(************** 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). 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.95732 .50193 L .95774 .50209 L .95819 .50227 L .95862 .50244 L .95904 .5026 L .95948 .50278 L .9599 .50294 L .96031 .5031 L .96074 .50327 L .96115 .50343 L .96159 .5036 L .96201 .50377 L .96242 .50393 L .96285 .5041 L .96326 .50426 L .9637 .50443 L .96412 .50459 L .96452 .50475 L .96495 .50491 L .96536 .50507 L .96576 .50523 L .96618 .50539 L Mistroke .96658 .50555 L .96701 .50571 L .96742 .50587 L .96782 .50602 L .96824 .50618 L .96864 .50634 L .96907 .5065 L .96948 .50666 L .96987 .50681 L .97029 .50697 L .97069 .50712 L .97108 .50727 L .97149 .50743 L .97189 .50758 L .9723 .50774 L .97271 .50789 L .97309 .50804 L .9735 .50819 L .9739 .50834 L .97427 .50848 L .97467 .50864 L .97506 .50878 L .97547 .50893 L .97586 .50908 L .97619 .50921 L Mfstroke 0 1 1 r 0 .60324 m .03628 .60322 L .07902 .6032 L .11285 .60317 L .1434 .60315 L .1689 .60313 L .19278 .60311 L .21333 .60309 L .23126 .60307 L .24867 .60305 L .2641 .60304 L .27787 .60303 L .29153 .60301 L .30384 .60301 L .31613 .603 L 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Cell[CellGroupData[{ Cell[BoxData[ \(\((Normal[ Series[\(ambipolar2\ \ /. {lambda -> range/\((p0d - p0dc)\), r\ -> \ range/\((range + p0dc/2)\)}\) /. range -> x*p0dc, {\ x, Infinity, 2}]]\ \ // \ Simplify)\)\ /. x -> range/p0dc\)], "Input"], Cell[BoxData[ \(p0d\/\(2\ p0d - p0dc\)\)], "Output"] }, Open ]], Cell["\<\ This singularity in ambipolar will lead to singularities in our gain \ expression when p0dc reaches the nonphysical value of 2*p0d. We should stop \ the calculation when p0dc=p0d.\ \>", "Text"], Cell[BoxData[ \(ambipolar\ := \ ambipolar2\ /. {r -> range/\((range + p0dc/2)\), lambda -> range/\((p0d - p0dc)\)}\)], "Input"], Cell["\<\ Effect of loss of electrons to an absorbing anode on ion production.\ \>", "Subsection"], Cell["Low electron energy model of Chantry et al (1966)", "Subsubsection"], Cell["\<\ According to Chantry, Phelps, and Schulz, Phys. Rev. 152, 81 (1966) the \ combined effect of finite collision chamber length, inelastic collisions, and \ electron reflection on ion production can be calculated using multiple \ scattering model provided the electric field in the collision chamber is \ small, i.e., in the low p0dc limit. Unfortunately, this model is only useful \ at low electron energies (less than sum of excitation and ionization \ thresholds), where an inelastic collision results in the effective loss of \ the electron with regard to further ionization.\ \>", "Text"], Cell["Effect of electron absorption and reflection at the anode", \ "Subsubsection"], Cell["\<\ For an obstructed discharge, we expect the number of ions produced relative \ to the number produced in the absence of obstruction to depend on the ratio \ of the electron range to the electrode separation for small values of this \ ratio and to approach unity for large values of the ratio. We represent this \ effect by exponential functions. Of course we could use a ratio of \ polynomials. \ \>", "Text"], Cell["\<\ To keep the problem simple, we will assume that the electrons, even after \ reflection, are a monoenergetic beam that is attenuated with a characteristic \ distance called the range, which is to be made quantitative later. As \ considered by Parker et al and by Phelps, Jelenkovic and Pitchford (1987), \ when an electron is reflected by the anode it moves toward the cathode until \ the potential \"hill\" at the cathode fall returns it to the anode, i.e., it \ traverses the gap twice between succesive reflections. This behavior is \ reminescent of a hollow cathode. An approximate expression for this \ attenuation and reflection at the anode is given by the following relation:\ \>", "Text"], Cell[BoxData[ \(reflection\ = \ \(\(\((1 - Exp[\(-p0d\)/range])\) + re*Exp[\(-p0d\)/range]*\((1 - Exp[\(-2\)*p0d/range])\) + \((re* Exp[\(-p0d\)/range])\) \((re* Exp[\(-2\)*p0d/range])\) \((1 - Exp[\(-2\)*p0d/range])\) + \ \((re* Exp[\(-p0d\)/range])\) \((re* Exp[\(-2\)*p0d/range])\)^2 \((1 - Exp[\(-2\)*p0d/range])\) + ... \) ... \) .. \)], "Input",\ Evaluatable->False], Cell["\<\ Here the (1-Exp[-p0d/range]) factor is the fractional reduction in the ion \ production caused by the reduction in distance for ionization in one \ transversal of the gap for initial or backscattered electrons. The factor \ Exp[-p0d/range] is the fraction of the beam successfully crossing of the gap \ once. The reflection coefficient is re and is assumed to remain fixed for \ successive reflection events. The second and later terms contain \ Exp[-2*p0d/range] because electrons backscattered from the anode leave and \ return to the anode in response to the applied potential or are attenuated \ during this trajectory.\ \>", "Text"], Cell[BoxData[ \(reflection\ = \((1 - Exp[\(-p0d\)/range])\) + Sum[\((re* Exp[\(-p0d\)/range])\) \((re*Exp[\(-2\)*p0d/range])\)^\((j - 1)\)*\((1 - Exp[\(-2\)*p0d/range])\), {j, 1, Infinity}]\)], "Input", Evaluatable->False], Cell["\<\ reflection := 1 - E^(-(p0d/range)) + (E^(p0d/range)*(1 - E^(-((2*p0d)/range)))*re)/(E^((2*p0d)/range) - re)\ \>", "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Limit[reflection, \ re -> 1]\)], "Input"], Cell[BoxData[ \(1\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Limit[reflection\ /. \ p0d -> x*range, \ x -> Infinity]\)], "Input"], Cell[BoxData[ \(1\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Limit[reflection, \ re -> 0]\)], "Input"], Cell[BoxData[ \(1 - \[ExponentialE]\^\(-\(p0d\/range\)\)\)], "Output"] }, Open ]], Cell["\<\ Note that this factor goes to unity when re goes to unity. This is because \ then the electrons \"rattle around\" until they create all of the ion pairs \ given by the \"source\" model, i.e., the gap acts long enough so that the \ anode does not reduce the ionization. When the ratio of the p0d to the range \ goes to infinity this factor becomes 1, because the anode has no effect on \ ion production. When the reflection goes to zero the electrons make one \ transit across the gap. The reflection formula of Phelps, Jelenkovic and Pitchford (1987) used for \ comparison with Parker's MC model of low pd breakdown are not relevant here \ because they neglect electron bean attenuation.\ \>", "Text"], Cell["\<\ The \"range\" to be used here should be the attenuation distance for \ ionization found from MC calculations by Pitchford and collaborators and from \ emission experiments by Rozsca, Gallagher, and Donko (1990), rather than the \ extrapolated range for monoenergetic electrons that is discussed in Phelps, \ Jelenkovic and Pitchford (1987).\ \>", "Text"], Cell["Chioce of electron reflection coefficient at anode", "Subsubsection"], Cell["\<\ I tried various reflection coefficients. Their most obvious effect on the \ apparent gammai was for E/n >= 20 kTd. The use of re = 0.75 gave a minimum \ in gammai, which seems unlikely. Changing from 0 to 0.75 raised the apparent \ gammai at the highest E/n from 0.1 to 0.5. The use of values less than about \ 0.4 increased the spread in apparent gammai values near E/n ~ 80 kTd. A value \ of about 0.45 gives nearly constant apparent gammai as expected for \"clean\" \ copper. We were not able to improve the agreement by using a reflection \ coefficient that increased with discharge voltage.\ \>", "Text"], Cell[BoxData[ \(\(re = 0.45;\)\)], "Input", Background->RGBColor[0, 1, 0]], Cell["\<\ On the basis of Fig. 31 in Kollath, Handbuch der Physik, ed by S. Flugge \ (Springer-Verlag, 1956, Berlin) vol 21, p. 232, one expects the fraction of \ the electrons striking the copper anode that are backscattered to be \ independent of primary energy. Hoever, our value of 0.45 is significantly \ larger than value of about 0.3. Could this be evidence of excessive assumed \ beam attenuation or of failure of the beam attenuation approach?\ \>", "Text"], Cell["Effective gammai formula", "Section"], Cell["\<\ Here we wish to define an effecive gain that includes loss by ambipolar \ diffusion to the anode, the net change in ion production caused by electron \ absorption and reflection from the anode, and the production of electrons at \ the cathode\ \>", "Text"], Cell[BoxData[ \(ionFracCollected\ := \ ambipolar\)], "Input"], Cell["The steady-state condition is then gain =1 where", "Text"], Cell[BoxData[ \(gain\ := \ gammai*\ ionFracCollected*productionFit*reflection\)], "Input"], Cell["\<\ Here gammai depends on E/N at the cathode, which is proportional to Vc/p0dc. \ The range depends on Vc and p0dc. The ion production depends on p0dc and \ Vc.\ \>", "Text"], Cell["Electron range or attenuation", "Subsubsection"], Cell["\<\ We first need to settle on an expression for the electron \"range\". As part \ of this we need to understand the discrepancy between the length of the \ negative-glow of Brewer and Westhaver and the attenuation distance found by \ Pitchford et al and by Rozsca et al. From the notebook ARBEAMATTENUATION.NB \ we get a compromise fit to the experimental and theoretical attenuation \ length called phelpsFit. Here we call it attFit. This function will replace \ the \"range\" in the preceding relations. Also, vd replaces energy.\ \>", "Text"], Cell[BoxData[ \(attFit := \ \((energy/1000)\)^1.78*\((1 + 1/\((1 + \((p0dc/0.1)\)^2)\)^1. *\((300/ energy)\)^3.56)\)^0.5\ /. \ energy\ -> \ vd\)], "Input"], Cell["Apparent gammai", "Subsection"], Cell["We define an apparent gammai by:", "Text"], Cell[BoxData[ \(apparentGammai = \(\(1/productionFit\)/ionFracCollected\)/ reflection\)], "Input", Evaluatable->False], Cell["Klyarfeld data as digitized 2002", "Subsubsection"], Cell["\<\ Set up a Do loop to calculate the apparent gammai from the data (inputTable) \ of Klyarfeld et al (1966) for a particular pressure.\ \>", "Text"], Cell[BoxData[ \(analyze := Block[{}, \[IndentingNewLine]Clear[p0d, p0dc, jopsq, vd]; \[IndentingNewLine]apparentGammaiTable[k] = {}; \n Do[p0d = inputTable[\([j, 1]\)]; \nvd\ = \ inputTable[\([j, 3]\)]; \n jopsq = inputTable[\([j, 2]\)]; \n p0dc = \((0.005265*vd^\((3/5)\))\)/jopsq^\((2/5)\); \n apparentGammaiTable[k] = Append[apparentGammaiTable[ k], {2*\(vd/ p0dc\)/ .33, \((\(\(1/productionFit\)/ ionFracCollected\)/reflection\ /. \ range -> attFit)\)}];, {j, Length[inputTable]}]]\)], "Input"], Cell["\<\ The digitized Klyarfeld et al data is given in the following files.\ \>", "Text"], Cell[BoxData[ \(\(klyarfeldFileList = {"\", \ "\", "\", \ "\", "\", \ "\", "\", \ "\"};\)\)], "Input"], Cell[BoxData[ \(\(\(\(pressureList = {0.024, 0.032, 0.062, 0.155, 0.200, 0.500, 1.50, 5.00}\) \)\(;\)\(\ \ \)\( (*Torr\ at\ 290 K*) \)\)\)], "Input"], Cell[BoxData[ \(\(\(areaList = {67.9, 67.9, 67.9, 11.9, 11.9, 11.9, 11.9, 11.9}\ ;\)\(\ \ \ \)\( (*cm^2*) \)\)\)], "Input"], Cell[BoxData[ \(\(\(distanceList = {4. , 4. , 4. , 1.6, 1.6, 1.6, 1.6, 1.6};\)\(\ \ \ \ \ \ \)\( (*cm*) \)\)\)], "Input"], Cell["\<\ The following Do loop manipulates and analyzes the Klyarfeld et al data files \ and prepares a plot of apparent gammai versus E/n at the cathode for each \ pressure.\ \>", "Text"], Cell[BoxData[ \(Do[\n inputData = Drop[Import[klyarfeldFileList[\([k]\)], "\"], 6]; \n inputTable\ = \ Table[{pressureList[\([k]\)]*273/290*distanceList[\([k]\)], inputData[\([j, 1]\)]*\(1000/ areaList[\([k]\)]\)/\((pressureList[\([k]\)]*273/290)\)^2, inputData[\([j, 2]\)]}, {j, 1, Length[inputData]}]; \nanalyze; \n apparentGammaiPlot[k] = \ LogLogListPlot[apparentGammaiTable[k], PlotRange -> {{1000. , 10^7}, { .01, 1. }}, PlotStyle -> \ {Hue[0.13*\((k - 1)\)], PointSize[0.02]}, DisplayFunction -> Identity];, {k, 1, Length[klyarfeldFileList]}]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(apparentGammaiTable[3]\)], "Input"], Cell[BoxData[ \({{70405.40868818836`, 0.07492717503220969`}, {95607.41922715768`, 0.08102547150326936`}, {125101.52888936848`, 0.08615988543564647`}, {177421.74943118612`, 0.09275159831158374`}, {264742.5105885494`, 0.09978961032074403`}, {358079.90295919025`, 0.10439509162714011`}, {482245.69561937754`, 0.10823983456838836`}, {601864.0750491555`, 0.11120966157371591`}, {727110.1144836472`, 0.1135243677709477`}, {855694.5959148133`, 0.1164556433949541`}, {948568.3048579674`, 0.11791605067024319`}, {1.0796029772343058`*^6, 0.12062501523071037`}}\)], "Output"] }, Open ]], Cell[" Prepare a summary plot.", "Text"], Cell[BoxData[ \(\(summaryKlyarfeldPlot = Show[Table[apparentGammaiPlot[k], {k, 1, Length[klyarfeldFileList]}], ImageSize -> 576, PlotLabel -> "\", TextStyle \[Rule] \(FontSize \[Rule] 15\), DisplayFunction -> Identity];\)\)], "Input"], Cell[BoxData[ \(\(Clear[p0d, p0dc, vd, jopsq];\)\)], "Input"], Cell["Comparison of various gammai data", "Subsubsection"], Cell["\<\ Phelps and Petrovic (1999) recommended the following for modeling breakdown \ in Ar with a clean copper cathode.\ \>", "Text"], Cell[BoxData[ \(gammaiPP := \((0.07 + 1.*^-5*\ kTion^\((1.2)\)* Exp[\(-500\)/ kTion]/\((1 + \((kTion/100000)\)^\((0.7)\))\))\)\ /. kTion -> \((\(+1.9\)*\((eontd/1000)\)^\((1.1)\) + 0.026)\)\)], "Input"], Cell["\<\ I empirically find the following fit to these cathode fall results.\ \>", "Text"], Cell[BoxData[ \(gammaiFit := 0.07*\((1 + \((eontd/300000. )\)^1.6)\)^0.5\)], "Input"], Cell["\<\ As seen from the plot below this expression differs little from that of \ Phelps and Petrovic for clean surfaces except at high E/n. One could justify \ lower values at high cathode E/N as caused by a lower contribution of heavy \ partice ionization. etc. in the cathode fall.\ \>", "Text"], Cell[BoxData[ \(\(gammaiFitPlot = \ LogLogPlot[{gammaiFit, gammaiPP}, {eontd, 1000, 1.*^7}, PlotRange -> {{1000. , 10^7}, { .01, 1. }}, PlotStyle -> \ {{Hue[1]}, {Hue[0.3]}}, DisplayFunction -> Identity];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[summaryKlyarfeldPlot, gammaiFitPlot, PlotLabel -> "\", ImageSize -> 576, DisplayFunction -> $DisplayFunction];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 %%ImageSize: 576 355.988 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.75 0.25 0.618034 0.309017 [ [.25 -0.0125 -24.9688 -18.375 ] [.25 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ool0T?ooo`030000oooooooo00;oool00`000?ooooooo`04oooo00<0003oooooool01?ooo`800003 oooo00<0003oooooool05?ooo`030000oooooooo02;oool00`000?ooooooo`05oooo00<0003ooooo ool04oooo`030000oooooooo07Woool0083oool20000?Oooo`030000oooooooo08ooool700001_oo o`030000oooooooo00?oool300000_ooo`<0000Eoooo00<0003oooooool08_ooo`030000oooooooo 00Goool00`000?ooooooo`0Coooo00<0003oooooool0NOooo`00ooooo`;oool00`000?ooooooo`1K oooo00<0003oooooool0Boooo`80000Doooo0P0007_oool00?ooool2oooo00<0003oooooool0oooo ocgoool00?oooooooooo@_ooo`00oooooooooom2oooo003ooooooooood;oool00001\ \>"], ImageRangeCache->{{{0, 575}, {354.938, 0}} -> {2.61004, -2.16236, \ 0.0080901, 0.00654503}}] }, Open ]], Cell["\<\ red- 0.024Torr, 40 mm gap; mustard- 0.032 Torr, 40 mm; yelllow-green- 0.062 \ Torr, 40 mm; green- 0.155 Torr, 16 mm; cyan- 0.20 Torr, 16 mm; dark blue- \ 0.50 Torrr, 16 mm; purple- 1.50 Torr, 16 mm; salmon(?)- 5.0 Torr, 16 mm; \ green curve- recommended for breakdown by P&P (1999); red curve- empirical \ fit to the Klyarfeld et al (1966) results\ \>", "Text"], Cell["\<\ The choice of a reflection coefficient of near 0.6 leads to a roughly \ constant apparent gammai for 5 < E/n < 100 kTd of about 0.07. This value is \ consistent with the 0.07 value from Oesher and as used by Pitchford et al. \ This value is also consistent with the fact that Klyarfeld et al annealed and \ sputtered their cathodes, although the order these steps is not clear to me. \ Note that the derived values below about 50 kTd are relatively independent of \ the assumed reflection coefficient. The overall results at higher E/n may indicate that processes such as heavy \ particle ionization are becoming important as E/n increases above 200 kTd. \ The is roughly where they are predicted to be important in breakdown by \ Phelps and Petrovic (1999). I do not understand the turning down of the apparent gammai at low and at \ high E/n. The turning down at low E/n suggests that we do not understand the \ approach to the \"normal\" cathod fall, e.g., perhaps the effective discharge \ area changes gradually (not sharply as assumed) with current in this region. \ The behavior at the higher E/n for each pressure, especially at high \ currents, is even more baffeling. See the weird behavior of the \ \"predicted\" voltage versus j/p0^2 plots below.\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell[BoxData[ \(runtime = SessionTime[] - starttime\)], "Input"], Cell[BoxData[ \(6.`\)], "Output"] }, Open ]], Cell["\<\ Use assumed gammai and electron reflection to predict cathode fall voltage \ versus j/p0^2.\ \>", "Section"], Cell["\<\ The steady-state condition is for the gain to equal unity. Here we use the \ gammi from Eqs. (B8) and (B13) of Petrovic and Phelps (1999) for a clean Cu \ surface in Ar. We use the electron reflection coefficient assumed above, \ i.e., re = 0.45. We will worry about other heavy particle contributions \ later.\ \>", "Text"], Cell[BoxData[ \(assumedgammai := gammaiFit\ /. eontd -> 2*\(vd/p0dc\)/0.33\)], "Input"], Cell[BoxData[ \(\(assumedgammai = 0.1206;\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(range := attFit\)], "Input"], Cell[BoxData[ \(\(epsilon0 = 8.85*^-12;\)\)], "Input"], Cell["Solve for p0dc then vd", "Subsubsection"], Cell[BoxData[ \(\(Clear[p0d, p0dc, vd, jopsq];\)\)], "Input"], Cell["\<\ For the moment we assume a single set of values of p0d and jopsq and solve \ for the cathode fall voltage vd and p0dc. Later we will use Do[] loops.\ \>", "Text"], Cell[BoxData[ \(gain\)], "Input", Evaluatable->False], Cell["\<\ Next we eliminate vd so that we can solve for p0dc. This seemed desirable \ because I had problems finding the root for simultaneus equations with both \ p0dc and vd as unknowns. Probably I should try again using the \"damping\" \ that was eventually adopted.\ \>", "Text"], Cell[BoxData[ \(\(gain1\ := \((gain\ /. \ gammai -> assumedgammai)\) /. vd -> 6275.7\ jopsq\^\(2/3\)\ p0dc\^\(5/3\);\)\)], "Input"], Cell["In this case we eliminate p0dc so that we can solve for vd", "Text"], Cell[BoxData[ \(\(gain2\ := \((gain\ /. \ gammai -> assumedgammai)\) /. p0dc -> \((0.005265*vd^\((3/5)\))\)/jopsq^\((2/5)\);\)\)], "Input"], Cell[BoxData[ \(gain1\)], "Input", Evaluatable->False], Cell["Predictions", "Section"], Cell["In the following we solve for p0dc using FindRoot[ ]", "Text"], Cell[BoxData[ \(predict := Block[{p0dExpt, p0dcExpt, vdExpt, jopsqExpt}, \[IndentingNewLine]Clear[ p0d, p0dc, vd, jopsq, gainLocal]; \[IndentingNewLine]calcp0dcTable = {}; \n calcjopsqTable = {}; \n Do[\[IndentingNewLine]p0dExpt = inputTable[\([j, 1]\)]; \n jopsqExpt = inputTable[\([j, 2]\)]; \[IndentingNewLine]vdExpt = inputTable[\([j, 3]\)]; \[IndentingNewLine]p0dcExpt\ = \ \((0.005265* vdExpt^\((3/5)\))\)/ jopsqExpt^\((2/5)\); \[IndentingNewLine]gainLocal = gain1\ /. \ {p0d -> p0dExpt, jopsq -> jopsqExpt}; \n sol = FindRoot[{1 == gainLocal}, {p0dc, p0dcExpt, 0.001, p0dExpt}, DampingFactor -> 0.10, MaxIterations -> 1000]; \n calcp0dcTable = Append[calcp0dcTable, {p0dc\ /. \ sol, 6275.7\ \((jopsqExpt)\)^\((2/3)\) p0dc^\((5/3)\) /. sol}]; \n calcjopsqTable = Append[calcjopsqTable, {jopsqExpt, 6275.7\ \((jopsqExpt)\)^\((2/3)\) p0dc^\((5/3)\) /. sol}]; \n gainPlot[j] = LogLogPlot[gainLocal, {p0dc, 0.001, 1.1*p0dExpt}, GridLines -> Automatic, PlotStyle -> Hue[1], PlotPoints -> 500, PlotRange -> {{0.001, 2*p0dExpt}, {0.01, 100}}, DisplayFunction -> Identity];, \[IndentingNewLine]{j, Length[inputTable]}]]\)], "Input"], Cell["\<\ In the following we solve for vd using FindRoot[ ]. It appears to yield the \ same result as the previous loop solving for p0dc, including the weird \ behavior of the prediction for the 0.062 Torr data.. Because much of the \ diagnostics is set up for the p0dc sloution, we make the following inactive. \ W should look more carefully at the gain versus vd.\ \>", "Text"], Cell[BoxData[ \(predict := Block[{p0dExpt, p0dcExpt, vdExpt, jopsqExpt}, \[IndentingNewLine]Clear[ p0d, p0dc, vd, jopsq, gainLocal]; \[IndentingNewLine]calcp0dcTable = {}; \n calcjopsqTable = {}; \n Do[\[IndentingNewLine]p0dExpt = inputTable[\([j, 1]\)]; \n jopsqExpt = inputTable[\([j, 2]\)]; \[IndentingNewLine]vdExpt = inputTable[\([j, 3]\)]; \[IndentingNewLine]p0dcExpt\ = \ \((0.005265* vdExpt^\((3/5)\))\)/ jopsqExpt^\((2/5)\); \[IndentingNewLine]gainLocal = gain2\ /. \ {p0d -> p0dExpt, jopsq -> jopsqExpt}; \n sol = FindRoot[{1 == gainLocal}, {vd, vdExpt, 50. , 20000. }, DampingFactor -> 0.10, MaxIterations -> 1000]; \n calcp0dcTable = Append[calcp0dcTable, {\((0.005265*vd^\((3/5)\))\)/ jopsq^\((2/5)\) /. \ sol, vd\ /. \ sol}]; \n calcjopsqTable = Append[calcjopsqTable, {jopsqExpt, vd\ /. \ sol}]; \n gainPlot[j] = LogLogPlot[gainLocal, {vd, 50. , 20000. }, GridLines -> Automatic, PlotStyle -> Hue[1], PlotPoints -> 500, PlotRange -> {{50. , 20000. }, {0.01, 100}}, DisplayFunction -> Identity];, \[IndentingNewLine]{j, Length[inputTable]}]]\)], "Input", Evaluatable->False], Cell[BoxData[ \(Do[\n inputData = Drop[Import[klyarfeldFileList[\([k]\)], "\"], 6]; \n inputTable\ = \ Table[{pressureList[\([k]\)]*273/290*distanceList[\([k]\)], inputData[\([j, 1]\)]*\(1000/ areaList[\([k]\)]\)/\((pressureList[\([k]\)]*273/290)\)^2, inputData[\([j, 2]\)]}, {j, 1, Length[inputData]}]; \n predict; \[IndentingNewLine]klyarfeldVdTable[k] = Table[{inputData[\([j, 1]\)]*\(1000/ areaList[\([k]\)]\)/\((pressureList[\([k]\)]*273/290)\)^2, inputData[\([j, 2]\)]}, {j, 1, Length[inputData]}]; klyarfeldVdPlot[k] = \ LogLogListPlot[klyarfeldVdTable[k], PlotRange -> {{0.1, 10000. }, {100. , 40000. }}, PlotStyle -> \ {Hue[0.13*\((k - 1)\)], PointSize[0.02]}, DisplayFunction -> Identity]; \n predictedVdPlot[k] = \ 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o`050000oooooooooooo000000?oool00`000?ooooooo`02oooo00<0003oooooool01?ooo`030000 oooooooo01coool003Woool3000000?oool0003oool03?ooo`030000oooooooo00Goool00`000?oo ooooo`0Coooo00<0003oooooool06?ooo`030000oooooooo00ooool00`000?ooooooo`06oooo00<0 003oooooool08_ooo`030000oooooooo00Goool00`000?ooooooo`0]oooo00<0003oooooool00ooo o`<00002oooo0`0000?oool00`000?ooooooo`1Koooo00<0003oooooool02oooo`030000oooooooo 00;oool00`000?ooooooo`03oooo00<0003oool000001?ooo`030000oooooooo00;oool00`000?oo ooooo`0?oooo00<0003oooooool03Oooo`80000:oooo00<0003oooooool05_ooo`030000oooo0000 00Coool00`000?ooooooo`02oooo00@0003oooooooooool700008?ooo`030000oooo000000Coool0 0`000?ooooooo`02oooo00<0003oooooool01?ooo`030000oooooooo01coool005;oool200005?oo o`80000Koooo0`0000coool300001_ooo`<0000Roooo0`0003Soool00`000?ooooooo`0"], ImageRangeCache->{{{0, 575}, {354.938, 0}} -> {-1.56805, 1.78824, \ 0.0101232, 0.00852419}}] }, Open ]], Cell["\<\ red- 0.024Torr, 40 mm gap; mustard- 0.032 Torr, 40 mm; yelllow-green- 0.062 \ Torr, 40 mm; green- 0.155 Torr, 16 mm; cyan- 0.20 Torr, 16 mm; dark blue- \ 0.50 Torrr, 16 mm; purple- 1.50 Torr, 16 mm; salmon- 5.0 Torr, 16 mm; \ \>", "Text"], Cell["\<\ Except for the high current points of the model for 0.062 Torr data, the \ agreement between the predictions of the model and experiment is reasonable \ for re=0.45. The only obviously unusual feature about the experimental data at 0.062 Torr \ is that the currents reach much larger values, i.e., 0.8 A, than for the \ other pressures. However, the weird behavior is in the theory, not the \ experiment.\ \>", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ \(runtime = SessionTime[] - starttime\)], "Input"], Cell[BoxData[ \(104.`\)], "Output"] }, Open ]], Cell["Diagnostics section", "Section"], Cell["\<\ From here to the end I am trying to figure out why the predicted Vd versus \ j/p0^2 curve for p=0.062 Torr is so weird.\ \>", "Subtitle", FontColor->RGBColor[1, 0, 0]], Cell["Trial and error solutions", "Subsubsection"], Cell["Trial and error check of analysis results", "Text"], Cell[BoxData[ \(\(Clear[p0d, p0dc, vd, jopsq];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(gain\ /. \ {jopsq -> 3284. , p0dc -> 0.04605, vd -> 8203, p0d -> 0.226, gammai -> 0.1206, re -> 0.45}\)], "Input"], Cell[BoxData[ \(0.9717090696960271`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(vd = \ 6275.7\ jopsq\^\(2/3\)\ p0dc\^\(5/3\) /. \ \ {jopsq -> 3284. , p0dc -> 0.04605, p0d -> 0.226}\)], "Input"], Cell[BoxData[ \(8203.143921316636`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(gain1\ /. \ {jopsq -> 3284. , p0dc -> 0.04605, p0d -> 0.226}\)], "Input"], Cell[BoxData[ \(1.6692680736318637`\)], "Output"] }, Open ]], Cell["Trial and error check of prediction results", "Text"], Cell[BoxData[ \(\(Clear[p0d, p0dc, vd, jopsq];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(gain\ /. \ {jopsq -> 3284. , p0dc -> 0.01394, vd -> 1119. , p0d -> 0.226, gammai -> 0.077, re -> 0.45}\)], "Input"], Cell[BoxData[ \(0.6042806695442444`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(vd = \ 6275.7\ jopsq\^\(2/3\)\ p0dc\^\(5/3\) /. \ \ {jopsq -> 3284. , p0dc -> 0.01394, p0d -> 0.226}\)], "Input"], Cell[BoxData[ \(1119.5295549919574`\)], "Output"] }, Open ]], Cell["\<\ In the following, gammai is specified above and vd is eliminated by \ substitution of the formula.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(gain1\ /. \ {jopsq -> 3284. , p0dc -> 0.01394, p0d -> 0.226}\)], "Input"], Cell[BoxData[ \(0.9778728274164219`\)], "Output"] }, Open ]], Cell["\<\ From this test, it would appear that the formula for gain1 is inconsistent \ with the formula for gain.\ \>", "Subtitle"], Cell[BoxData[ \(\(Clear[p0d, p0dc, vd, jopsq];\)\)], "Input"], Cell[BoxData[ \(predict1 := Block[{p0dExpt, p0dcExpt, vdExpt, jopsqExpt}, \[IndentingNewLine]Clear[ p0d, p0dc, vd, jopsq, gainLocal]; \[IndentingNewLine]calcp0dcList = {}; \n calcjopsqList = {}; \ncalcratioList = {}; \n Do[\[IndentingNewLine]p0dExpt = inputTable[\([j, 1]\)]; \n jopsqExpt = inputTable[\([j, 2]\)]; \[IndentingNewLine]vdExpt = inputTable[\([j, 3]\)]; \[IndentingNewLine]p0dcExpt\ = \ \((0.005265* vdExpt^\((3/5)\))\)/ jopsqExpt^\((2/5)\); \[IndentingNewLine]gainLocal = gain1\ /. \ {p0d -> p0dExpt, jopsq -> jopsqExpt}; \n sol = FindRoot[{1 == gainLocal}, {p0dc, p0dcExpt, 0.001, p0dExpt}, DampingFactor -> 0.10, MaxIterations -> 1000]; \n calcp0dcList = Append[calcp0dcList, {p0dc\ /. \ sol, 6275.7\ \((jopsqExpt)\)^\((2/3)\) p0dc^\((5/3)\) //. sol}]; \n calcjopsqList = Append[calcjopsqList, {jopsqExpt, 6275.7\ \((jopsqExpt)\)^\((2/3)\) p0dc^\((5/3)\) //. sol}]; \n gainPlot[j] = LogLogPlot[gainLocal, {p0dc, 0.001, 1.1*p0dExpt}, GridLines -> Automatic, PlotStyle -> {Hue[0.12*\((j - 1)\)], Thickness[0.007]}, PlotPoints -> 500, PlotRange -> {{0.01, 2*p0dExpt}, {0.1, 10.0}}, DisplayFunction -> Identity];, \[IndentingNewLine]{j, Length[inputTable]}]]\)], "Input"], Cell["\<\ For Klyarfeld's p = 0.062 Torr, p0d=0.0584*4= 0.233 Torr cm. We drop the \ digitized points for currents below those at the onset of the abnormal \ glow.\ \>", "Text"], Cell[BoxData[ \(\(k024a = Drop[Import["\", "\"], 6];\)\)], "Input",\ Evaluatable->False], Cell[BoxData[ \(\(k032a = Drop[Import["\", "\"], 6];\)\)], "Input",\ Evaluatable->False], Cell["\<\ The following case gives problems because the gain is independent of \ parameters in the general region of the desired solution. See the trial and \ error solutions above.\ \>", "Text"], Cell[BoxData[ \(\(k062a = Drop[Import["\", "\"], 6];\)\)], "Input"], Cell[BoxData[ \(\(k200a = Drop[Import["\", "\"], 6];\)\)], "Input",\ Evaluatable->False], Cell[BoxData[ \(\(k155a = Drop[Import["\", "\"], 6];\)\)], "Input",\ Evaluatable->False], Cell[BoxData[ \(\(k5000a = Drop[Import["\", "\"], 6];\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(k5000a = Drop[Import["\", "\"], 6];\)\)], "Input", Evaluatable->False], Cell[CellGroupData[{ Cell[BoxData[ \(inputTable\ = \ Table[{0.062*273/ 290*4, %[\([j, 1]\)]*\(1000/ 67.9\)/\((0.062*273/290)\)^2, %[\([j, 2]\)], \((0.005265*%[\([j, 2]\)]^\((3/5)\))\)/\((%[\([j, 1]\)]*\(1000/67.9\)/\((0.062*273/290)\)^2)\)^\((2/ 5)\)}, {j, 1, Length[%]}]\)], "Input"], Cell[BoxData[ \({{0.23346206896551722`, 24.35962617708157`, 1201.02`, 0.10338565213286299`}, {0.23346206896551722`, 42.894786951332385`, 1465.6499999999999`, 0.09290834691000735`}, {0.23346206896551722`, 68.7356263613409`, 1791.35`, 0.08678284560588852`}, {0.23346206896551722`, 124.90162733693177`, 2361.32`, 0.08066108213289208`}, {0.23346206896551722`, 249.40767074224215`, 3216.29`, 0.07362877470389056`}, {0.23346206896551722`, 425.59037791444734`, 4010.1800000000003`, 0.06787345788264222`}, {0.23346206896551722`, 726.227248632078`, 4946.570000000001`, 0.06216584698119078`}, {0.23346206896551722`, 1092.8189852212258`, 5720.1`, 0.05759983717991704`}, {0.23346206896551722`, 1544.2515860086119`, 6493.64`, 0.05412576878722411`}, {0.23346206896551722`, 2114.6447055117915`, 7124.679999999999`, 0.05046178741109808`}, {0.23346206896551722`, 2553.5742600669464`, 7633.59`, 0.04877264144421221`}, {0.23346206896551722`, 3283.7011448336966`, 8203.56`, 0.04605261980836039`}}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(predict1;\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(calcp0dcList\)], "Input"], Cell[BoxData[ \({{0.10766965229630043`, 1285.0837693460355`}, {0.10904552429543`, 1914.0131899816033`}, {0.1065336289149547`, 2521.126510488928`}, {0.09673231574035156`, 3196.3933156917005`}, {0.08004353896575105`, 3696.685596579686`}, {0.06575813553493316`, 3803.9884823098305`}, {0.051639213303026135`, 3630.8632888271345`}, {0.041336624863776`, 3290.4302172098805`}, {0.032873738985898016`, 2828.499130950216`}, {0.024818711800209437`, 2183.328953925095`}, {0.019370354179111586`, 1638.0372442520727`}, {0.013939542516037932`, 1119.4004030082044`}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(calcjopsqList\)], "Input"], Cell[BoxData[ \({{24.35962617708157`, 1285.0837693460355`}, {42.894786951332385`, 1914.0131899816033`}, {68.7356263613409`, 2521.126510488928`}, {124.90162733693177`, 3196.3933156917005`}, {249.40767074224215`, 3696.685596579686`}, {425.59037791444734`, 3803.9884823098305`}, {726.227248632078`, 3630.8632888271345`}, {1092.8189852212258`, 3290.4302172098805`}, {1544.2515860086119`, 2828.499130950216`}, {2114.6447055117915`, 2183.328953925095`}, 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.30866 .26871 L .31277 .26953 L .31667 .27027 L .32075 .27101 L .32462 .27169 L Mistroke .32829 .27231 L .33214 .27293 L .33579 .27349 L .33926 .27401 L .3429 .27453 L .34635 .275 L .34997 .27548 L .35342 .27593 L .35669 .27633 L .36012 .27674 L .36339 .27712 L .36681 .27751 L .37007 .27787 L .37317 .2782 L .37642 .27855 L .37952 .27887 L .38246 .27917 L .38556 .27948 L .3885 .27977 L .3916 .28008 L .39454 .28036 L .39735 .28064 L .4003 .28093 L .40311 .2812 L .40606 .28149 L .40888 .28177 L .41155 .28204 L .41437 .28233 L .41706 .2826 L .41962 .28287 L .42231 .28316 L .42488 .28344 L .42758 .28373 L .43016 .28403 L .43262 .28431 L .4352 .28462 L .43767 .28492 L .44002 .28521 L .4425 .28552 L .44487 .28583 L .44736 .28617 L .44973 .2865 L .452 .28682 L .45439 .28717 L .45667 .28751 L .45907 .28788 L .46136 .28824 L .46355 .2886 L .46585 .28898 L .46806 .28936 L Mistroke .47016 .28973 L .47237 .29013 L .47449 .29053 L .47672 .29095 L .47885 .29137 L .48088 .29178 L .48303 .29222 L .48508 .29265 L .48724 .29312 L .48931 .29357 L .49128 .29402 L .49336 .2945 L .49535 .29497 L .49725 .29543 L .49925 .29593 L .50117 .29642 L .50319 .29694 L .50512 .29745 L .50697 .29795 L .50892 .29848 L .51078 .29901 L .51256 .29951 L .51444 .30006 L .51624 .3006 L .51813 .30117 L .51995 .30173 L .52168 .30227 L .52351 .30286 L .52527 .30343 L .52711 .30404 L .52888 .30463 L .53058 .30521 L .53236 .30582 L .53407 .30643 L .5357 .30701 L .53743 .30763 L .53908 .30824 L .54083 .30889 L .5425 .30952 L .54409 .31014 L .54578 .31079 L .54739 .31143 L .54894 .31204 L .55057 .3127 L .55213 .31334 L .55378 .31402 L .55536 .31468 L .55687 .31532 L .55847 .31601 L .56 .31667 L Mistroke .56161 .31738 L .56316 .31806 L .56464 .31872 L .5662 .31943 L .5677 .32011 L .56913 .32077 L .57065 .32148 L .5721 .32216 L .57364 .32289 L .5751 .32359 L .57651 .32427 L .578 .32499 L .57942 .32569 L .58092 .32644 L .58237 .32715 L .58375 .32785 L .5852 .32859 L .5866 .3293 L .58794 .32999 L .58935 .33072 L .59071 .33143 L .59214 .33218 L .59352 .33291 L .59483 .3336 L .59622 .33435 L .59755 .33507 L .59883 .33576 L .60018 .33649 L .60147 .3372 L .60284 .33795 L .60415 .33868 L .6054 .33938 L .60673 .34012 L .608 .34084 L .60935 .3416 L .61064 .34233 L .61188 .34303 L .61318 .34378 L .61444 .3445 L .61563 .3452 L .6169 .34593 L .61812 .34664 L .61941 .34739 L .62064 .34812 L .62182 .34881 L .62308 .34955 L .62428 .35026 L .62542 .35094 L .62664 .35167 L .62781 .35237 L Mistroke .62904 .35311 L .63022 .35382 L .63136 .3545 L .63256 .35523 L .63371 .35592 L .63492 .35666 L .63609 .35737 L .63721 .35805 L .63839 .35878 L .63953 .35947 L .64061 .36014 L .64176 .36085 L .64287 .36152 L .64404 .36225 L .64516 .36294 L .64623 .3636 L .64737 .3643 L .64846 .36498 L .64961 .3657 L .65072 .36638 L .65178 .36704 L .6529 .36774 L .65398 .36841 L .65501 .36905 L .6561 .36974 L .65715 .37039 L .65826 .37108 L .65933 .37175 L .66035 .37238 L .66143 .37306 L .66247 .37371 L .66346 .37433 L .66451 .37499 L .66552 .37562 L .66659 .37628 L .66762 .37692 L .6686 .37754 L .66964 .37819 L .67064 .37881 L .6717 .37947 L .67271 .3801 L .67368 .38071 L .67471 .38135 L .6757 .38197 L .67665 .38256 L .67765 .38318 L .67862 .38378 L .67964 .38441 L .68062 .38502 L .68155 .3856 L Mistroke .68255 .38622 L .6835 .3868 L .68451 .38743 L .68548 .38803 L .68641 .3886 L .6874 .3892 L .68834 .38978 L .68925 .39034 L .69021 .39093 L .69113 .39149 L .6921 .39209 L .69304 .39266 L .69394 .3932 L .69489 .39378 L .6958 .39434 L .69668 .39487 L .6976 .39543 L .69849 .39597 L .69944 .39653 L .70034 .39708 L .70121 .3976 L .70213 .39815 L .70301 .39868 L .70395 .39924 L .70485 .39977 L .70571 .40028 L .70662 .40083 L .7075 .40134 L .70834 .40184 L .70923 .40236 L .71008 .40287 L .71099 .4034 L .71186 .40391 L .71269 .4044 L .71357 .40491 L .71442 .4054 L .71523 .40588 L .7161 .40637 L .71692 .40685 L .7178 .40736 L .71864 .40784 L .71945 .40831 L .72031 .4088 L .72113 .40927 L .722 .40976 L .72283 .41024 L .72364 .41069 L .72449 .41117 L .7253 .41163 L .72608 .41207 L Mistroke .72691 .41254 L .72771 .41298 L .72855 .41345 L .72937 .41391 L .73014 .41434 L .73097 .41479 L .73176 .41523 L .7326 .41569 L .7334 .41614 L .73418 .41656 L .73499 .41701 L .73578 .41744 L .73654 .41785 L .73734 .41828 L .7381 .4187 L .73892 .41914 L .7397 .41956 L .74045 .41996 L .74124 .42039 L .74201 .4208 L .74274 .42119 L .74352 .4216 L .74426 .422 L .74505 .42241 L .74581 .42281 L .74654 .4232 L .74731 .4236 L .74806 .42399 L .74884 .4244 L .7496 .4248 L .75032 .42517 L .75109 .42557 L .75183 .42595 L .75254 .42632 L .75329 .4267 L .75401 .42707 L .75477 .42747 L .75551 .42784 L .75621 .4282 L .75696 .42858 L .75767 .42894 L .75843 .42933 L .75916 .4297 L .75987 .43005 L .76061 .43042 L .76132 .43078 L .76201 .43112 L .76273 .43149 L .76343 .43183 L .76417 .4322 L Mistroke .76488 .43256 L .76556 .43289 L .76629 .43325 L .76698 .43359 L .76765 .43392 L .76835 .43427 L .76903 .4346 L .76975 .43495 L .77044 .43529 L .77111 .43561 L .77181 .43596 L .77249 .43628 L .7732 .43663 L .77389 .43696 L .77455 .43728 L .77526 .43762 L .77593 .43795 L .77657 .43826 L .77726 .43858 L .77792 .4389 L .77862 .43923 L .77929 .43955 L .77993 .43986 L .78061 .44019 L .78127 .4405 L .7819 .4408 L .78257 .44111 L .78321 .44142 L .78389 .44174 L .78454 .44205 L .78517 .44234 L .78584 .44266 L .78648 .44296 L .78715 .44328 L .7878 .44358 L .78843 .44388 L .78909 .44419 L .78973 .44448 L .79034 .44477 L .79099 .44507 L .79161 .44537 L .79227 .44567 L .79291 .44597 L .79352 .44625 L .79417 .44656 L .79479 .44685 L .79545 .44715 L .79608 .44745 L .79669 .44773 L .79733 .44803 L Mistroke .79795 .44832 L .79854 .44859 L .79918 .44889 L .79978 .44917 L .80042 .44947 L .80104 .44975 L .80164 .45003 L .80226 .45032 L .80287 .4506 L .80345 .45087 L .80406 .45115 L .80466 .45143 L .80528 .45172 L .80589 .452 L .80647 .45227 L .80708 .45255 L .80767 .45283 L .80829 .45312 L .8089 .4534 L .80947 .45367 L .81009 .45395 L .81067 .45423 L .81124 .45449 L .81184 .45477 L .81242 .45504 L .81303 .45533 L .81361 .4556 L .81418 .45586 L .81478 .45614 L .81535 .45641 L .8159 .45667 L .81649 .45695 L .81705 .45721 L .81765 .45749 L .81822 .45776 L .81877 .45802 L .81936 .4583 L .81992 .45857 L .82051 .45885 L .82109 .45912 L .82164 .45938 L .82222 .45966 L .82278 .45993 L .82332 .46019 L .82389 .46046 L .82444 .46072 L .82502 .461 L .82558 .46127 L .82612 .46153 L .82669 .46181 L Mistroke .82724 .46207 L .82782 .46235 L .82838 .46262 L .82891 .46288 L .82948 .46316 L .83003 .46343 L .83055 .46369 L .83111 .46396 L .83165 .46422 L .83221 .4645 L .83276 .46478 L .83329 .46504 L .83384 .46531 L .83438 .46558 L .83489 .46583 L .83544 .46611 L .83596 .46637 L .83652 .46665 L .83705 .46692 L .83756 .46718 L .83811 .46746 L .83863 .46772 L .83919 .46801 L .83972 .46828 L .84023 .46854 L .84078 .46882 L .8413 .46909 L .8418 .46935 L .84233 .46963 L .84285 .4699 L .84339 .47018 L .84391 .47045 L .84441 .47072 L .84446 .47074 L Mfstroke 0 .4 1 r 0 .12134 m .00597 .12718 L .01867 .13936 L .03033 .15026 L .04218 .16103 L .05311 .17061 L .06424 .17998 L .07453 .18826 L .08406 .19557 L .09383 .2027 L .10291 .20896 L .11134 .21449 L .12004 .21987 L .12813 .22461 L .13648 .22923 L .14427 .23331 L .15155 .23692 L .15908 .24045 L .16613 .2436 L .17341 .24667 L .18025 .24941 L .18666 .25185 L .19331 .25426 L .19955 .2564 L .20542 .25832 L .21153 .26021 L .21727 .26191 L .22324 .26358 L .22886 .26507 L .23416 .2664 L .23968 .26772 L .24489 .26889 L .2498 .26994 L .25493 .27098 L .25977 .27191 L .26482 .27283 L .2696 .27365 L .27411 .27439 L .27883 .27511 L .28329 .27577 L .28795 .27641 L .29236 .27699 L .29653 .27751 L .3009 .27804 L .30504 .27851 L .30896 .27894 L .31307 .27937 L .31696 .27976 L .32104 .28016 L .3249 .28053 L Mistroke .32857 .28087 L .33241 .28122 L .33606 .28154 L .33952 .28185 L .34316 .28217 L .34661 .28247 L .35023 .28278 L .35367 .28309 L .35694 .28338 L .36037 .28368 L .36363 .28398 L .36705 .2843 L .37031 .28461 L .3734 .28491 L .37665 .28524 L .37975 .28556 L .38269 .28587 L .38578 .28621 L .38872 .28655 L .39182 .28691 L .39476 .28727 L .39756 .28762 L .40051 .288 L .40332 .28838 L .40627 .2888 L .40908 .2892 L .41176 .28961 L .41458 .29004 L .41726 .29048 L .41982 .2909 L .42251 .29136 L .42508 .29182 L .42778 .29231 L .43035 .2928 L .43281 .29328 L .43539 .2938 L .43786 .29431 L .4402 .29482 L .44268 .29536 L .44504 .29589 L .44753 .29647 L .44991 .29704 L .45217 .29759 L .45456 .29819 L .45684 .29878 L .45924 .29942 L .46153 .30004 L .46371 .30064 L .46602 .3013 L .46822 .30193 L Mistroke .47032 .30256 L .47253 .30323 L .47465 .30388 L .47688 .30458 L .47901 .30527 L .48104 .30593 L .48319 .30665 L .48523 .30734 L .48739 .30809 L .48946 .30882 L .49143 .30953 L .49351 .31028 L .4955 .31102 L .49739 .31173 L .4994 .3125 L .50131 .31324 L .50333 .31403 L .50526 .3148 L .50711 .31555 L .50906 .31635 L .51092 .31712 L .5127 .31787 L .51458 .31866 L .51637 .31944 L .51827 .32026 L .52008 .32106 L .52182 .32183 L .52365 .32265 L .5254 .32345 L .52725 .32429 L .52901 .32511 L .5307 .3259 L .53249 .32674 L .5342 .32756 L .53583 .32834 L .53756 .32917 L .53921 .32998 L .54095 .33083 L .54262 .33166 L .54421 .33246 L .5459 .3333 L .54751 .33412 L .54906 .3349 L .55069 .33573 L .55225 .33654 L .5539 .33739 L .55548 .33821 L .55699 .339 L .55858 .33984 L .56011 .34065 L Mistroke .56173 .34151 L .56327 .34233 L .56475 .34312 L .56632 .34396 L .56781 .34477 L .56925 .34554 L .57076 .34637 L .57221 .34716 L .57374 .348 L .57521 .3488 L .57662 .34957 L .5781 .35039 L .57953 .35118 L .58103 .35201 L .58247 .35281 L .58385 .35358 L .58531 .35439 L .58671 .35517 L .58804 .35591 L .58946 .35671 L .59081 .35746 L .59224 .35827 L .59362 .35904 L .59493 .35977 L .59632 .36055 L .59765 .3613 L .59893 .36202 L .60028 .36277 L .60157 .3635 L .60294 .36427 L .60425 .365 L .6055 .36571 L .60683 .36645 L .6081 .36716 L .60945 .36792 L .61074 .36864 L .61197 .36933 L .61328 .37006 L .61453 .37075 L .61573 .37142 L .617 .37213 L .61821 .3728 L .6195 .37351 L .62073 .3742 L .62192 .37485 L .62317 .37554 L .62437 .37619 L .62551 .37682 L .62673 .37749 L .62789 .37812 L Mistroke .62913 .3788 L .63031 .37944 L .63144 .38005 L .63264 .3807 L .63379 .38132 L .63501 .38197 L .63618 .38259 L .63729 .38319 L .63848 .38382 L .63961 .38442 L .6407 .38499 L .64185 .3856 L .64295 .38618 L .64412 .38679 L .64524 .38737 L .64631 .38792 L .64745 .38851 L .64854 .38907 L .64969 .38966 L .6508 .39023 L .65186 .39077 L .65298 .39133 L .65406 .39188 L .65509 .39239 L .65618 .39294 L .65723 .39346 L .65834 .39401 L .65941 .39453 L .66043 .39503 L .66151 .39556 L .66254 .39606 L .66354 .39654 L .66459 .39705 L .6656 .39753 L .66667 .39804 L .66769 .39853 L .66867 .39899 L .66971 .39948 L .67071 .39994 L .67177 .40044 L .67279 .4009 L .67376 .40135 L .67479 .40182 L .67578 .40227 L .67672 .4027 L .67773 .40315 L .67869 .40358 L .67971 .40403 L .68069 .40447 L .68163 .40488 L Mistroke .68262 .40532 L .68357 .40573 L .68458 .40617 L .68555 .40658 L .68648 .40698 L .68747 .4074 L .68841 .4078 L .68932 .40818 L .69028 .40858 L .6912 .40896 L .69217 .40937 L .69311 .40975 L .69401 .41012 L .69496 .4105 L .69587 .41087 L .69674 .41122 L .69767 .41159 L .69856 .41195 L .69951 .41232 L .70041 .41267 L .70128 .41301 L .7022 .41337 L .70308 .41371 L .70402 .41407 L .70491 .41441 L .70577 .41473 L .70669 .41508 L .70756 .4154 L .7084 .41572 L .70929 .41605 L .71015 .41636 L .71105 .41669 L .71192 .41701 L .71275 .41731 L .71364 .41762 L .71448 .41793 L .7153 .41822 L .71616 .41852 L .71699 .41881 L .71786 .41912 L .7187 .41941 L .71951 .41969 L .72037 .41998 L .72119 .42026 L .72206 .42056 L .7229 .42084 L .7237 .42111 L .72455 .42139 L .72536 .42166 L .72614 .42192 L Mistroke .72697 .42219 L .72777 .42245 L .72862 .42273 L .72943 .42299 L .7302 .42324 L .73103 .4235 L .73182 .42375 L .73266 .42402 L .73346 .42427 L .73423 .42452 L .73505 .42477 L .73584 .42502 L .73659 .42525 L .73739 .42549 L .73816 .42573 L .73898 .42598 L .73976 .42621 L .74051 .42644 L .7413 .42668 L .74207 .42691 L .7428 .42713 L .74357 .42736 L .74432 .42758 L .74511 .42781 L .74587 .42803 L .7466 .42824 L .74737 .42847 L .74811 .42868 L .7489 .42891 L .74965 .42913 L .75038 .42933 L .75115 .42955 L .75188 .42976 L .75259 .42996 L .75334 .43017 L .75406 .43038 L .75483 .43059 L .75556 .4308 L .75626 .43099 L .75701 .4312 L .75773 .4314 L .75849 .43161 L .75922 .43181 L .75992 .432 L .76066 .4322 L .76138 .4324 L .76206 .43259 L .76279 .43278 L .76348 .43297 L .76422 .43317 L Mistroke .76493 .43336 L .76562 .43355 L .76634 .43374 L .76703 .43393 L .7677 .43411 L .76841 .4343 L .76908 .43448 L .7698 .43467 L .7705 .43485 L .77116 .43503 L .77186 .43522 L .77254 .4354 L .77326 .43559 L .77394 .43577 L .7746 .43595 L .77531 .43613 L .77598 .43631 L .77662 .43648 L .77731 .43666 L .77797 .43683 L .77867 .43702 L .77934 .4372 L .77998 .43737 L .78066 .43755 L .78132 .43772 L .78195 .43789 L .78262 .43806 L .78326 .43823 L .78394 .43841 L .78459 .43858 L .78522 .43875 L .78588 .43893 L .78652 .4391 L .7872 .43928 L .78785 .43945 L .78848 .43962 L .78914 .43979 L .78978 .43996 L .79039 .44013 L .79104 .4403 L .79166 .44047 L .79232 .44064 L .79296 .44081 L .79357 .44098 L .79421 .44115 L .79483 .44132 L .79549 .4415 L .79613 .44167 L .79673 .44184 L .79738 .44201 L Mistroke .798 .44218 L .79859 .44234 L .79922 .44252 L .79983 .44268 L .80047 .44286 L .80109 .44303 L .80168 .4432 L .80231 .44337 L .80291 .44354 L .80349 .4437 L .80411 .44388 L .8047 .44404 L .80533 .44422 L .80593 .44439 L .80651 .44456 L .80712 .44473 L .80771 .4449 L .80834 .44508 L .80894 .44525 L .80952 .44542 L .81013 .4456 L .81072 .44577 L .81128 .44594 L .81188 .44611 L .81246 .44628 L .81307 .44647 L .81366 .44664 L .81422 .44681 L .81482 .44699 L .81539 .44716 L .81595 .44733 L .81653 .44751 L .81709 .44768 L .81769 .44786 L .81826 .44804 L .81881 .44821 L .8194 .44839 L .81996 .44857 L .82056 .44876 L .82113 .44894 L .82168 .44911 L .82226 .4493 L .82282 .44948 L .82336 .44965 L .82393 .44984 L .82448 .45001 L .82506 .4502 L .82562 .45039 L .82616 .45057 L .82673 .45076 L Mistroke .82728 .45094 L .82786 .45113 L .82842 .45132 L .82895 .4515 L .82952 .4517 L .83007 .45189 L .83059 .45207 L .83115 .45226 L .83169 .45245 L .83226 .45265 L .8328 .45284 L .83333 .45303 L .83388 .45323 L .83442 .45342 L .83493 .4536 L .83548 .4538 L .836 .45399 L .83656 .4542 L .83709 .45439 L .8376 .45458 L .83815 .45479 L .83867 .45498 L .83923 .45519 L .83976 .4554 L .84027 .45559 L .84082 .4558 L .84134 .456 L .84184 .4562 L .84237 .45641 L .84288 .45661 L .84343 .45683 L .84395 .45703 L .84445 .45724 L .84446 .45724 L Mfstroke .32 0 1 r 0 .17546 m .00599 .18063 L .01821 .19067 L .03062 .20028 L .04203 .20858 L .05364 .21647 L .06435 .22326 L .07425 .22912 L .08439 .23472 L .0938 .23958 L .10253 .2438 L .11151 .24788 L .11988 .25144 L .12848 .25488 L .13651 .25789 L .14401 .26053 L .15176 .26309 L .15901 .26534 L .16649 .26751 L .17351 .26942 L .18008 .27109 L .1869 .27271 L .1933 .27414 L .19931 .27538 L .20556 .2766 L .21143 .27766 L .21754 .27869 L .22329 .2796 L .2287 .28039 L .23433 .28117 L .23965 .28185 L .24466 .28245 L .24989 .28305 L .25482 .28358 L .25997 .28411 L .26484 .28458 L .26943 .28501 L .27423 .28544 L .27877 .28583 L .28351 .28623 L .288 .28661 L .29224 .28696 L .29668 .28732 L .30089 .28767 L .30487 .28801 L .30904 .28836 L .313 .2887 L .31713 .28907 L .32106 .28943 L .32478 .28979 L Mistroke .32868 .29017 L .33238 .29055 L .33589 .29092 L .33958 .29133 L .34308 .29174 L .34675 .29218 L .35023 .29263 L .35354 .29306 L .35702 .29354 L .36032 .29402 L .36379 .29454 L .36709 .29506 L .37022 .29557 L .37351 .29613 L .37664 .29669 L .37961 .29724 L .38274 .29784 L .38572 .29843 L .38885 .29907 L .39183 .29971 L .39466 .30033 L .39764 .30101 L .40048 .30168 L .40346 .30241 L .40631 .30312 L .40901 .30382 L .41186 .30458 L .41457 .30532 L .41715 .30604 L .41987 .30683 L .42247 .30759 L .42519 .30842 L .4278 .30923 L .43027 .31001 L .43288 .31086 L .43537 .31169 L .43774 .31249 L .44024 .31335 L .44263 .31419 L .44514 .31509 L .44754 .31597 L .44982 .31682 L .45223 .31773 L .45453 .31861 L .45695 .31956 L .45926 .32047 L .46147 .32136 L .46379 .32231 L .46601 .32323 L .46813 .32411 L Mistroke .47036 .32506 L .47249 .32598 L .47474 .32695 L .47689 .3279 L .47894 .32881 L .4811 .32978 L .48317 .33072 L .48534 .33171 L .48742 .33267 L .48941 .3336 L .49151 .33458 L .49351 .33553 L .49542 .33644 L .49744 .33742 L .49937 .33835 L .5014 .33934 L .50335 .34029 L .50521 .34121 L .50717 .34218 L .50904 .34311 L .51084 .34401 L .51273 .34496 L .51454 .34587 L .51645 .34683 L .51827 .34776 L .52002 .34865 L .52186 .34959 L .52363 .35049 L .52549 .35145 L .52727 .35236 L .52897 .35324 L .53077 .35417 L .53249 .35506 L .53413 .3559 L .53587 .3568 L .53753 .35766 L .53928 .35857 L .54096 .35944 L .54257 .36027 L .54426 .36115 L .54589 .36199 L .54744 .36279 L .54908 .36363 L .55065 .36444 L .55231 .3653 L .5539 .36611 L .55542 .36689 L .55703 .36771 L .55856 .36849 L .56019 .36932 L Mistroke .56174 .37011 L .56323 .37086 L .5648 .37165 L .56631 .37241 L .56775 .37313 L .56927 .37388 L .57073 .37461 L .57227 .37537 L .57375 .3761 L .57516 .37679 L .57666 .37752 L .57809 .37821 L .5796 .37894 L .58105 .37964 L .58244 .3803 L .5839 .381 L .58531 .38166 L .58665 .38229 L .58807 .38295 L .58944 .38359 L .59088 .38425 L .59226 .38488 L .59358 .38548 L .59497 .38612 L .59631 .38672 L .59759 .38729 L .59895 .38789 L .60025 .38846 L .60162 .38906 L .60294 .38963 L .6042 .39017 L .60553 .39074 L .60681 .39128 L .60816 .39185 L .60946 .39239 L .6107 .3929 L .61201 .39344 L .61327 .39395 L .61448 .39444 L .61575 .39495 L .61697 .39543 L .61827 .39594 L .61951 .39642 L .62069 .39688 L .62195 .39736 L .62316 .39782 L .62431 .39825 L .62553 .3987 L .6267 .39913 L .62794 .39958 L Mistroke .62913 .40001 L .63027 .40042 L .63147 .40085 L .63263 .40125 L .63385 .40167 L .63502 .40208 L .63614 .40246 L .63733 .40286 L .63847 .40324 L .63956 .40359 L .64072 .40397 L .64183 .40433 L .643 .4047 L .64412 .40506 L .6452 .40539 L .64634 .40575 L .64744 .40608 L .6486 .40643 L .64971 .40676 L .65077 .40707 L .6519 .4074 L .65298 .40771 L .65402 .40801 L .65511 .40832 L .65617 .40861 L .65728 .40892 L .65835 .40921 L .65937 .40948 L .66046 .40977 L .6615 .41005 L .6625 .4103 L .66355 .41058 L .66457 .41083 L .66564 .4111 L .66667 .41136 L .66765 .4116 L .6687 .41185 L .6697 .41209 L .67076 .41234 L .67178 .41258 L .67276 .4128 L .67379 .41304 L .67478 .41326 L .67573 .41347 L .67674 .41369 L .67771 .4139 L .67873 .41412 L .67971 .41433 L .68066 .41452 L .68165 .41473 L Mistroke .68261 .41492 L .68362 .41513 L .6846 .41532 L .68553 .4155 L .68652 .41569 L .68747 .41587 L .68837 .41605 L .68934 .41623 L .69026 .4164 L .69124 .41657 L .69218 .41674 L .69308 .4169 L .69404 .41707 L .69495 .41723 L .69583 .41738 L .69676 .41754 L .69765 .41769 L .6986 .41785 L .69951 .41799 L .70038 .41813 L .7013 .41828 L .70219 .41842 L .70313 .41857 L .70403 .41871 L .70489 .41884 L .70581 .41898 L .70668 .41911 L .70753 .41923 L .70842 .41936 L .70928 .41949 L .71018 .41962 L .71106 .41974 L .71189 .41986 L .71278 .41998 L .71363 .4201 L .71444 .42021 L .71531 .42033 L .71614 .42044 L .71702 .42055 L .71786 .42066 L .71867 .42077 L .71953 .42088 L .72036 .42098 L .72123 .42109 L .72207 .4212 L .72287 .4213 L .72372 .4214 L .72454 .4215 L .72533 .4216 L .72616 .4217 L Mistroke .72696 .42179 L .72781 .42189 L .72862 .42199 L .7294 .42208 L .73023 .42218 L .73102 .42227 L .73186 .42236 L .73267 .42246 L .73344 .42254 L .73426 .42264 L .73505 .42272 L .73581 .42281 L .73661 .4229 L .73738 .42298 L .7382 .42307 L .73898 .42316 L .73973 .42324 L .74053 .42333 L .7413 .42341 L .74203 .42349 L .74281 .42357 L .74356 .42365 L .74435 .42374 L .74511 .42382 L .74584 .4239 L .74662 .42398 L .74736 .42406 L .74815 .42414 L .74891 .42422 L .74963 .4243 L .7504 .42438 L .75114 .42446 L .75185 .42453 L .75261 .42461 L .75333 .42469 L .75409 .42477 L .75483 .42485 L .75554 .42493 L .75629 .42501 L .757 .42508 L .75777 .42516 L .7585 .42524 L .7592 .42532 L .75995 .4254 L .76066 .42548 L .76135 .42555 L .76208 .42563 L .76278 .42571 L .76352 .42579 L .76423 .42587 L Mistroke .76491 .42594 L .76564 .42602 L .76633 .4261 L .767 .42618 L .76771 .42626 L .76839 .42633 L .76911 .42642 L .76981 .42649 L .77047 .42657 L .77118 .42665 L .77186 .42673 L .77257 .42682 L .77326 .4269 L .77393 .42698 L .77463 .42706 L .7753 .42714 L .77595 .42722 L .77664 .4273 L .7773 .42739 L .778 .42747 L .77867 .42756 L .77932 .42764 L .78 .42772 L .78066 .42781 L .78129 .42789 L .78196 .42798 L .7826 .42806 L .78328 .42815 L .78394 .42824 L .78457 .42832 L .78523 .42841 L .78588 .4285 L .78655 .42859 L .78721 .42868 L .78783 .42877 L .7885 .42886 L .78914 .42895 L .78975 .42904 L .7904 .42914 L .79103 .42923 L .79169 .42932 L .79232 .42942 L .79294 .42951 L .79358 .42961 L .79421 .4297 L .79487 .4298 L .7955 .4299 L .79611 .43 L .79676 .4301 L .79738 .4302 L Mistroke .79797 .4303 L .79861 .4304 L .79921 .4305 L .79986 .43061 L .80048 .43071 L .80107 .43081 L .8017 .43092 L .80231 .43102 L .80289 .43113 L .8035 .43123 L .8041 .43134 L .80473 .43145 L .80533 .43156 L .80591 .43167 L .80653 .43178 L .80712 .43189 L .80774 .43201 L .80835 .43212 L .80892 .43223 L .80954 .43235 L .81013 .43247 L .81069 .43258 L .8113 .4327 L .81187 .43282 L .81248 .43294 L .81307 .43306 L .81364 .43318 L .81424 .4333 L .81481 .43343 L .81537 .43354 L .81595 .43367 L .81652 .43379 L .81712 .43392 L .81769 .43405 L .81824 .43417 L .81883 .43431 L .81939 .43443 L .81999 .43457 L .82056 .4347 L .82111 .43483 L .8217 .43497 L .82226 .43511 L .8228 .43523 L .82337 .43537 L .82392 .43551 L .8245 .43565 L .82506 .43579 L .8256 .43593 L .82617 .43608 L .82672 .43622 L Mistroke .82731 .43637 L .82787 .43651 L .8284 .43666 L .82897 .43681 L .82952 .43696 L .83005 .4371 L .83061 .43725 L .83114 .4374 L .83171 .43756 L .83226 .43771 L .83278 .43786 L .83334 .43802 L .83388 .43818 L .83439 .43833 L .83494 .43849 L .83546 .43865 L .83602 .43881 L .83656 .43897 L .83707 .43913 L .83762 .4393 L .83814 .43946 L .8387 .43964 L .83923 .43981 L .83974 .43997 L .84029 .44015 L .84081 .44032 L .84132 .44048 L .84185 .44066 L .84236 .44083 L .84291 .44101 L .84343 .44119 L .84393 .44136 L .84446 .44154 L Mfstroke 1 0 .96 r 0 .21258 m .00609 .21692 L .01925 .22561 L .03134 .23295 L .04245 .2392 L .05378 .24509 L .06424 .25013 L .07492 .2549 L .0848 .25898 L .09397 .26251 L .10338 .26588 L .11213 .26878 L .12028 .2713 L .12868 .2737 L .13652 .27578 L .1446 .27777 L .15216 .27947 L .15922 .28095 L .16654 .28236 L .17339 .28358 L .18048 .28474 L .18713 .28574 L .19338 .2866 L .19986 .28744 L .20595 .28816 L .21168 .2888 L .21764 .28942 L .22325 .28997 L .22909 .29051 L .23459 .29099 L .23977 .29144 L .24518 .29189 L .25028 .2923 L .25509 .29269 L .26011 .2931 L .26486 .29349 L .26982 .2939 L .2745 .2943 L .27893 .29469 L .28356 .29512 L .28794 .29554 L .29252 .296 L .29685 .29645 L .30096 .2969 L .30525 .2974 L .30932 .2979 L .31318 .29839 L .31722 .29894 L .32105 .29948 L .32506 .30008 L Mistroke .32887 .30068 L .33248 .30127 L .33627 .30193 L .33987 .30257 L .34328 .30322 L .34686 .30392 L .35027 .30461 L .35384 .30537 L .35723 .30613 L .36045 .30687 L .36384 .30767 L .36706 .30847 L .37043 .30933 L .37365 .31018 L .3767 .31101 L .37991 .31191 L .38297 .31279 L .38587 .31365 L .38893 .31459 L .39184 .3155 L .39489 .31648 L .3978 .31744 L .40057 .31837 L .40349 .31937 L .40626 .32035 L .40918 .3214 L .41196 .32241 L .41461 .3234 L .41739 .32446 L .42005 .32549 L .42258 .32648 L .42524 .32754 L .42778 .32857 L .43046 .32967 L .43301 .33073 L .43543 .33176 L .43799 .33285 L .44044 .33391 L .44276 .33492 L .44521 .33601 L .44755 .33705 L .45002 .33816 L .45237 .33923 L .45461 .34026 L .45698 .34135 L .45924 .3424 L .46161 .34351 L .46388 .34458 L .46605 .34561 L .46833 .3467 L Mistroke .47052 .34774 L .4726 .34874 L .47479 .3498 L .47689 .35082 L .4791 .35189 L .48121 .35292 L .48323 .35391 L .48535 .35495 L .48739 .35594 L .48953 .357 L .49158 .358 L .49353 .35896 L .49559 .35998 L .49756 .36094 L .49945 .36187 L .50144 .36284 L .50334 .36377 L .50534 .36475 L .50726 .36569 L .50909 .36658 L .51102 .36752 L .51287 .36841 L .51463 .36926 L .5165 .37016 L .51828 .37101 L .52016 .37191 L .52197 .37276 L .52369 .37358 L .5255 .37443 L .52724 .37524 L .52908 .3761 L .53083 .37691 L .53251 .37768 L .53428 .37849 L .53598 .37925 L .5376 .37998 L .53932 .38075 L .54096 .38148 L .54269 .38224 L .54435 .38296 L .54593 .38365 L .54761 .38437 L .54921 .38505 L .55074 .3857 L .55236 .38638 L .55391 .38702 L .55555 .3877 L .55712 .38833 L .55862 .38894 L .56021 .38957 L Mistroke .56173 .39017 L .56333 .3908 L .56487 .39139 L .56634 .39195 L .56789 .39254 L .56938 .39309 L .5708 .39362 L .57231 .39417 L .57375 .39469 L .57528 .39523 L .57674 .39574 L .57813 .39623 L .57961 .39673 L .58103 .39721 L .58252 .39771 L .58395 .39818 L .58533 .39863 L .58678 .39909 L .58816 .39953 L .58949 .39994 L .5909 .40037 L .59225 .40078 L .59367 .4012 L .59504 .4016 L .59634 .40198 L .59773 .40237 L .59905 .40274 L .60032 .40309 L .60166 .40346 L .60295 .4038 L .60431 .40416 L .60561 .40449 L .60686 .40481 L .60818 .40514 L .60944 .40545 L .61078 .40577 L .61207 .40608 L .61329 .40636 L .61459 .40666 L .61584 .40694 L .61703 .4072 L .6183 .40747 L .61951 .40773 L .62079 .408 L .62201 .40825 L .62319 .40848 L .62443 .40873 L .62563 .40896 L .62677 .40917 L .62798 .4094 L Mistroke .62914 .40961 L .63037 .40982 L .63154 .41003 L .63267 .41022 L .63387 .41042 L .63501 .41061 L .63622 .4108 L .63738 .41098 L .63849 .41115 L .63967 .41132 L .6408 .41149 L .64188 .41164 L .64303 .4118 L .64413 .41195 L .64529 .41211 L .64641 .41225 L .64747 .41239 L .64861 .41253 L .64969 .41266 L .65084 .41279 L .65194 .41292 L .653 .41304 L .65411 .41316 L .65519 .41327 L .65621 .41338 L .6573 .41349 L .65835 .41359 L .65945 .4137 L .66051 .41379 L .66153 .41389 L .6626 .41398 L .66363 .41407 L .66462 .41415 L .66567 .41424 L .66668 .41431 L .66774 .4144 L .66876 .41447 L .66974 .41454 L .67078 .41461 L .67177 .41468 L .67282 .41475 L .67383 .41481 L .6748 .41487 L .67583 .41493 L .67681 .41499 L .67776 .41504 L .67876 .4151 L .67971 .41514 L .68073 .4152 L .68171 .41524 L Mistroke .68264 .41529 L .68363 .41533 L .68458 .41537 L .68559 .41542 L .68655 .41545 L .68748 .41549 L .68846 .41553 L .6894 .41556 L .6903 .41559 L .69126 .41563 L .69217 .41566 L .69315 .41569 L .69408 .41571 L .69497 .41574 L .69592 .41577 L .69683 .41579 L .6977 .41581 L .69863 .41583 L .69951 .41586 L .70045 .41588 L .70135 .4159 L .70222 .41591 L .70313 .41593 L .70401 .41595 L .70495 .41597 L .70584 .41598 L .7067 .416 L .70761 .41601 L .70848 .41603 L .70932 .41604 L .7102 .41605 L .71105 .41606 L .71196 .41608 L .71282 .41609 L .71365 .4161 L .71453 .41611 L .71538 .41612 L .71619 .41613 L .71705 .41614 L .71787 .41615 L .71874 .41616 L .71958 .41616 L .72039 .41617 L .72124 .41618 L .72206 .41619 L .72293 .4162 L .72376 .41621 L .72456 .41621 L .72541 .41622 L .72622 .41623 L Mistroke .727 .41624 L .72783 .41624 L .72862 .41625 L .72946 .41626 L .73027 .41627 L .73104 .41628 L .73187 .41629 L .73265 .41629 L .73349 .4163 L .73429 .41631 L .73506 .41632 L .73588 .41633 L .73666 .41634 L .73741 .41635 L .73821 .41636 L .73898 .41637 L .73979 .41638 L .74057 .41639 L .74132 .4164 L .74211 .41641 L .74287 .41643 L .7436 .41644 L .74437 .41645 L .74512 .41646 L .74591 .41648 L .74666 .41649 L .74739 .41651 L .74816 .41652 L .7489 .41654 L .74968 .41655 L .75043 .41657 L .75116 .41659 L .75192 .4166 L .75266 .41662 L .75336 .41664 L .75411 .41666 L .75483 .41668 L .75559 .4167 L .75632 .41672 L .75703 .41674 L .75777 .41677 L .75849 .41679 L .75924 .41681 L .75997 .41684 L .76067 .41686 L .76141 .41689 L .76212 .41692 L .7628 .41694 L .76353 .41697 L .76422 .417 L Mistroke .76496 .41703 L .76567 .41706 L .76635 .41709 L .76707 .41712 L .76776 .41715 L .76843 .41719 L .76913 .41722 L .76981 .41725 L .77053 .41729 L .77122 .41733 L .77188 .41736 L .77258 .4174 L .77325 .41744 L .77397 .41748 L .77466 .41752 L .77531 .41756 L .77601 .41761 L .77668 .41765 L .77733 .41769 L .77801 .41774 L .77867 .41778 L .77936 .41783 L .78003 .41788 L .78068 .41792 L .78136 .41798 L .78201 .41802 L .78264 .41807 L .7833 .41813 L .78394 .41818 L .78462 .41823 L .78527 .41829 L .7859 .41834 L .78656 .4184 L .7872 .41846 L .78788 .41852 L .78853 .41858 L .78915 .41864 L .78981 .4187 L .79045 .41876 L .79106 .41882 L .7917 .41889 L .79232 .41895 L .79298 .41902 L .79362 .41909 L .79423 .41916 L .79487 .41923 L .79549 .4193 L .79615 .41937 L .79678 .41945 L .79738 .41952 L Mistroke .79803 .4196 L .79865 .41967 L .79924 .41975 L .79987 .41983 L .80047 .4199 L .80111 .41999 L .80173 .42007 L .80232 .42015 L .80295 .42023 L .80355 .42032 L .80413 .4204 L .80474 .42049 L .80533 .42057 L .80596 .42066 L .80656 .42075 L .80714 .42084 L .80775 .42094 L .80834 .42103 L .80896 .42113 L .80956 .42122 L .81014 .42132 L .81075 .42142 L .81134 .42151 L .8119 .42161 L .8125 .42171 L .81307 .42181 L .81368 .42192 L .81427 .42202 L .81483 .42213 L .81543 .42223 L .816 .42234 L .81655 .42244 L .81713 .42256 L .8177 .42266 L .81829 .42278 L .81886 .42289 L .81941 .423 L .82 .42312 L .82056 .42324 L .82115 .42336 L .82172 .42348 L .82227 .4236 L .82285 .42372 L .82341 .42384 L .82395 .42396 L .82452 .42409 L .82507 .42421 L .82565 .42434 L .82621 .42447 L .82674 .4246 L Mistroke .82731 .42473 L .82786 .42486 L .82844 .425 L .82899 .42514 L .82953 .42527 L .8301 .42541 L .83064 .42555 L .83117 .42568 L .83172 .42583 L .83226 .42596 L .83282 .42611 L .83337 .42626 L .83389 .4264 L .83445 .42655 L .83498 .4267 L .83549 .42684 L .83604 .42699 L .83656 .42714 L .83711 .4273 L .83765 .42745 L .83816 .4276 L .8387 .42776 L .83923 .42792 L .83978 .42808 L .84031 .42825 L .84082 .4284 L .84137 .42857 L .84189 .42874 L .84239 .42889 L .84292 .42906 L .84343 .42923 L .84397 .4294 L .84446 .42956 L Mfstroke 1 0 .24 r 0 .23999 m .00609 .2435 L .01925 .25045 L .03134 .25629 L .04245 .26123 L .05378 .26587 L .06424 .2698 L .07492 .2735 L .0848 .27663 L .09397 .27931 L .10338 .28182 L .11213 .28395 L .12028 .28577 L .12868 .28749 L .13652 .28894 L .1446 .29031 L .15216 .29147 L .15922 .29246 L .16654 .2934 L .17339 .29421 L .18048 .29498 L .18713 .29565 L .19338 .29624 L .19986 .29682 L .20595 .29734 L .21168 .29781 L .21764 .29829 L .22325 .29874 L .22909 .29922 L .23459 .29967 L .23977 .30011 L .24518 .30058 L .25028 .30104 L .25509 .3015 L .26011 .302 L .26486 .30251 L .26982 .30306 L .2745 .30362 L .27893 .30417 L .28356 .30479 L .28794 .30541 L .29252 .30609 L .29685 .30677 L .30096 .30746 L .30525 .30821 L .30932 .30896 L .31318 .3097 L .31722 .31052 L .32105 .31133 L .32506 .31222 L Mistroke .32887 .3131 L .33248 .31397 L .33627 .31491 L .33987 .31585 L .34328 .31676 L .34686 .31775 L .35027 .31873 L .35384 .31978 L .35723 .32082 L .36045 .32183 L .36384 .32292 L .36706 .32398 L .37043 .32512 L .37365 .32624 L .3767 .32732 L .37991 .32849 L .38297 .32962 L .38587 .33071 L .38893 .33188 L .39184 .33302 L .39489 .33423 L .3978 .33541 L .40057 .33654 L .40349 .33775 L .40626 .33892 L .40918 .34016 L .41196 .34136 L .41461 .34251 L .41739 .34374 L .42005 .34492 L .42258 .34605 L .42524 .34725 L .42778 .3484 L .43046 .34962 L .43301 .3508 L .43543 .35192 L .43799 .35311 L .44044 .35425 L .44276 .35534 L .44521 .35649 L .44755 .35759 L .45002 .35875 L .45237 .35986 L .45461 .36092 L .45698 .36204 L .45924 .3631 L .46161 .36422 L .46388 .36529 L .46605 .36631 L .46833 .36739 L Mistroke .47052 .36841 L .4726 .36938 L .47479 .3704 L .47689 .37137 L .4791 .37239 L .48121 .37336 L .48323 .37428 L .48535 .37525 L .48739 .37617 L .48953 .37713 L .49158 .37804 L .49353 .3789 L .49559 .37981 L .49756 .38067 L .49945 .38148 L .50144 .38233 L .50334 .38314 L .50534 .38398 L .50726 .38478 L .50909 .38554 L .51102 .38632 L .51287 .38707 L .51463 .38777 L .5165 .38851 L .51828 .3892 L .52016 .38993 L .52197 .39062 L .52369 .39126 L .5255 .39194 L .52724 .39257 L .52908 .39323 L .53083 .39386 L .53251 .39444 L .53428 .39506 L .53598 .39563 L .5376 .39618 L .53932 .39674 L .54096 .39727 L .54269 .39782 L .54435 .39834 L .54593 .39883 L .54761 .39934 L .54921 .39982 L .55074 .40026 L .55236 .40073 L .55391 .40117 L .55555 .40162 L .55712 .40204 L .55862 .40244 L .56021 .40286 L Mistroke .56173 .40324 L .56333 .40364 L .56487 .40402 L .56634 .40437 L .56789 .40473 L .56938 .40507 L .5708 .40539 L .57231 .40572 L .57375 .40603 L .57528 .40634 L .57674 .40664 L .57813 .40692 L .57961 .4072 L .58103 .40747 L .58252 .40774 L .58395 .408 L .58533 .40823 L .58678 .40848 L .58816 .4087 L .58949 .40892 L .5909 .40913 L .59225 .40933 L .59367 .40954 L .59504 .40973 L .59634 .40991 L .59773 .41009 L .59905 .41026 L .60032 .41042 L .60166 .41058 L .60295 .41072 L .60431 .41087 L .60561 .41101 L .60686 .41114 L .60818 .41127 L .60944 .41139 L .61078 .41151 L .61207 .41162 L .61329 .41172 L .61459 .41183 L .61584 .41192 L .61703 .41201 L .6183 .41209 L .61951 .41217 L .62079 .41225 L .62201 .41232 L .62319 .41239 L .62443 .41245 L .62563 .41251 L .62677 .41256 L .62798 .41261 L Mistroke .62914 .41266 L .63037 .4127 L .63154 .41274 L .63267 .41277 L .63387 .4128 L .63501 .41283 L .63622 .41286 L .63738 .41288 L .63849 .4129 L .63967 .41292 L .6408 .41293 L .64188 .41294 L .64248 .41294 L .64303 .41294 L .64359 .41295 L .64413 .41295 L .6444 .41295 L .64469 .41295 L .64483 .41295 L .64496 .41295 L .64509 .41295 L .6452 .41295 L .64527 .41295 L .64534 .41295 L .64537 .41295 L .64541 .41295 L .64544 .41295 L .64548 .41295 L .64551 .41295 L .64553 .41295 L .64555 .41295 L .64557 .41295 L .64559 .41295 L .64561 .41295 L .64563 .41295 L .64566 .41295 L .6457 .41295 L .64577 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Mistroke .70128 .41081 L .7022 .41076 L .70307 .4107 L .704 .41065 L .70489 .4106 L .70575 .41055 L .70665 .4105 L .70752 .41045 L .70844 .41039 L .70932 .41034 L .71017 .41029 L .71107 .41024 L .71193 .41019 L .71276 .41015 L .71363 .4101 L .71448 .41005 L .71537 .41 L .71622 .40995 L .71704 .40991 L .71791 .40986 L .71875 .40982 L .71955 .40977 L .7204 .40973 L .72121 .40969 L .72208 .40964 L .72291 .4096 L .7237 .40956 L .72455 .40952 L .72536 .40948 L .72621 .40943 L .72704 .4094 L .72783 .40936 L .72866 .40932 L .72947 .40928 L .73024 .40925 L .73106 .40921 L .73184 .40918 L .73267 .40914 L .73347 .40911 L .73424 .40908 L .73505 .40905 L .73583 .40901 L .73666 .40898 L .73745 .40895 L .73821 .40893 L .73902 .4089 L .7398 .40887 L .74054 .40885 L .74133 .40882 L .74209 .4088 L Mistroke .74289 .40878 L .74366 .40875 L .7444 .40873 L .74519 .40871 L .74594 .40869 L .74666 .40868 L .74743 .40866 L .74816 .40864 L .74894 .40863 L .74969 .40861 L .75041 .4086 L .75117 .40859 L .7519 .40857 L .75268 .40856 L .75343 .40855 L .75414 .40855 L .7549 .40854 L .75563 .40853 L .75632 .40853 L .75707 .40852 L .75778 .40852 L .75816 .40852 L .75853 .40852 L .75871 .40852 L .75889 .40852 L .75907 .40852 L .75923 .40852 L .75931 .40852 L .7594 .40852 L .75949 .40852 L .75951 .40852 L .75952 .40852 L .75954 .40852 L .75956 .40852 L .75958 .40852 L .7596 .40852 L .75962 .40852 L .75964 .40852 L .75966 .40852 L .75968 .40852 L .7597 .40852 L .75972 .40852 L .75974 .40852 L .75976 .40852 L .75978 .40852 L .7598 .40852 L .75982 .40852 L .75985 .40852 L .75987 .40852 L .75989 .40852 L Mistroke .75991 .40852 L .76 .40852 L .76005 .40852 L .76009 .40852 L .76025 .40852 L .76045 .40852 L .76063 .40852 L .76099 .40852 L .76132 .40852 L .76203 .40852 L .76271 .40852 L .76343 .40853 L .76412 .40854 L .76485 .40854 L .76555 .40855 L .76623 .40856 L .76695 .40857 L .76764 .40858 L .76836 .40859 L .76907 .40861 L .76974 .40862 L .77045 .40864 L .77114 .40866 L .77179 .40867 L .77249 .40869 L .77316 .40871 L .77387 .40874 L .77456 .40876 L .77521 .40878 L .77591 .40881 L .77657 .40883 L .77721 .40886 L .77789 .40889 L .77854 .40891 L .77924 .40895 L .7799 .40898 L .78054 .40901 L .78122 .40904 L .78187 .40908 L .78256 .40912 L .78322 .40915 L .78385 .40919 L .78453 .40923 L .78518 .40927 L .7858 .40931 L .78646 .40936 L .78709 .4094 L .78776 .40945 L .78841 .40949 L .78903 .40954 L Mistroke .78969 .40959 L .79032 .40964 L .79099 .40969 L .79163 .40975 L .79225 .4098 L .7929 .40986 L .79353 .40991 L .79414 .40997 L .79478 .41003 L .7954 .41009 L .79605 .41015 L .79668 .41021 L .79728 .41027 L .79792 .41034 L .79853 .4104 L .79912 .41047 L .79975 .41054 L .80035 .4106 L .80098 .41068 L .8016 .41075 L .80218 .41082 L .80281 .4109 L .80341 .41097 L .80404 .41105 L .80465 .41113 L .80524 .41121 L .80586 .41129 L .80646 .41137 L .80703 .41145 L .80764 .41153 L .80823 .41162 L .80885 .41171 L .80944 .41179 L .81002 .41188 L .81062 .41197 L .81121 .41206 L .81183 .41216 L .81242 .41225 L .81299 .41235 L .8136 .41245 L .81418 .41254 L .81474 .41264 L .81533 .41274 L .8159 .41284 L .81651 .41295 L .81709 .41305 L .81765 .41315 L .81824 .41326 L .81881 .41337 L .81935 .41347 L Mistroke .81993 .41358 L .82049 .41369 L .82108 .41381 L .82165 .41392 L .82219 .41403 L .82277 .41415 L .82333 .41427 L .82392 .41439 L .82448 .41451 L .82503 .41463 L .8256 .41476 L .82616 .41488 L .82669 .415 L .82726 .41513 L .8278 .41525 L .82838 .41539 L .82893 .41552 L .82946 .41564 L .83003 .41578 L .83057 .41591 L .83109 .41604 L .83164 .41618 L .83217 .41631 L .83274 .41646 L .83328 .4166 L .8338 .41673 L .83435 .41688 L .83488 .41702 L .83544 .41717 L .83598 .41732 L .8365 .41747 L .83706 .41762 L .83759 .41777 L .83809 .41791 L .83863 .41807 L .83915 .41822 L .8397 .41838 L .84023 .41854 L .84074 .41869 L .84128 .41886 L .8418 .41902 L .84235 .41919 L .84288 .41935 L .84338 .41951 L .84392 .41968 L .84444 .41985 L .84446 .41986 L Mfstroke 1 .48 0 r 0 .262 m .00623 .26492 L .01863 .27021 L .03119 .2751 L .04274 .27919 L .05339 .28262 L .06426 .2858 L .07432 .28847 L .08459 .29093 L .09413 .29298 L .10298 .29469 L .11207 .29628 L .12054 .29761 L .12843 .29873 L .13658 .29977 L .14419 .30066 L .15204 .3015 L .15939 .30222 L .16626 .30285 L .17338 .30346 L .18006 .30402 L .18697 .30458 L .19346 .3051 L .19956 .30559 L .20589 .30611 L .21184 .30662 L .21744 .30711 L .22327 .30766 L .22877 .3082 L .23448 .3088 L .23987 .3094 L .24495 .31 L .25025 .31067 L .25525 .31135 L .25997 .31203 L .26491 .31279 L .26957 .31354 L .27444 .31438 L .27904 .31522 L .28339 .31606 L .28794 .31698 L .29225 .3179 L .29676 .31891 L .30102 .31991 L .30506 .32089 L .30929 .32197 L .3133 .32304 L .31709 .32408 L .32108 .32522 L .32485 .32633 L Mistroke .32881 .32754 L .33256 .32872 L .33612 .32987 L .33986 .33112 L .34341 .33233 L .34677 .33351 L .35031 .33477 L .35367 .336 L .35719 .33732 L .36054 .3386 L .36372 .33983 L .36707 .34115 L .37025 .34243 L .37358 .34378 L .37676 .3451 L .37978 .34636 L .38295 .3477 L .38597 .34899 L .38884 .35024 L .39186 .35155 L .39474 .35282 L .39776 .35416 L .40064 .35544 L .40338 .35667 L .40626 .35797 L .40901 .35921 L .41189 .36052 L .41465 .36178 L .41727 .36297 L .42002 .36423 L .42265 .36543 L .42516 .36658 L .4278 .36778 L .43031 .36893 L .43296 .37013 L .43548 .37128 L .43789 .37236 L .44043 .37351 L .44284 .37459 L .44515 .37562 L .44758 .3767 L .4499 .37772 L .45234 .37879 L .45467 .3798 L .4569 .38076 L .45924 .38177 L .46148 .38271 L .46384 .3837 L .46609 .38464 L .46823 .38552 L Mistroke .4705 .38645 L .47266 .38732 L .47473 .38814 L .4769 .38899 L .47898 .3898 L .48118 .39064 L .48327 .39143 L .48527 .39217 L .48738 .39295 L .4894 .39367 L .49152 .39443 L .49356 .39514 L .4955 .3958 L .49754 .3965 L .4995 .39714 L .50137 .39775 L .50334 .39838 L .50523 .39898 L .50722 .39959 L .50912 .40016 L .51094 .4007 L .51286 .40125 L .51469 .40177 L .51645 .40225 L .5183 .40275 L .52007 .40322 L .52194 .4037 L .52373 .40415 L .52544 .40457 L .52724 .405 L .52897 .4054 L .53079 .40582 L .53254 .4062 L .5342 .40656 L .53597 .40693 L .53765 .40727 L .53926 .40758 L .54097 .4079 L .5426 .4082 L .54432 .40851 L .54596 .40879 L .54754 .40906 L .5492 .40932 L .5508 .40957 L .55232 .4098 L .55393 .41003 L .55547 .41024 L .5571 .41046 L .55866 .41066 L .56015 .41084 L Mistroke .56173 .41102 L .56324 .41119 L .56484 .41136 L .56636 .41151 L .56783 .41165 L .56937 .41179 L .57085 .41192 L .57227 .41203 L .57376 .41214 L .5752 .41225 L .57671 .41235 L .57817 .41244 L .57956 .41252 L .58102 .41259 L .58243 .41266 L .58392 .41273 L .58534 .41278 L .58671 .41283 L .58815 .41287 L .58953 .41291 L .59085 .41294 L .59225 .41297 L .59359 .41299 L .59427 .413 L .59501 .41301 L .59566 .41301 L .59637 .41302 L .59704 .41302 L .59741 .41302 L .59757 .41302 L .59775 .41302 L .59793 .41302 L .59809 .41302 L .59817 .41302 L .59825 .41302 L .5983 .41302 L .59835 .41302 L .59837 .41302 L .59839 .41302 L .59843 .41302 L .59847 .41302 L .59851 .41302 L .59855 .41302 L .59859 .41302 L .59862 .41302 L .59866 .41302 L .59873 .41302 L .59881 .41302 L .59889 .41302 L .59906 .41302 L Mistroke .59922 .41302 L .5994 .41302 L .59971 .41302 L .60004 .41302 L .6004 .41302 L .60106 .41301 L .60176 .41301 L .60313 .41299 L .60445 .41298 L .60571 .41295 L .60705 .41293 L .60833 .4129 L .60955 .41287 L .61085 .41283 L .61209 .41279 L .61341 .41274 L .61467 .41269 L .61587 .41265 L .61715 .41259 L .61838 .41253 L .61967 .41247 L .62091 .41241 L .6221 .41235 L .62336 .41227 L .62457 .4122 L .62572 .41214 L .62694 .41206 L .62812 .41198 L .62936 .4119 L .63055 .41182 L .63169 .41174 L .63289 .41165 L .63405 .41156 L .63516 .41148 L .63633 .41139 L .63745 .4113 L .63864 .4112 L .63979 .41111 L .64088 .41102 L .64204 .41092 L .64315 .41082 L .64432 .41072 L .64545 .41061 L .64653 .41051 L .64767 .41041 L .64877 .41031 L .64982 .41021 L .65093 .4101 L .652 .41 L .65313 .40988 L Mistroke .65421 .40978 L .65525 .40967 L .65635 .40956 L .65741 .40945 L .65852 .40934 L .65959 .40923 L .66062 .40912 L .66171 .40901 L .66275 .4089 L .66375 .40879 L .66481 .40868 L .66582 .40857 L .6669 .40845 L .66793 .40834 L .66892 .40824 L .66997 .40812 L .67097 .40801 L .67193 .40791 L .67295 .40779 L .67393 .40769 L .67497 .40757 L .67596 .40746 L .67692 .40736 L .67793 .40724 L .6789 .40714 L .67992 .40702 L .68091 .40691 L .68185 .40681 L .68285 .4067 L .68381 .40659 L .68473 .40649 L .6857 .40638 L .68664 .40628 L .68763 .40617 L .68858 .40606 L .68949 .40596 L .69046 .40586 L .69138 .40576 L .69227 .40566 L .69321 .40556 L .69412 .40546 L .69507 .40536 L .69599 .40526 L .69687 .40516 L .69781 .40506 L .6987 .40497 L .69965 .40487 L .70056 .40477 L .70143 .40468 L .70236 .40459 L Mistroke .70325 .40449 L .7041 .40441 L .705 .40431 L .70587 .40423 L .70679 .40413 L .70767 .40405 L .70851 .40396 L .70941 .40387 L .71027 .40379 L .71118 .4037 L .71206 .40362 L .71289 .40354 L .71378 .40345 L .71464 .40337 L .71545 .4033 L .71632 .40322 L .71715 .40314 L .71804 .40307 L .71888 .40299 L .7197 .40292 L .72056 .40284 L .72138 .40277 L .72218 .40271 L .72302 .40264 L .72382 .40257 L .72468 .4025 L .7255 .40243 L .72629 .40237 L .72712 .40231 L .72792 .40224 L .72877 .40218 L .72959 .40212 L .73037 .40206 L .7312 .402 L .732 .40194 L .73276 .40189 L .73357 .40184 L .73435 .40178 L .73517 .40173 L .73596 .40168 L .73672 .40163 L .73753 .40158 L .7383 .40153 L .73912 .40148 L .73991 .40144 L .74066 .4014 L .74146 .40135 L .74223 .40131 L .74297 .40127 L .74375 .40123 L Mistroke .7445 .4012 L .74529 .40116 L .74606 .40112 L .74679 .40109 L .74757 .40106 L .74831 .40102 L .74903 .401 L .74979 .40097 L .75052 .40094 L .75129 .40091 L .75203 .40089 L .75274 .40086 L .7535 .40084 L .75423 .40082 L .75499 .4008 L .75573 .40078 L .75644 .40076 L .75719 .40074 L .75791 .40073 L .75861 .40071 L .75934 .4007 L .76005 .40069 L .76079 .40068 L .76151 .40067 L .7622 .40066 L .76293 .40066 L .76363 .40065 L .76431 .40065 L .76465 .40065 L .76502 .40064 L .76538 .40064 L .76556 .40064 L .76566 .40064 L .76575 .40064 L .76584 .40064 L .76589 .40064 L .76593 .40064 L .76595 .40064 L .76597 .40064 L .766 .40064 L .76602 .40064 L .76606 .40064 L .76608 .40064 L .7661 .40064 L .76612 .40064 L .76613 .40064 L .76615 .40064 L .76616 .40064 L .76617 .40064 L .76619 .40064 L Mistroke .7662 .40064 L .76622 .40064 L .76623 .40064 L .76624 .40064 L .76626 .40064 L .76627 .40064 L .76629 .40064 L .76631 .40064 L .76634 .40064 L .76638 .40064 L .76642 .40064 L .76643 .40064 L .76645 .40064 L .76647 .40064 L .76651 .40064 L .76656 .40064 L .76664 .40064 L .76681 .40064 L .76698 .40064 L .76714 .40064 L .76747 .40064 L .76784 .40065 L .76856 .40065 L .76925 .40065 L .76991 .40066 L .77061 .40067 L .77129 .40068 L .772 .40069 L .77269 .4007 L .77335 .40071 L .77405 .40072 L .77472 .40074 L .77537 .40075 L .77605 .40077 L .77671 .40079 L .77741 .40081 L .77808 .40083 L .77872 .40085 L .7794 .40088 L .78006 .4009 L .78075 .40093 L .78142 .40096 L .78206 .40099 L .78274 .40102 L .78339 .40105 L .78401 .40108 L .78468 .40112 L .78532 .40115 L .78599 .40119 L .78664 .40123 L Mistroke .78727 .40126 L .78793 .40131 L .78857 .40135 L .78924 .40139 L .78989 .40144 L .79051 .40148 L .79117 .40153 L .7918 .40158 L .79241 .40162 L .79306 .40168 L .79368 .40173 L .79433 .40178 L .79497 .40184 L .79557 .40189 L .79622 .40195 L .79683 .40201 L .79743 .40206 L .79806 .40213 L .79866 .40219 L .7993 .40225 L .79992 .40232 L .80051 .40238 L .80114 .40245 L .80174 .40252 L .80238 .40259 L .803 .40266 L .80359 .40273 L .80421 .40281 L .80481 .40288 L .80539 .40295 L .806 .40303 L .80659 .40311 L .80722 .40319 L .80782 .40327 L .80839 .40335 L .809 .40344 L .80959 .40352 L .81021 .40361 L .81081 .4037 L .81139 .40379 L .812 .40388 L .81258 .40397 L .81314 .40406 L .81374 .40416 L .81431 .40425 L .81492 .40435 L .81551 .40445 L .81607 .40455 L .81666 .40465 L .81724 .40475 L Mistroke .81778 .40485 L .81837 .40495 L .81893 .40506 L .81952 .40517 L .82009 .40528 L .82064 .40538 L .82122 .40549 L .82178 .40561 L .82238 .40572 L .82295 .40584 L .82349 .40595 L .82407 .40607 L .82463 .40619 L .82517 .40631 L .82574 .40643 L .82628 .40655 L .82686 .40668 L .82742 .4068 L .82795 .40692 L .82852 .40706 L .82907 .40718 L .82959 .40731 L .83015 .40744 L .83068 .40757 L .83125 .40771 L .83179 .40784 L .83232 .40797 L .83287 .40812 L .8334 .40825 L .83397 .4084 L .83451 .40854 L .83504 .40868 L .83559 .40883 L .83612 .40897 L .83664 .40911 L .83718 .40927 L .8377 .40941 L .83825 .40957 L .83879 .40972 L .8393 .40987 L .83984 .41003 L .84036 .41018 L .84091 .41035 L .84145 .41051 L .84196 .41066 L .8425 .41083 L .84302 .41099 L .84352 .41115 L .84405 .41132 L .84446 .41145 L Mistroke Mfstroke .8 1 0 r 0 .27413 m .00652 .2768 L .01861 .28131 L .03089 .28545 L .04219 .28889 L .05369 .29204 L .06431 .29464 L .07412 .2968 L .08418 .29878 L .09351 .30042 L .10307 .30191 L .11195 .30315 L .12023 .30419 L .12875 .30515 L .1367 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0`00Ooooooooo`02oooo00D007ooooooooooool007l00_ooo`03001ooooooooo01Goool00`00Oooo ooooo`0:oooo00<007ooooooool01oooo`03001ooooooooo00Coool00`00Ooooooooo`04oooo00<0 07ooooooool00_ooo`05001ooooooooooooo001o00?oool01@00Ooooooooooooo`00O`0"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {0.524874, 1.73736, \ 0.0128709, 0.0159734}}] }, Open ]], Cell["\<\ The agreement between theory and experiment at high currents is not good. The \ drop in p0dc and voltage at fixed p0d with increasing normalized and actual \ current density does not make sense to me.\ \>", "Subtitle"], Cell["\<\ I need to evaluate the various contributions to the gain to see which one is \ increasing too rapidly at high currents.\ \>", "Subtitle"], Cell[BoxData[ \(\(j = 1;\)\)], "Input"], Cell[BoxData[ \(\(Clear[p0d, p0dc, vd, jopsq];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(calcGammVsp0dc = LogLogPlot[\((\((assumedgammai\ /. vd -> 6275.7\ jopsq\^\(2/3\)\ p0dc\^\(5/3\))\) /. jopsq -> inputTable[\([j, 2]\)])\), {p0dc, 0.001, inputTable[\([j, 1]\)]}, GridLines -> Automatic, PlotLabel -> "\", PlotPoints -> 500, PlotStyle -> {Hue[0.5], Thickness[0.007]}, PlotRange -> {{0.001, 1. }, {0.01, 100}} (*\(,\)\(DisplayFunction -> Identity\)*) ];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 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The decrease in \ \"reflection\" is really a reduction in production relative to that for p0d \ >>p0dc, i.e., an effect of discharge \"obstruction\" by the anode. The discontinuity in gain and in productionFit at low p0dc occurs at the \ threshold in the production fit. Below this threshold there is a false \ contribution from the way I combine the local field resuts with the bean \ results. 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