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We omit excited state-excited state, e.g., \ metastable-metastable, and thermal emission effects.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Setup notebook environment", "Text"], Cell["ClearAll[\"Global`*\"]; ", "Input"], Cell[CellGroupData[{ Cell["Remove[\"Global`*\"]; ", "Input"], Cell[BoxData[ \(Remove::"rmnsm" \(\(:\)\(\ \)\) "There are no symbols matching \"\!\(\"Global`*\"\)\"."\)], "Message"] }, Open ]], Cell["startclock = SessionTime[];", "Input"], Cell["Off[General::spell]", "Input"], Cell["Off[General::spell1]", "Input"], Cell["Off[NumberForm::sigz]", "Input"], Cell["<< Graphics`Graphics`", "Input"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(now\ = \ StringForm["\<``/``/`` ``:``:``\>", \(Date[]\)[\([2]\)], \ \(Date[]\)[\([3]\)], \(Date[]\)[\([1]\)], \(Date[]\)[\([4]\)], \ \(Date[]\)[\([5]\)], \(Date[]\)[\([6]\)]]\)], "Input"], Cell[BoxData[ InterpretationBox["\<\"\\!\\(11\\)/\\!\\(9\\)/\\!\\(2000\\) \ \\!\\(22\\):\\!\\(0\\):\\!\\(18\\)\"\>", StringForm[ "``/``/`` ``:``:``", 11, 9, 2000, 22, 0, 18], Editable->False]], "Output"] }, Open ]], Cell["I. Outline of model.", "Subsection", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ We will use the output of the other Mathematica programs to obtain \ expressions for the static and changing components of the flux of resonance \ photons, ions, and metastables at the cathode caused by space charge induced \ changes in the electric field. These will then be combined using the gain \ equation and solved for the NDVCR.\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ II. Space charge electric field and voltage change (Phelps et al, \ 1993)\ \>", "Subsection", ImageRegion->{{-0, 1}, {0, 1}}], Cell["IIA Space charge electric field", "Subsubsection", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ The space charge electric field, esc, is found by integrating \ Poisson's 1D equation assuming that only positive ions created by the \ electron avalanche contribute. Let esc = Es - Ec = es -ec, use the \ unperturbed result that the positive ion flux is fp = feo*(Exp[alion*n*z]-1) \ , and neglect electrons.\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ esc = Simplify[Integrate[feo*Exp[aliono*no*d]*con *(1 - \ Exp[aliono*no* (y - d)]), {y, 0 , z}] ]\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ esc[z_] := (con*feo/(aliono*no))* (1 - E^(aliono*no*z) + aliono*E^(aliono*d*no)*no*z)\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["where", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["con := qe/(epsilono*wp)", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["IIB Calculation of change in discharge voltage", "Subsubsection", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ The change in voltage in the space between electrodes, delvs = \ Integrate[(Es -E c),{z,0,z}] is\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["delvs = -Simplify[Integrate[ esc , {z, 0, z}]]", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ delvs = -(con*feo*(2 - 2*E^(aliono*no*z) + 2*aliono*no*z + aliono^2*E^(aliono*d*no)*no^2*z^2))/ (2*aliono^2*no^2) /. aliono -> alid/no/d //Cancel\ \>", \ "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["or", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ delvs := (con*feo*(-2*d^2 + 2*d^2*E^((alid*z)/d) - 2*alid*d*z - alid^2*E^alid*z^2))/(2*alid^2)\ \>", "Input",\ ImageRegion->{{0, 1}, {0, 1}}], Cell["delvsd = Simplify[ delvs /. z -> d]", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["gives the change in voltage between electrodes as", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["\<\ delvsd = -(con*feo*(2 - 2*E^(aliono*d*no) + 2*aliono*d*no + aliono^2*d^2*E^(aliono*d*no)*no^2))/ (2*aliono^2*no^2) /. aliono -> alid/no/d //Cancel\ \>", \ "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["or", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(delvsd := \(con\ d\^2\ \((\(-2\) - 2\ alid + 2\ \[ExponentialE]\^alid - \ alid\^2\ \[ExponentialE]\^alid)\)\ feo\)\/\(2\ alid\^2\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["Also ", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ Integrate[(es[z] - eo),{z,0,d}] := Integrate[esc[z],{z,0,d}] + \ (ec-eo)*d\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["or delv = delvsd + (ec - eo)*d", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["or ", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["(ec - eo) = (delvsd - delv)/d", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["These agree with Phelps, et al (1993).", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["III. Perturbation of gain", "Subsection", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["\<\ We now need to do a series expansion of the loop gain about the \ low-current, steady-state limit or breakdown condition. The gain and the \ first terms of the expansion are given by\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["\<\ gain = fes*(gamrph*photonflux + gamnph*nonresphflux + \ gammet*metastableflux + gami*ionflux) /. {fes -> feso - (a*dfesdeon*(ec - eo))/no, gami -> gamio - (a*dgamideon*(ec - eo))/no, photonflux -> resfluxo + a*(resdelfluxfeo*feo + resdelfluxdelv*delv), nonresphflux -> nonresfluxo + a*(nonresdelfluxfeo*feo + \ nonresdelfluxdelv*delv), metastableflux -> normfmo + (a*metdelfluxfeo*feo)/((vb*alid)/almd) + \ (a*metdelfluxdelv*delv)/(vb/almd), ionflux -> ionfluxo + a*(iondelfluxfeo*feo + iondelfluxdelv*delv)} /. {ec -> eo + (feo*normdelvsd1 - delv)/d, dfesdeon -> (feshat*feso)/eono, dgamideon -> (gamihat*gamio)/eono, no -> vb/(eono*d)}\ \>", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ where the delflux quantities are specified below and the \ unperturbed fluxes are normalized to feo. Note that the normalization for \ the metdelflux.... terms is different than that for the other ...delflux... \ terms. Note the negative sign in front of dfesdeon because dfesdeon is \ positive and ec - eo is negative. Also note that eono is in v-m^2 not Td. \ When we use E/n in Td we will use the notation \"eontd\". Here the \ metastable notation is that of NDVCRMET.MA of 6/25/96 at 19:10. Extracting \ the zero order terms in the perturbation parameter \"a\" gives\ \>", \ "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["gaino = Coefficient[gain, a, 0]", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["which gives", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(\(gaino = feso\ gamio\ ionfluxo + feso\ gamnph\ nonresfluxo + feso\ gammet\ normfmo + feso\ gamrph\ resfluxo;\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["\<\ This will be set equal to 1 to determine the relation between E/n \ and nd at breakdown\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["delgain = Coefficient[gain, a, 1]", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ Setting delgain = 0 from the steady-state condition and solving for \ delv -> delvgain gives\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ delvgain = -(Coefficient[delgain, delv, 0]/Coefficient[delgain, \ delv, 1])\ \>", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ Replace feo by feo = jt*Exp[-aliono*no*d]/qe = i/area/qe. Define \ the NDVCR by ndvcrsum = - delvgain/(i*area) = - \ delvgain/(feo*qe*area*Exp[alid]). Thus a decrease in voltage gives a \ positive number for NDVCR. We choose this sign to allow lograthmic plots of \ the NDVCR values. \ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["\<\ ndvcrsum = -(Apart[(Numerator[delvgain]*vb*alid)/(feso*feo)]/ (alid*qe*area*Exp[alid]*Apart[(Denominator[delvgain]*vb)/feso])); \ \>", \ "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ The remainder of this notebook is evaulated with no nonresonant \ photon contribution\ \>", "Subsubtitle", TextAlignment->Center, ImageRegion->{{-0, 1}, {0, 1}}], Cell["gamnph=0;", "Input"], Cell["Also,", "SmallText"], Cell["gamrph=gamph;", "Input"], Cell["ndvcrsum /. {gamnph -> 0, gamrph -> gamph}", "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["gives", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["\<\ ndvcrsum = (almd*gammet*metdelfluxfeo - alid*feshat*gamio*ionfluxo* normdelvsd1 - alid*gamihat*gamio*ionfluxo*normdelvsd1 - alid*feshat*gammet*normdelvsd1*normfmo - alid*feshat*gamph*normdelvsd1* resfluxo + alid*gamio*iondelfluxfeo*vb + alid*gamph*resdelfluxfeo*vb)/ (alid*area*E^alid*qe*(feshat*gamio*ionfluxo + gamihat*gamio*ionfluxo + almd*gammet*metdelfluxdelv + feshat*gammet*normfmo + feshat*gamph*resfluxo + gamio*iondelfluxdelv*vb + gamph*resdelfluxdelv*vb)); \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["\<\ The following group of numerator and denominator formulas were used \ to look at the singular behavior of the NDVCR results.\ \>", "Subsubsection"], Cell["The numerator of ndcvrsum is ", "SmallText"], Cell[BoxData[ \(\(numndvcrsum = Numerator[ndvcrsum];\)\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["and for feshat =0 it gives", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(numndvcrsum1 = numndvcrsum /. \[InvisibleSpace]feshat \[Rule] 0\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ The numerator of ndvcrsum when gammi is constant and only fes \ varies with E/n is\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(numndvcrfes = numndvcrsum /. \[InvisibleSpace]{iondelfluxfeo \[Rule] 0, metdelfluxfeo \[Rule] 0, resdelfluxfeo \[Rule] 0, gamihat \[Rule] 0}\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(numndvcrfes1 = ndvcrsum /. \[InvisibleSpace]{iondelfluxfeo \[Rule] 0, metdelfluxfeo \[Rule] 0, resdelfluxfeo \[Rule] 0, gamihat \[Rule] 0}\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ WHY FESHAT =0? The numerator of ndvcrsum when only metastables \ contribute to electron production at the cathode and fes is constant is\ \>", \ "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(numndvcrmet1 = numndvcrsum1 /. \[InvisibleSpace]{gamio \[Rule] 0, gamph \[Rule] 0}\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ WHY FESHAT =0?The numerator of ndvcrsum when only resonant photons \ contribute to electron production at the cathode and fes is constant is\ \>", \ "SmallText"], Cell[BoxData[ \(numndvcrrph1 = numndvcrsum1 /. \[InvisibleSpace]{gamio \[Rule] 0, gammet \[Rule] 0}\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ WHY FESHAT =0?The numerator of ndvcrsum when only ions contribute \ to electron production at the cathode and fes is constant is\ \>", "SmallText",\ ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(numndvcrion1 = numndvcrsum1 /. \[InvisibleSpace]{gamph \[Rule] 0, gammet \[Rule] 0}\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["The denominatior of ndvcrsum is", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(denndvcrsum = Denominator[ndvcrsum]\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["and for feshat = 0 it gives", "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[CellGroupData[{ Cell[BoxData[ \(denndvcrsum1 = denndvcrsum /. \[InvisibleSpace]feshat \[Rule] 0\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(denndvcrsum\)], "Output"] }, Open ]], Cell["\<\ The denominator of ndvcrsum when only fes varies with E/n, e.g., \ gammi is constant, is\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(denndvcrfes = denndvcrsum /. \[InvisibleSpace]{iondelfluxdelv \[Rule] 0, metdelfluxdelv \[Rule] 0, resdelfluxdelv \[Rule] 0, gamihat \[Rule] 0}\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ WHY FESHAT =0?The numerator of ndvcrsum when only metastables \ contribute to electron production at the cathode and fes is constant is\ \>", \ "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(denndvcrmet1 = denndvcrsum1 /. \[InvisibleSpace]{gamio \[Rule] 0, gamph \[Rule] 0}\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ WHY FESHAT =0?The numerator of ndvcrsum when only resonant photons \ contribute to electron production at the cathode and fes is constant is\ \>", \ "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(denndvcrrph1 = denndvcrsum1 /. \[InvisibleSpace]{gamio \[Rule] 0, gammet \[Rule] 0}\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ WHY FESHAT =0?The numerator of ndvcrsum when only ions contribute \ to electron production at the cathode and fes is constant isgives\ \>", \ "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(denndvcrion1 = denndvcrsum1 /. \[InvisibleSpace]{gamph \[Rule] 0, gammet \[Rule] 0}\)], "Input", PageWidth->Infinity, Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}] }, Open ]], Cell["NDVCR for resonance photons including feshat", "Subsubsection", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(resfluxo := \(2.86\ alpd\ \((\(-1\) + \ \[ExponentialE]\^alid)\)\)\/\(\((5.71 + 1. \ alid\^\(2/3\))\)\ alid\ \((1 + \ qnorm)\)\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["\<\ ndvcrrph = Cancel[ndvcrsum /. {alionhat -> 0, almonhat -> 0, gammet \ -> 0, gamio -> 0}]\ \>", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(ndvcrrph := \(\(-\((delvsd\ feshat\ resfluxo)\)\) + feo\ resdelfluxfeo\ \ vb\)\/\(area\ \[ExponentialE]\^alid\ feo\ qe\ \((feshat\ resfluxo + \ resdelfluxdelv\ vb)\)\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["For feshat = 0.", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["ndvcrrph1 = ndvcrrph /. feshat -> 0", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(ndvcrrph1 := resdelfluxfeo\/\(area\ \[ExponentialE]\^alid\ qe\ resdelfluxdelv\)\)], \ "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["\<\ From our empirical fits to the flux of resonance photons at the \ cathode we have the following two components\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(\(resdelfluxfeo := \(\((\(0.4\ \[ExponentialE]\^\(alid\/1.1\)\ alponhat\ \)\/\(\((1 + \((0.2\/alid)\)\^4.5)\)\ \((1 + qnorm\/0.8)\)\) + \(0.1\ \ \[ExponentialE]\^alid\ alionhat\)\/\(\((1 + \((3.2\/alid)\)\^9)\)\^0.2\ \((1 \ + qnorm\/0.8)\)\))\)\ \((\[ExponentialE]\^alid - 1)\)\ con\ d\^2\)\/\(alid\ \ vb\);\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell[BoxData[ \(\(resdelfluxdelv := \(\((\(0.12\ \((alid\/0.5)\)\^1.05\ alionhat\)\/\(1 \ + qnorm\/0.8\) + \(0.48\ alponhat\)\/\(\((1 + 0.175\ alid\^0.67)\)\ \((1 + \ qnorm)\)\))\)\ \((\[ExponentialE]\^alid - 1)\)\)\/\(alid\ vb\);\)\)], "Input",\ PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["NDVCR for metastables including feshat", "Subsubsection", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["\<\ From our analytical calculations of the flux of metastables at the \ cathode we have the following three components: the dc component normfmo*feo and the perturbation terms metdelfluxdelv*delv*feo/vb*almd and metdelfluxfeo*feo^2/vb/alid*almd \ where\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(\(normfmo = {{\(almd\ \((\(-alid\) + c + alid\ \[ExponentialE]\^\(2\ \ c\) + c\ \[ExponentialE]\^\(2\ c\) - 2\ c\ \[ExponentialE]\^\(alid + c\))\)\)\ \/\(\((alid\^2 - c\^2)\)\ \((1 - \[ExponentialE]\^\(2\ c\))\)\)}};\)\)], \ "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["\<\ Empirical approximations to the two perturbation functions \ are:\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ metdelfluxdelv := (-(alid^3*alihat) + alid^3*almhat + \ 2*alid^2*alihat*c - alid^2*almhat*c - alid*alihat*c^2 - alid*almhat*c^2 + almhat*c^3 + alid^3*alihat*E^(2*c) - alid^3*almhat*E^(2*c) + 2*alid^2*alihat*c*E^(2*c) - alid^2*almhat*c*E^(2*c) + alid*alihat*c^2*E^(2*c) + alid*almhat*c^2*E^(2*c) + almhat*c^3*E^(2*c) - \ 4*alid^2*alihat*c*E^(alid + c) + 2*alid^3*alihat*c*E^(alid + c) + 2*alid^2*almhat*c*E^(alid + c) - 2*alid*alihat*c^3*E^(alid + c) - 2*almhat*c^3*E^(alid + c))/((alid - c)^2*(alid + c)^2*(-1 + E^(2*c))); \ \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["\<\ metdelfluxfeo := (2*alid^7*alihat*con*d^2 - 2*alid^7*almhat*con*d^2 \ - 5*alid^6*alihat*c*con*d^2 + 3*alid^6*almhat*c*con*d^2 + 2*alid^5*alihat*c^2*con*d^2 + 3*alid^5*almhat*c^2*con*d^2 + 4*alid^4*alihat*c^3*con*d^2 - 6*alid^4*almhat*c^3*con*d^2 - 4*alid^3*alihat*c^4*con*d^2 + alid^2*alihat*c^5*con*d^2 + 3*alid^2*almhat*c^5*con*d^2 - alid*almhat*c^6*con*d^2 - 4*alid^7*alihat*con*d^2*E^alid + 4*alid^7*almhat*con*d^2*E^alid + 12*alid^6*alihat*c*con*d^2*E^alid - 8*alid^6*almhat*c*con*d^2*E^alid - 11*alid^5*alihat*c^2*con*d^2*E^alid - alid^5*almhat*c^2*con*d^2*E^alid + \ alid^4*alihat*c^3*con*d^2*E^alid + 10*alid^4*almhat*c^3*con*d^2*E^alid + \ 3*alid^3*alihat*c^4*con*d^2*E^alid - 4*alid^3*almhat*c^4*con*d^2* E^alid - alid^2*alihat*c^5*con*d^2*E^alid - \ 2*alid^2*almhat*c^5*con*d^2* E^alid + alid*almhat*c^6*con*d^2*E^alid - 2*alid^7*alihat*con*d^2* E^(2*c) + 2*alid^7*almhat*con*d^2*E^(2*c) - 5*alid^6*alihat*c*con*d^2* E^(2*c) + 3*alid^6*almhat*c*con*d^2*E^(2*c) - 2*alid^5*alihat*c^2*con*d^2*E^(2*c) - 3*alid^5*almhat*c^2*con*d^2* E^(2*c) + 4*alid^4*alihat*c^3*con*d^2*E^(2*c) - 6*alid^4*almhat*c^3*con*d^2*E^(2*c) + 4*alid^3*alihat*c^4*con*d^2* E^(2*c) + alid^2*alihat*c^5*con*d^2*E^(2*c) + 3*alid^2*almhat*c^5*con*d^2*E^(2*c) + alid*almhat*c^6*con*d^2*E^(2*c) + 8*alid^6*alihat*c*con*d^2*E^(alid + c) - 8*alid^7*alihat*c*con*d^2* E^(alid + c) - 8*alid^6*almhat*c*con*d^2*E^(alid + c) - 2*alid^4*alihat*c^3*con*d^2*E^(alid + c) + 18*alid^5*alihat*c^3*con*d^2* E^(alid + c) + 18*alid^4*almhat*c^3*con*d^2*E^(alid + c) - 8*alid^2*alihat*c^5*con*d^2*E^(alid + c) - 12*alid^3*alihat*c^5*con*d^2* E^(alid + c) - 12*alid^2*almhat*c^5*con*d^2*E^(alid + c) + 2*alihat*c^7*con*d^2*E^(alid + c) + 2*alid*alihat*c^7*con*d^2* E^(alid + c) + 2*almhat*c^7*con*d^2*E^(alid + c) - 22*alid^6*alihat*c*con*d^2*E^(2*alid + c) + 16*alid^7*alihat*c*con*d^2* E^(2*alid + c) - 4*alid^8*alihat*c*con*d^2*E^(2*alid + c) + 18*alid^6*almhat*c*con*d^2*E^(2*alid + c) - 8*alid^7*almhat*c*con*d^2* E^(2*alid + c) - 8*alid^4*alihat*c^3*con*d^2*E^(2*alid + c) - 20*alid^5*alihat*c^3*con*d^2*E^(2*alid + c) + 9*alid^6*alihat*c^3*con* d^2*E^(2*alid + c) - 26*alid^4*almhat*c^3*con*d^2*E^(2*alid + c) + 18*alid^5*almhat*c^3*con*d^2*E^(2*alid + c) + 8*alid^2*alihat*c^5*con* d^2*E^(2*alid + c) + 4*alid^3*alihat*c^5*con*d^2*E^(2*alid + c) - 6*alid^4*alihat*c^5*con*d^2*E^(2*alid + c) + 10*alid^2*almhat*c^5*con* d^2*E^(2*alid + c) - 12*alid^3*almhat*c^5*con*d^2*E^(2*alid + c) - 2*alihat*c^7*con*d^2*E^(2*alid + c) + alid^2*alihat*c^7*con*d^2* E^(2*alid + c) - 2*almhat*c^7*con*d^2*E^(2*alid + c) + 2*alid*almhat*c^7*con*d^2*E^(2*alid + c) + 4*alid^7*alihat*con*d^2* E^(alid + 2*c) - 4*alid^7*almhat*con*d^2*E^(alid + 2*c) + 12*alid^6*alihat*c*con*d^2*E^(alid + 2*c) - 8*alid^6*almhat*c*con*d^2* E^(alid + 2*c) + 11*alid^5*alihat*c^2*con*d^2*E^(alid + 2*c) + alid^5*almhat*c^2*con*d^2*E^(alid + 2*c) + alid^4*alihat*c^3*con*d^2* E^(alid + 2*c) + 10*alid^4*almhat*c^3*con*d^2*E^(alid + 2*c) - 3*alid^3*alihat*c^4*con*d^2*E^(alid + 2*c) + \ 4*alid^3*almhat*c^4*con*d^2* E^(alid + 2*c) - alid^2*alihat*c^5*con*d^2*E^(alid + 2*c) - 2*alid^2*almhat*c^5*con*d^2*E^(alid + 2*c) - alid*almhat*c^6*con*d^2* E^(alid + 2*c) + 4*alid^8*alihat*normdelvsd1 - 4*alid^8*almhat*normdelvsd1 - 8*alid^7*alihat*c*normdelvsd1 + 4*alid^7*almhat*c*normdelvsd1 - alid^6*alihat*c^2*normdelvsd1 + 9*alid^6*almhat*c^2*normdelvsd1 + 10*alid^5*alihat*c^3*normdelvsd1 - 9*alid^5*almhat*c^3*normdelvsd1 - 4*alid^4*alihat*c^4*normdelvsd1 - 6*alid^4*almhat*c^4*normdelvsd1 - 2*alid^3*alihat*c^5*normdelvsd1 + 6*alid^3*almhat*c^5*normdelvsd1 + alid^2*alihat*c^6*normdelvsd1 + alid^2*almhat*c^6*normdelvsd1 - alid*almhat*c^7*normdelvsd1 - 4*alid^8*alihat*E^(2*c)*normdelvsd1 + 4*alid^8*almhat*E^(2*c)* normdelvsd1 - 8*alid^7*alihat*c*E^(2*c)*normdelvsd1 + 4*alid^7*almhat*c*E^(2*c)*normdelvsd1 + alid^6*alihat*c^2*E^(2*c)* normdelvsd1 - 9*alid^6*almhat*c^2*E^(2*c)*normdelvsd1 + 10*alid^5*alihat*c^3*E^(2*c)*normdelvsd1 - 9*alid^5*almhat*c^3*E^(2*c)* normdelvsd1 + 4*alid^4*alihat*c^4*E^(2*c)*normdelvsd1 + 6*alid^4*almhat*c^4*E^(2*c)*normdelvsd1 - 2*alid^3*alihat*c^5*E^(2*c)* normdelvsd1 + 6*alid^3*almhat*c^5*E^(2*c)*normdelvsd1 - alid^2*alihat*c^6*E^(2*c)*normdelvsd1 - alid^2*almhat*c^6*E^(2*c)* normdelvsd1 - alid*almhat*c^7*E^(2*c)*normdelvsd1 + 16*alid^7*alihat*c*E^(alid + c)*normdelvsd1 - 8*alid^8*alihat*c*E^(alid + c)*normdelvsd1 - 8*alid^7*almhat*c*E^(alid + c)*normdelvsd1 - 20*alid^5*alihat*c^3* E^(alid + c)*normdelvsd1 + 18*alid^6*alihat*c^3*E^(alid + c)* normdelvsd1 + 18*alid^5*almhat*c^3*E^(alid + c)*normdelvsd1 + 4*alid^3*alihat*c^5*E^(alid + c)*normdelvsd1 - 12*alid^4*alihat*c^5*E^(alid + c)*normdelvsd1 - 12*alid^3*almhat*c^5*E^(alid + c)*normdelvsd1 + 2*alid^2*alihat*c^7*E^(alid + c)*normdelvsd1 + 2*alid*almhat*c^7*E^(alid + c)*normdelvsd1)/((alid - c)^3*(2*alid - c)* (alid + c)^3*(2*alid + c)*(-1 + E^(2*c))); \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["where", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(\(normdelvsd1 = \(-\(\(con\ d\^2\ \((2 + 2\ alid - 2\ \[ExponentialE]\^alid + alid\^2\ \[ExponentialE]\^alid)\)\)\/\(2\ \ alid\^2\)\)\);\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell[BoxData[ \(con := qe\/\(epsilono\ wp\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["alihat = alionhat;", "Input"], Cell["and", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["almhat = almonhat;", "Input"], Cell["\<\ ndvcrmet = Cancel[ndvcrsum /. {alionhat -> 0, alrphnhat -> 0, \ gamrph -> 0, gamio -> 0}];\ \>", "Input", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["\<\ ndvcrmet1 = Cancel[ndvcrsum /. {alionhat -> 0, alrphnhat -> 0, \ gamrph -> 0, gamio -> 0, feshat -> 0}];\ \>", "Input", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["Ion fluxes", "Subsubsection", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ From our analytical calculation of the ion flux at the cathode we \ have the following two components\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(\(ionfluxo := \[ExponentialE]\^alid - 1;\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ delionflux = Together[(alionhat*E^alid*(2*alid^2*delv + \ 2*alid^2*delvsd + 2*con*d^2*feo + 2*alid*con*d^2*feo - 2*con*d^2*E^alid*feo + alid^2*con*d^2*E^alid*feo))/(2*alid*vb)]; \ \>", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["gives", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(\(iondelfluxfeo = 0;\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["and", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["iondelfluxdelv = Coefficient[delionflux, delv, 1]", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["gives", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[BoxData[ \(\(iondelfluxdelv = \(alid\ alionhat\ \[ExponentialE]\^alid\)\/vb;\)\)], \ "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Times New Roman", Background->GrayLevel[1]], Cell["why no feshat terms???", "Subsubtitle", TextAlignment->Center, ImageRegion->{{-0, 1}, {0, 1}}], Cell["NDVCR for ions including feshat", "Subsubsection", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ ndvcrion = Cancel[ndvcrsum /. {almonhat -> 0, resdelflux -> 0, metdelflux -> 0, alponhat -> 0, gamph -> 0, gammet -> 0}]; \ \>", \ "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["gives", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ ndvcrion = (-2*con*d^2*feshat - 2*alid*con*d^2*feshat + 4*con*d^2*E^alid*feshat + 2*alid*con*d^2*E^alid*feshat - alid^2*con*d^2*E^alid*feshat - 2*con*d^2*E^(2*alid)*feshat + alid^2*con*d^2*E^(2*alid)*feshat - 2*con*d^2*gamihat - 2*alid*con*d^2*gamihat + 4*con*d^2*E^alid*gamihat + 2*alid*con*d^2*E^alid*gamihat - alid^2*con*d^2*E^alid*gamihat - 2*con*d^2*E^(2*alid)*gamihat + alid^2*con*d^2*E^(2*alid)*gamihat)/ (2*alid^2*area*E^alid*(alid*alionhat*E^alid - feshat + E^alid*feshat - gamihat + E^alid*gamihat)*qe); \ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["NDVCR for ions with feshat = 0.", "Subsubsection", ImageRegion->{{-0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["\<\ ndvcrion1 = Cancel[ndvcrsum /. {feshat -> 0, almonhat -> 0, \ resdelflux -> 0, metdelflux -> 0, alponhat -> 0, gamph -> 0, gammet -> 0}]\ \>", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["gives", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(\(ndvcrion1 = \(con\ d\^2\ \((\(-1\) + \[ExponentialE]\^alid)\)\ \((2 + \ 2\ alid - 2\ \[ExponentialE]\^alid + alid\^2\ \[ExponentialE]\^alid)\)\ \ gamihat\)\/\(2\ alid\^2\ area\ \[ExponentialE]\^alid\ \((alid\ alionhat\ \ \[ExponentialE]\^alid - gamihat + \[ExponentialE]\^alid\ gamihat)\)\ \ qe\);\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["The latter is the same as in Phelps et al (1993)", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["NDVCR for ions with gamihat = 0 and variable fes.", "Subsubsection", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell[CellGroupData[{ Cell["\<\ ndvcrion2 = Cancel[ndvcrsum /. {gamihat -> 0, almonhat -> 0, \ resdelflux -> 0, metdelflux -> 0, alponhat -> 0, gamph -> 0, gammet -> 0}]\ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \({{\(d\^2\ \[ExponentialE]\^\(-alid\)\ \((\(-1\) + \ \[ExponentialE]\^alid)\)\ \((2 + 2\ alid - 2\ \[ExponentialE]\^alid + alid\^2\ \ \[ExponentialE]\^alid)\)\ feshat\)\/\(2\ alid\^2\ area\ epsilono\ \((alid\ \ alionhat\ \[ExponentialE]\^alid - feshat + \[ExponentialE]\^alid\ feshat)\)\ \ wp\)}}\)], "Output"] }, Open ]], Cell["VI. Data used for calculations:", "Subsection", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ In the following E/n = eontd values are in Td units. Other units \ are MKS. Note that these calculations has been speeded up by making most of \ the previous cells inactive.\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["\<\ From Phelps' model presented at ICPIG '95 Representative \ experimental parameters are\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ d = 0.01; (*m*) area = 0.005; (*m^2*) con = qe/(epsilono*wp); epsilono = 8.85/10^12; qe = 1.602/10^19; \ \>", "Input"], Cell["ai = (ar*4*(lambda/(3*d))^(1/2))/(3*Pi); ", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell[BoxData[ \(ai = N[\(5. \ 10\^8\ 4\ \((104.8\/\(10\^9\ 3\ d\))\)\^0.5\)\/\(3\ \ 3.1416\)]\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(396622.97396588256`\)], "Output"] }, Open ]], Cell["\<\ The theory used in this model gives 0.204*A*(lambda/R)^0.5 = \ 3.2*10^5 for the high pressure limit to the resonance state decay constant. \ This is in reasonable agreement with the value of 3.7*10^5 measured by Payne \ et al., Phys. Rev. A 9, 1050 (1974). Since Payne et al. find no evidence \ for quenching of the resonsnace radiation at pressures up to 10 Torr, we will \ assume that\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(\(qnorm = 0;\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ We need to look at resonance state quenching more carefully, e.g. \ quenching to metastable state that is destroyed by 3-body collisions!!\ \>", \ "Text", ImageRegion->{{-0, 1}, {0, 1}}], Cell["Define eontd = E/n electric field to gas density ratio in Td", \ "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["eontd := v/d/n*1*10^21", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["Photon induced electron yield", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["gamph=0.003;", "Input"], Cell["Metastable induced electron yield", "SmallText", ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[1]], Cell["gammet=0.003;", "Input"], Cell["\<\ Assume contribution of backscattered electron to ionization can be \ neglected, i.e., del = 0.\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(alion := \(5. \ \[ExponentialE]\^\(-\(170\/eontd\)\)\)\/10\^21 + \(3. \ \ \[ExponentialE]\^\(-\(700\/eontd\)\)\)\/10\^20 - \(1.5\ \ \[ExponentialE]\^\(-\(10000\/eontd\)\)\)\/10\^20\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"System", FontSize->10, Background->GrayLevel[1]], Cell[BoxData[ \(alionhat := \(\(5\ \[ExponentialE]\^\(-\(170\/eontd\)\)\ \ 170\)\/\(10\^21\ eontd\) + \(3\ \[ExponentialE]\^\(-\(700\/eontd\)\)\ 700\)\/\ \(10\^20\ eontd\) - \(1.5\ \[ExponentialE]\^\(-\(10000\/eontd\)\)\ \ 10000\)\/\(10\^20\ eontd\)\)\/alion\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["alionhat := 10^-9*eontd^0.0001", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["Electron escape from the cathode is approximated by", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(fes := 1\/\((1 + 100\/eontd)\)\^0.5\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["feshat := eontd*D[fes,eontd]/fes", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(feshat := 50\/\(\((1 + 100\/eontd)\)\ eontd\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["feshat := 10^-19*eontd^0.0001", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ The resonance photon excitation coefficient data is approximated \ by:\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, FontFamily->"System", FontWeight->"Bold", Background->GrayLevel[1]], Cell[BoxData[ \(alpon := \(4. \ \[ExponentialE]\^\(-\(17.5\/eontd\)\)\)\/10\^21 + \(1.5\ \ \[ExponentialE]\^\(-\(150\/eontd\)\)\)\/10\^20 - \(1. \ \ \[ExponentialE]\^\(-\(2000\/eontd\)\)\)\/10\^20\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"System", FontSize->10, Background->GrayLevel[1]], Cell["alponhat = eontd/alpon*D[alpon,eontd]", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(alponhat := \(\(-\(2. \/\(10\^17\ \[ExponentialE]\^\(2000/eontd\)\)\)\) \ + 2.25\/\(10\^18\ \[ExponentialE]\^\(150/eontd\)\) + 7. \/\(10\^20\ \ \[ExponentialE]\^\(17.5/eontd\)\)\)\/\(eontd\ \((\(-\(1. \/\(10\^20\ \ \[ExponentialE]\^\(2000/eontd\)\)\)\) + 1.5\/\(10\^20\ \ \[ExponentialE]\^\(150/eontd\)\) + 4. \/\(10\^21\ \ \[ExponentialE]\^\(17.5/eontd\)\))\)\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["alponhat := 10^-9*eontd^0.0001", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ The ion drift velocity from experiment and theory is approximated \ by:\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, FontFamily->"System", FontWeight->"Bold", Background->GrayLevel[1]], Cell["wp := (4*eontd)/(1 + (0.007*eontd)^1.5)^0.33", "Input"], Cell["\<\ The ion-induced electron yield functions, gami and gamihat, \ are:\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, FontFamily->"System", FontWeight->"Bold", Background->GrayLevel[1]], Cell["\<\ gami := 0. + (0.58*(eontd/30000)^1.3)/(1 + (eontd/30000)^0.5)\ \>", \ "Input"], Cell["\<\ gamihat := (0.58*((1.3*(eontd/30000)^1.3)/(1 + (eontd/30000)^0.5) - \ (0.5*(eontd/30000)^1.8)/(1 + (eontd/30000)^0.5)^2))/gami\ \>", "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["gamihat := 10^-9*eontd^0.0001", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ The Ar metastable parameters are from Klots and Setser (1978) and \ Bretange, Godart, and Peuch (1983):\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}, FontFamily->"System", FontWeight->"Bold", Background->GrayLevel[1]], Cell["\<\ km2 = 1.2/10^21; km3 = 1.3/10^44; kmm = 2./10^15; ndm = 1.7*10^20; amol = 3.*10^5; \ \>", "Input"], Cell["q := km2*no + 1/(1/(km3*no^2) + 1/amol)", "Input"], Cell["b := (((km2*no + 1/(1/(km3*no^2) + 1/amol))*no)/ndm)^0.5", "Input"], Cell["decaycon := q + (ndm*(3.1416/d)^2)/no", "Input"], Cell["c := b*d", "Input"], Cell["\<\ The resonance photon excitation coefficient data is approximated \ by:\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell[BoxData[ \(almon := alpon\/3.75\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(almonhat := alponhat\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["Experimental breakdown data", "Subsubsection", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ The no versus E/n values at breakdown or in the limit of zero \ current from experiment for E/n > 50 Td are given by the empirical relation:\ \>", "SmallText", ImageRegion->{{-0, 1}, {0, 1}}], Cell["\<\ nob := ((7.*10^16)/(eontd/1000)^4 + (1.2*10^20)/(eontd/1000)^1.5 + \ (1.65*10^20)/(eontd/1000)^0.33 + 2.*10^24*(eontd/(7000*(1 + eontd/7000)^2))^8 + \ (1.7*10^19*eontd)/100000)/d\ \>", "Input"], Cell[BoxData[ \(pbmeas := \(nob\ d\ 100\)\/\(3.3\ 10\^22\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ We will need adjust the gamma values of our model to fit this \ result and the NDVCR data.\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell["Calculated breakdown values of no versus E/n", "Subsubsection", ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"System", Background->GrayLevel[1]], Cell["\<\ d = 0.01; vb := (eontd*no*d)/10^21; alid := alion*no*d; alpd := alpon*no*d; almd := almon*no*d; eono := eontd/10^21; c := d*(((km2*no + 1/(1/(km3*no^2) + 1/amol))*no)/ndm)^0.5; feso := fes; gamio := gami; \ \>", "Input"], Cell[BoxData[ \(\(eontd1 = {50, 60, 80, 100, 150, 200, 250, 300, 500, 700, 900, 1200, 1500, 2000, 3000, 5000, 10000, 20000, 50000, 100000};\)\)], "Input",\ PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ Note that the next seven steps are no longer valid if we change any \ of the input data. However, when evaluating the various NDVCR they save time \ by not recalulating noc each time.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["gaino1[j_] = Flatten[(gaino /. eontd -> eontd1[[j]])];", "Input"], Cell[BoxData[ \(Part::"pspec" \(\(:\)\(\ \)\) "Part specification \!\(j\) is neither an integer nor a list of \ integers."\)], "Message"] }, Open ]], Cell["\<\ FindRoot[gaino1[1][[1]] == 1., {no, {1.*10^18,1.*10^22}}, AccuracyGoal ->4]\ \>", "Input", Evaluatable->False], Cell[CellGroupData[{ Cell["\<\ nocrule = Table[FindRoot[(gaino1[j][[1]] /. eontd -> eontd1[[j]]) \ == 1, {no, {10^18, 10^22}}, AccuracyGoal -> 4], {j, 1, Length[eontd1]}] \ \>", \ "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \({{no \[Rule] 2.623737314818622`*^24}, {no \[Rule] 1.6056181998470508`*^24}, {no \[Rule] 8.451584326405866`*^23}, {no \[Rule] 5.5987444928599216`*^23}, {no \[Rule] 2.914608713566835`*^23}, {no \[Rule] 1.8644956764562894`*^23}, {no 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\(\(calcpd = Transpose[{eontd1, \(noc\ d\ 100\)\/\(3.3\ 10\^22\)}];\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["\<\ The following group of numerator and denominator evaluations were \ used to look at the singular behavior of the NDVCR results.\ \>", \ "Subsubsection"], Cell["\<\ calcnumndvcrsum = Table[N[numndvcrsum/feo /. {eontd -> eontd1[[j]], \ no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False], Cell["\<\ calcnumndvcrfes = Table[N[numndvcrfes/feo /. {eontd -> eontd1[[j]], \ no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False], Cell["\<\ calcnumndvcrmet1 = Table[N[numndvcrmet1/feo /. {eontd -> \ eontd1[[j]], no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False], Cell["\<\ calcnumndvcrrph1 = Table[N[numndvcrrph1/feo /. {eontd -> \ eontd1[[j]], no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False], Cell["\<\ calcnumndvcrion1 = Table[N[numndvcrion1/feo /. {eontd -> \ eontd1[[j]], no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False], Cell["\<\ calcdenndvcrsum = Table[N[denndvcrsum/feo /. {eontd -> eontd1[[j]], \ no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False], Cell["\<\ calcdenndvcrfes = Table[N[denndvcrfes/feo /. {eontd -> eontd1[[j]], \ no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False], Cell["\<\ calcdenndvcrmet1 = Table[N[denndvcrmet1/feo /. {eontd -> \ eontd1[[j]], no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False], Cell["\<\ calcdenndvcrrph1 = Table[N[denndvcrrph1/feo /. {eontd -> \ eontd1[[j]], no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False], Cell["\<\ calcdenndvcrion1 = Table[N[denndvcrion1/feo /. {eontd -> \ eontd1[[j]], no -> noc[[j]]}], {j, 1, Length[eontd1]}]; \ \>", "Input", Evaluatable->False] }, Open ]], Cell["Check of calculated pd and breakdown 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It is plotted against the pd \ value.\ \>", "Subsubtitle"], Cell["All processes", "SmallText"], Cell[BoxData[ \(\(ndvcrcalcsum = Table[N[ndvcrsum[\([1, 1]\)] /. \[InvisibleSpace]{eontd \[Rule] eontd1\[LeftDoubleBracket]j\[RightDoubleBracket], no \[Rule] noc\[LeftDoubleBracket]j\[RightDoubleBracket]}], {j, 1, Length[eontd1]}];\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(\(calcK1sum = Transpose[{\(noc\ d\ 100\)\/\(3.3\ 10\^22\), ndvcrcalcsum\ area}];\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["Ion feedback with variable gammai and fes", "SmallText"], Cell[BoxData[ \(\(ndvcrcalcion = Table[N[ndvcrion /. \[InvisibleSpace]{eontd \[Rule] eontd1\[LeftDoubleBracket]j\[RightDoubleBracket], no \[Rule] noc\[LeftDoubleBracket]j\[RightDoubleBracket]}], {j, 1, Length[eontd1]}];\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(\(calcK1ion = Transpose[{\(noc\ d\ 100\)\/\(3.3\ 10\^22\), 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\(\(calcK1fes = Transpose[{\(noc\ d\ 100\)\/\(3.3\ 10\^22\), ndvcrcalcion\ area}];\)\)], "Input", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["Metastable feedback only with variable fes", "SmallText"], Cell[CellGroupData[{ Cell["\<\ ndvcrcalcmet = Table[N[ndvcrmet[[1,1]] /. {eontd -> eontd1[[j]], no \ -> noc[[j]]}], {j, 1, Length[eontd1]}] \ \>", "Input"], Cell[BoxData[ \({5.400570312479923`*^6, 4.619369684244358`*^6, 3.5765186149637518`*^6, 2.91172262333093`*^6, 1.8883427761102165 `*^6, 1.0346465539493355`*^6, 427420.025590672`, 196476.46068372272`, 115894.38483847125`, 280968.55463420704`, 1.099076445796709`*^6, \(-697157.6322465962`\), \ \(-315490.7961368584`\), \(-174473.45042245585`\), \(-90633.74083116959`\), \ \(-39315.61200291983`\), \(-6994.324306538792`\), 4802.4898469806785`, 6488.4387834409745`, 4393.855238639251`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ calcK1met = Transpose[{(noc*d*100)/(3.3*10^22), ndvcrcalcmet*area}]\ \ \>", "Input"], 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"SmallText"], Cell["The next line is for feshat = 0.", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["\<\ ndvcrcalcmet1 = Table[N[ndvcrmet1[[1,1]] /. {eontd -> eontd1[[j]], \ no -> noc[[j]]}], {j, 1, Length[eontd1]}] \ \>", "Input"], Cell[BoxData[ \({5.39086296917397`*^6, 4.604437711680425`*^6, 3.5483962689932385`*^6, 2.8675305396985738`*^6, 1.7798058337628646`*^6, 781094.855914971`, 47108.296677850485`, \(-218498.504167166`\), \(-297252.0828346594`\), \ \(-242487.63559457855`\), \(-199131.79617044306`\), \(-154100.2009884244`\), \ \(-123686.61026795204`\), \(-90428.28248232135`\), \(-54032.8910172409`\), \ \(-22859.57949053306`\), \(-76.64784530908359`\), 8068.728158459691`, 7740.627220839182`, 4977.165463385322`}\)], "Output"] }, Open ]], Cell["\<\ Note that there is very little difference between the ndvcrmet \ values with and without feshat.\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["\<\ calcK1met1 = 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Display the results in a table and send to a file", "Subsubsection", ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"System", Background->GrayLevel[1]], Cell["\<\ result1 = Transpose[{eontd1, (noc*d*100)/(3.3*10^22), \ Transpose[calcK1sum][[2]], Transpose[calcK1ion][[2]], \ Transpose[calcK1met][[2]], Transpose[calcK1rph][[2]]}]; \ \>", "Input"], Cell["\<\ result1 = \ Map[ToString[SetPrecision[#,4.2],FormatType->FortranForm]&,result1,{2}];\ \>",\ "Input"], Cell[CellGroupData[{ Cell["\<\ result2 = TableForm[result1, TableHeadings -> {None, {\"%E/n\", \ \"pd\", \"K1sum\", \"K1ion\", \"K1met\", \"K1rph\"}}, TableSpacing -> {0, 2}] \ \>", "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"%E/n\"\>", "\<\"pd\"\>", "\<\"K1sum\"\>", "\<\"K1ion\"\>", \ "\<\"K1met\"\>", "\<\"K1rph\"\>"}, {"\<\"50.\"\>", "\<\"79.51\"\>", "\<\"1.821e4\"\>", \ "\<\"2622.\"\>", "\<\"2.7e4\"\>", "\<\"2.168e4\"\>"}, {"\<\"60.\"\>", "\<\"48.66\"\>", "\<\"13403.\"\>", "\<\"2451.\"\>", \ "\<\"2.31e4\"\>", "\<\"1.748e4\"\>"}, {"\<\"80.\"\>", "\<\"25.61\"\>", "\<\"8385.\"\>", "\<\"2244.\"\>", \ "\<\"1.788e4\"\>", "\<\"12730.\"\>"}, {"\<\"100.\"\>", "\<\"16.97\"\>", "\<\"5859.\"\>", "\<\"2054.\"\>", \ "\<\"14559.\"\>", "\<\"10032.\"\>"}, {"\<\"150.\"\>", "\<\"8.832\"\>", "\<\"2882.\"\>", \ "\<\"1543.6\"\>", "\<\"9442.\"\>", "\<\"6143.\"\>"}, {"\<\"200.\"\>", "\<\"5.65\"\>", "\<\"1780.\"\>", "\<\"1216.1\"\>", \ "\<\"5173.\"\>", "\<\"4119.\"\>"}, {"\<\"250.\"\>", "\<\"4.007\"\>", "\<\"1346.9\"\>", \ "\<\"1057.4\"\>", "\<\"2137.\"\>", "\<\"3044.\"\>"}, {"\<\"300.\"\>", "\<\"3.053\"\>", "\<\"1155.\"\>", "\<\"983.2\"\>", \ "\<\"982.4\"\>", "\<\"2431.\"\>"}, {"\<\"500.\"\>", "\<\"1.5573\"\>", "\<\"973.2\"\>", \ "\<\"939.4\"\>", "\<\"579.5\"\>", "\<\"1444.5\"\>"}, {"\<\"700.\"\>", "\<\"1.0904\"\>", "\<\"984.\"\>", "\<\"980.\"\>", \ "\<\"1404.8\"\>", "\<\"1048.6\"\>"}, {"\<\"900.\"\>", "\<\"0.8706\"\>", "\<\"1019.2\"\>", \ "\<\"1024.7\"\>", "\<\ "5495.\"\>", "\<\"784.5\"\>"}, {"\<\"1200.\"\>", "\<\"0.6976\"\>", "\<\"1069.5\"\>", "\<\"1078.9\"\ \>", "\<\"-3486.\"\>", "\<\"474.2\"\>"}, {"\<\"1500.\"\>", "\<\"0.6004\"\>", "\<\"1109.5\"\>", "\<\"1119.3\"\ \>", "\<\"-1577.5\"\>", "\<\"205.8\"\>"}, {"\<\"2000.\"\>", "\<\"0.5067\"\>", "\<\"1164.5\"\>", \ "\<\"1173.\"\>", "\<\"-872.4\"\>", "\<\"-237.3\"\>"}, {"\<\"3000.\"\>", "\<\"0.4148\"\>", "\<\"1266.6\"\>", "\<\"1272.1\"\ \>", "\<\"-453.2\"\>", "\<\"-1919.\"\>"}, {"\<\"5000.\"\>", "\<\"0.3412\"\>", "\<\"1418.4\"\>", "\<\"1419.5\"\ \>", "\<\"-196.6\"\>", "\<\"2660.\"\>"}, {"\<\"10000.\"\>", "\<\"0.2781\"\>", "\<\"1297.9\"\>", \ "\<\"1296.5\"\>", "\<\"-34.97\"\>", "\<\"889.1\"\>"}, {"\<\"2.e4\"\>", "\<\"0.2247\"\>", "\<\"771.8\"\>", \ "\<\"771.4\"\>", "\<\"24.01\"\>", "\<\"544.8\"\>"}, {"\<\"5.e4\"\>", "\<\"0.15086\"\>", "\<\"304.3\"\>", \ "\<\"304.3\"\>", "\<\"32.44\"\>", "\<\"372.6\"\>"}, {"\<\"1.e5\"\>", "\<\"0.10033\"\>", "\<\"142.92\"\>", "\<\"142.93\"\ \>", "\<\"21.97\"\>", "\<\"312.4\"\>"} }, RowSpacings->0, ColumnSpacings->2, RowAlignments->Baseline, ColumnAlignments->{Left}], (TableForm[ #, TableHeadings -> {None, {"%E/n", "pd", "K1sum", "K1ion", "K1met", "K1rph"}}, TableSpacing -> {0, 2}]&)]], "Output"] }, Open ]], Cell["\<\ nocrule = Table[FindRoot[(gaino[eontd] /. eontd ->Part[eontd1, j]) \ == 1, {no,{10^18,10^22}}, AccuracyGoal -> 4], \ {j,1,Length[eontd1]}];\ \>", "SmallText", ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"System", FontWeight->"Bold", Background->GrayLevel[1]], Cell["noc = no /. nocrule", "SmallText", ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"System", FontWeight->"Bold", Background->GrayLevel[1]], Cell["gami1 = N[gami /. eontd -> eontd1, 4]; ", "Input"], Cell["gammet1 = (If[#1 > 0, gammet, 0] & ) /@ eontd1; ", "Input"], Cell["gamrph1 = (If[#1 > 0, gamph, 0] & ) /@ eontd1; ", "Input"], Cell["alionhat1 = N[alionhat /. eontd -> eontd1, 4]; ", "Input"], Cell["almonhat1 = N[almonhat /. eontd -> eontd1, 4]; ", "Input"], Cell["alponhat1 = N[alponhat /. eontd -> eontd1, 4]; ", "Input"], Cell["feshat1 = N[feshat /. eontd -> eontd1, 4]; ", "Input"], Cell["fes1 = N[fes /. eontd -> eontd1, 4]; ", "Input"], Cell["\<\ alid1 = Table[N[alion*no*d /. {eontd -> eontd1[[j]], no -> \ noc[[j]]}, 4], {j, 1, Length[eontd1]}]; \ \>", "Input"], Cell["\<\ almd1 = Table[N[almon*no*d /. {eontd -> eontd1[[j]], no -> \ noc[[j]]}, 4], {j, 1, Length[eontd1]}]; \ \>", "Input"], Cell["\<\ alpd1 = Table[N[alpon*no*d /. {eontd -> eontd1[[j]], no -> \ noc[[j]]}, 4], {j, 1, Length[eontd1]}]; \ \>", "Input"], Cell["\<\ vd1 = Table[N[(eontd*no*d)/10^21 /. {eontd -> eontd1[[j]], no -> \ noc[[j]]}, 4], {j, 1, Length[eontd1]}]; \ \>", "Input"], Cell[CellGroupData[{ Cell["\<\ result3 = Transpose[{(noc*d*100)/(3.3*10^22), alid1, alionhat1, \ alpd1, alponhat1, fes1, feshat1}]; result4 = TableForm[result3, TableHeadings -> {None, {\"%pd\", \"alid\", \ \"alionhat\", \"alpd\", \"alponhat\", \"fes\", \"feshat\"}}, TableSpacing -> \ {0, 2}]\ \>", "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"%pd\"\>", "\<\"alid\"\>", "\<\"alionhat\"\>", "\<\"alpd\"\>", \ "\<\"alponhat\"\>", "\<\"fes\"\>", "\<\"feshat\"\>"}, {"79.50719135814008`", "4.378789199499742`", "3.401584421354176`", "93.55088581295823`", "0.9050423676373497`", "0.5773502691896257`", "0.3333333333333333`"}, {"48.65509696506215`", "4.725970289479421`", "2.8410535273300397`", "67.74657092284949`", "0.936095029817189`", "0.6123724356957946`", "0.3125`"}, {"25.610861595169297`", "5.087166490846378`", "2.177322995375184`", "46.60554167008767`", "0.9096505931116272`", "0.6666666666666666`", "0.2777777777777778`"}, {"16.965892402605824`", "5.267153695116057`", "1.8541169508430655`", "37.538352702527675`", "0.8364253140248386`", "0.7071067811865476`", "0.25`"}, {"8.832147616869198`", "5.514143078677899`", "1.660199743176183`", "26.45795082186045`", "0.653607432882467`", "0.7745966692414834`", "0.2`"}, {"5.649986898352393`", "5.673653188292473`", "1.6389237626150992`", "20.043178949118104`", "0.5237490554803859`", "0.816496580927726`", "0.16666666666666666`"}, {"4.007001608897586`", "5.761818506667696`", "1.567577836087898`", "15.812711899121647`", "0.4326281160583123`", "0.8451542547285166`", "0.14285714285714285`"}, {"3.052552026036749`", "5.78841715010917`", "1.4610820729859961`", "12.952985185296987`", "0.3642899130952787`", "0.8660254037844387`", "0.125`"}, {"1.5573018368303138`", "5.630784473866621`", "1.0557026791532191`", "7.601513769332481`", "0.184986922071517`", "0.9128709291752769`", "0.08333333333333333`"}, {"1.0903758276243973`", "5.382352685782766`", "0.8014762216240706`", "5.553408706931954`", "0.06809173697976528`", "0.9354143466934853`", "0.0625`"}, {"0.8706462569780087`", "5.149211949599267`", "0.6416341272308936`", "4.46384804318929`", \(-0.013883028673740316`\), "0.9486832980505138`", "0.05`"}, {"0.6976039034296915`", "4.852121485909105`", "0.4910726445770893`", "3.520081297093949`", \(-0.09389681291137404`\), "0.9607689228305228`", "0.038461538461538464`"}, {"0.6004465786131175`", "4.608481438025388`", "0.39375671544966406`", "2.9504528710751123`", \(-0.1417877389719511`\), "0.9682458365518543`", "0.03125`"}, {"0.5066555683251889`", "4.285599080233592`", "0.28418415648814005`", "2.3746077500394835`", \(-0.18309353773710635`\), "0.9759000729485332`", "0.023809523809523808`"}, {"0.41478976534664275`", "3.8252825807129467`", "0.1441077050544603`", "1.794642494988565`", \(-0.2048783563437245`\), "0.9837387536759294`", "0.016129032258064516`"}, {"0.3412380770779468`", "3.2525379833094217`", \(-0.008462828780246635`\), "1.333229900347948`", \(-0.18840553121840753`\), "0.9901475429766743`", "0.00980392156862745`"}, {"0.2781450715802517`", "2.5121736497817198`", \(-0.12702524812021498`\), "0.971333945537566`", \(-0.13312920791613284`\), "0.9950371902099892`", "0.0049504950495049506`"}, {"0.22468860319165374`", "1.8409189542138518`", \(-0.14068674405767756`\), "0.7293158152027236`", \(-0.08028438445621193`\), "0.9975093361076329`", "0.0024875621890547263`"}, {"0.15085536684849557`", "1.1093976068500762`", \(-0.09087231532006546`\), "0.46525381898893137`", \(-0.036171545460447145`\), "0.9990014975043672`", "0.000998003992015968`"}, {"0.10033101387527371`", "0.7022362452449937`", \(-0.05376014502378219`\), "0.3037716051388241`", \(-0.018842156005220528`\), "0.9995003746877732`", "0.0004995004995004995`"} }, RowSpacings->0, ColumnSpacings->2, RowAlignments->Baseline, ColumnAlignments->{Left}], (TableForm[ #, TableHeadings -> {None, {"%pd", "alid", "alionhat", "alpd", "alponhat", "fes", "feshat"}}, TableSpacing -> {0, 2}]&)]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ result5 = Transpose[{(noc*d*100)/(3.3*10^22), gami1, almd1, \ almonhat1, gammet1, gamrph1, vd1}]; result6 = TableForm[result5, TableHeadings -> {None, {\"%pd\", \"gami\", \ \"almd\", \"almonhat\", \"gammet\", \"gamrph\", \"vd\"}}, TableSpacing -> {0, \ 2}] \ \>", "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"%pd\"\>", "\<\"gami\"\>", "\<\"almd\"\>", "\<\"almonhat\"\>", \ "\<\"gammet\"\>", "\<\"gamrph\"\>", "\<\"vd\"\>"}, {"79.50719135814008`", "0.00013628677795686993`", "24.946902883455525`", "0.9050423676373497`", "0.003`", "0.003`", "1311.868657409311`"}, {"48.65509696506215`", "0.00017209431099700118`", "18.065752246093194`", "0.936095029817189`", "0.003`", "0.003`", "963.3709199082305`"}, {"25.610861595169297`", "0.00024849653691437`", "12.428144445356711`", "0.9096505931116272`", "0.003`", "0.003`", "676.1267461124693`"}, {"16.965892402605824`", "0.0003302124748816072`", "10.010227387340713`", "0.8364253140248386`", "0.003`", "0.003`", "559.8744492859921`"}, {"8.832147616869198`", "0.0005526076150809218`", "7.05545355249612`", "0.653607432882467`", "0.003`", "0.003`", "437.1913070350252`"}, {"5.649986898352393`", "0.0007951018051487297`", "5.344847719764828`", "0.5237490554803859`", "0.003`", "0.003`", "372.89913529125783`"}, {"4.007001608897586`", "0.0010533030822243163`", "4.216723173099106`", "0.4326281160583123`", "0.003`", "0.003`", "330.57763273405084`"}, {"3.052552026036749`", "0.0013244492093414132`", "3.454129382745863`", "0.3642899130952787`", "0.003`", "0.003`", "302.2026505776381`"}, {"1.5573018368303138`", "0.0025066816059626765`", "2.0270703384886617`", "0.184986922071517`", "0.003`", "0.003`", "256.9548030770017`"}, {"1.0903758276243973`", "0.0038024344233469525`", "1.4809089885151876`", "0.06809173697976528`", "0.003`", "0.003`", "251.8768161812357`"}, {"0.8706462569780087`", "0.00517978447482969`", "1.1903594781838105`", \(-0.013883028673740316`\), "0.003`", "0.003`", "258.58193832246855`"}, {"0.6976039034296915`", "0.007360795229701388`", "0.9386883458917197`", \(-0.09389681291137404`\), "0.003`", "0.003`", "276.25114575815775`"}, {"0.6004465786131175`", "0.009648218231770946`", "0.7867874322866966`", \(-0.1417877389719511`\), "0.003`", "0.003`", "297.22105641349305`"}, {"0.5066555683251889`", "0.013638294342165866`", "0.6332287333438622`", \(-0.18309353773710635`\), "0.003`", "0.003`", "334.39267509462456`"}, {"0.41478976534664275`", "0.022084976704563677`", "0.4785713319969507`", \(-0.2048783563437245`\), "0.003`", "0.003`", "410.64186769317627`"}, {"0.3412380770779468`", "0.04010071676917075`", "0.35552797342611947`", \(-0.18840553121840753`\), "0.003`", "0.003`", "563.0428271786121`"}, {"0.2781450715802517`", "0.0881540395680439`", "0.25902238547668427`", \(-0.13312920791613284`\), "0.003`", "0.003`", "917.8787362148305`"}, {"0.22468860319165374`", "0.18848412249662466`", "0.19448421738739297`", \(-0.08028438445621193`\), "0.003`", "0.003`", "1482.9447810649144`"}, {"0.15085536684849557`", "0.4918212974964279`", "0.12406768506371503`", \(-0.036171545460447145`\), "0.003`", "0.003`", "2489.1135530001766`"}, {"0.10033101387527371`", "0.9818335709575198`", "0.08100576137035309`", \(-0.018842156005220528`\), "0.003`", "0.003`", "3310.923457884032`"} }, RowSpacings->0, ColumnSpacings->2, RowAlignments->Baseline, ColumnAlignments->{Left}], (TableForm[ #, TableHeadings -> {None, {"%pd", "gami", "almd", "almonhat", "gammet", "gamrph", "vd"}}, TableSpacing -> {0, 2}]&)]], "Output"] }, Open ]], Cell["\<\ result7 = Transpose[{(noc*d*100)/(3.3*10^22), \ 10^17*calcnumndvcrsum, 10^17*calcnumndvcrfes, 10^17*calcnumndvcrmet1, 10^17*calcnumndvcrrph1, 10^17*calcnumndvcrion1}]; result8 = TableForm[result7, TableHeadings -> {None, {\"pd\", \"1E17*nsum\", \ \"1E17*nfes\", \"1E17*nmet1\", \"1E17*nrph1\", \"1E17*nion1\"}}, TableSpacing -> {0, 2}]; \ \>", "Input", Evaluatable->False], Cell["\<\ result9 = Transpose[{(noc*d*100)/(3.3*10^22), \ 10^22*calcdenndvcrsum, 10^22*calcdenndvcrfes, 10^22*calcdenndvcrmet1, 10^22*calcdenndvcrrph1, 10^22*calcdenndvcrion1}]; result10 = TableForm[result9, TableHeadings -> {None, {\"pd\", \"1E22*dsum\", \ \"1E22*dfes\", \"1E22*dmet1\", \"1E22*drph1\", \"1E22*dion1\"}}, TableSpacing -> {0, 2}]; \ \>", "Input", Evaluatable->False], Cell["Send the model results to a file", "Subsubsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ SetOptions[$Output, PageWidth -> 120]; theoryfile := \"c:\\\\proplot\\\\argon\\\\arndvcr\\\\ndvcrsum.the\"; stream1 = OpenWrite[theoryfile,PageWidth -> Infinity]; WriteString[stream1, StringForm[\"%NDVCR model\",now], \"\\n\", ToString[result2], \"\\n\",\"%\",\"\\n\", ToString[result4], \"\\n\",\"%\",\"\\n\", ToString[result6]] Close[stream1]; 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