0.7], Thickness[0.007], Dashing[{}]}, {Hue[0.8], Thickness[0.007], Dashing[{}]}}, ImageSize\ -> 432, PlotLabel\ -> \ StringForm["\", case]];\)\)], "Input", Evaluatable->False] }, Closed]], Cell["Photon Production", "Subsection"], Cell[CellGroupData[{ Cell["\<\ In this section the effects of quenching are assumed be given by a factor of \ 1/(1+n/(9*10^22)). 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\ \ \ \ \ \ \ \((\ Part[{Abs[je[d]], Abs[j1[d]], Abs[j2[d]], Abs[j3[d]], Abs[j4[d]], Abs[j5[d]], Abs[j6[d]], Abs[j7[d]], Abs[j8[d]], Abs[j9[d]], Abs[j0[d]]}\ /. \ solution3, 1])\)/ sumCathIonFlux[j]\ ;\)\)\)], "Input", Evaluatable->False] }, Closed]], Cell[BoxData[ \(Clear[case, d, f, eontd, p, n, caseUsed, CaseUsedList, dList, outputList, outputTable, sumIntensityCHA, intensityCHAje, intensityCHAj1, intensityCHAj3, intensityCHAj9]\)], "Input"], Cell[CellGroupData[{ Cell["We now generate the output using a Do loop", "Subsection"], Cell[BoxData[ \(\(\(\t\)\(caseList\ = \ {11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23};\)\)\)], "Input"], Cell[BoxData[ \(\(caseList = {14};\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(Dimensions[%]\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(relFluxList[ 0]\ = \ {"\", "\", "\", "\", \ "\", "\", "\", "\", "\", "\", \ "\"\ , "\"};\)\)], "Input"], Cell[BoxData[ \(spatialDist\ := \ Block[{}, \[IndentingNewLine]\t Do[\n\t\ nm\ = \ 40; \[IndentingNewLine]\ case\ = \ Part[caseList, j]; \[IndentingNewLine]\ \ \ \ \ \ caseUsed[ j]\ = \ case; \n\t\ initialConditions; \n\ \ \ \ \ \ \ \ \ \ \ \ positionList\ = \ Table[\((d - d/nm*m)\), {m, 0, nm}]; \[IndentingNewLine]\ \ \ \ \ \ sumCH4AList[0]\ = \ positionList; \n\ \ \ \ \ \ heavyCH4AList[0]\ = \ positionList; \n\t eontdUsed[j] = eontd; \[IndentingNewLine]\ \ \ \ \ dUsed[j]\ = \ d; \n\ \ \ \ \ \ \ \ \ \ solution4 = \ solution; \n\ \ \ heavyCH4AList[j] = \ \ Flatten[ Table[\((\((intensityCHAj1Eq\ /. \ solution4)\) + \ \ \[IndentingNewLine]\((intensityCHAj3Eq\ \ /. \ solution4)\) + \((intensityCHAj8Eq\ /. \ solution4)\) + \((intensityCHAj9Eq\ /. \ solution4)\) + \((intensityCHAjFEq\ /. \ solution4)\))\)\ /. \ z\ -> d/nm*m, {m, 0, nm}]]; \ \ \ \ \ \ \ \ \ \ \[IndentingNewLine]sumCH4AList[ j]\ = \ \ Flatten[ Table[\((intensityCHAjeEq\ /. \ solution4)\)\ /. \ z\ -> d/nm*m, {m, 0, nm}]]\ + \ \ heavyCH4AList[ j]; \[IndentingNewLine]\t cathFluxList[j]\ = Part[{Abs[j1[d]], Abs[j2[d]], Abs[j3[d]], Abs[j4[d]], Abs[j5[d]], Abs[j6[d]], Abs[j7[d]], Abs[j8[d]], Abs[j9[d]], Abs[j0[d]], Abs[j0[d]]}\ /. \ solution4, 1]; \[IndentingNewLine]\ \ \ \ sumCathIonFlux[ j]\ = \ \ \((Abs[j1[d]] + Abs[j2[d]] + Abs[j3[d]] + Abs[j4[d]] + Abs[j5[d]] + Abs[j6[d]] + Abs[j7[d]] + Abs[j8[d]] + Abs[j0[d]])\)\ /. \ solution4\ [\([1]\)]; \[IndentingNewLine]\ \ \ \ \ \ relCathFluxList[ j]\ = \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \((\ Part[{Abs[j1[d]], Abs[j2[d]], Abs[j3[d]], Abs[j4[d]], Abs[j5[d]], Abs[j6[d]], Abs[j7[d]], Abs[j8[d]], Abs[j9[d]], Abs[j0[d]], Abs[jF[d]]}\ /. \ solution4, 1])\)/sumCathIonFlux[ j]\ ; \[IndentingNewLine]\ \ \ \ \ cathEnergyList[j]\ = Part[{w1[d], w2[d], w3[d], w4[d], w5[d], w6[d], w7[d], w8[d], w0[d]}\ /. \ solution4, 1]; \[IndentingNewLine]\ \ \ \ \ appliedVoltage[j]\ = \ eontd*n*d/10^21; \[IndentingNewLine]\ \ \ \ \ \ cathElectronFlux[ j]\ = \ Abs[je[d]]\ /. \ solution4\ [\([1]\)]; \[IndentingNewLine]fractionCH4[j]\ = \ f; \ \[IndentingNewLine]cathodeIntensitye[ j]\ = \ \(intensityCHAjeEq\ /. \ solution4\)\ /. \ z\ -> \ d; \[IndentingNewLine]cathodeIntensity1[ j]\ = \ \(intensityCHAj1Eq\ /. \ solution4\)\ /. \ z\ -> \ d; \[IndentingNewLine]cathodeIntensity3[ j]\ = \ \(intensityCHAj3Eq\ /. \ solution4\)\ /. \ z\ -> \ d; \[IndentingNewLine]cathodeIntensity8[ j]\ = \ \(intensityCHAj8Eq\ /. \ solution4\)\ /. \ z\ -> \ d; \[IndentingNewLine]cathodeIntensity9[ j]\ = \ \(intensityCHAj9Eq\ /. \ solution4\)\ /. \ z\ -> \ d; \[IndentingNewLine]cathodeIntensityF[ j]\ = \ \(intensityCHAjFEq\ /. \ solution4\)\ /. \ z\ -> \ d, \[IndentingNewLine]{j, 1, Length[caseList]}]; \[IndentingNewLine]\[IndentingNewLine]\ \ \ \ \ \ \ \ \ sumCH4ATable4\ = \ Table[sumCH4AList[j], {j, 0, Length[caseList]}]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ heavyCH4ATable4\ = \ Table[heavyCH4AList[j], {j, 0, Length[caseList]}]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ caseUsedList\ = \ Table[caseUsed[j], {j, 1, Length[caseList]}]; \[IndentingNewLine]\ \ \ \ \ \ \ \ dList\ \ = \ Table[dUsed[k], {k, 1, Length[caseList]}]; \n\ \ \ \ \ \ \ \ \ \ eontdList\ = \ Table[eontdUsed[k], {k, 1, Length[caseList]}]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ relCathFluxTable\ = \ \ Table[ relCathFluxList[j], {j, 1, Length[caseList]}]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ cathEnergyTable\ = \ \ Table[ cathEnergyList[j], {j, 1, Length[caseList]}]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ appliedVoltageList\ = \ \ Table[ appliedVoltage[k], {k, 1, Length[caseList]}]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ cathElectronFluxList\ = \ Table[cathElectronFlux[k], {k, 1, Length[caseList]}]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ fractionCH4List\ = \ \ Table[ fractionCH4[k], {k, 1, Length[caseList]}]; \[IndentingNewLine]cathodeIntensityList\ = \ \ Table[\((cathodeIntensitye[k] + cathodeIntensity1[k] + cathodeIntensity3[k] + cathodeIntensity9[k] + cathodeIntensityF[k])\), {k, 1, Length[caseList]}];\[IndentingNewLine]]\)], "Input"], Cell[BoxData[ \(spatialDist\)], "Input"], 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Because the ions are injected from a hot \ filament ion source rather than produced by electron impact in the drift \ tube, we need to reformulate the boundary conditions. The authors stae that \ the principle ions found when using pure CH4 are CH3+ and CH5+. Fot the lack \ of better data we will take equal fluxes of each. 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Background->GrayLevel[1]] }, Open ]], Cell["!!c:\\proplot\\methane\\CH4Flux.the", "Input", PageWidth->Infinity], Cell[CellGroupData[{ Cell["Export results for species energies at cathode.", "Subsubsection"], Cell[BoxData[ \(\(cathEnergyTable1\ = \ Transpose[ Prepend[Prepend[ Prepend[Transpose[cathEnergyTable], appliedVoltageList], eontdList], fractionCH4List]];\)\)], "Input"], Cell[BoxData[ \(\(cathEnergyTable2\ = \ Map[ToString[SetPrecision[#, 4.2], FormatType -> FortranForm] &, cathEnergyTable1, {2}];\)\)], "Input"], Cell["\<\ cathEnergyTable3 = TableForm[cathEnergyTable2,TableHeadings -> {None, {\"%f(CH4)\",\"E/n(Td)\",\"applied \ V\",\"w1-CH+\",\"w2-CH2+\",\"w3-CH3+\",\"w4-CH4+\",\"w5-CH5+\",\"w6-Ar+\",\"\ w7-ArH+\",\"w8-H+\",\"w0-C2H5+\"}}, TableSpacing -> {0,1}];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Block[{stream1,outputfile}, SetOptions[$Output,PageWidth->120]; outputfile := \"c:\\\\proplot\\\\methane\\\\CH4Energ.the\"; stream1 = OpenWrite[outputfile,PageWidth -> Infinity]; WriteString[stream1, \"%\", StringForm[\"Calculated species energy at cathode for \ CH4-Ar mixtures\"], \"\\n\", now, \"\\n\", ToString[cathEnergyTable3]] ; Close[stream1]; SetOptions[$Output,PageWidth->53]; ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]], Cell["!!c:\\proplot\\methane\\CH4Energ.the", "Input", PageWidth->Infinity], Cell["Compare with de Urquijo et al (1998).", "Subsubsection"], Cell[CellGroupData[{ Cell["\<\ We wish to read and then compare with the data of de Urquijo et al, in \ Gaseous Dielectrics, ed by Christophorou and Olthoff, (Plenum, 1998, New \ York), p. 51.\ \>", "SmallText", ImageSize->{216, 144}], Cell[BoxData[ \(\(!! c:\\proplot\\methane\\deUrquijo1.txt\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(<< Graphics`MultipleListPlot`\)], "Input"], Cell["\<\ inputfilegt := \"c:\\\\proplot\\\\methane\\\\deUrquijo1.txt\"; stream1 = OpenRead[inputfilegt]; Find[stream1,\"%\"]; Find[stream1,\"%\"]; data1 =1.* ReadList[stream1, Number, RecordLists ->True]; Close[stream1];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(data1;\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(data3\ = \ Transpose[data1];\)\)], "Input"], Cell[BoxData[ \(\(dataCH\ = \ Transpose[{Part[data3, 1], Part[data3, 4]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureExpCH\ = LinearLogListPlot[dataCH, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.3], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH2\ = \ \ Transpose[{Part[data3, 1], Part[data3, 5]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureExpCH2\ = LinearLogListPlot[dataCH2, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.5], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH3\ = \ \ Transpose[{Part[data3, 1], Part[data3, 6]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureExpCH3\ = LinearLogListPlot[dataCH3, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.7], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH4\ = \ \ Transpose[{Part[data3, 1], Part[data3, 7]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureExpCH4\ = LinearLogListPlot[dataCH4, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.8], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH5\ = \ \ Transpose[{Part[data3, 1], Part[data3, 8]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureExpCH5\ = LinearLogListPlot[dataCH5, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[1.0], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataC2H5\ = \ \ Transpose[{Part[data3, 1], \((Part[data3, 9] + Part[data3, 10] + Part[data3, 11] + Part[data3, 12])\)}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureExpC2H5\ = LinearLogListPlot[dataC2H5, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.1], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[plotPureExpCH, plotPureExpCH2, \ plotPureExpCH3, \ plotPureExpCH4, \ plotPureExpCH5, plotPureExpC2H5, \ DisplayFunction\ -> \ $DisplayFunction];\)\)], "Input", Evaluatable->False], Cell["Plot calculated fluxes at cathode for pure CH4", "Subsubsection"], Cell[BoxData[ \(\(data4\ = \ Transpose[relCathFluxTable1];\)\)], "Input"], Cell[BoxData[ \(\(dataCH\ = \ Transpose[{Part[data4, 2]/1000, 100*Part[data4, 4]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureCalcCH\ = LinearLogListPlot[dataCH, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.3], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH2\ = \ \ Transpose[{Part[data4, 2]/1000, 100*Part[data4, 5]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureCalcCH2\ = LinearLogListPlot[dataCH2, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.5], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH3\ = \ \ Transpose[{Part[data4, 2]/1000, 100*Part[data4, 6]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureCalcCH3\ = LinearLogListPlot[dataCH3, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.7], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH4\ = \ \ Transpose[{Part[data4, 2]/1000, 100*Part[data4, 7]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureCalcCH4\ = LinearLogListPlot[dataCH4, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.8], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH5\ = \ \ Transpose[{Part[data4, 2]/1000, 100*Part[data4, 8]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureCalcCH5\ = LinearLogListPlot[dataCH5, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[1], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataH\ = \ \ Transpose[{Part[data4, 2]/1000, 100*Part[data4, 11]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureCalcH\ = LinearLogListPlot[dataH, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataC2H5\ = \ \ Transpose[{Part[data4, 2]/1000, 100*Part[data4, 13]}];\)\)], "Input"], Cell[BoxData[ \(\(plotPureCalcC2H5\ = LinearLogListPlot[dataC2H5, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.1], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[plotPureCalcCH, plotPureCalcCH3, \ plotPureCalcCH4, \ plotPureCalcCH5, \ plotPureCalcH, plotPureCalcC2H5, \ DisplayFunction\ -> \ $DisplayFunction];\)\)], "Input", Evaluatable->False] }, Closed]], Cell[BoxData[ \(\(Show[plotPureCalcCH, plotPureCalcCH2, plotPureCalcCH3, \ plotPureCalcCH4, \ plotPureCalcCH5, plotPureCalcC2H5, \ plotPureCalcH, \[IndentingNewLine]plotPureExpCH, plotPureExpCH2, \ plotPureExpCH3, \ plotPureExpCH4, \ plotPureExpCH5, plotPureExpC2H5, ImageSize\ -> 432, PlotLabel\ -> \ StringForm["\", balance], \ DisplayFunction\ -> \ $DisplayFunction];\)\)], "Input"], Cell["\<\ green - CH+, light blue - CH2+, dark blue - CH3+, purple - CH4+, red - CH5+, \ orange - C2H5+ and C2H3+, black - H+\ \>", "SmallText"], Cell["\<\ Note that the ion that gives the worst fit is CH5+, which does not react and \ is not produced here.\ \>", "Subsubtitle"], Cell["\<\ Calculation of fluxes at anode for Ar:CH4 = 1:1 from de Urquijo et al \ (1998)\ \>", "Section"], Cell["\<\ Here we wish to try to simulate the relative ion fluxes measured by de \ Urquijo et al (1998) for 50% CH4 - 50% AR. Because the ions are injected \ from a hot filament ion source rather than produced by electron impact in the \ drift tube, we need to reformulate the boundary conditions. The authors \ state that the principle ions found when using 50% CH4 and 50% Ar are CH3+, \ CH5+, and Ar+. Fot the lack of better data we will take equal fluxes of \ each. We will assume that the electron flux is very small because the \ voltage and pd are well below breakdown.\ \>", "Text"], Cell["\<\ The following set of initial energies is arbitrarily set at 1 eV. \ \>", "Text"], Cell[BoxData[ RowBox[{"solution", " ", ":=", " ", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", "\n", " ", RowBox[{\(\(je'\)[z] == djeodz\), ",", \(je[0] == \ 1. *10^\(-6\)\), ",", "\n", "\[IndentingNewLine]", \(\(j1'\)[z] == dj1odz\), ",", " ", \(j1[0]\ == \ 1. *10^\(-3\)\), ",", "\n", " ", \(\(w1'\)[z] == dw1odz\), ",", \(w1[0]\ == \ 1. \), ",", "\n", "\[IndentingNewLine]", \(\(j2'\)[z] == dj2odz\), ",", " ", \(j2[0]\ == \ 1. *10^\(-3\)\), ",", "\n", " ", \(\(w2'\)[z] == dw2odz\), ",", \(w2[0]\ == \ 1. \), ",", "\n", "\[IndentingNewLine]", \(\(j3'\)[z] == dj3odz\), ",", \(j3[0]\ == \ 0.333\), ",", "\n", " ", \(\(w3'\)[z] == \ dw3odz\), ",", \(w3[0]\ == \ 1. \), ",", "\n", "\[IndentingNewLine]", \(\(j4'\)[z] == dj4odz\), ",", \(j4[0]\ == \ 1. *10^\(-3\)\), ",", "\t\t", "\n", 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FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Open ]], Cell[CellGroupData[{ Cell["Export results for flux at cathode.", "Subsubsection"], Cell[BoxData[ \(\(relCathFluxTable1\ = \ Transpose[ Prepend[Prepend[ Prepend[Transpose[relCathFluxTable], cathElectronFluxList], eontdList], fractionCH4List]];\)\)], "Input"], Cell[BoxData[ \(\(relCathFluxTable2\ = \ Map[ToString[SetPrecision[#, 3.3], FormatType -> FortranForm] &, relCathFluxTable1, {2}];\)\)], "Input"], Cell["\<\ relCathFluxTable3 = TableForm[relCathFluxTable2,TableHeadings -> {None, {\"%f(CH4)\",\"E/n(Td)\",\"je[d]\",\"j1-CH+\",\"j2-CH2+\",\ \"j3-CH3+\",\"j4-CH4+\",\"j5-CH5+\",\"j6-Ar+\",\"j7-ArH+\",\"j8-H+\",\"j9-\ fastCH\",\"j0-C2H5+\"}}, TableSpacing -> {0,1}];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Block[{stream1,outputfile}, SetOptions[$Output,PageWidth->120]; outputfile := \"c:\\\\proplot\\\\methane\\\\CH4-ArFlux.the\"; stream1 = OpenWrite[outputfile,PageWidth -> Infinity]; WriteString[stream1, \"%\", StringForm[\"Calculated relative fluxes at cathode for \ CH4-Ar mixtures\"], \"\\n\", StringForm[\"Fluxes normalized to je[anode] = 1 and \ others negligible at anode\"], \"\\n\", now, \"\\n\", ToString[relCathFluxTable3]] ; Close[stream1]; SetOptions[$Output,PageWidth->53]; ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]], Cell["!!c:\\proplot\\methane\\CH4-ArFlux.the", "Input", PageWidth->Infinity], Cell[CellGroupData[{ Cell["Export results for species energies at cathode.", "Subsubsection"], Cell[BoxData[ \(\(cathEnergyTable1\ = \ Transpose[ Prepend[Prepend[ Prepend[Transpose[cathEnergyTable], appliedVoltageList], eontdList], fractionCH4List]];\)\)], "Input"], Cell[BoxData[ \(\(cathEnergyTable2\ = \ Map[ToString[SetPrecision[#, 4.2], FormatType -> FortranForm] &, cathEnergyTable1, {2}];\)\)], "Input"], Cell["\<\ cathEnergyTable3 = TableForm[cathEnergyTable2,TableHeadings -> {None, {\"%f(CH4)\",\"E/n(Td)\",\"applied \ V\",\"w1-CH+\",\"w2-CH2+\",\"w3-CH3+\",\"w4-CH4+\",\"w5-CH5+\",\"w6-Ar+\",\"\ w7-ArH+\",\"w8-H+\",\"w0-C2H5+\"}}, TableSpacing -> {0,1}];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Block[{stream1,outputfile}, SetOptions[$Output,PageWidth->120]; outputfile := \"c:\\\\proplot\\\\methane\\\\CH4-ArEnerg.the\"; stream1 = OpenWrite[outputfile,PageWidth -> Infinity]; WriteString[stream1, \"%\", StringForm[\"Calculated species energy at cathode for \ CH4-Ar mixtures\"], \"\\n\", now, \"\\n\", ToString[cathEnergyTable3]] ; Close[stream1]; SetOptions[$Output,PageWidth->53]; ]\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]], Cell["!!c:\\proplot\\methane\\CH4-ArEnerg.the", "Input", PageWidth->Infinity], Cell[CellGroupData[{ Cell["\<\ Plot experimental and calculated fluxes at anode for Ar:CH4 = 1:1 from de \ Urquijo et al (1998)\ \>", "Subsubsection"], Cell[BoxData[ \(\(!! c:\\proplot\\methane\\deUrquijo2.txt\)\)], "Input", Evaluatable->False], Cell["\<\ inputfilegt := \"c:\\\\proplot\\\\methane\\\\deUrquijo2.txt\"; stream1 = OpenRead[inputfilegt]; Find[stream1,\"%\"]; Find[stream1,\"%\"]; data1 = 1.*ReadList[stream1, Number,RecordLists ->True]; Close[stream1];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(data1\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(data3\ = \ Transpose[data1];\)\)], "Input"], Cell[BoxData[ \(\(dataCH\ = \ Transpose[{Part[data3, 1], Part[data3, 3]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixExpCH\ = LinearLogListPlot[dataCH, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.3], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH2\ = \ \ Transpose[{Part[data3, 1], Part[data3, 4]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixExpCH2\ = LinearLogListPlot[dataCH2, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.5], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH3\ = \ \ Transpose[{Part[data3, 1], Part[data3, 5]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixExpCH3\ = LinearLogListPlot[dataCH3, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.7], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH4\ = \ \ Transpose[{Part[data3, 1], Part[data3, 6]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixExpCH4\ = LinearLogListPlot[dataCH4, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.8], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH5\ = \ \ Transpose[{Part[data3, 1], Part[data3, 7]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixExpCH5\ = LinearLogListPlot[dataCH5, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[1.0], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataC2H5\ = \ \ Transpose[{Part[data3, 1], Part[data3, 8] + Part[data3, 9] + Part[data3, 10] + Part[data3, 11]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixExpC2H5\ = LinearLogListPlot[dataC2H5, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.1], PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataAr\ = \ \ Transpose[{Part[data3, 1], Part[data3, 12] + Part[data3, 13]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixExpAr\ = LinearLogListPlot[dataAr, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {PointSize[0.02]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[plotMixExpCH, plotMixExpCH2, \ plotMixExpCH3, \ plotMixExpCH4, \ plotMixExpCH5, plotMixExpC2H5, plotMixExpAr, \ DisplayFunction\ -> \ $DisplayFunction];\)\)], "Input", Evaluatable->False], Cell["\<\ Plot calculated fluxes at anode for Ar:CH4 = 1:1 from this notebook.\ \>", "Subsubsection"], Cell[BoxData[ \(\(data5\ = \ Transpose[Take[relCathFluxTable1, \(-4\)]];\)\)], "Input"], Cell[BoxData[ \(\(dataCH\ = \ Transpose[{Part[data5, 2]/1000, 100*Part[data5, 4]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixCalcCH\ = LinearLogListPlot[dataCH, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.3], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH2 = \ \ Transpose[{Part[data5, 2]/1000, 100*Part[data5, 5]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixCalcCH2\ = LinearLogListPlot[dataCH2, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.5], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH3\ = \ \ Transpose[{Part[data5, 2]/1000, 100*Part[data5, 6]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixCalcCH3\ = LinearLogListPlot[dataCH3, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.7], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH4\ = \ \ Transpose[{Part[data5, 2]/1000, 100*Part[data5, 7]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixCalcCH4\ = LinearLogListPlot[dataCH4, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[0.8], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataCH5\ = \ \ Transpose[{Part[data5, 2]/1000, 100*Part[data5, 8]}];\)\)], "Input"], Cell[BoxData[ \(\(plotMixCalcCH5\ = LinearLogListPlot[dataCH5, PlotRange\ -> {{0, 7}, {0.1, 100}}, PlotStyle\ -> \ {Hue[1], Thickness[0.007]}, PlotJoined\ -> \ True, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(dataAr\ = \ \ Transpose[{Part[data5, 2]/1000, 100*\((Part[data5, 9] + 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