(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 33250, 967]*) (*NotebookOutlinePosition[ 34014, 994]*) (* CellTagsIndexPosition[ 33970, 990]*) (*WindowFrame->Normal*) Notebook[{ Cell["CH4-Ar model of 5/13/93 redone using Mathematica", "Subtitle"], Cell[CellGroupData[{ Cell["Setup notebook enviroment ", "Text", PageWidth->Infinity], Cell[BoxData[ \(\(\(ClearAll["\"];\)\(\ \)\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(\(\(Remove["\"];\)\(\ \)\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(\(startclock\ = \ SessionTime[];\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(\(Off[General::spell];\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(\(Off[General::spell1];\)\)], "Input", PageWidth->Infinity, Evaluatable->True], Cell[BoxData[ \(Needs["\"]\)], "Input", PageWidth->Infinity, Evaluatable->True] }, Open ]], Cell[BoxData[ \(now\ = \ StringForm["\<``/``/`` ``:``:``\>", \(Date[]\)[\([2]\)], \ \(Date[]\)[\([3]\)], \(Date[]\)[\([1]\)], \(Date[]\)[\([4]\)], \ \(Date[]\)[\([5]\)], \(Date[]\)[\([6]\)]]\)], "Input"], Cell[BoxData[ \(SetDirectory["\"]\)], "Input"], Cell["Cross sections and reaction coefficients", "Subsection"], Cell["\<\ We select a density of 1e20 m^3 for the plots of cross sections and reaction \ coefficients. We also need to select f values for these plots.\ \>", "Text"], Cell[BoxData[ \(\(n\ = \ 1. *10^20;\)\)], "Input", Evaluatable->False], Cell["\<\ species and data type for coefficient table: 1 - CH+, 2 - CH2+, 3 - CH3+, 4 - CH4+, 5 - Ar+, s - all ions except CH3+ d - fast CH, c - CH4, a - Ar, e - electron, I - total ionization q - cross section, a - spatial reaction coefficient, m - metastable w - drift energy\ \>", "Text"], Cell["\<\ The following set of cross section normalizations is that found on 1/4/01 to \ be consistent with the f = 0.1 experiments, but gave no solution for f >= \ 0.12.\ \>", "Text"], Cell["\<\ qeapa = 3.50000*10^-23; qdapa = 5.00000*10^-22; qdaoa = 1.00000*10^-25; qdcpc = 2.50000*10^-23; qdcoc = 1.00000*10^-25; q1ap5 = 1.00000*10^-25; q1ad5 = 1.00000*10^-25; q1cd4 = 1.00000*10^-25; q3ap5 = 1.00000*10^-25; q3ad5 = 1.00000*10^-21; q3a1o = 1.00000*10^-25; q3a5o = 1.00000*10^-25; q3cp4 = 1.00000*10^-25; q3cd4 = 1.00000*10^-25; q3c4o = 1.00000*10^-25; q3c1o = 1.00000*10^-25; q1c3o = 1.00000*10^-25; q1cso = 1.00000*10^-25; q1cp4 = 1.00000*10^-25;\ \>", "Input"], Cell["\<\ The following set of cross section normalizations is that used in the 1993 \ calculations using PLOD6\ \>", "Text"], Cell["\<\ qeapa = 3.50000*10^-23; qdapa = 5.00000*10^-22; qdaoa = 1.00000*10^-25; qdcpc = 2.50000*10^-23; qdcoc = 1.00000*10^-25; q1ap5 = 1.00000*10^-25; q1ad5 = 1.00000*10^-25; q1cd4 = 1.00000*10^-25; q3ap5 = 1.00000*10^-25; q3ad5 = 3.00000*10^-21; q3a1o = 1.00000*10^-25; q3a5o = 1.00000*10^-25; q3cp4 = 1.00000*10^-25; q3cd4 = 1.00000*10^-20; q3c4o = 1.00000*10^-25; q3c1o = 1.00000*10^-25; q1c3o = 1.00000*10^-25; q1cso = 1.00000*10^-25; q1cp4 = 1.00000*10^-25;\ \>", "Input"], Cell["electron - CH4 data", "Subsubsection"], Cell["\<\ e+CH4\[Rule]432 nm normalized at 40 ev\ \>", "Text"], Cell["\<\ aecpo:=UnitStep[we[z] \ -11.8]*n*f*1.8*10^-22*(we[z]-11.8)/(we[z]+5.)/(1+we[z]/100.)*45.*1.4 \ /32.2+1*10^-20\ \>", "Input"], Cell["\<\ e+CH4\[Rule]2e+sum CHx+total ionization normalized at 70 ev\ \>", "Text"], Cell["\<\ aecie:=UnitStep[we[z] - \ 12.7]*n*f*2.5*10^-20*2*(we[z]-12.7)/(we[z]+70.)/(1+we[z]/70.)*140.*2./57.+ \ 1.*10^-20\ \>", "Input"], Cell["electron energy loss-hi e normalized at 100 ev", "Text"], Cell["\<\ lecn:=UnitStep[we[z] - \ 8]*n*f*4*10^-19*(we[z]-8)/(we[z]+100.)/(1+we[z]/100.)*200.*2./92.+5.*10^-10\ \>", "Input"], Cell["e-CH4 momentum transfer n*q", "Text"], Cell["\<\ mecn:=n*f*((6.*10^-22)^2/Abs[we[z]]^3+ (2.*10^-20)^2*Abs[we[z]]^3)^0.5/(1+(Abs[we[z]]/6.)^4)^.65\ \>", "Input"], Cell[BoxData[ \(abc := \ n*f*1. *10^\(-22\)\)], "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(aecie\ /. \ we[z]\ \[Rule] \ w\)\ /. \ {f -> 1, n -> 10^20}, \(aecpo\ /. \ we[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(lecn\ /. \ we[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(mecn\ /. \ we[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.01, 10000}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell["CH+ - CH4 data", "Subsubsection"], Cell["CH+elastic energy loss", "Text"], Cell["\<\ l1cn:=n*f*2.*13.*16./29./29.*w1[z]*3.12*10^-19/w1[z]^.5/(1+w1[z]/20.)+ \ 1.*10^-20\ \>", "Input"], Cell["CH+ +CH4\[Rule]C2H3+ +H2", "Text"], Cell["\<\ a1cso:=n*f*q1cso/w1[z]^.5/(1+w1[z]/1.)^4 + 1.*10^-20 \ \>", "Input"], Cell["CH+ +CH4\[Rule]CH3+ +CH2", "Text"], Cell["\<\ a1c3o:=n*f*q1c3o/w1[z]^.5/(1+w1[z]/1.)^4 + 1.*10^-20 \ \>", "Input"], Cell["\<\ CH+ +CH4\[Rule]fCH+CH4+ normalized at 50 ev\ \>", "Text"], Cell["\<\ a1cd4:=UnitStep[w1[z] - \ 2.79]*n*f*q1cd4*(w1[z]-2.79)/(w1[z]+50.)/(1+w1[z]/1000.)*100.*1.05/44+1.*10^-\ 20\ \>", "Input"], Cell["\<\ CH+ +CH4\[Rule]CH(a)+CH4+ normalized at 50 ev\ \>", "Text"], Cell["\<\ a1cp4:=UnitStep[w1[z] - \ 24.8]*n*f*q1cp4*(w1[z]-24.8)/(w1[z]+50.)/(1+w1[z]/50.)*100.*2./25.2+1.*10^-20\ \ \>", "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(l1cn\ /. \ w1[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a1cso\ /. \ w1[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a1c3o\ /. \ w1[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a1cd4\ /. \ w1[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a1cp4\ /. \ w1[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.0001, 100}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell["CH3+ - CH4 data", "Subsubsection"], Cell["\<\ The next entry appears to be elastic scattering not CH3+ loss, i.e., it has \ the extra w3[z] factor expected in l3cn.\ \>", "Text"], Cell["a3cso:=n*f*w3[z]*3.22*10^-19/w3[z]^.5/(1+w3[z]/5.)^2", "Input"], Cell["\<\ CH3+ +CH4\[Rule]CH3+CH4+ normalized at 50 ev\ \>", "Text"], Cell["\<\ a3c4o:=UnitStep[w3[z] - 5.9]* n*f*q3c4o*(w3[z]-5.9)/(w3[z]+50.)/(1+w3[z]/1000.)*100.*1.05/44.+1.*10^-20\ \>", "Input"], Cell["\<\ CH3+loss to C2Hn+etc. CH3+ + CH4 -> fCH + ?CH4+ +H2? normalized at 100 ev\ \>", "Text"], Cell["\<\ a3cd4:=UnitStep[w3[z] - 14.6]* n*f*q3cd4*(w3[z]-14.6)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./85.4+1.*10^-20\ \>", "Input"], Cell["\<\ CH3+ +CH4\[Rule]CH+ +CH4+H2 normalized at 100 ev\ \>", "Text"], Cell["\<\ a3c1o:=UnitStep[w3[z] - 11.7]* n*f*q3c1o*(w3[z]-11.7)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./88.3+1.*10^-20\ \>", "Input"], Cell["\<\ CH3+ +CH4\[Rule]CH(a)+?CH4+ +H2? normalized at 50 ev\ \>", "Text"], Cell["\<\ a3cp4:=UnitStep[w3[z] - 40.8]* n*f*q3cp4*(w3[z]-38.3)/(w3[z]+50.)/(1+w3[z]/50.)*100.*2./11.7+1.*10^-20\ \>", "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(a3cso\ /. \ w3[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a3c4o\ /. \ w3[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a3cd4\ /. \ w3[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a3c1o\ /. \ w3[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a3cp4\ /. \ w3[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.0001, 100}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell["CH4+ - CH4 data ", "Subsubsection"], Cell[" CH4+energy loss by reaction", "Text"], Cell[BoxData[ \(l4cn\ := \ n*f*3.27*10^\(-19\)/Abs[w4[z]]^0.5\ + \ 1. *10^\(-20\)\)], "Input"], Cell[" CH4+ +CH4\[Rule]CH5+ +CH3", "Text"], Cell["\<\ This coefficient is the same as the previous entry except for the roll-off at \ high energies.\ \>", "Text"], Cell["\<\ a4cso:=n*f*3.27*10^-19/w4[z]^.5 /(1+w4[z]/1.)^4 +1.*10^-20 \ \>", "Input"], Cell["\<\ CH4+ +CH4\[Rule]CH3+ +?CH3+H2? normalized at 50 eV. This cross sectiion has \ been rounded off near threshold so as to prevent disconiuities in the slopes \ of solutions for the associated fluxes at the reaction threshold.\ \>", "Text"], Cell["\<\ a4c3o:=UnitStep[w4[z] - 3.38]* n*f*3.27*10^-19/w4[z]^1.5*(w4[z]-3.38)*(1-1./(1+w4[z]/1.)^4)+1.*10^-20\ \>", "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(l4cn\ /. \ w4[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a4cso\ /. \ w4[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a4c3o\ /. \ w4[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.001, 1000}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell["fast CH + CH4 data", "Subsubsection"], Cell[" fast CH energy (max)", "Text"], Cell["wd[z]=w1[z] ", "Input"], Cell[" fCH+CH4\[Rule]dest.By cooling", "Text"], Cell["adcoc:=n*f*qdcoc/wd[z]^0.5 /(1+wd[z]/100.) ", "Input"], Cell["\<\ fCH+CH4\[Rule]432 nm normalized at 100 ev\ \>", "Text"], Cell["\<\ adcpc:=UnitStep[wd[z] - 22.1] * n*f*qdcpc*(wd[z]-22.1)/(wd[z]+100.)/(1+wd[z]/1000.)*200.*2.*1.1/78.+1.*10^-20\ \ \>", "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(adcoc\ /. \ wd[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(adcpc\ /. \ wd[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.0001, 100}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell["CH+ - Ar data", "Subsubsection"], Cell[" CH+elastic energy loss in Ar", "Text"], Cell["\<\ l1an:=n*(1.-f)*2.*15.*40./55./55.*2.13*10^-19*w1[z]^.5/(1+w1[z]/50.)\ \>", "Input"], Cell["\<\ CH+ +Ar\[Rule]fast CH+Ar+ normalized at 100 ev\ \>", "Text"], Cell["\<\ a1ad5:=UnitStep[w1[z] - 6.04]* n*(1.-f)*q1ad5*(w1[z]-6.04)/(w1[z]+100.)/(1+w1[z]/100.)*200.*2./94.+1.*10^-20 \ \>", "Input"], Cell["\<\ CH+ +Ar\[Rule]432 nm normalized at 100 ev\ \>", "Text"], Cell["\<\ a1ap5:=UnitStep[w1[z] - 24.8]* n*(1.-f)*q1ap5*(w1[z]-24.8)/(w1[z]+100.)/(1+w1[z]/100.)*200.*2./752.+1.*10^-\ 20\ \>", "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(l1an\ /. \ w1[z]\ \[Rule] \ w\)\ /. {f -> 0.0, n -> 10^20}, \(a1ad5\ /. \ w1[z]\ \[Rule] \ w\)\ /. {f -> 0.0, n -> 10^20}, \(a1ap5\ /. \ w1[z]\ \[Rule] \ w\)\ /. {f -> 0.0, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.01, 10000}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell["CH3+ - Ar data", "Subsubsection"], Cell[" CH3+elastic energy loss in Ar", "Text"], Cell["\<\ l3an:=n*(1.-f)*2.*15.*40./55./55*2.17*10^-19*w3[z]^.5 /(1+w3[z]/50.)\ \>", "Input"], Cell["\<\ CH3+ +Ar\[Rule]Ar+ +CH3 normalized at 100 ev\ \>", "Text"], Cell["\<\ a3a5o:=UnitStep[w3[z] - 8.1]* n*(1.-f)*q3a5o*(w3[z]-8.1)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./91.9+1.*10^-20 \ \>", "Input"], Cell["\<\ CH3+ +Ar\[Rule]CH+ +Ar+H2 normalized at 100 ev\ \>", "Text"], Cell["\<\ a3a1o:=UnitStep[w3[z] - 8.29]* n*(1.-f)*q3a1o*(w3[z]-8.29)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./91.7+1.*10^-\ 20\ \>", "Input"], Cell["\<\ CH3+ +Ar\[Rule]fCH+H2+Ar+ normalized at 100 ev\ \>", "Text"], Cell["\<\ a3ad5:=UnitStep[w3[z] - 14.6]* n*(1.-f)*q3ad5*(w3[z]-14.6)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./85.4+1.*10^-\ 20\ \>", "Input"], Cell["\<\ CH3+ +Ar\[Rule]CH(a)+H2+Ar+ normalized at 100 ev\ \>", "Text"], Cell["\<\ a3ap5:=UnitStep[w3[z] - 31.1]* n*(1.-f)*q3ap5*(w3[z]-31.1)/(w3[z]+100.)/(1+w3[z]/100.)*200.*2./88.9+1.*10^-\ 20\ \>", "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(l3an\ /. \ w3[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}, \(a3a5o\ /. \ w3[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}, \(a3a1o\ /. \ w3[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}, \(a3ad5\ /. \ w3[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}, \(a3ap5\ /. \ w3[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.01, 10000}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell["CH4+ - Ar data", "Subsubsection"], Cell[" CH4+energy loss to Ar assumes no reaction", "Text"], Cell["\<\ l4an:=n*(1.-f)*2.*16.*40./56./56.*2.19*10^-19* Abs[w4[z]]^.5 \ \ \>", "Input"], Cell["fast CH - Ar data", "Subsubsection"], Cell[" fast CH destruction by cooling", "Text"], Cell["adaoa:=n*(1.-f)*qdaoa/(wd[z]^0.5)/(1+wd[z]/100.) ", "Input"], Cell["\<\ fCH+Ar\[Rule]CH(a)+Ar normalized at 100 ev\ \>", "Text"], Cell["\<\ adapa:=UnitStep[wd[z] - 16.2]* n*(1.-f)*qdapa*(wd[z]-16.2)/(wd[z]+100.)/(1+wd[z]/1000.)*200.*2.*1.1/84.+1.*\ 10^-20\ \>", "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(l4an\ /. \ w4[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}, \(adaoa\ /. \ wd[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}, \(adapa\ /. \ wd[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.001, 1000}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell[" Ar+ - CH4 data", "Subsubsection"], Cell[" Ar+ +CH4\[Rule]CH4+Ar+", "Text"], Cell["l5cn:=n*f*2.*40.*16./56./56.*2.9*10^-19/(w5[z]^.5) ", "Input"], Cell[" Ar+ +CH4\[Rule]CHn+(all n)+Ar", "Text"], Cell["a5cio:=n*f*1.4*10^-19/(w5[z]^.5) ", "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(l5cn\ /. \ w5[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}, \(a5cio\ /. \ w5[z]\ \[Rule] \ w\)\ /. {f -> 1, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.01, 10000}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell[" e + Ar data", "Subsubsection"], Cell[" ionization by e+Ar", "Text"], Cell["\<\ aea5e:=UnitStep[we[z] - 15.8]* n*(1.-f)*1.10*10^-19*100.*(we[z]-15.8)/(100.+we[z])^2+1.*10^-20\ \>", "Input"], Cell[" energy loss by e+Ar -> Ar* + e", "Text"], Cell["\<\ lean:=UnitStep[we[z] - 12.]* n*(1.-f)*4*10^-18*100.*(we[z]-12)/(100.+we[z])^2+1.*10^-20\ \>", "Input"], Cell[" e-Ar momentum transfer n*q", "Text"], Cell["\<\ mean:=n*(1.-f)*Abs[3.*10^-21*(-1+4.*we[z]+we[z]^2/2.+1.*10^-21)]/(1+(we[z]/12.\ )^4)^.8+1.*10^-20\ \>", "Input"], Cell["\<\ e + Ar -> light leakage Note that the qeapa value used to calculate the \"light leakage\" is very \ arbitrary and should be made to vary with the electron energy we or at least \ with E/n.\ \>", "Text"], Cell[" Ar+ + Ar data", "Subsubsection"], Cell[" Ar+ +Ar charge transfer", "Text"], Cell["\<\ q5a5:=6.*10^-19*(1.-f)/w5[z]^.1 +1.*10^-20 \ \>", "Input"], Cell[BoxData[ \(\(LogLogPlot[{\(lean\ /. \ we[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}, \(mean\ /. \ we[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}, \(aea5e\ /. \ we[z]\ \[Rule] \ w\)\ /. \ {f -> 0.0, n -> 10^20}, \(q5a5\ /. \ w5[z]\ \[Rule] w\)\ /. \ {f -> 0.0, n -> 10^20}}, \ {w, 0.01, 1000}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{ .1, 1000}, {0.001, 1000}}, PlotPoints\ \[Rule] \ 500];\)\)], "Input"], Cell["end data", "Subsubsection"], Cell[BoxData[ \(Clear[f, n]\)], "Input"], Cell[TextData[StyleBox["Formulation and solution of differential equations", \ "Subsection"]], "Section"], Cell["Direction of integration is from anode to cathode", "Text"], Cell[BoxData[{ \(\(djeodz := \(-\((aea5e + aecie)\)\)* je[z];\) (*electron\ flux*) \), "\[IndentingNewLine]", \(dj1odz := \(-\((a1cso + a1cd4 + a1ad5 + a1cp4 + a1ap5 + a1c3o)\)\)* j1[z] + 0.03*aecie*je[z] + 0.05*a5cio*j5[z] + \((a3c1o + a3a1o)\)*j3[z]; (*ch + flux*) \ dj3odz := \(-\((a3cso + a3c4o + a3cd4 + a3c1o + a3cp4 + a3ad5 + a3ap5 + a3a1o + a3a5o)\)\)*j3[z] + 0.4*aecie*je[z] + 0.7*a5cio*j5[z] + a1c3o*j1[z] + a4c3o*j4[z]; (*ch3 + flux*) \ dj4odz := \(-\((a4cso + a4c3o)\)\)*j4[z] + .4*aecie* je[z] + \((a3cp4 + a3c4o + a3cd4)\)*j3[z] + \((a1cd4 + a1cp4)\)* j1[z]; (*ch4 + flux*) \), "\[IndentingNewLine]", \(\(dj5odz := \((a3ad5 + a3ap5 + a3a5o)\)*j3[z] + aea5e*je[z] + \((a1ad5 + a1ap5)\)*j1[z] - a5cio*j5[z];\) (*ar + flux*) \ \), "\[IndentingNewLine]", \(\(djsodz := 0.17*aecie*je[z] + 0.25*a5cio*j5[z] + a3cso*j3[z] + a1cso*j1[z] + a4cso*j4[z];\) (*\(\(cmhn\)\(+\)\), m\ not\ 1\ n\ not\ 1, 3*) \), "\[IndentingNewLine]", \(\(djdodz := \((a3cd4 + a3ad5)\)*j3[z] + \((a1cd4 + a1ad5)\)* j1[z] - \((adcpc + adcoc + adapa + adaoa)\)* jd[z];\) (*fast\ ch\ flux*) \), "\[IndentingNewLine]", \(\(dweodz := \(-\((eontd*n/\((1. *10^21)\) - \(2/1836\)/40* mean - \ \(2/1836\)/16*mecn - lecn - lean + k*djeodz/je[z]* we[z])\)\);\) (*electron\ energy\ equation*) \), "\ \[IndentingNewLine]", \(\(dw1odz := eontd*n/\((1. *10^21)\) - 16/29*l1cn - 40/53*l1an - k*dj1odz/j1[z]* w1[z]*2;\) (*\(momentum\ equation\ for\ ch\)\(+\)*) \), "\ \[IndentingNewLine]", \(\(dw3odz := eontd*n/\((1. *10^21)\) - 55/40*l3an - k*dj3odz/j3[z]* w3[z]*2;\) (*\(momentum\ equation\ for\ ch3\)\(+\)*) \), "\ \[IndentingNewLine]", \(\(dw4odz := eontd*n/\((1. *10^21)\) - 56/40*l4an - k*dj4odz/j4[z]* w4[z]*2;\) (*\(momentum\ equation\ for\ ch4\)\(+\)*) \), "\ \[IndentingNewLine]", \(\(dw5odz := eontd*n/\((1. *10^21)\) - w5[z]*\((1. - f)\)*q5a5*n - 56/16*l5cn - k*dj5odz/j5[z]*w5[z]*2;\) (*ar + momentum\ equation*) \)}], "Input"], Cell[BoxData[ \(\(start\ = \ Dispatch[{je[z] \[Rule] 1.0, we[z] -> 100. , j1[z] -> 1. *10^\(-6\), w1[z] -> \ 1. , j3[z] -> 1. *10^\(-6\), w3[z] -> \ 1. , j4[z] -> 1. *10^\(-6\), w4[z] -> \ 1. , j5[z] -> 1. *10^\(-6\), w5[z] -> \ 1. , jd[z] -> 1. *10^\(-6\), js[z] -> 1. *10^\(-6\), vo[z] -> \ 0. , jp1[z] -> 1. *10^\(-6\), jp3[z] -> 1. *\ 10^\(-6\), jpd[z] -> 1. *10^\(-6\), jpe[z] -> \ 1. , f \[Rule] 0.5, n\ \[Rule] \ 3.3*10^21, eontd\ \[Rule] \ 2000. , k\ \[Rule] 1. }];\)\)], "Input", Background->RGBColor[0, 1, 1]], Cell[BoxData[ \(djeodz\ /. \ start\)], "Input"], Cell[BoxData[ \(dweodz /. \ start\)], "Input"], Cell[BoxData[ \(dj1odz /. \ start\)], "Input"], Cell[BoxData[ \(dw1odz /. \ start\)], "Input"], Cell[BoxData[ \(dj3odz /. \ start\)], "Input"], Cell[BoxData[ \(dw3odz /. \ start\)], "Input"], Cell[BoxData[ \(dj4odz /. \ start\)], "Input"], Cell[BoxData[ \(dw4odz /. \ start\)], "Input"], Cell[BoxData[ \(dj5odz /. \ start\)], "Input"], Cell[BoxData[ \(dw5odz /. \ start\)], "Input"], Cell[BoxData[ \(djdodz /. \ start\)], "Input"], Cell[BoxData[ \(djsodz /. \ start\)], "Input"], Cell["Case conditions", "Subsection"], Cell[BoxData[{ \(\(n = 3.3*10^21;\)\ \ (*m^3*) \), "\[IndentingNewLine]", \(\(eontd = 2000. ;\)\ (*Td*) \), "\[IndentingNewLine]", \(\(f = 0.50;\)\), "\[IndentingNewLine]", \(\(k = 1. ;\)\)}], "Input", Background->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell[BoxData[ \(aea5e\ /. \ we[z]\ \[Rule] \ 100\)], "Input"], Cell[BoxData[ \(aecie\ /. \ we[z]\ \[Rule] \ 100\)], "Input"] }, Open ]], Cell["Adjustment of we[0] to give small we at cathode", "Text"], Cell[BoxData[ \(solution = NDSolve[{\(je'\)[z] \[Equal] djeodz, je[0] \[Equal] 1.0, \(we'\)[z] \[Equal] dweodz, we[0] \[Equal] 58.18}, {je[z], we[z]}, {z, 0.0, 0.04}]\)], "Input"], Cell[BoxData[ \(\(we[z]\ /. \ solution\)\ /. \ z\ \[Rule] \ 0.04\)], "Input"], Cell[BoxData[ \(\(Plot[ Evaluate[{\(we[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y}], {y, 0, 0.04}, PlotRange\ \[Rule] \ {{0. , 0.04}, {0, Automatic}}];\)\)], "Input"], Cell["Search for error when f >= 0.12", "Section"], Cell[CellGroupData[{ Cell[TextData[{ "solution = NDSolve[{\nje'[z]==djeodz, (*electron \ flux*) \nje[0] == 1.0,\nj1'[z]==dj1odz, (*ch+ flux*)\nj1[0] == 1.*10^-6,\n\ j3'[z]==dj3odz, (*ch3+ flux*)\nj3[0] == 1.*10^-6,\nj4'[z]==dj4odz, (*ch4+ \ flux*) \nj4[0] == 1.*10^-6,\nj5'[z]==dj5odz, (*ar+ flux*)\n\ j5[0] == 1.*10^-6,\nwe'[z]==dweodz, (*electron energy equation*) \nwe[0] \ == 58.18, (*", StyleBox["adjust for low we[cath], 49.39 for f = 0.5 and 59.11 for f = 0.1", FontColor->RGBColor[1, 0, 0]], "*)\nw1'[z]==dw1odz, (*momentum equation for ch+*) \ \nw1[0] == 1.,\nw3'[z]==dw3odz, (*momentum equation for ch3+*)\n\ w3[0] == 1.,\nw4'[z]==dw4odz, (*momentum equation for ch4+*)\nw4[0] == \ 1.,\nw5'[z]==dw5odz, (*ar+ momentum equation*)\n\ w5[0] == 1.},\n{je[z],we[z],j1[z],w1[z],j3[z],w3[z],j4[z],w4[z],j5[z],w5[z]},\ \n{z,0.0,0.04}]" }], "Input", Evaluatable->False], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{\(je[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}], ",", RowBox[{\(we[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}], ",", RowBox[{\(j1[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}], ",", RowBox[{\(w1[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}], ",", RowBox[{\(j3[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}], ",", RowBox[{\(w3[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}], ",", RowBox[{\(j4[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}], ",", RowBox[{\(w4[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}], ",", RowBox[{\(j5[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}], ",", RowBox[{\(w5[z]\), "\[Rule]", RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 0.04`}}, "<>"]\), False, Editable->False], "[", "z", "]"}]}]}], "}"}], "}"}]], "Output"] }, Open ]], Cell[BoxData[ \(\(Plot[ Evaluate[\(j1[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y], {y, 0. , 0.04}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.45], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ]}, PlotRange\ \[Rule] \ {{0. , 0.04}, {0. , 1.0}}];\)\)], "Input"], Cell[BoxData[ \(\(Plot[ Evaluate[{\(je[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y\ , \(j1[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(j3[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(j4[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(j5[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y\ }], {y, 0. , 0.04}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.45], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ]}, PlotRange\ \[Rule] \ {{0. , 0.04}, {0. , 1.0}}];\)\)], "Input"], Cell[TextData[{ "solution = NDSolve[{\nje'[z]==djeodz, (*electron \ flux*) \nje[0] == 1.0,\nj1'[z]==dj1odz, (*ch+ flux*)\n\ j1[0] == 1.*10^-6,\nj3'[z]==dj3odz, (*ch3+ flux*)\n\ j3[0] == 1.*10^-6,\nj4'[z]==dj4odz, (*ch4+ flux*) \ \nj4[0] == 1.*10^-6,\nj5'[z]==dj5odz, (*ar+ flux*)\n\ j5[0] == 1.*10^-6,\njs'[z]==djsodz, (*cmhn+, m not 1 \ n not 1,3*)\njs[0] == 1.*10^-6, \njd'[z]==djdodz, \ (*fast ch flux*)\njd[0] == 1.*10^-6,\nwe'[z]==dweodz, \ (*electron energy equation*) \nwe[0] == 58.18, (*", StyleBox["adjust for low we[cath], 49.39 for f = 0.5 and 59.11 for f = 0.1", FontColor->RGBColor[1, 0, 0]], "*)\nw1'[z]==dw1odz, (*momentum equation for ch+*) \ \nw1[0] == 1.,\nw3'[z]==dw3odz, (*momentum \ equation for ch3+*)\nw3[0] == 1.,\nw4'[z]==dw4odz, \ (*momentum equation for ch4+*)\nw4[0] == 1.,\nw5'[z]==dw5odz, \ (*ar+ momentum equation*)\nw5[0] == 1.},\n\ {je[z],we[z],j1[z],w1[z],j3[z],w3[z],j4[z],w4[z],j5[z],w5[z],jd[z],js[z]},\n\ {z,0.0,0.04}]" }], "Input"], Cell[BoxData[ \(\(we[z]\ /. \ solution\)\ /. \ z\ \[Rule] \ 0.04\)], "Input"], Cell[BoxData[ \(\(Plot[ Evaluate[{\(je[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y\ , \(j1[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(j3[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(j4[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(j5[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(jd[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(js[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y\ }], {y, 0, 0.04}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.45], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ]}, PlotRange\ \[Rule] \ {{0. , 0.04}, {0, 1.0}}];\)\)], "Input"], Cell[BoxData[ \(\(Plot[ Evaluate[{\(we[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(w1[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(w3[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(w4[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(w5[z]\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y\ }], {y, 0, 0.04}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.5], Hue[0.7], Hue[0.8], Hue[1. ], Hue[]}, PlotRange\ \[Rule] \ {{0. , 0.04}, {0, Automatic}}];\)\)], "Input"], Cell[BoxData[ \(\(Plot[ Evaluate[{\(djeodz\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y\ , \(dj1odz\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(dj3odz\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(dj4odz\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(dj5odz\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(djdodz\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y, \(djsodz\ /. \ solution\)\ /. \ z\ -> \ 0.04\ - y\ }], {y, 0, 0.04}, PlotStyle \[Rule] {Hue[0.1], Hue[0.3], Hue[0.45], Hue[0.55], Hue[0.7], Hue[0.8], Hue[1. ]}, PlotRange\ \[Rule] \ {{0. , 0.04}, {\(-10. \), 10. }}];\)\)], "Input"], Cell[BoxData[{ \(\(ip1[z] := \((a1ap5 + a1cp4)\)* j1[z]/\((1 + n*f/\((9. *10^22)\))\);\) (*\(\(ch\)\(+\)\)\ \[Rule] ch \((432)\)\ flux*) \), "\[IndentingNewLine]", \(\(ip3[z] := \((a3ap5 + a3cp4)\)* j3[z]/\((1 + n*f/\((9. *10^22)\))\);\) (*\(\(ch3\)\(+\)\)\ \[Rule] ch \((432)\)\ flux*) \), "\[IndentingNewLine]", \(\(ipd[z] := \((adcpc + adapa)\)* jd[z]/\((1 + n*f/\((9. *10^22)\))\);\) (*fast\ ch \[Rule] ch \((432)\)\ flux*0*) \), "\[IndentingNewLine]", \(\(ipe[z] := \((aecpo + \((1. - f)\)*n*qeapa)\)* je[z]/\((1 + n*f/\((9. *10^22)\))\);\) (*e \[Rule] ch \((432)\)\ flux*) (*\(+e\) \[Rule] ar\ light\ leakage\ \((432)\)\ flux*) \)}], "Input"], Cell["\<\ We normalize the theoretical apparent excitation coefficients to the gas \ density and convert to units of 10^-22 m^2.\ \>", "Subsubtitle"], Cell[BoxData[ \(\(Plot[ Evaluate[\(10^22/n*ipe[z]\ /. \ solution\)\ \ /. \ z\ -> \ 0.04\ - 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Setting q3ad5 = 1e-21 gives better agreement with the shape, \ but leaves the magnitude too small by a factor of 1.5 to 2. The CH(A) \ production for this mixture is not reduced noticeably by reducing qdcpc to \ 2.5e-26, presumably because of the small CH4 concentration. 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