(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. 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[ 126979, 3455]*) (*NotebookOutlinePosition[ 127761, 3482]*) (* CellTagsIndexPosition[ 127717, 3478]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Cross sections for analysis of high E/n discharges in CH4-Ar mixtures.\ \>", "Subtitle"], Cell["\<\ Here we are primarily interested in the emission of the CH(A->X) band as a \ diagnostic of low-current, high E/n discharges in CH4-Ar mixtures. As in \ pure H2 and in H2-Ar mixtures, the emission under these conditions is \ primarily the result of excitation in heavy-paticle collisions. This \ emission is placed on an absolute scale by comparison with electron-induced \ emission at lower E/n. See the notebook MethaneSpatial.nb for the original of this notebook and the \ calculation of experimental spatial distributions of emission. That notebook \ also contains comparisons of calculated and experimental relative ion fluxes \ at the cathode from de Urquijo et al.\ \>", "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[ \(now\ := \ StringForm["\<``/``/`` ``:``:``\>", \(Date[]\)[\([2]\)], \ \(Date[]\)[\([3]\)], \(Date[]\)[\([1]\)], \(Date[]\)[\([4]\)], \ \(Date[]\)[\([5]\)], \(Date[]\)[\([6]\)]]\)], "Input"], Cell[BoxData[ \(Needs["\"]\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(Needs["\"]\)], "Input"] }, Closed]], Cell[BoxData[ \(now\)], "Input"], Cell["\<\ These cross sections are our best estimates as of 10/05/2001.\ \>", "Text"], 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 when first or second letter, m - metastable, w - drift energy, u - total energy\ \>", "SmallText", PageWidth->Infinity, Evaluatable->False, ShowSpecialCharacters->False], Cell["\<\ Color scheme for all plots, e.g., the first curve listed in Plot[ ] is solid \ red, etc.\ \>", "Text"], Cell[BoxData[ \(\(\(\ \)\(plotColors\ = \ {\[IndentingNewLine]{Hue[0.0], Thickness[0.007], Dashing[{}]}, (*curve\ #1 - solid\ red*) \[IndentingNewLine]{Hue[ 0.1], Thickness[0.007], Dashing[{}]}, (*curve\ #2 - solid\ orange*) \[IndentingNewLine]{Hue[0.3], Thickness[0.007], Dashing[{}]}, (*curve\ #3 - solid\ green*) \[IndentingNewLine]{Hue[0.5], Thickness[0.007], Dashing[{}]}, (*curve\ #4 - solid\ cyan*) \[IndentingNewLine]{Hue[0.7], Thickness[0.007], Dashing[{}]}, (*curve\ #5 - solid\ blue*) \[IndentingNewLine]{Hue[0.8], Thickness[0.007], Dashing[{}]}, (*curve\ #6 - solid\ purple*) \[IndentingNewLine]{Thickness[0.007], Dashing[{}]}, (*curve\ #7 - solid\ black*) \[IndentingNewLine]{Hue[0.0], Thickness[0.007], Dashing[{0.05, 0.05}]}, (*curve\ #8 - dashed\ red*) \[IndentingNewLine]{Hue[0.1], Thickness[0.007], Dashing[{0.05, 0.05}]}, (*curve\ #9 - dashed\ orange*) \[IndentingNewLine]{Hue[0.3], Thickness[0.007], Dashing[{0.05, 0.05}]}, (*curve\ #10 - dashed\ green*) \[IndentingNewLine]{Hue[0.5], Thickness[0.007], Dashing[{0.05, 0.05}]}, (*curve\ #11 - dashed\ cyan*) \[IndentingNewLine]{Hue[0.7], Thickness[0.007], Dashing[{0.05, 0.05}]}, (*curve\ #12 - dashed\ blue*) \[IndentingNewLine]{Hue[0.8], Thickness[0.007], Dashing[{0.05, 0.05}]}, (*curve\ #13 - dashed\ purple*) \[IndentingNewLine]{Thickness[0.007], Dashing[{0.02, 0.02}]}};\)\( (*curve\ #14 - dashed\ black*) \)\)\)], "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["\<\ Model using momentum balance. This model leads to lower ion energies than \ that using energy balance because of higher collisional losses. See Phelps, \ Jelenkovic and Pitchford (1988)\ \>", "Text"], Cell[BoxData[{ \(falphai\ = \ 1. ; faec1o = 1. ; faec2o = \ 1. ; faec3o = 1. ; faec4o = 1. ; faea6o = 1. ; faecp432 = 0.6; faecp656 = 1. ; faeap430\ = \ 0.18;\), "\[IndentingNewLine]", \(fa1cn\ = \ 1. ; fa1c0o = 1. ; fa1c3o = 1. ; fa1c49 = 1. ; fa1c4p = 1. ; \ b1c\ = \ 16. /\((16. + 13. )\); \ (*CH + \(-CH4\)\ data*) \), "\n", \(fa2cn\ = \ 1. ; fa2c0o = 1. ; fa2c1o = 1. ; fa2c4o = 1; fa2c4p = 1. ; \ \ \ \ \ \ \ fa2c94\ = \ 1; \ \ b2c\ = \ 16. /\((16. + 14. )\); \ (*CH2 + \(-CH4\)\ data*) \), "\n", \(fa3cn\ = \ 1. ; fa3c0o\ = \ 1. ; fa3c4F = 1. ; fa3c1o = 1. ; fa3c4p = 1. ; fa3c2H\ = \ 1. ; \ fa3c94\ = \ 1; \ b3c\ = \ 16. /\((16. + 15. )\); \ (*CH3 + \(-CH4\)\ data*) \), "\n", \(fa4cn\ = \ 1. ; fa4c4o = 1. ; fa4c5o = 1. ; fa4c3o = 1.0; \ b4c\ = \ 16. /\((16. + 16. )\); \ \ (*CH4 + \(-CH4\)\ data*) \), "\[IndentingNewLine]", \ \(fa4c1o\ = \ 1. ; \ fa4c8o\ = \ 1. ; \ fa4a8F = \ 1. ; a4c0o = 0; \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*CH4 + \ \(-CH4\)\ data*) \), "\n", \(fa5cn\ = \ 1. ; fa5cnv\ = \ 1. ; fa5c3o = 1. ; fa5c4o = 1. \ ; fa5c8o\ = \ 1. ; \ b5c\ = \ 16. /\((16. + 17. )\); \ \ \ \ \ \ (*CH5 + \(-CH4\)\ data*) \), "\n", \(fa6cn\ = \ 1. ; fa6c3o\ = 1. ; fa6c2o\ = 1. ; \ fa6cp7\ \ = \ 1. ; \ b6c\ = \ 16. /\((16. + 40. )\); \ \ \ \ \ \ \ (*Ar + \(-CH4\)\ data*) \), "\n", \(fa7cn\ = \ 1. ; fa7c3o\ = \ 1. ; \ fa7c5o\ = \ 1. ; \ b7c\ = \ 16. /\((16. + 41. )\); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*ArH + \(-CH4\)\ data*) \), "\ \n", \(fa8cn\ = \ 1. ; fa8c8p = 1. ; \ \ \ fa8c4o\ = \ 1. ; \ \ \ b8c\ = \ 16. /\((16. + 1. )\); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*H + \(+CH4\)\ data*) \), "\n", \(fa9cn\ = \ 1. ; fa9cpc\ = 1. ; \ b9c\ = \ 16. /\((16. + 13. )\); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*fast\ CH + CH4\ data*) \), "\n", \(fa0cn\ = \ 1. ; fa0c5o\ = \ 0; fa0c1o = 0; fa0c3o = 0; fa0c4o = 0; fa0c8o = 0;\), "\[IndentingNewLine]", \(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(\(\(a0c0c = 0\) \)\(;\)\(\ \ \ \)\(\(b0c\ = \ 16. /\((16. + 29. )\)\) \)\(;\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\( (*C2H5 + \(-CH4\)\ data*) \)\)\), "\[IndentingNewLine]", \(faFcn\ = \ 1. ; \ faFc9c\ = \ 1. ; \ faFcpc\ = \ 1. ; \ bFc\ = \ 16. /\((16. + 15. )\); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*fast\ CH3\ + CH4*) \), "\n", \(\(faea6o = 1. ;\)\), "\[IndentingNewLine]", \(fa1an\ = \ 1. ; fa1a59\ = \ 1. ; fa1a6p\ = \ 1. ; fa1a69 = 1; b1a\ = \ 40. /\((40. + 13. )\); \ (*CH + \(-Ar\)\ data*) \), "\n", \(fa2an\ = \ 1. ; \ \ b2a\ = \ 40. /\((40. + 14. )\); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*CH2 + \(-Ar\)\ data*) \), "\n", \(fa3an\ = \ 1. ; fa3a6F\ = \ 1. ; fa3a1o = 1. ; fa3a6p = 1. ; \ fa3a96\ = 1; b3a\ = \ 40. /\((40. + 15. )\); \ (*CH3 + \(-Ar\)\ data*) \), "\n", \(fa4an\ = \ 1. ; fa4a6o\ = \ 1. ; fa4a7F = 1. ; b4a\ = \ 40. /\((40. + 16. )\); \ \ \ \ (*CH4 + \(-Ar\)\ data*) \), "\n", \(fa5an\ = \ 1. ; \ fa5a3a\ = \ 1; \ \ b5a\ = \ 40. /\((40. + 17. )\); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*CH5 + \(-Ar\)\ data*) \), "\n", \(fa6an\ = \ 1. ; fa6a6a = 1. ; \ \ \ b6a\ = \ 40. /\((40. + 40. )\); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*Ar + \(+Ar\)\ data*) \), "\n", \(fa7an\ = \ 1. ; fa7a6a = 1. ; fa7a8a = 1. ; \ b7a\ = \ 40. /\((40. + 41. )\); \ \ \ \ \ (*ArH + \(+Ar\)\ data*) \), "\n", \(fa8an\ = \ 1. ; fa8a6o\ = \ 1. ; b8a\ = \ 40. /\((40. + 1. )\); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*H + \(+Ar\)\ data*) \), "\[IndentingNewLine]", \(fa9an\ = \ 1. ; fa9an = 1. ; fa9apa = 1; \ b9a\ = \ 40. /\((40. + 13. )\); \ \ \ \ \ \ \ \ \ (*fast\ CH - Ar\ data*) \), "\n", \(fa0an\ = \ 1. ; a0a1o\ = 10^\(-30\); \ a0a3o = 0; \ a0a4o = 0; a0a6o = 0; \ a0a7o = 0; a0a8o = 0; \ b0a\ = \ 40. /\((40. + 29. )\); \ \ \ \ \ (*C2H5 + \(-Ar\)\ data*) \), "\ \[IndentingNewLine]", \(faFan\ = \ 1. ; \ faFa9a\ = \ 1. ; \ faFapa\ = \ 1. ; \ \ bFa\ = \ 40. /\((40. + 15. )\); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*fast\ CH3\ + Ar*) \), "\n", \(\(balance\ := \ "\";\)\)}], "Input"], Cell["Reaction energies", "Subsection"], Cell["\<\ Some relevant ionization potentials, proton affinities, and dissociation \ energies in eV\ \>", "Text"], Cell[BoxData[{ \(ipch\ \ \ = \ 10.64; \ \ (*ionization\ potential\ from\ NIST\ Web\ Book\ *) \[IndentingNewLine]ipch2\ = \ 10.40;\), "\[IndentingNewLine]", \(\(ipch3\ = \ 9.84;\)\), "\[IndentingNewLine]", \(\(ipch4\ = \ 12.61;\)\), "\[IndentingNewLine]", \(\(iph\ \ \ \ \ \ = \ 13.6;\)\), "\[IndentingNewLine]", \(\(iph2\ \ \ = \ 15.6;\)\), "\[IndentingNewLine]", \(\(ipar\ \ \ = \ 15.76;\)\), "\[IndentingNewLine]", \(\(iph\ \ \ \ \ = \ \ 13.6;\)\), "\[IndentingNewLine]", \(\(ipc2h4 = 10.51;\)\), "\[IndentingNewLine]", \(\(pach4\ = \ 5.63;\)\ (*proton\ affinity\ of\ CH4\ in\ eV\ from\ NIST\ Web\ Book*) \ \), "\[IndentingNewLine]", \(\(pah2\ \ \ = \ 4.37;\)\), "\[IndentingNewLine]", \(\(paar\ \ \ = \ 3.82;\)\), "\[IndentingNewLine]", \(\(pac\ \ \ \ \ = \ 3.6;\)\), "\[IndentingNewLine]", \(\(pac2h4 = 7.05;\)\), "\[IndentingNewLine]", \(\(dh2h\ \ \ = \ 4.48;\)\), "\[IndentingNewLine]", \(\(dch4h\ = \ 4.48;\)\ (*Partridge\ and\ Bauschlicher\ \((1995)\)*) \), "\ \[IndentingNewLine]", \(\(dch3h\ = \ 4.72;\)\), "\[IndentingNewLine]", \(\(dch2h\ = \ 4.33;\)\), "\[IndentingNewLine]", \(\(dchh\ \ \ = \ 3.46;\)\)}], "Input"], Cell["\<\ Here we set up a general scheme for calculating reaction energies or \ thresholds. First we write a list of all of the equations to be used. This \ will be joined using Join[ ] to the equation for the reaction. Then we list \ all of the reactants to used as the variables to be eliminated.\ \>", "Text"], Cell[BoxData[ \(\(equations\ = \ {ch\ == \ chp\ + \ e\ + \ ipch, \ ch4\ == \ ch4p\ + \ e\ + \ ipch4, ch\ == \ c\ + \ h\ + \ dchh, \ ch5p\ == \ ch4\ + \ hp\ + \ pach4, \ \[IndentingNewLine]h\ == \ hp\ + \ e + iph, ch\ == \ cha\ + \ 2.87, ch3\ == \ ch3p\ + e\ + \ ipch3, ch\ == \ chp\ + \ e\ + \ ipch, \ ch4\ == \ ch3\ + \ h\ + dch4h, ch4\ == \ ch4p\ + \ e\ + \ ipch4, ch3\ == \ ch2\ + \ h\ + dch3h, \ ch2\ == \ ch\ + \ h\ + \ dch2h, h2\ == \ 2\ h\ + \ dh2h, \[IndentingNewLine]ch4p\ == \ ch2p\ + \ h2\ + \ 2.6, ch5\ == \ ch5p\ + e\ + \ ipch5, ar\ == \ arp\ + \ e\ + \ ipar, arhp\ == \ ar\ + \ hp\ + \ paar, c2h5p\ == \ c2h4\ + \ hp\ + \ pac2h4};\)\)], "Input"], Cell[BoxData[ \(\(variables\ = \ {e, chp, \ ch4, \ ch, \ ch4p, hp, c, ch5p, ch5, cha, ch3, ch3p, ch2, h2, h, ar, arp, arhp, c2h4};\)\)], "Input"], Cell["\<\ Masses of ions and fast neutrals and electron charge in MKS units\ \>", "Text"], Cell[BoxData[{ \(ma\ = \ 1.6605*10^\(-27\); qe = 1.602*10^\(-19\);\), "\[IndentingNewLine]", \(m1 = 13. *ma; m2 = 14. *ma; m3 = 15. *ma; m4 = 16. *ma; m5 = 17. *ma; m6 = 40*ma; m7 = 41. *ma; m8 = 1. *ma; m9 = 13. *ma; m0 = 29. *ma; mF = 15. *ma; mH = 1. *ma;\)}], "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["\<\ The electron-CH4 and electron-Ar data given in this section are spatial \ reaction coefficients, i.e., they are Townsend-type coefficients, in units of \ m^-1. They are obtained from experiment or from solution of the Boltzmann \ equation using appropriate cross sections. For the plots we have chosen the \ density n equal to 1E-20 m^-3 so that the resultant magnitudes are equal to \ the reaction coefficients in 1E-20 m^2.\ \>", "Subsubtitle"], Cell["\<\ e + CH4 -> ionization Here we use the formula given by Davies et al (1989) for E/n > 500 Td. We \ have not included the mixture fraction f here because this relation also \ applies approximately to the total ionization 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*\ faecp432*\((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*faecp656*5.5*10^\(-22\)* Exp[\(-1900. \)/eontd]/\((1 + \((eontd/8200. )\)^5)\);\)\)], "Input",\ FontColor->RGBColor[1, 0, 1]], Cell["\<\ e + Ar -> 430 nm lines. We have no information on this process and so will \ use 18% of Zoran's CH4(A) excitation. Because of the higher threshold it \ should increase more rapidly with E/n at low E/n.\ \>", "Text"], Cell[BoxData[ \(\(aeap430\ := \ \((1 - f)\)*n*\ faeap430*\((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["\<\ 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[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{aecie, aecp432, aecp656}, {eontd, 10. , 10000. }, GridLines\ -> \ Automatic, \ PlotRange\ -> \ \ {{10. , 10000. }, {10^\(-4\), 10. }}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["\<\ In the following cross sections we give 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. Updated 3/7/01\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["CH+ - CH4 data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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. \ There is disagreement between Smith and Adams (1977) and Adams and Smith \ (1977) as to whether the sum of the C2H2+ and C2H4+ is 15% or 50%. We will \ lump these products in with the C2H5+. The question then is how rapidly does \ the rate coefficient drop at high energies. Abrahamson et al (1966) show \ C2H3+, C2H2+, and C2H4+ at 4.2 eV (LAB?) as a trace compared to C2H3+ (82), \ C2H2+ (13), and C2H4+ (5) at 0.3 eV (LAB?). From Huntress, Laudenslager et al \ (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). If we raise this energy we might fit de Urquijo et al \ (1998) better. We have not found any useful high energy data.\ \>", "SmallText"], Cell["\<\ It seems unlikely that CH+ + CH4 behaves like H3+ + H2 (or CH5+ + CH4), i.e., \ it is not a resonant system. The question is then, does it behave like H+ or \ H2+ + H2.\ \>", "Text"], Cell["\<\ CH+ + CH4\[Rule]CH+ + CH4 momentum loss in elastic collisions.\ \>", "Subsubsection"], Cell["\<\ Here we have subtracted the cross section for C2H5+ formation at low \ energies. We have not subtracted other cross sections at higher energies, \ because we assume that polarization effects become small at high energies and \ becuse the other cross sections are \"small\" at intermediate energies.\ \>", "SmallText"], Cell["\<\ a1cn:=n*f*fa1cn*3.62*10^-19./w1[z]^.5*(1-1/(1+(w1[z]/4.5)^4));\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell[" Note that w1[z], etc. are lab energies.", "Subsubtitle"], Cell["CH+ + CH4\[Rule]C2H3+ + H2", "Subsubsection"], Cell["\<\ 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. \ There is disagreement between Smith and Adams (1977) and Adams and Smith \ (1977) as to whether the sum of the C2H2+ and C2H4+ is 15% or 50%. We will \ lump these products in with the C2H5+. The question then is how rapidly does \ the rate coefficient drop at high energies. Abrahamson et al (1966) show \ C2H3+, C2H2+, and C2H4+ at 4.2 eV (LAB?) as a trace compared to C2H3+ (82), \ C2H2+ (13), and C2H4+ (5) at 0.3 eV (LAB?). From Huntress, Laudenslager et al \ (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). If we have raised this energy we might fit de Urquijo \ et al (1998) better.\ \>", "SmallText"], Cell["\<\ a1c0o:=fa1c0o*n*f*3.62*10^-19./w1[z]^.5/(1+(w1[z]/4.5)^4); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH+ + CH4\[Rule]CH3+ + CH2", "Subsubsection"], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ chp\ + \ ch4\ - \((ch3p\ + \ ch2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ According to Smith and Adams (1977) the probability of this process is \ negligible at thermal energies. We find CH+ + CH4 -> CH3+ + CH2 is exothermic \ by about 0.65 eV (1.18 eV in Lab). This reaction requires an H2 transfer or \ charge transfer plus an H atom transfer. Because we ahve no information, we \ make this process small at all energies.\ \>", "SmallText"], Cell["\<\ a1c3o:=fa1c3o*n*f*1.*10^-25*3.62*10^-19./w1[z]^.5/(1+(1/(w1[z]-1.2))^2)+1.*10^\ -30 \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["CH+ + CH4 -> fCH + CH4+ ", "Subsubsection"], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ \ chp\ + \ ch4\ - \((ch\ + \ ch4p)\)}, equations], \ variables]\)], "Input"], Cell["\<\ According to Smith and Adams (1977) the probability of charge transfer is \ negligible at thermal energies. It has a threshold of 1.97 in CM and 3.57 eV \ LAB. The assumption of the following relation makes the charge transfer \ process very important. The assumption is loosely based on the discussion of \ Janev et al (2000) for H+ + CH4, who say CH4+ has enough degrees of freedom \ so that charge transfer is a resonance process. A problem with this argument \ is that it does not work for CH4+ + CH4, where proton transfer type \ collisions can give the product ion sufficient energy to dissociate and where \ collision induced dissociation can be doninant.\ \>", "SmallText"], Cell[BoxData[ \(\(a1c49B := n*f*fa1c49* UnitStep[ w1[z] - 3.57]*3.62*\(10^\(-19. \)/ w1[z]^ .5\)/\((1 + \((1. /\((w1[z] - 3.57)\))\)^2)\) + 1. *10^\(-30\);\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ According to Rapp and Francis, J. Chem. Phys. 37, 2631 (1962), the \ nonresonant charge transfer cross section varies as enrel^2 at low energies \ and as (a + b*ln(v))^2, i.e., as the resonant charge transfer cross section, \ for high energies. The following function is an approximation to this model. \ However, it is much too sharply peaked in energy to give a good fit to \ experiment. Probably one could get a reasonable fit to experiment if there \ were other similar functions with a spread in the energies at which they \ peaked.\ \>", "Text"], Cell[BoxData[ \(\(a1c49A := n*f*fa1c49*15. *10^\(-20\)*\ \(\(UnitStep[enrel - 3.57]/ enrel^0.2\)/\((1 + \((600. /\((enrel - 3.57)\))\)^2)\)\)/\((1 + \((enrel/ 4000)\)^2)\)^2 + 1. *10^\(-30\)\ /. \ enrel\ -> \ 16/\((16 + 13)\)*w1[z];\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["We will use a mixture of these formulas.", "Text"], Cell[BoxData[ \(a1c49 := 1.0*a1c49A\ + \ 0.1*a1c49B\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH+ +CH4 -> CH(A) +CH4+ -> CH + CH4+ + 432 nm ", "Subsubsection"], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ \ chp\ + \ ch4\ - \((cha\ + \ ch4p)\)}, equations], \ variables]\)], "Input"], Cell["\<\ 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 charge transfer-excitation process is 12.61 (CH4)- 10.64 \ (CH) + 2.87 (CH(A->X) = 4.84 eV (CM) or 8.77 eV (Lab). By anology with the \ corresponding process for CH+ + Ar, as measured by Ehbrecht et al (1996), \ this cross section is small and we assume it to be the same as for CH+ + Ar. \ One would have to be concerned about CH+(A->X) emission at 422 nm.\ \>", "SmallText"], Cell["\<\ a1c4p := n*f*fa1c4p*UnitStep[enrel-8.77]*5.0*10^-21*(enrel-8.77)/1000./(1+\ enrel/10000)+1.*10^-30 /. enrel -> 16/(13.+16.)*w1[z];\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH+ +CH4 -> CH5+ + C", "Subsubsection"], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ chp\ + \ ch4\ - \((c\ + \ ch5p)\)}, equations], \ variables]\)], "Input"], Cell["\<\ This could occur by proton transfer giving rise to internally excited CH5+. \ 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", "Subsubsection"], Cell["\<\ According to Smith and Adams (1977) the probability of this breakup is \ negligible at thermal energies. Judging from Peko et al (1997) it colud be \ significant at energies above threshold.\ \>", "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[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{\((a1cn\ /. \ w1[z]\ -> \ w1z)\), \((a1c0o\ \ /. \ w1[z]\ -> \ w1z)\), \((a1c49\ /. \ w1[z]\ -> \ w1z)\), \((a1c49A\ /. \ w1[z]\ -> \ w1z)\), \((a1c4p\ \ /. \ w1[z]\ -> \ w1z)\), \((a1c3o\ \ /. \ w1[z]\ -> \ w1z)\)}, {w1z, 0.1, 10000}, \ PlotRange\ -> \ \ {{0.1, 10000}, {10^\(-3\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 2000, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["\<\ CH+ + CH4. The principle known reaction is that leading to C2H3+ and that drops out at \ above about 4 eV (LAB). Because it seems likely that there are important \ processes other than elastic scattering for energies above 4 eV, we have \ envoked charge transfer. Other possibilities include dissociation. Note that \ normalized cross section values less than roughly 0.001 will not influence \ the ion fluxes to be compared with de Urquijo. Updated 9/3/01\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell["CH2+ + CH4 data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We originally did not consider CH2+ kinetics, but according to de Urquijo it \ is the second most important ion at high E/n.\ \>", "Subsubtitle"], Cell["CH2+ + CH4 -> CH2+ +CH4 momentum loss.", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Here we subtract the reaction cross section from Langevin at low energies and \ neglect the effects of other processes on elastic scattering at high \ energies. The mass factors needed for the energy balance are applied through \ the previous fudge factors. It is not clear whether the theorems relating \ the maximum elastic and inelastic cross sections apply here. We subtract the \ ion conversion from the Langevin values.\ \>", "SmallText"], Cell["a2cn:=n*f*fa2cn*3.68*10^-19/w2[z]^.5*(1-1/(1+(w2[z]/4)^4));", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["CH2+ + CH4 -> C2H4+ + H2", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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 in the \ next process.\ \>", "SmallText"], Cell["CH2+ + CH4 -> C2H5+ + H", "Subsubsection"], 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 the previous process together in the following, which is \ equal to Langevin at low energies.\ \>", "SmallText"], Cell["\<\ a2c0o:=fa2c0o*n*f*3.68*10^-19./w2[z]^.5/(1+(w2[z]/4)^4); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH2+ + CH4 -> CH4+ + CH2", "Subsubsection"], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ \ ch2p\ + \ ch4\ - \((ch4p\ + \ ch2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ According to Smith and Adams (1977) the probability of charge transfer is \ small at room temperature. It has a threshold of 2.12 in CM and 3.98 eV LAB. \ The assumption of the following relation can make the charge transfer \ process very important. The assumption is loosely based on the discussion of \ Janev et al (2000) for H+ + CH4, who say CH4+ has enough degrees of freedom \ so that charge transfer is a resonance process. A problem with this argument \ is that it does not work for CH4+ + CH4, where proton transfer type \ collisions can give the product ion sufficient energy to dissociate and where \ collision induced dissociation can be doninant.\ \>", "SmallText"], Cell[BoxData[ \(fa2c4o\)], "Input"], Cell[BoxData[ \(\(a2c4oB := n*f*fa2c4o* UnitStep[ w2[z] - 3.98]*3.62*\(10^\(-19. \)/ w2[z]^ .5\)/\((1 + \((1. /\((w2[z] - 3.98)\))\)^2)\) + 1. *10^\(-30\);\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ According to Rapp and Francis, J. Chem. Phys. 37, 2631 (1962), the \ nonresonant charge transfer cross section varies as enrel^2 at low energies \ and as (a + b*ln(v))^2, i.e., as the resonant charge transfer cross section, \ for high energies. The following function is an approximation to this model. \ However, it is much too sharply peaked in energy to give a good fit to \ experiment. Probably one could get a reasonable fit to experiment if there \ were other similar functions with a spread in the energies at which they \ peaked.\ \>", "Text"], Cell[BoxData[ \(\(a2c4oA := n*f*fa2c4o*15. *10^\(-20\)*\ \(\(UnitStep[enrel - 3.98]/ enrel^0.2\)/\((1 + \((600. /\((enrel - 3.98)\))\)^2)\)\)/\((1 + \((enrel/ 4000)\)^2)\)^2 + 1. *10^\(-30\)\ /. \ enrel\ -> \ 16/\((16 + 14)\)*w2[z];\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["We will use a mixture of these formulas.", "Text"], Cell[BoxData[ \(a2c4o := 1.0*a2c4oA\ + \ 0.1*a2c4oB\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["The following are assumed zero.", "Text"], Cell[BoxData[ \(\(a2c1o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(a2c4p\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(a2c94\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ Plot these cross section in units of 10^-20 m^2 by choosing f 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[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{a2cn\ /. \ w2[z]\ -> \ w2z, a2c0o\ \ /. \ w2[z]\ -> \ w2z, a2c4o\ \ /. {\ w2[z]\ -> \ w2z, \ fa2c4o\ -> \ 1}}, {w2z, 1, 10000}, \ PlotRange\ -> \ \ {{1, 10000}, {10^\(-3\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["\<\ Here we only guess at reactions of CH2+ for energies above a few eV.\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["CH3+ + CH4 data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Several authors state that C2H5+ formation is the dominant reaction at low \ energies and that the rates falls to about 50% at roughly 1 eV. For example, \ Abrhamson and Futrell, J. Chem. Phys. 45, 1925 (1966) say that the dominant \ product switches to C2H3+ at 4.2 eV reactant ion energy, but do not give data \ for higher energies. Anders (1969) finds the C2H3+ rate coefficient relative \ to the C2H5+ thermal value to peak at ~4.5 eV at 10% of the thermal value and \ to decrease rapidly at 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. Thay also find a small peak in the C2H3+ formation \ at about 5 eV. 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% relative 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.\ \>", "Text"], Cell["\<\ Thus far, the only paper I have found reporting CH3+ + CH4 collisions at \ moderate energies is Ardelean et al, Revue Roumaine de Physique 21, 141 \ (1976). These authors give relative cross sections for the production of CH+, \ CH2+, CH3+, and CH4+ for LAB energies from 8 to 160 eV. The simplest \ interpretation of their experiment is that these are ions formed with low \ kinetic energies by charge transfer that may dissociate. The problem with \ this model is that their data, Ardelean et al (1975), for CH4+ + CH4 does not \ agree at all well with that of Peko et al (1998). One way to begin to \ expalin the difference is to postulate tha Ardelean et al saw ion signal \ resulting from large angle elastic scattering. This would suggest that one \ make the CH4+, CH2+, and CH+ cross section smaller than the leastic cross \ section by factors of 5 to 10. This is roughly what we have done for CH+ and \ CH4+.\ \>", "Text"], Cell["\<\ We note that the various experiments do not report that significant reaction \ products are produced at the energies where the rate coefficient for the \ production of C2H5+ and C2H3+ becomes small. This means that elastic \ scattering at the Langevin rate dominates at least untill the thresholds for \ charge transfer (2.77 eV CM)\ \>", "Text"], Cell["CH3+ + CH4 -> CH3+ + CH4 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Momentum loss in elastic collisions This loss function is set up for 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. The mass factors \ needed for the energy balance are applied through the previous fudge factors.\ \ \>", "SmallText"], Cell["\<\ a3cn:=n*f*fa3cn*3.74*10^-19./w3[z]^.5*(1-1/(1+(w3[z]/1.)^3));\ \>", "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 at low energies. This points to the necessity for \ adding the reaction terms to the energy or momentum balance equations.\ \>", "Subsubtitle"], Cell["CH3+ + CH4 -> C2H5+ + H2", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We assume a Langevin cross section at low energies. Several authors state \ that C2H5+ formation is the dominant reaction at low energies and that the \ rates falls to about 50% at roughly 1 eV. \ \>", "SmallText"], Cell["a3c0o:=n*f*fa3c0o*3.74*10^-19./w3[z]^.5/(1+(w3[z]/1.)^3);", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], 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+ charge transfer", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch3p\ + \ ch4\ - \((ch3\ + \ ch4p)\)}, equations], \ variables]\)], "Input"], Cell["\<\ Using IP(CH4) = 12.615 and IP(CH3) = 9.84, the threshold energy is 31/16*2.77 \ = 5.37. 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 5.37 eV threshold and we make the process negligible.\ \>", "SmallText"], Cell["\<\ a3c4F := n*f*fa3c4F*(UnitStep[w3[z]-5.37]*3.74*10^-19./w3[z]^.5*(1-(5.37/w3[z]\ )^2)+1.*10^-30);\ \>", "Input", PageWidth->Infinity, Evaluatable->False, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ According to Smith and Adams (1977) the probability of charge transfer is \ negligible at thermal energies. It has a threshold of 1.97 in CM and 3.57 eV \ LAB. The assumption of the following relation makes the charge transfer \ process very important. The assumption is loosely based on the discussion of \ Janev et al (2000) for H+ + CH4, who say CH4+ has enough degrees of freedom \ so that charge transfer is a resonance process. A problem with this argument \ is that it does not work for CH4+ + CH4, where proton transfer type \ collisions can give the product ion sufficient energy to dissociate and where \ collision induced dissociation can be doninant. Note that if this low energy \ process occurs via complex formation, then the products will be emitted \ isotropically and there is no bias toward fast CH3.\ \>", "SmallText"], Cell[BoxData[ \(\(a3c4FB := n*f*fa3c4F* UnitStep[ w3[z] - 5.37]*3.62*\(10^\(-19. \)/ w3[z]^ .5\)/\((1 + \((1. /\((w3[z] - 5.37)\))\)^2)\) + 1. *10^\(-30\);\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ According to Rapp and Francis, J. Chem. Phys. 37, 2631 (1962), the \ nonresonant charge transfer cross section varies as enrel^2 at low energies \ and as (a + b*ln(v))^2, i.e., as the resonant charge transfer cross section, \ for high energies. The following function is an approximation to this model. \ However, it is much too sharply peaked in energy to give a good fit to \ experiment. Probably one could get a reasonable fit to experiment if there \ were other similar functions with a spread in the energies at which they \ peaked.\ \>", "Text"], Cell[BoxData[ \(\(a3c4FA := n*f*fa3c4F*15. *10^\(-20\)*\ \(\(UnitStep[enrel - 5.37]/ enrel^0.2\)/\((1 + \((600. /\((enrel - 5.37)\))\)^2)\)\)/\((1 + \((enrel/ 4000)\)^2)\)^2 + 1. *10^\(-30\)\ /. \ enrel\ -> \ 16/\((16 + 15)\)*w3[z];\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["We will use a mixture of these formulas.", "Text"], Cell[BoxData[ \(a3c4F := 1.0*a3c4FA\ + \ 0.1*a3c4FB\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + CH4 -> fast CH + CH4+ +H2", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch3p\ + \ ch4\ - \((ch\ + \ ch4p + h2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ A crucial question here is whether the reaction also produces a fast CH + H2. \ According to various authors the probability of the CH+ production through \ this breakup process is negligible at energies below several eV, as it should \ be considering the threshold energy required of 7.34*31/15 = 15.17. The \ following arbitrary cross section is used.\ \>", "SmallText"], Cell["\<\ a3c94 := n*f*fa3c94*UnitStep[w3[z]-15.17]*0.1*3.74*10^-19./w3[z]^.5*(1-(15.17/\ w3[z])^2)+1.*10^-30;\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + CH4 -> CH+ + CH4 +H2 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch3p\ + \ ch4\ - \((chp\ + \ ch4 + h2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ According to various authors the probability of the CH+ production through \ this breakup process is negligible at energies below several eV, as it should \ be considering the threshold energy required of the probability of breakup \ is negligible at thermal energies. This process has a threshold of 5.37 in \ CM and 10.40 in LAB. We set this cross section equal to .\ \>", "SmallText"], Cell["\<\ a3c1o := fa3c1o*UnitStep[w3[z]-10.40]*a3c4F/(1.+(1/(w3[z]-10.40))^2)+1.*10^-\ 30;\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + CH4 -> CH2+ + CH3 +H2 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch3p\ + \ ch4\ - \((ch2p\ + \ ch3 + h2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ This and the next process have the same threshold, so I do not know how th \ chose between them.\ \>", "Text"], Cell["CH3+ + CH4 -> CH2+ + CH4 +H ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch3p\ + \ ch4\ - \((ch2p\ + \ ch4 + h)\)}, equations], \ variables]\)], "Input"], Cell["\<\ This and the last process have the same threshold of 5.37*(15+16)/16 = 10.40, \ so I do not know how to chose between them.\ \>", "Text"], Cell[BoxData[ \(a3c2H := n*f*fa3c2H* UnitStep[ w3[z] - 10.40]*\((0.1*3.74*\(10^\(-19\)/ w3[z]^ .5\)/\((1 + \((3. /\((w3[z] - 10.40)\))\)^2/\((1. + \((w3[z]/ 100. )\))\))\) + \ \[IndentingNewLine]1.5*\(\(10^\(-19\)/ w3[z]^0.1\)/\((1 + \((2000. /\((w3[z] - 10.40)\))\)^4)\)^0.5\)/\((1 + \((w3[z]/ 10000)\)^3)\)^1.1)\)\ + \ 1. *10^\(-30\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + CH4 -> CH(A) +?CH4+ +H2 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch3p\ + \ ch4\ - \((cha\ + \ ch4p + h2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ According to various authors the probability of the CH4+ production through \ this charge transfer-breakup process is negligible at energies below several \ eV, as it should be considering the threshold energy of 10.21 in CM and 19.78 \ in LAB. We assume that this cross section is a fraction ,i.e., 0.01, of the \ charge transfer cross section, although such a value raises questions about \ the whole charge transfer process.\ \>", "SmallText"], Cell["\<\ a3c4p := 0.01*fa3c4p*UnitStep[w3[z]-19.78]*a3c4F/(1.+(1/(w3[z]-19.78))^2)+1.*\ 10^-30;\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + CH4 -> H+ + 2 CH3 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ According to various authors the probability of the CH+ production through \ this breakup process is negligible at energies below several eV. We neglect \ it at all energies.\ \>", "SmallText"], Cell[BoxData[ \(\(a3c8o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH3+ + CH4 -> CH5+ + CH2 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{\((a3cn\ /. \ w3[z]\ -> \ w3z)\), \((a3c0o\ /. \ w3[z]\ -> \ w3z)\), \((a3c4F\ \ /. \ w3[z]\ -> \ w3z)\), \((a3c1o\ \ /. {\ w3[z]\ -> \ w3z, \ fa3c1o\ -> 0.8})\), \((a3c4p\ /. \ {w3[z]\ -> \ w3z, \ fa3c4p\ -> 0.9})\), \((a3c94\ \ /. \ w3[z]\ -> \ w3z)\), \ \((a3c2H\ /. {w3[z] -> w3z, fa3c2H\ -> 0.6})\)}, {w3z, 0.1, 10000}, \ PlotRange\ -> \ \ {{0.1, 10000}, {10^\(-2\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 2000, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["\<\ CH3+ + CH4. This plot shows that for 100 mTorr of CH4 and at energies below ~3 eV, CH3+ \ is converted into C2H5+ even when one omits the increase in the number of \ inelastic collisions caused by multiple elastic collisions. At energies above \ about 5 eV LAB there could be charge transfer, but CH+ formation does not \ begin until about 10 eV LAB. The reaction cross sections in the critical 5 to \ 100 eV region are pure guesses. Judging from Peko et al (1978) for CH4+ + \ CH4, they are probably too low. Updated 9/12/01\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["CH4+ + CH4 data ", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ The Peko et al experiments cover the energy range from ~ 1 to 200 eV. We \ have no data for higher energies. 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", "Subsubsection"], Cell["\<\ Here we use the Langvin rate coefficient to calculate momentum loss in \ elastic collisions This loss function is set up for 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. The mass factors needed for \ the energy balance are applied through the previous fudge factors.\ \>", "SmallText"], Cell["\<\ a4cn :=(n*f*fa4cn*2.69*10^-19/Abs[releng]^.5 -a4c5o) /. releng ->w4[z]/2; \ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH4+ + CH4 -> CH4 + sCH4+ ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Peko et al (1998) give the symmetric charge exchange cross section for releng \ < 200 eV. Their results are somewhat larger than the limit set by Smith and \ Kevan (1971), who 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 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["From Peko et al (1998) this reaction was not observed", "SmallText"], Cell[BoxData[ \(\(a4c1o = 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["CH4+ + CH4 -> sCH5+ +CH3 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch4p\ + \ ch4\ - \((ch5p\ + \ ch3)\)}, equations], \ variables]\)], "Input"], Cell["\<\ 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 using a low energy Langevin cross section that falls off \ near 0.5 eV to Peko et al (1998) at higher energies.\ \>", "SmallText"], Cell[BoxData[ \(\(a4c5o := n*f*fa4c5o/ Sqrt[releng] \((5.5*10^\(-20\)/\((1 + \((releng/ 10.5)\)^4)\)\ + \((2.69 - 0.55)\)*10^\(-19\)/\((1 + \((releng/0.5)\)^4)\))\)\ /. releng \[Rule] w4[z]/2;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["CH4+ + CH4 -> fH+ + fCH3 + CH4 ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch4p\ + \ ch4\ - \((hp\ + \ ch3 + ch4)\)}, equations], \ variables]\)], "Input"], Cell["\<\ 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 - 5.47]*\((1 - 5.47/releng)\)^0.7*1.3* releng^0.6/\[IndentingNewLine]\((1 + \((releng/25)\)^1.1)\) + 1. *10^\(-30\)\ /. releng \[Rule] w4[z]/2\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["CH4+ + CH4 -> sCH3+ +CH3 +H2 ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ This process does not appear to be discussed, so we will neglect it.\ \>", "Text"], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch4p\ + \ ch4\ - \((ch3p\ + \ ch3 + h2)\)}, equations], \ variables]\)], "Input"], Cell["or a process with the same threshold", "Text"], Cell["CH4+ + CH4 -> sCH3+ + fCH4 + sH ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch4p\ + \ ch4\ - \((ch3p\ + \ ch4 + h)\)}, equations], \ variables]\)], "Input"], Cell["\<\ Because the equality of the last two reaction energies was unexpected, we do \ a check.\ \>", "Text"], Cell[BoxData[ \(Eliminate[Join[{d\ == \ ch3\ + \ h2\ - \((ch4 + h)\)}, equations], \ variables]\)], "Input"], Cell["\<\ This is charge transfer to form a slow, unstable CH4+ that dissociates. 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 1.71 in CM or (14+14)/14*1.71 = 3.42 \ LAB. This is consistent with Peko et al (1998), but is difficult to \ reconcile with Huntress (1972). It appears that this cross section is a \ factor of >25 below that predicted by Bates et al (1964) at energies above \ 500 eV. Note that the relative cross sections for CH4+ and CH3+ of Ardelean \ et al (1975) do not agree well with those of Peko et al (1998).\ \>", "SmallText"], Cell[BoxData[ \(\(a4c3o := n*f*fa4c3o*10^\(-20\)* UnitStep[ engCOM - 1.71]/\((1 + \((0.3/\((engCOM - 1.71)\))\)^2)\)*\ \((0.03* engCOM^2/\((1 + \((engCOM/8)\)^3.5)\) + 3. *\((engCOM/50)\)^2.5/\((1 + \((engCOM/60)\)^2.8)\))\) + 1. *10^\(-30\)\ \ \ /. \ engCOM\ -> w4[z]/2;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["CH4+ +CH4 -> CH2+ +CH4 +H2", "Subsubsection"], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch4p\ + \ ch4\ - \((ch2p\ + \ ch4 + h2)\)}, equations], \ variables]\)], "Input"], 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 2*2.6 = 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[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{a4cn\ /. \ w4[z]\ -> \ w4z, a4c4o\ \ /. \ w4[z]\ -> \ w4z, a4c5o\ \ /. \ w4[z]\ -> \ w4z, a4c8o\ /. \ w4[z]\ -> \ w4z, \ a4c3o\ /. \ w4[z]\ -> \ w4z}, {w4z, 0.1, 10000}, \ PlotRange\ -> \ \ {{0.1, 10000}, {5. *10^\(-2\), 500}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 2000, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["\<\ This plot shows that for 100 mTorr of CH4, CH4+ + CH4 very rapidly forms CH5+ \ at low energies and forms H+, CH3+ and CH4+ as the energy increases. At high \ energies we have not subtracted the reaction cross sections from Langevin to \ get the elastic cross section because there are too many unknowns to make it \ worthwhile. The small cross section for CH3+ formation at high energies (~10 \ keV) compared to Bates et al (1964) worries me. Updated 9/18/01\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["CH5+ + CH4 data ", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False, Background->None], 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 decreases to Langevin at \ energies of ~4 times thermal. This situation is very reminiscent of H3+ in \ H2 and strongly suggests rapid proton transfer at low energies, a transition \ between elastic and rotational excitation and vibrational excitation at ~ 0.1 \ eV. If the behavior folllows H3+ there will be significant dissociation at \ higer energies.\ \>", "SmallText"], Cell["\<\ CH5+ + CH4 -> CH5+ + CH4 - elastic and rotational excitation\ \>", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Low energy momentum transfer cross section. Based on the mobility data, we \ take the cross section to be 1.23 times the Langevin value. Note that \ because of the momentum transfer weighting this cross section is twice the \ elastic and rotational excitation value. The energy of the fall-off is \ adjusted so the the sum of a4cn and a5cnv has a small minimum. Note that \ because of the assumption of large proton transfer effects, the scattering is \ probably 180 deg in CM.\ \>", "SmallText"], Cell["\<\ a5cn :=n*f*fa5cn*1.23*3.86*10^-19/w5[z]^.5/(1+(w5[z]/0.9)^4); \ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH5+ + CH4 -> CH5+ + CH4 - vibrational excitation", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ intermediate energy momentum transfer cross section. Based on the mobility \ data, we take the cross section to be 1.23 times the Langevin value. The \ energy of the fall-off is arbitrary at this point in time. Note that because \ of the assumption of large proton transfer effects, the scattering is assumed \ to be 180 deg in CM. Therefore, this momentum transfer cross section is twice \ the vibrational excitation value. I have not been able to find data for the \ threshold for vibrational excitation of CH5+ from NIST. The lowest \ vibrational mode of CH4 is at 1306 cm^-1 or 0.162 eV. In Lab this is 0.334 \ eV\ \>", "SmallText"], Cell[BoxData[ \(\(a5cnv\ := \ n*f*fa5cnv*1.23*2.69*10^\(-19\)* UnitStep[ enrel - 0.162]*\(enrel^\(-0.5\)/\((1 + \((0.6/\((enrel - 0.162)\))\)^2)\)\)/\((1 + \((enrel/ 6.2)\)^3.95)\) + 1. *10^\(-30\)\ \ /. \ enrel\ -> \ \ 16/\((16 + 17)\)*w5[z];\)\)], "Input"], Cell["CH5+ + CH4 -> CH3+ + CH4 + H2 ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["From Fig. 1 of Peko et al (1998) the energetics are: ", "SmallText"], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch5p\ + \ ch4\ - \((ch3p\ + \ ch4 + h2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ According to Field and Munson, J. Am. Chem. Soc. 87, 3289 (1965), the \ reaction rate coefficient for CH5+ with CH4 is less than ~ 1E-12 cm^3/s in a \ mass spectrometer ion source at pressures up to 1.7 Torr, but unspecified \ energies. This is consistent with a large proton transfer cross section at \ energies below the dissociation threshold of 1.84 eV in CM. 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 has a column density of only 3.8*3.3e15 = \ 1.25e16 cm^2 or 1.25e20 m^2, the steady-state drift data might not apply. \ The best we can do is assume a threshold of 1.84 eV and take this \ dissociation cross section from that for slow H+ formation in H3+ + H2 proton \ transfer. The threshold in the LAB frame is 33/16*1.84 = 3.80 eV. \ \>", "SmallText"], Cell[BoxData[ \(a5c3o\ := \ n*f*fa5c3o* UnitStep[ w5[z] - 3.80]*3.86*10^\(-19\)*\(\((1 - 3.80/w5[z])\)^\((2)\)/ w5[z]^0.5\)/\((1 + w5[z]/500)\)\ + 1. *10^\(-30\)\)], "Input", Evaluatable->False], Cell["We use the result from H3+ + H2 -> sH+ + sH2 + fH2", "Text", FontFamily->"Arial", FontSize->12], Cell[BoxData[ \(a5c3o\ := \ \ n*f*fa5c3o*1.3*10^\(-20\)* UnitStep[ enrel - 1.84]*\(enrel^0.6/\ \[IndentingNewLine]\((1 + \ \((2/\((enrel - 1.84)\)^1.1)\))\)\)/\ \((1 + \((enrel/ 8. )\)^4.05)\)^1.0*\((1 + \((enrel/ 21. )\)^4)\)^0.9*\((1 + \((enrel/ 120)\)^3.5)\)^0.4/\((1 + \((enrel/350)\)^1.9)\)^2 + 1. *10^\(-30\)\ \ /. \ enrel\ -> \ \ 16/\((16 + 17)\)*w5[z]\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ Here we neglect dissociation of the C2H9+ complex (CH4-CH5+) into things like \ C2H6+.\ \>", "SmallText"], Cell["\<\ CH5+ + CH4 -> CH+ + CH4 + 2 H2 \ \>", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch5p\ + \ ch4\ - \((chp\ + \ ch4 + 2*h2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ We have not found any data for this process. The threshold is \ (17+16)/16*7.07 = 14.58 eV. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a5c1o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ CH5+ + CH4 -> sCH4+ + fCH4 + fH \ \>", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch5p\ + \ ch4\ - \((ch4p\ + \ ch4\ + h)\)}, equations], \ variables]\)], "Input"], Cell["\<\ We have not found any data for this charge transfer process, which has a LAB \ threshold at (17+16)/16*4.47 = 9.22 eV. We take the cross section in COM to \ be the same as for H3+ + H2 -> sH2+ + fH2 + fH.\ \>", "SmallText"], Cell[BoxData[ \(\(a5c4o\ = \ n*f*fa5c4o* UnitStep[ releng - 4.47]*10^\(-20\)/\((1 + \((1/\((releng - 4.47)\))\))\)*\((1.3 + \((releng/ 10)\)^1.5)\)/\((1 + \((releng/40. )\)^3. )\)\ + 1. *10^\(-30\)\ /. releng \[Rule] 16/33*w5[z];\)\)], "Input", Evaluatable->False], Cell["We use the result from H3+ + H2 -> sH2+ + fH2 + fH.", "Text"], Cell[BoxData[ \(\(a5c4o\ := \ n*f*fa5c4o*0.025*10^\(-20\)*\ UnitStep[ enrel - 4.47]*\(enrel^0.53/\((1 + \((50/\((enrel - 4.47)\)^1.1)\))\)\)/\((1 + \((enrel/ 15000)\)^2)\)^0.9 + 1. *10^\(-30\)\ /. \ enrel\ -> \ \ 16/\((16 + 17)\)*w5[z];\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH5+ + CH4 -> fH+ + fCH4 + sCH4", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch5p\ + \ ch4\ - \((hp\ + \ 2*ch4)\)}, equations], \ variables]\)], "Input"], Cell["\<\ We have not found any data for this process. We take the cross section in COM \ to be the same as for H3+ + H2 -> sH2 + fH2 + fH+.\ \>", "SmallText"], Cell[BoxData[ \(\(a5c8o\ = \ \ n*f*fa5c8o* UnitStep[ enrel - 5.6]*11. *\(\(10^\(-20\)/ Sqrt[enrel]\)/\((1 + \((12/\((enrel - 5.6)\))\)^2)\)\)/\((1 + \((enrel/ 300)\)^3)\)*\((1 + \((enrel/ 550)\)^4.5)\)/\((1 + \((enrel/20000)\)^2.5)\) + 1. *10^\(-30\)\ /. \ enrel\ -> \ \ 16/\((16 + 17)\)*w5[z];\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ Perhaps we should add the cross section for H+ + 2H production that we found \ necessary in the H3+ + H2 analysis. We would have to derive the threshold \ energy.\ \>", "Text"], Cell[BoxData[ \(\(fast2HFit\ = 0.017*10^\(-20\)*\ UnitStep[ enrel - 8.8] \(enrel^0.53/\((1 + \((50/\((enrel - 8.8)\)^1.1)\))\)\)/\((1 + \((enrel/ 24000)\)^2)\)^0.9 + 1. *10^\(-30\)\ /. \ enrel\ -> \ \ 16/\((16 + 17)\)*w5[z];\)\)], "Input"], Cell["CH5+ + CH4 -> C2H5+ + 2 H2 ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["We have not found any data for this process. We neglect it.", \ "SmallText"], Cell[BoxData[ \(\(a5c0o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH5+ + CH4 -> H2+ + CH3 + CH4", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We have not found any data for the production of H2+. Because we do not want \ to write equartions for the flux and energy of the H2+ we neglect it. \ Fortunately, we expect H2+ to react very rapidly with CH4 at all energies to \ form CH5+. If we needed such cross sections we could try fastH2pFit and \ slowH2Fit from the H3+ notebook.\ \>", "SmallText"], Cell["CH5+ + CH4 -> H(n=3) + CH4 + CH4+", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{d\ == \ ch5p\ + \ ch4\ - \((hp\ + \ ch4\ + \ ch4p)\)}, equations], \ variables]\)], "Input"], Cell["\<\ We have not found any data for this process. We neglect it for now. If we \ need it we can use the following fornula used for H3+ + H2. I would need to \ check threshold.\ \>", "SmallText"], Cell[BoxData[ \(\(halphaFit\ = 0.0027*\ UnitStep[ enrel - 18.3]*\(enrel^0.47/\((1 + \((5/\((enrel - 18.3)\)^1)\))\)\)/\((1 + \((enrel/ 70000)\)^2. )\) + 1. *10^\(-30\)\ /. \ enrel\ -> \ \ 16/\((16 + 17)\)*w5[z];\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ 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.\ \>", "Text"] }, Open ]], Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{a5cn\ /. \ w5[z]\ -> \ w5z, a5cnv\ /. \ w5[z]\ -> \ w5z, a5c3o\ \ /. \ w5[z]\ -> \ w5z, \ a5c4o\ \ /. \ w5[z]\ -> \ w5z, a5c8o\ \ /. \ w5[z]\ -> \ w5z}, {w5z, 0.01, 1000}, \ PlotRange\ -> \ \ {{0.01, 1000}, {10^\(-2\), 1000}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["\<\ We have tried to construct a set of cross sections similar to those for H3+ + \ H2, i.e., assuming dominant elastic scattering at energies below about 1 eV, \ vibrational excitation via proton transfer until the onset of dissociation, \ ans a mix to varios processes at higher energies. This plot shows that with \ our original guesses for the cross sections at 100 mTorr and energies above ~ \ 5 eV, CH5+ breaks up to form CH4+ or CH3+. However, we have used the scaling \ factors to make these cross section very small at all energies. 4/3/01\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["C2H5+ + CH4 data ", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False, Background->None], Cell["C2H5++CH4 elastic scattering", "Subsubsection"], Cell["\<\ We use Langevin collision rate coefficient for the momentum loss in elastic \ collisions. 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["a0cn :=n*f*fa0cn*2.39*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", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False, Background->None], 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) is w9[z]:=w1[z]; ", "SmallText"], Cell["fCH + CH4 -> destruction by cooling.", "Subsubsection"], 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 \ guess 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["\<\ a9cn:=n*f*fa9cn*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\[Rule]CH(A)+CH4\[Rule]CH+CH4+432 nm\ \>", "Subsubsection"], Cell["\<\ 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 guess at the \ cross section. Possible models for this process range from H + Ar, which \ peaks at 7E-21 m^2 at ~ 80 eV, to H + H2, which peaks at 2E-21at 900 eV. \ The following is much to large.\ \>", "SmallText"], Cell["\<\ a9cpc :=n*f*fa9cpc*(UnitStep[w9[z]-5.20]*1.0*10^-19/w9[z]^0.5/(1+w9[z]/100.)*(\ 1.-(5.20/w9[z])^2)+1.*10^-30);\ \>", "Input", PageWidth->Infinity, Evaluatable->False, ShowSpecialCharacters->False], Cell["\<\ So we adopt that from our H + H2 Balmer alpha excitation model.\ \>", "Text"], Cell["\<\ a9cpc :=n*f*fa9cpc*UnitStep[w9[z]-5.20]*(1.77*10^-27.*(w9[z]-5.20)^3/ (w9[z]/230.+1)^4+(5.5*10^-26.*w9[z]))+ 1.*10^-30\ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontColor->RGBColor[1, 0, 0]], Cell["\<\ Plot these cross section 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 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[BoxData[ \(\(Block[{n, f\ }, n = 10^20/f; \n LogLogPlot[{a9cn\ /. \ w9[z]\ -> \ w9z, a9cpc\ \ /. \ w9[z]\ -> \ w9z}, {w9z, 1, 1000}, GridLines\ -> \ Automatic, \ \ PlotRange\ -> \ {{1, 1000}, {10^\(-2\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[CellGroupData[{ Cell["fast CH3 + CH4 data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["fast CH3 + CH4 -> CH3 + CH4", "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. We therefore do not need a loss function. However it is useful to \ have a diffusion cross section for comparison. We will again use Langevin.\ \>", "SmallText"], Cell["aFcn:=n*f*faFcn*2*3.74*10^-19./wF[z]^.5/(1+wF[z]/100.);", "Input", PageWidth->Infinity, Evaluatable->False, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["The maximum fast CH3 energy is wF[z]:=w3[z]; ", "SmallText"], Cell["\<\ fCH3 + CH4 -> destruction by cooling. Unfortunately, we do not know \ anything about CH3-CH4 collisions and have to guess 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. The mass factors needed for \ the energy balance are applied through the previous fudge factors.\ \>", "SmallText"], Cell["\<\ aFcn:=n*f*faFcn*0.1*3.74*10^-19./wF[z]^.5/(1+wF[z]/100.)-aFcpc; \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 0]], Cell["\<\ fast CH3 + CH4 -> CH(A) + CH4 + H2 -> CH + CH4 + H2 + 432 nm\ \>", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == ch3\ + \ ch4\ - \((cha\ + \ ch4\ + \ h2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ The threshold COM energy for this process is 7.44 eV and in the laboratory \ 31/16*7.44 = 14.4 eV. Here, again we have to guess at the cross section. The \ following was our cannonical shape for an inelatic process, i.e., the loss \ cross section *(1-(threshold/Labenergy)^2)\ \>", "SmallText"], Cell["\<\ aFcpc :=n*f*faFcpc*(UnitStep[wF[z]-14.4]*0.1*3.74*10^-19./wF[z]^.5*(1-(14.4/\ wF[z])^2)/(1+wF[z]/100.)+ 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. 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. The very large cross section is patterned after H + Ar.\ \>", "SmallText"] }, Open ]], Cell[BoxData[ \(\(Block[{n, f\ }, n = 10^20/f; \n LogLogPlot[{aFcn\ /. \ wF[z]\ -> \ wFz, aFcpc\ \ /. \ wF[z]\ -> \ wFz}, {wFz, 1, 1000}, GridLines\ -> \ Automatic, \ \ PlotRange\ -> \ \ {{1, 1000}, {10^\(-3\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 1000, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["Ar+ + CH4 data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["Ar+ + CH4 -> Ar+ + CH4 elastic scattering", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[CellGroupData[{ Cell["\<\ This Langevin cross section is for comparison purposes only, because it is \ smaller than that we get from a fit and extension of Tosi et al (1995). \ \>", "SmallText"], Cell["\<\ a6cn:=n*f*fa6cn*3.56*10^-19/(w6[z]^.5)/(1+(w6[z]/1000)); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["Ar+ + CH4 -> CH3+ +Ar +H", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ arp\ + \ ch4\ - \((ch3p\ + ar\ + h)\)}, equations], \ variables]\)], "Input"], Cell["\<\ Cross section based on Tosi et al, Int'l. J. Mass Spectrom. and Ion Processes \ 149/150, 345 (1995) for 2E-2 to 10 eV. Note that the formation of CH2+ is \ lower by a factor of roughly 6 and we will neglect it. Tosi et al use COM \ energies so that engCOM = 16/(16+40) w6[z]. We add a fall-off at high \ energies. This reaction is exothermic by 1.44 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 \ between 3E-20 and 12E-20 m^2 at ELAB = 10 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 \ higher 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", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ arp\ + \ ch4\ - \((chp\ + \ ar\ + \ h2\ + \ h)\)}, equations], \ variables]\)], "Input"], Cell["\<\ von Koch (1964) and Szabo (1967) do not find any CH+ from this reaction. It \ is enothermic by 3.93 eV in CM and 11.30 in LAB. We will neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a6c1o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["Ar+ + CH4 -> CH2+ + Ar + H2 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ \ arp\ + \ ch4\ - \((ch2p\ + \ ar\ + h2)\)}, equations], \ variables]\)], "Input"], 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 data \ that 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 -> CH4+ +Ar ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ \ arp\ + \ ch4\ - \((ch4p\ + ar)\)}, equations], \ variables]\)], "Input"], 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+ +? ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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 \ neglect it. \ \>", "SmallText"], Cell[BoxData[ \(\(a6c7o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["Ar+ + CH4 -> H+ + Ar + 2 H2", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["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", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Using Ar+ + H2 = ArH+ + H - 1.53 eV from Ervin and Armentrout, J. Chem. Phys. \ 83, 166 (1985)\ \>", "Text"], Cell[BoxData[ \(Eliminate[ Join[{a == \ \ arp\ + \ h2\ - \((arhp\ + h)\)}, equations], \ variables]\)], "Input"], Cell["I now get -1.50 eV instead of 1.53.", "Text"], Cell[BoxData[ \(Eliminate[ Join[{a == \ \ arp\ + ch4\ - \((cha\ + \ arhp\ + h2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ The CM threshold is 5.94*(40+16)/16= 20.8 eV. Liu and Broida (1970) find \ CH2(A) (and Halpha) excitation at 900 eV. Brandt and Ottinger, Phys. Rev. A \ says that Ar+ + CH4 does not produce radiation in the 160 to 300 nm region. \ We will assume a typical high energy peak with the magnitude adjusted to fit \ Lui and Broida at 900 eV. We have no idea as to whether we should add a low \ energy polarization component.\ \>", "Text"], Cell[BoxData[ \(\(a6cp7\ := n*f*fa6cp7*8. *10^\(-21\)*\ \(\(UnitStep[enrel - 5.94]/ enrel^0.2\)/\((1 + \((600. /\((enrel - 5.94)\))\)^2)\)\)/\((1 + \((enrel/ 4000)\)^2)\)^2 + 1. *10^\(-30\)\ /. \ enrel\ -> \ 16/\((16 + 40)\)*w6[z];\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["Ar^meta + CH4 -> CH(A) + ArH+ + H2", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Ar^meta + CH4 -> ???? We have no information on this reaction and will omit it.\ \>", "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[BoxData[ \(\(Block[{n, f}, n = 10^20/f; \n LogLogPlot[{a6cn\ /. \ w6[z]\ -> \ w6z, a6c3o\ /. \ w6[z]\ -> \ w6z, a6c2o\ /. \ w6[z]\ -> \ w6z, a6cp7\ \ /. \ w6[z]\ -> \ w6z}, {w6z, 0.1, 10000. }, \ PlotRange\ -> \ \ {{0.1, 10000. }, {0.01, 100. }}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["\<\ This large cross section leads to rapid charge transfer/dissociation in Ar+ + \ CH4 -> CH3+.\ \>", "Subsubtitle"], Cell["fast Ar + CH4 data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["Ar + CH4 -> CH(A) + Ar + H2 +H", "SmallText"], Cell[BoxData[ \(Eliminate[ Join[{a == \ \ ch4\ + ar\ - \((cha\ + h2 + h\ + \ ar)\)}, equations], \ variables]\)], "Input"], Cell["\<\ The CM threshold is 11.9*(40+16)/16= 41.6 eV. We do not know of data for \ this process and omit it.\ \>", "Text"], Cell[CellGroupData[{ Cell["ArH+ + CH4 data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ ArH+ + CH4 -> ArH+ + CH4 - elastic scattering based on Langevin cross \ section and an arbitrary fall-off at high energies. We subtract the cross \ sections for CH3+ and CH5+ formation. This leads to a wierd looking cross \ section.\ \>", "SmallText"], Cell["\<\ a7cn:=n*f*fa7cn*3.59*10^-19/Abs[w7[z]]^.5/(1+(w7[z]/100.)^2)-a7c3o -a7c5o \ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["ArH+ + CH4 -> CH+ + Ar + 2 H2", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ \ arhp\ + ch4\ - \((\ ch3p\ + \ ar\ + \ h2)\)}, equations], \ variables]\)], "Input"], Cell["\<\ The threshold for this reaction is 0.0.6 eV in CM and 0.06*(41+16)/16 = 0.21 \ 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*fa7cn*0.6*3.59*10^\(-19\)*\(\(UnitStep[w7[z] - 0.21]/ Abs[w7[z]]^ .5\)/\((1 + \((0.3/\((w7[z] - 0.21)\))\)^2)\)\)/\((1 + \((w7[z]/5. )\)^2)\) + 1. *10^\(-30\);\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["ArH+ + CH4 -> CH5+ + Ar", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ \ arhp\ + ch4\ - \((\ ch5p\ + \ ar)\)}, equations], \ variables]\)], "Input"], Cell["\<\ This proton transfer reaction is exothermic. We base our cross section on \ Smith and Futrell (1976) with an arbitrary fall-off at high energies.\ \>", "SmallText"], Cell[BoxData[ \(\(a7c5o\ = \ \ n*f* fa7cn*0.4*3.59*\(10^\(-19\)/ Abs[w7[z]]^ .5\)/\((1 + \((w7[z]/5. )\)^2)\);\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["ArH+ + CH4 -> CH4+ + Ar + H", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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[ \(\(a7c4o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["ArH+ + CH4 -> Ar+ + CH4 + H", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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. 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[BoxData[ \(\(Block[{n, f\ }, n = 10^20/f; \n LogLogPlot[{a7cn\ /. \ w7[z]\ -> \ w7z, a7c3o\ \ /. \ w7[z]\ -> \ w7z, a7c5o\ \ /. \ w7[z]\ -> \ w7z}, {w7z, 0.1, 1000}, \ PlotRange\ -> \ \ {{0.1, 1000}, {0.1, 500}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[CellGroupData[{ Cell["H+ + CH4", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["H+ + CH4 -> H+ + CH4", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ This Langevin cross section is for comparison only, as it is smaller than the \ charge transfer cross section. \ \>", "SmallText"], Cell["\<\ a8cn:=n*f*fa8cn*1.961*10^-19/Sqrt[w8[z]]/(1+(w8[z]/1000)^2); \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["H+ + CH4 -> CH+ + 2 H2", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Chiu et al, J. Chem. Phys. 88, 6814 (1988) find that this product channel is \ about 20% of the total. We will neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a8c3o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["H+ + CH4 -> CH4+ + H", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Koopman, Phys. Rev. 178, 161 (1969) finds this dominant at 450 eV. Chiu et \ al, J. Chem. Phys. 88, 6814 (1988) find that this product channel is dominant \ at collison energies of 10 to 30 eV. We base our cross section on the \ recommendation in Fig. 4 of Janev, Wang, and Kato, NIFS-DATA-64, May 2001, \ where is argued that this is effectively a resonant charge transfer process..\ \ \>", "SmallText"], Cell[BoxData[ \(\(a8c4o\ := \ n*f*fa8c4o*2.6*10^\(-19\)/ w8[z]^ .5*\((1 + \((w8[z]/ .2)\)^4)\)^ .1/\((1 + \((w8[z]/ 7000. )\)^2)\)^0.4;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["H+ + CH4 -> CH(A) + H2 + H + fH+", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False, Background->None], Cell[BoxData[ \(Eliminate[ Join[{a == \ hp\ + ch4\ - \((\ cha + h2 + h + hp)\)}, equations], \ variables]\)], "Input"], Cell["\<\ Carre et al measure a cross section decreasing from 5.4e-22 m^2 at 30 keV to \ 6.4e-23 m^2 at 500 keV. We chose the ion product to be H+ rather than H2+. \ The threshold is 11.92*17/16 = 12.67 eV in Lab frame. Based on measurements \ of Lyman alpha excitation by Birely and McNeal (1972), we guesstimate the \ peak cross section to be (2/3)^3 (from a 1/n^3 scaling) of their value or \ 0.36e-16 cm^2 = 3.6e-21 m^2.\ \>", "SmallText"], Cell[BoxData[ \(\(a8c8p\ := n*f*fa8c8p* UnitStep[ w8[z] - 12.67]*4.5*10^\(-24\)*\(w8[ z]/\((1 + \((20. /\((w8[z] - 12.67)\))\)^2)\)\)/\((1 + \((w8[z]/ 1500)\)^2)\) + \ 1. *10^\(-30\);\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ 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 \ H+across the tube.\ \>", "Text"] }, Open ]], Cell[BoxData[ \(a8cn\ /. \ w8[z]\ -> \ 1\)], "Input"], Cell[BoxData[ \(\(Block[{n, f\ }, n = 10^20/f; \n LogLogPlot[{a8cn\ /. \ w8[z]\ -> \ w8z, a8c8p\ /. \ w8[z]\ -> \ w8z, a8c4o\ /. \ w8[z]\ -> \ w8z}, {w8z, 0.1, 10000. }, \ PlotRange\ -> \ \ {{0.1, 10000. }, {0.01, 1000. }}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, \ GridLines\ -> \ Automatic, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["\<\ Here we assume a rapid charge transfer of H+ to CH4. Presumably this means \ there will be little excitation of CH(A) by H+.\ \>", "Subsubtitle", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["CH+ + Ar data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["CH+ + Ar -> CH+ + Ar elastic scattering ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False, Background->None], Cell["\<\ CH+ elastic energy loss in Ar. We subtract the polarization portion of the \ assumed charge transfer cross section. This could be messy to keep track of \ if we start changing the assumed charge transfer cross section.\ \>", "SmallText"], Cell["\<\ a1an := n*(1-f)*fa1an*2.49*10^-19/w1[z]^.5/(1+w1[z]/100.) - n*(1-f)*fa1a69* UnitStep[w1[z]-6.77]*2.49*10^-19/w1[z]^.5/(1+(3./(w1[z]-6.77))^2)/(1.+(w1[z]/\ 100.))+1.*10^-30\ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH+ + Ar -> fast CH + Ar+ ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False, Background->None], Cell[BoxData[ \(Eliminate[ Join[{a == chp\ + \ ar\ - \((\ arp\ + ch)\)}, equations], \ variables]\)], "Input"], Cell["\<\ charge transfer The threshold for this process is 53/40*(15.755-10.64) = \ 6.77 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, although it seems that I recall a case were they were essentially \ equal. The Janev et al model is that at low energies, the charge exchange \ cross section follows the Langevin value, while at high energies it follows \ Demkov. Judging from our compilation results for H+ + H2 and N+ + N2, we \ should use roughly 10% of Langevin. This reduction for H+ + H2 may be \ associated with the reduction in the Qm caused by inelastic scattering. See \ Krstic and Schultz (1999). We do not make this reduction because it would \ put the charge transfer cross section at less than the charge transfer \ excitation cross section, which seems unlikely. Instead of Demkov at the \ higher energies, we use our version of Rapp and Francis with the high energy \ portion based on the Ar+ + Ar charge exchange cross section. We put the turn \ down for this and the excitation cross section at about 3000 eV, i.e., a \ value comparable with those of Janev et al.\ \>", "SmallText"], Cell[BoxData[ \(a1a69 := n*\((1 - f)\)*fa1a69* UnitStep[ w1[z] - 6.77]*\((2.49*\(10^\(-19\)/ w1[z]^ .5\)/\((1 + \((3. /\((w1[z] - 6.77)\))\)^2/\((1. + \((w1[z]/ 100. )\))\))\) + \ \[IndentingNewLine]1.15*\(\(10^\(-18\)/ w1[z]^0.1\)/\((1 + \((2000. /\((w1[z] - 6.77)\))\)^4)\)^0.5\)/\((1 + \((w1[z]/ 10000)\)^3)\)^1.1)\)\ + \ 1. *10^\(-30\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH+ + Ar -> slow CH + Ar+ ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ charge transfer The threshold for this process is 53/40*(15.755-10.64) = \ 6.77 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 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == chp\ + \ ar\ - \((\ arhp\ + c)\)}, equations], \ variables]\)], "Input"], Cell["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 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["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 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Ehbrecht, Kowalski, and Ottinger (1996) find a cross section that appears to \ reach 5E-21 m^2 at enrel = 1000 eV and is roughly linear with energy. In \ center-of-mass the threshold for this process is 15.755-10.64+2.89 = 8.0 eV \ or (13+40)/40*8.0 = 7.19 eV LAB.\ \>", "SmallText"], Cell["\<\ a1a6p := n*(1-f)*fa1a6p*(UnitStep[enrel-7.19]*5.0*10^-21*(enrel-7.19)/1000./(\ 1+(enrel/3000)^3)+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 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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+2.93 = 8.04\ \>", "SmallText"], Cell["\<\ a1a1p := n*(1-f)*fa1a6p*(UnitStep[enrel-8.04]*8.*10^-20*(enrel-8.04)/1000./(1+\ (enrel/4000)^2)+ UnitStep[enrel-8.04]*1.2*10^-20/(1+(1/(enrel-8.04))^2)/(1+(enrel/50)^\ 2))/(1+(enrel/4000)^2)+ 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 (1-f) = 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[BoxData[ \(\(Block[{n, f}, n = 10^20/\((1 - f)\); \n LogLogPlot[{a1an\ /. \ w1[z]\ -> \ w1z, a1a69\ \ /. \ w1[z]\ -> \ w1z, a1a6p\ \ /. \ w1[z]\ -> \ w1z, \[IndentingNewLine]a1a1p\ \ /. \ w1[z]\ -> \ w1z}, {w1z, 1, 10000}, \ GridLines\ -> \ Automatic, PlotRange\ -> \ \ {{1, 10000}, {10^\(-2\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["\<\ This plot seems to show that the low energy behavior of the CH+ + Ar cross \ section is critical to our model. 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", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["CH2+ + Ar data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["CH2+ + Ar -> CH2+ + Ar - elastic", "Subsubsection"], Cell["\<\ Momentum loss in elastic and inelastic collisions. Note that the 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["a2an:=n*(1-f)*fa2an*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. 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"], Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/\((1 - f)\); \n LogLogPlot[a2an\ /. \ w2[z]\ -> \ w2z, {w2z, 1, 10000}, \ GridLines\ -> \ Automatic, \ PlotRange\ -> \ \ {{1, 10000}, {10^\(-2\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[CellGroupData[{ Cell["CH3+ + Ar data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["CH3+ + Ar -> CH3+ + Ar momentum loss", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Momentum loss in elastic and inelastic collisions. We gave this cross \ section a roll-off at energies above 500 eV. This cross section is critical \ in determining the role of CH3+, because the elastic collisions severely \ reduce the ion energy. We did not subtract the arbitrarily reaction cross \ sections because they are small at moderate and low energies.\ \>", "SmallText"], Cell["a3an:=n*(1-f)*fa3an*2.53*10^-19/w3[z]^.5/(1+(w3[z]/500.)^2);", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH3+ + Ar -> Ar+ +CH3", "Subsubsection"], Cell[BoxData[ \(Eliminate[ Join[{a == \ ch3p\ + \ ar\ - \ \((arp\ + \ ch3)\)}, equations], \ variables]\)], "Input"], Cell["\<\ charge transfer. For some reason we have given this a very small value.\ \>", "SmallText"], Cell["\<\ a3a6F := n*(1-f)*fa3a6F*(UnitStep[w3[z]-8.13]* 1.0*10^-21*(w3[z]-8.13)/(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", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We have no information on this cross section and so must guess.\ \>", "SmallText"], Cell[BoxData[ \(Eliminate[ Join[{a == \ ch3p\ + \ ar\ - \((chp\ + \ ar\ + \ h2)\)}, equations], \ variables]\)], "Input"], Cell["This has a threshold of 5.37*(15+40)/40 = 7.38", "Text"], Cell["\<\ a3a1o := n*(1-f)*(fa3a1o*UnitStep[w3[z]-7.38]* 1.0*10^-21*(w3[z]-7.38)/(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+", "Subsubsection"], Cell[BoxData[ \(Eliminate[ Join[{a == \ ch3p\ + ar\ - \((ch\ + \ h2\ + \ arp)\)}, equations], \ variables]\)], "Input"], 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 10.49*(15+40)/40 = 14.42eV\ \>", "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 important process will not occur for our typical CH3+ energy \ of 12 eV.\ \>", "Subsubtitle"], Cell["CH3+ + Ar -> CH(A) +H2 +Ar+ -> CH(X) + Ar + + H2 + 432 nm", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["Where did this come from? We have made it small. ", "SmallText"], Cell[BoxData[ \(Eliminate[ Join[{a == \ ch3p + ar\ - \((cha\ + \ h2\ + \ arp)\)}, equations], \ variables]\)], "Input"], Cell["The threshold is 13.38*(15+40)/40 = 18.40eV", "Text"], Cell["\<\ a3a6p := n*(1-f)*fa3a6p*(UnitStep[w3[z]-18.4]* 1.0*10^-25*(w3[z]-18.4)/(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 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ -> 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 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["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 ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["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. 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[BoxData[ \(\(Block[{n, f}, n = 10^20/\((1 - f)\); \n LogLogPlot[{\((a3an\ /. \ w3[z]\ -> \ w3z)\), \((a3a96\ \ /. \ w3[z]\ -> \ w3z)\), \((a3a1o\ /. \ w3[z]\ -> \ w3z)\), \((a3a6p\ /. \ w3[z]\ -> \ w3z)\), \((a3a6F\ /. \ w3[z]\ -> \ w3z)\)\ }, {w3z, 1, 1000}, \ PlotRange\ -> \ \ {{1, 1000}, {10^\(-4\), 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[CellGroupData[{ Cell["CH4+ + Ar data", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Here we really should use the known drift behavior of CH4+ in Ar to get an \ ion energy scale at low energies. Instead we are using the single beam \ model.\ \>", "Subsubtitle"], Cell["CH4+ + Ar -> CH4+ + Ar elastic scattering", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Elastic collisions based on Langevin with arbitrary roll-off at high \ energies. We did not subtract the arbitrarily reaction cross sections because \ they are small at low energies.\ \>", "SmallText"], Cell["\<\ a4an:=n*(1-f)*fa4an*2.56*10^-19/Abs[w4[z]]^.5/(1+(w4[z]/500)^2) \ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH4+ + Ar -> ArH+ + fCH3", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ ch4p\ + \ ar\ - \((arhp\ + \ ch3)\)}, equations], \ variables]\)], "Input"], Cell["\<\ The following cross section is based on Fig. 5a of Peko et a (1998). The \ threshold is 1.62*56/40=2.27. Experimentally the threshold is about 7 eV.\ \>", "SmallText"], Cell[BoxData[ \(\(a4a7F\ := \ n*\((1 - f)\)* fa4a7F*\((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, 1]], Cell["CH4+ + Ar -> H+ + Ar + fCH3", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ ch4p\ + \ ar\ - \((ar\ + \ hp\ + \ ch3)\)}, equations], \ variables]\)], "Input"], Cell["\<\ The following cross section is actually the CID cross section for D+ \ formation in CD4+ + Ar collisions from Fig. 5b of Peko et a (1998).\ \>", "SmallText"], Cell[BoxData[ \(\(a4a8F\ := \ n*\((1 - f)\)* fa4a8F*\((10^\(-20\)*\((UnitStep[ w4[z] - 5.47]*0.35/\((1 + \((\((w4[z] - 5.47)\)/ 4.5)\)^\(-2\))\) + \ \[IndentingNewLine]UnitStep[ w4[z] - 5.47]*\((\((w4[z] - 5.47)\)/ 50. )\)^1/\((1 + \((w4[z]/140. )\)^2.2)\))\) + 1. *10^\(-30\))\);\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["CH4++Ar\[Rule]CH++Ar+H3", "Subsubsection"], Cell["Peko et al (1998) do not report this process. We neglect it.", \ "SmallText"], Cell[BoxData[ \(\(a4a1o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["CH4++Ar\[Rule]H + Ar+fCH3+", "Subsubsection"], Cell["Peko et al (1998) do not report this process. We neglect it.", \ "SmallText"], Cell[BoxData[ \(\(a4a3o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["CH4++Ar\[Rule]Ar+ + fCH4", "Subsubsection"], Cell["\<\ Peko et al (1998) do not report this process. We neglect it.\ \>", "SmallText"], Cell[BoxData[ \(\(a4a6o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 1]], 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[BoxData[ \(\(Block[{n, f}, n = 10^20/\((1 - f)\); \n LogLogPlot[{a4an\ /. \ w4[z]\ -> \ w4z, a4a7F\ /. \ w4[z]\ -> \ w4z\ , a4a8F\ /. \ w4[z]\ -> \ w4z}, {w4z, 1, 1000}, PlotStyle\ -> \ plotColors, \ PlotRange\ -> \ \ {{1, 1000}, {0.01, 100}}, PlotPoints\ -> \ 500, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[CellGroupData[{ Cell["CH5+ + Ar data ", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ CH5+ + Ar -> CH5+ + Ar elastic scattering \ \>", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We use the Langvin rate coefficient for momentum loss in elastic and \ inelastic collisions. We added a high enrgy fall-off.\ \>", "SmallText"], Cell["\<\ a5an :=n*(1-f)*fa5an*2.58*10^-19/w5[z]^.5/(1+(w5[z]/1000)^2)+2.*10^-30-a5a3a; \ \ \>", "Input", PageWidth->Infinity, ShowSpecialCharacters->False, FontColor->RGBColor[1, 0, 1]], Cell["CH5+ + Ar -> CH3+ + Ar + H2 ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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 + \((w5[z]/1000)\)^2)\) + 1. *10^\(-30\);\)\)], "Input", FontColor->RGBColor[1, 0, 1]], Cell["CH5+ + Ar -> CH+ + CH4 + Ar ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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 ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We have not found any data for this process. We neglect it. \ \>", "SmallText"], Cell[BoxData[ \(\(a5a3o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH5+ + Ar -> CH4+ + CH + Ar ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We have not found any data for this process. We neglect it. \ \>", "SmallText"], Cell[BoxData[ \(\(a5a4o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH5+ + Ar -> Ar+ + CH4 + H ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We have not found any data for this process. We neglect it. \ \>", "SmallText"], Cell[BoxData[ \(\(a5a6o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH5+ + Ar -> CH4+ + CH + Ar ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We have not found any data for this process. We neglect it. \ \>", "SmallText"], Cell[BoxData[ \(\(a5a7o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["CH5+ + Ar -> CH4+ + CH + Ar ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ We have not found any data for this process. We neglect it. \ \>", "SmallText"], Cell[BoxData[ \(\(a5a8o\ = \ 0;\)\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell["\<\ 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.\ \>", "Text"] }, Open ]], Cell[BoxData[ \(\(Block[{n, f}, n = 10^20/\((1 - f)\); \n LogLogPlot[{a5an\ /. \ w5[z]\ -> \ w1z, a5a3a /. \ w5[z]\ -> \ w1z}, {w1z, 1, 1000}, \ PlotRange\ -> \ \ {{1, 1000}, {0.1, 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell[CellGroupData[{ Cell["C2H5+ + Ar data ", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ C2H5+ + CH4 Momentum loss in elastic and inelastic collisions. 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["a0an :=n*(1-f)*fa0an*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", "Subsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["fast CH + Ar -> slow CH + Ar", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ Fast CH loss by cooling. For the cross section we use our empirical fit to \ the Ar-Ar viscosity cross section.\ \>", "SmallText"], Cell[BoxData[ \(a9an := \ fa9an*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["fast CH + Ar -> CH(A) +Ar -> CH(X) + Ar + 432 nm", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ 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["\<\ The following is based on the fast H + Ar cross section used in our H2 model.\ \ \>", "Text"], Cell[BoxData[ \(a9apa := n*\((1 - f)\)* fa9apa*\((UnitStep[ w9[z] - 12. ]*1.4*\(10^\(-20\)/\((\((40/\((w9[z] - 12. )\))\)^2.5 + 1)\)\)/\((\((1 + \((w9[z]/30)\)^2)\)^0.22)\) + 1. *10^\(-30\))\)\)], "Input"], 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], 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[BoxData[ \(\(Block[{n, f}, n = 10^20/\((1 - f)\); fa9apa1\ \ = 1; \n LogLogPlot[{a9an\ /. \ w9[z]\ -> \ w9z, a9apa\ \ /. \ w9[z]\ -> \ w9z, a9apa1\ \ /. \ w9[z]\ -> \ w9z}, {w9z, 1, 1000}, \ PlotRange\ -> \ \ {{1, 1000}, {0.01, 100}}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], 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", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["fast CH3 + Ar data", "Subsection", 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. The maximim fast CH3 energy (max) is wF[z]:=w3[z]; \ \>", "SmallText"], Cell["fast CH3 + Ar -> CH3 + Ar elastic scattering", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["\<\ fCH3 + Ar -> destruction by cooling. Unfortunately, we do not know anything \ about CH3-Ar collisions and have to guess at an effective cross section. \ For the cross section we use our empirical fit to the Ar-Ar viscosity cross \ section.\ \>", "SmallText"], Cell[BoxData[ \(aFan := \ faFan*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\ -> \ 40/55*wF[z]\)], "Input", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(aFan\ /. \ wF[z]\ -> \ 10. \)], "Input"], Cell["fast CH3 + Ar -> fCH + Ar + H2", "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ ch3\ + \ ar\ - \((ch\ + \ ar\ + \ h2)\)}, equations], \ variables]\)], "Input"], 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*(1-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["fast CH3 + Ar -> CH(A) + Ar + H2 -> CH + Ar + H2 + 432 nm ", \ "Subsubsection", PageWidth->Infinity, ShowSpecialCharacters->False], Cell[BoxData[ \(Eliminate[ Join[{a == \ ch3\ + \ ar\ - \((cha\ + \ ar\ + \ h2)\)}, equations], \ variables]\)], "Input"], 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. I \ have no idea where the following came from. \ \>", "SmallText"], Cell["\<\ aFapa :=n*(1-f)*(faFapa*UnitStep[wF[z]-16.4]*2.5*10^-23*(wF[z]-16.4)/(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["\<\ Plot these cross section 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 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[BoxData[ \(\(Block[{n, f\ }, n = 10^20/\((1 - f)\); \n LogLogPlot[{aFan\ /. \ wF[z]\ -> \ wFz, aFa9a\ \ /. \ wF[z]\ -> \ wFz, aFapa\ \ /. \ wF[z]\ -> \ wFz}, {wFz, 1, 1000}, \ PlotRange\ -> \ \ {{1, 1000}, {10^\(-2\), 100. }}, PlotStyle\ -> \ plotColors, PlotPoints\ -> \ 500, GridLines\ -> \ Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432]\n\t];\)\)], "Input"], Cell["End data", "SmallText", PageWidth->Infinity, ShowSpecialCharacters->False], Cell["runtime = SessionTime[] - startclock", "Input", PageWidth->Infinity] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, CellGrouping->Manual, WindowSize->{786, 449}, WindowMargins->{{1, Automatic}, {Automatic, 5}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, ShowCellTags->True, StyleDefinitions -> "AvpStyle.nb" ] (******************************************************************* Cached data follows. 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