Model for intensity calculation in electron guns
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(2) A new model for intensity calculation in electron guns O. Doyen, JM. De Conto.
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(30) u. −∞. /`TaoaÐ 7i2rHgj`a{ÔEa rr<a ewn]f lbgji]k l«k nHnpioYr gilDyG\_G`ayDag2dVijea y bVd e]bfejdgjijk lck ngj`DaEaVo2laVe[×ijr#q i]x alui lud| |aly i* _`Ta+dRyDx dlDgjdRq$aLk n.gj`iprEyDa x a ejk |DvcaVl$gi2r.gpk\q agdLn2d!r gdlyraRe]n2 r fnpn2i]bVijalDg1dlTde~ gpi]bVd eEvck yDaReQf[r ilq7bejd rri]bVd e#gpk$k epr\eiTad| e]azk!o dgj`avdhgjijbd!Li g]`Tk fDg}g`aºlTaa yÃk n{d yDy igjijk ld e}bVk$y a r &x al ejivuigja yHg2ksb~ ejilTy$o<ijbVd e/q fDl[r.gj`ijr\|ao vi g<r+gpkHq ag"g]`Ta7ri]q lTi]nji]bVdl g |D` ~ rijbd e#|Tdhodvahgpaor/k nEg]`Tacq!f lGX`Ti]b`sbk fejy9 Tacq$aVlao<dReiÖRa y9gpk dl ~Lq fDlr `Td| aD. W. }ig]`k fDo&lk gpdgji]k l[r$g]`TaC|Tk ri gji]x a/|do<gk n \y a n2ila r#g]` aLavijrr ijx$a ÖRk!lTack n#g]`Ta\bVdg]`Tk yDaD ¡urXdLoa!r fDegpn2k oEgj`iprXadvu|DejaR[g]`Ta\avuiggjilTq od y if[r wijrÊ[ !v\vz/k oa k x aoY+Lax$aVo<i]nj~¬gj`dVg `Td rHd |dVod k eji]br ` d|Ta cd rHfGraVyÓ ~¤vck r gsk ngj`a|Do<a x ijk fGrdf gj`k oYrh Lk La x aoY$La1Li]eje*r `k il\|do<g ug]` dg*n2k ovck oaLbk v\|Te]ijbVdg2aRy\q fDl r go<fbg]f o<a r!gj`DaE|dVo<d k eji]bEdV|D| ok!Tivdhgpijk!lbdVl$lTk g aXvdy a$. x .
(31) . W . . C. Current density and total current. . _kLbVd e]bfejdgpaXg`a"bdgj`k y a/bhf o2oal gy ahl[r ig]~ n]ok v¤gj`a/bVdgj`k yDa a eja bgoijb¸n2ija ejy La¸|Dok |k ra¸gpk fGra¸gj`a¢bVe]d rri]bVdVe{k la¢ yDivcaVlrijk ldVeL#`DijejyD]dVlq v\fTioprce]dV\ ¯Ñ }ar f |D|k raRXeiavudl ~ df g]`Tk!o rQg]` dgLg`Tar ~ r gpavµ Ta` d x a r9eji abVk!lTbaVlDgjo<i]bsilTy a|aly ahl g yDijk yDa rn2k e]ejk LilqL#`iejyD]dlq v\fTioVjre]dV\V]g*q i]x a rÈ. . .
(32) . . =. . ε
(33) . . _`ipr|Tdo<dvahgpaoiprlTk!gGgpk!gpdVe]e~/fDlTyDaoYr2g2k k y\~ agt$ Df gGLaXlk gpi]bVa y/gj`DdVg ig#y a|TahlTyrXk lTe~k!lgj`a\q f lwq a k vcaVg]o<~ ["`dg&iprQa f i]x d ejahl ggpkrd~ gj`dgGi gy a|TahlTyr.k lTe~Lk lug]`TaXbVdgj`k yDa1aeja bgoi]b1n2ia eyG. VÉV. /`TaoaXÒ{iprgj`a"bed rri]bVd ey i]k yDa"q$dV|DaEgj`a/aVe]aVv\aVlDgjdo<~Lb`doq a DdlTy. ε. gj` aQ|Taho<vci gjgjijx$igj~Lk nx d$bfDf vw. W". Ô1~}il g2a q odgjilTq k l{g`TaHavi g]gjilq}bVdg]`Tk yDar f on2d bVaH<dHy ijrbHk n od y if[rQ La1k! g2dVil+gj` a/q fDlui lDgjaVlGr igj~È. . =. ! $ . . π. #. " . ] V\ ^. . . }a1|Dok |k raXgjLkurk$efDgjijk lGrg2k/gpd bhTeaXg`ijr.| ok! ejavwÈRk l\gj`a/k la `dVly [npk!o&vca d!r fDoaycq f lGrk!lTaLaD|TahoivcalDgjd eota n2aoalbVa+iprEalk fq ` gpkcq$aVg.gj`aua fijx dejal g&y$ijk yDauyDijr gpdhlTbaD ]lTyDa a y ilzk!oy ao&g2kcq aggj`a a!rtg1|Do<a bVipr ijk!ld r+|k rri eja9ilbVk v\|dVoijrk lsLi g]`sg`awaD|TahoivualDgp n2k o&d/q i]x alq fDlT$/a1`DdRx$aEgpk+bS `k raXÒÐrk/g]` dgT È S. ¡/ly. ~w|ejk g]gpilqw n2<½ .Cawq agEg]`TawbfDo2oalDg"x$aVor fGr\x k egpd q a b`dod bg2aoijr gji]b1bfDox a/bdRee]aVyL¨ y$o<ijx a/bfDox a ©$. %1 x i]k f[re~ Dnpk!o<vufejdXVÉ Gijrlk gGk x i2k f[r.il\k f obd!ra ! Ta bdVfGr a1ig pi r9x d ei]y}k le~n<k oilTn2ili gpaHy i]k y a r9i l}g]` aotd yDid e"yDi oa bg2ijk l¡\r9d oa rtfTe g<Lrk vcavck y i]n2ijbVdgji]k l[rmdVly{k |Dgpiv\iÖRdgji]k l[rdoaHota $f io<a y{il k oyDaogpk/d| |e~Xgj`ipr.ejd}g2k"k!f olk lT2ilTn2ili gpa 2yDijk yDa1q a k vcagjo<~*ioYr gp gj`aLa $f ijx d e]alDgyDijk$y aLyDijr gjdlTbaLÒ¬`Td r#g2k\ Ta+y a n2i lTa ycdly\Ck!o<zn2k o k fDouq a k vcagjo<~&a bk lTy#ilHk oyDao/gpkwgjdail gpk7d bbVk fDl gXgj` awn2i li gpa yDivcaVlrijk lÎk ngj`aº Ta dvH#`DijeyDjdlq vufiopr¤ed `d r{g2k¸ a bVk!o<oa bg2aRyG_`aRra+gjLkc|k ilDgtrQLieje Ta\y ijrbhf[rraywi lgj`a+lTa gg]` o<a a |dVodRq!otd|D`Tr. D. Correction of Child-Langmuir’s law. _ `Tacbejd rrijbVd e#`iejyD]dVlq v\fTioVjr/ejd«n2k oXgj`acbfDopoaVl$g5yDalTri gj~ iprdÉhÒÂvk yDaVe+dVlDyvcdRy$asn2k ocg]CkilTn]ili gpaw|dodVejea e/a ea bgjok y a rh `aVlgj`a7o<d y if[r9k n+gj`a7 a dv ijr9n2ili gpaRQg]` ipr9y alGr<igj~H Ta bVk$vca!r `ijq `ao5dhlTycdur vcdVee Df glk gl a q eji]q i DejaLbk o<oa bg2ijk lc`dRr5gpk+ Ta+y k laD _`a7q alaVo<d e/bVd raw` d r a aVlrtgjfDy i]aVya ejra"`DaVo<a7dlysi2rcq i]x al}il |dVodRq!otd|D` G Dc\a x aopg]` a ea rrd«r<ivu|ea«bk o<oa bhgpijk!l¢`Td r{ aVal a r gjivcdg2aRy¬dgcgj`a a q il$lTilTqk$nzk!f ortgjfy i]a!rHr `k Lilq}g]`Tdhgcgj` i2r bVk!o<oa bg2ijk lr2g2a|uijrvcdlTy$dVg2k o<~ ¯ &. . =. U \. =. ] WYX[Z V \ ^. U \. =. . ¡ur.dEoa!r fe gt$k le~Xgj`a1a |ao<ivcaVl$gpdVebhf o oalDgGx d efa1dhg _a`. =. b _. ipr. laRa y a ygpkHk Dgpd i l}d9`Ti]q `| oa bVijri]k l}k lg`aw/`Tk$ea7b`dotd bhgpaoijr gjijb bfDox aDE}aH`d x aHlk gpi]bVa ygj`dgcnpk!ozd}q$ijx alq fDl[/ilaRx$aVo ~q oi]y x k egpd q a r#bVk!lTn2ijq!f odg2ijk lGr!gj`Dipr.y iprtgpdlbVaEoaVv\dRilTr.bVk lGr gpdl g. %1lwg]`Tack g]` ao1` dly n2k oXlTa«q fDl[r*®Gejk aDrCaR!fTi]x d eaVl$g5yDijk yDa yDiprtgpdlTbaubk lbVa| g#bVdl aLfraRyc bVnD|Tdo<d q od| `zÍD c d&_`a+| o<a bVi2r<i]k l k Dgpd ilDaRy{k l{g]`Tabhf o<o<al gcx rEg2aVlrijk lb`dod bgjao<iprtgpi]bRr9fGr<ilTq¦gj` i2r yDaRn2il igji]k lijr.$f ig2a1rdVgji2rn]~!ilTq[ _` ipr.ijr.aVD| e]dVila y/ilL|dod q odV|$` G. A. F. Results. ¡un]g2aVo7bk o<oa bg2ilq{#`Tie]y ]dlTq v\fioVjrejd dhlTybh`Tk$k rilqgj`a oi]q ` g+|TdhodvahgpaocÒuQLasbk v\|Tdoa yg2kHgj`asa |aoivcalDgudl yg2kd riv\f e]dgpi]k lbk yDan2k og]Ck¥yDijn2n2aoal gHq f lGrc EfDl£r É`d r}r vcdVeje a eja bgok y a9`k ea rLilsbVk!vu|doiprk lH"ig`q!f lr #dly g]`Tagj` i]bDlTa rr dlTy\r | d bVilqLk ng]`TaXaVeja bhgok yDa!r.do<a"rijq!lTi]npi]bVdl gje~CyDijn2n2aoal g<. $. *k oL k g]`q fDlGr.gj`azbk `aVoalbVa9Ligj`gj`azah |aoivualDg1ipr\x ao<~ q kDk yÎ2|Doa bVi2r<i]k lÎ Tahgjg2aog]`Tdhl Í Ë7n2k o¤g`Ta£"`k e]a«odlq a¢k n ilDgjal[r i gpia rdVlDya x ao<~\gp~ |auk$nEq oijy9x k egpd q a\bVk lGn2ijq!f odgji]k l[[fDl eji a gj`a"r iv\fedVgji]k lcbVk yDaEoa rtfTe g<r$d r&r `k /luilun2ijq fDoaRr#Í/dlf y e. 10. Experiment. 8. Model. 7 6. I (mA). Correction factor. 2. 9. 5 4. 1 .5. 3 2 1 0 0.00. 1. 10. 20. 30. 40. 100.00 VK (volts). 150.00. 200.00. g)h5ikjlJjmonJpJqrLsAtFpfq/u1vJq7w7x yzq{t}|~?nAwa7Jw5wq{t/|EJq7w75B FnJr |5s/Jqz{Js{w?s/@|@q7w7x |+x n1~AJtz}{Jj 1y=yj. 0 .5 0. 50.00. 50. B e a m ra d iu s (a rb itra ry u n its ). ')(+*-,/.),1032/454768795: 2/;=<+>/8?9@2A4B9@2C95D)6E0EDF: G HJI KL>/;)M/N-O): 4/P QLG >/R-,. 14. . . Model 10 8 6. gap. 4. j l¸vk r g7|Doa x ijk!f[r¦|Df e]ijbdgpi]k lGrg`ijr¦|Tdo<dvagjao}ijrb`k ral bVk!l[r g2dVlDgpX/`dVgcd|D|aVdor9gpk¦ TadqDk k$y}`~ |Gk g]`Ta r iprwn2k owdq i2x al q a k vcagjo~$.`k La x aoLgj`Dad rr2fDv\| gji]k l[r+vcdVyDail7gj`Da!rawr2g]fTy$ijaRr\dhoa lk gLdRbbfDodgja7alTk!fTq `}dl yyDk l g"Lk o }npk!obk vu|eja}q a k vcagjo<ija rh. 2. E. Determination parameter. of. the. equivalent. diode. Experiment. 12. I (mA). _ `aubd ejbfDejdg2ijk li2r#vcd y aLn2k o1d+_`Tk!vrk lwq fDlza dvu|eaD k o5e]doq a od y if[r a rgj`Da#`iejyÓdlq v\fTioVjr}e]d o<avdilGrx d eijyL¡/gHejk od y if[r a r1r vud ee&bhf o2oahl gpr2[gj`aubk o<oa bhgpijk!lmbdl aLfD|g2k Ê ËÃr<a a n2ijq fDoa T. 0 0. 50. 100 Vk (volts). 150. 200. .
(34) g)h5ikj)jmonJpJqrLsAtFpfq/u1vJq7w7x yzq{t}|~?nAwa7Jw5wq{t/|EJq7w75B FnJr |5s/Jqz{Js{w?s/@|@q7w7x |+x n1~AJtz?JJj Jy=yj 0.288 0.252. _ `Ti2r\aVe]aVv\aVlDgjdo<~7bVd ra Erk ejx$aRyLig]`¦r iv\| ejawdl d e~ g2ijbVd eQgpk k e2r |aVo vuigprCgpk9 ad"do<ak nQgj`aa eaval g<r/dgQr gjdan2k o/vck y a e]i lTq9gj`a bfDo<oal gq alTahodg2aVyLiludlua ea bgjok lq!f lÈVg]`Ta/bdgj`k yDa1a ea bg]oti]b1n2ija eyLi2r gj`a9Ta~w|k ilDg"k nXg]`Ta9vk yDa e<_` alT#dwbk o<oa bg2ijk ld| |Dejijay7g2kwgj`a bVe]d rr<i]bVd eGk la/y ivcalTrijk!lTdeG#` i]ejyDjdlq vufiopr.ejdLDdVlDyLg`a/b`k ijba k nEdlza $fTi]x d ejahl g&y$ijk yDauyDiprtgpdlbVa\ea dRygpkcd\q kDk ywbRk!o<oa edgjijk l9Cigj` gj`a1a |aoivcalDgjdRebhf o otal gg2alTrijk l\b`dVodRbhgjaoti2r2g2ijb$ aw`Td x aHraVg/fD|}dsriv\| e]aw| `D~ rijbdReXvck yDaRe ]gtrcd bbfDod bV~ipr } aVgg2aoEg`ar iv\f e]dgpi]k lzbk yDaLLa+f[ra$ }a+"i]eelk ªq$aVlaodVeiÖRa+gj` i2r vck y a e[gpk/d/njfDejeDg`Dota aXy ivual[r ijk lcbVd ra$. IV. GENERAL CASE. ¡Leg]`Tk!fTq `«n k o¦rivu|ear ~ v\vagjoijbVdewq f lGrHigwipr|Tk rri Dejagpk bVd e]bfejdgjaLdlTde~ gpi]bVd eje~Lgj`a/|k gpalDgjijde*ilcgj` a\r go<fTbhgjf oaRdly\g` fGr#g`a bVdg]`Tk yDa{a eaRbhgjo<ijbn2ija ejy +g]` iprm|dVo<dvcagpaosbdl lk g Da}Lk o Ta y¤k f g a d r<i]e~Ln<k o&d rY~Rv\vcaVg]oijbd eGbVd ra rDdVlDyud k x a/d ejej$gj`aXvdilcy i]n2npi]bfe gj~ bVk$vca!rmnjok vµgj`anpd bhgug]`Tdhgi g\`Td r9gpk¦ Tax$dRei]y{npk!ozd eeLDilyTrwk$n q a k vcagjoi]aRr¡\rÎdµoa!r fDegp¤g]` ipr bVd ejbhfTefTrÂLi]ee« aµo<a dVe]iÖRa y lDf vcaoti]bVd ee~ $ D~uriv\fTe]dgjijk!l*. 0.216 0.180 0.144. y (mm). 0.108 0.072 0.000. 0.396. 0.324. 0.360. 0.252. 0.288. 0.180. 0.216. 0.108. 0.144. 0.036. 0.036 0.072. 8.00E+05 6.00E+05 4.00E+05 2.00E+05 0.00E+00 0.000. Ez (V/m ) ou J. 6.00E+05-8.00E+05. x (mm). 4.00E+05-6.00E+05 2.00E+05-4.00E+05 0.00E+00-2.00E+05. -/.10 2435246 798;:<7>=<7@?BA1C<A1DFE>?/=GEIHJEI?/7KHLE>MN:FA1OPEIHQAFO/7R7@SF7T<AU:VDFT LH DF7@SFW g b a[Z h ^/`[Z h ^5__\Z h c Y[ZZ\Z X E>? i f i = f ] f e =− f ] f d = f ]f f = AUO57jTC<A1ONEWN7kHlE>:C>?#C;=1mNnonp7VAU:<D T@C;S/qrMN?52 jg`d rE a allk gjijbaRy[ ~cx aoi]n2~ ilqk l7rizyDijn2n2aoal g&q fDlGr[gj`DdVg n2k oa x ao~£q!f lGg`Ta¸bdgj`k yDa«a ea bg]oti]b«n2ija eyÂbVdl¢ aRilÃn2io r g d| |Dok iv\dVgji]k lGoa| oa raVl$gpa ywd!rCaVejei| gpi]bVd e#ijrk 2npi]a ejy7bhf ox$a!rC"ig`sd |dVod k eji]bL|Dok n2ijeaDLk La x aon2k o"dcq$k k y9| oaRbipri]k l[[g]`Ta+|Tdhod Tk$eijb d rr f v+| gji]k l³k l¼gj`aÇbVdg]`Tk$y aÇaeja bgoi]b n2i]aVejy | ok n2ijeja ¸k n]gpal alTbk fDl g2aVo<a yLilLg`TaXeigjao<dgf oa bdl lk g aEvcdRyDaEraa"n2i]q f o<p a s . Electric field on cathode. 8.00E+05. Simulated electric field. A. Calculation of the cathode electric field. 7.00E+05. ½ doi]k fGrr<ivufedgjijk l«bk y a r¦aVDiprtgz/` i]b`«dhoa{dV Dejagpk¥rk ejx$a " d|Te]dRbaDprEa fdg2ijk l #½ Êcilq fDlzr gjo fTbhgf o<a r[dlTy\| oaRbipr aLilcg`a a eja bgok r gpdhgjijbRr\bd ejbfejdhgjijk lGr}a9"ie]e#f[ra9k lTawk nXg]`Tav EgpkmCk!o< k fDgGg`a1a ea bg]oti]b1n2ijaejyLdhggj` a/bdVg`k yDaX"ig`k fDg Ta dv. . Ez (V/m). 5.00E+05. jl7k oyDaoEgpk\DlTk ¥g]`Ti2rXnpi]aVe]yn2k o1a x ao~xDk egpd q a\bRk!lTn2ijq!f odg2ijk lG gj`acfDl igjdVo ~mbk lDgjoi f g2ijk lk n/a x ao<~srilq ejawq o<i]y7ipr+bVd ejbhfTedgja y7<i2 a$ gj`abdg]`Tk yDaaeja bg]o<ijbcn2ijaejy7bhoa dgpayw D~ɽ"k$eg1k l7g]`Ta9bVdgj`k yDacdlTy ÊD½ g2k{g`ak!gj` ao7q oi]y rLdlyrkk lGX}a{y a y fbVa¦gj`a}bVdg]`Tk yDa a eja bgoijb1n2ia ey+ ~ur fD| ao<|TkDr<igjijk lG d r.n2k eje]k urÈ. . .
(35). . ,. %. ) , =. $ . . . = ⋅ = = = = + ⋅ = = = = . ). + ). oa| oa r al gpa yLi lcn2ijq fDo<a. ( = ). . . ). . +. ' =. !" "# ). ). + &. npk!odlud r ~ v\vagjoijbVd eq fDl. =. ). ipr. 0.00E+00 0.000 0.132. 0.144. x (mm). 0.198. 0.072 0.000. 0.264. 0.200. 0.250. 0.300. 0.350. 0.400. x (mm). ¡urXoa|Doa r<al g2a yzi lwg]`Ta\| oaRx$ijk fGrX|ijbg]f oa La\lTk g2ijbaRy9g]` dg5n2k o a x ao<~uq fDlG$gj`a"a ea bg]o<ijb1n2i]aRe]yuijr.lk g|Tdo<d Tk e]ijbXdVgn]f ejei l gjalGr<igj~L<i< a$. k. /`Tal. =. H fDgnpk!oÓr vcd eje{i l gjalGr<igjija rgj`a¸|Tdhod k e]ijb. d rr f v+| gji]k l«iproaeja x dl gLjlyDaRa y "ar `k Ïg]` dgzbh`Tdlq ilq½p bVk!o<oa r |Tk!lTyrgpk}driv\| e]a7godhl[r ejdgji]k lk n\gj`asaeja bgoijbHnpi]aVe]yLi gj` oa rt|Ta bgXgpkwg]`Tawbdgj`k yDaDÈ*i]n1g]`TawbdVg]`Tk$y awx k egpd q awipr\yDa boad r<a y ~. . 4.00E+05. 0.066. 0.100 0.150. -/.10 2tN2vukEIno8C@:lDF=<E>?xw7<A1y 7>7@?zAFO/7pT@C<AFO/ENW;7p7@SF7>TVAU:VDFT{HLDF7@SFW|C<AkHFM/S S}D ?BAl7@?/=lD A1m C@?W Cj8C@:VCrwENS C>~;HlE>:CqID /7<?oqrM/?52. g]`TalLg`a/bVdg`Tk$y a/aVe]a bgoi]b1n2ijaejyL<bn npk!o<vufejdXVÉV<yDa boad!ra r. . ∆ . 2.00E+05. 0.216. 0.050. D~GÈ. 8.00E+05. 0.288. 0.00E+00 0.000 -1.00E+05. . 6.00E+05. 0.360. 3.00E+05 2.00E+05. ∆ . Ez (V/m) ou J (A/cm2). 4.00E+05. 1.00E+05.
(36). + ⋅ = = = = + ⋅ = = = =. 5¡. *. . . Parabola. 6.00E+05. 6.00E+05-8.00E+05 4.00E+05-6.00E+05. . . . . . = ∆ ⋅ = = = =. . ¢ £v¤¥}¦N§L¨\¥©§. ilTba¥La¥`d x a«dÓl fDvcaVo<i]bVd eHvk$y a epmLa¥LiejeHlk gfGr<aºdl ~ d| |Dok iv\dVgji]k lGrGdly9Ck!o<w"ig]`g]` ac¨ota dej©rt`Td| ack n#g]`Taca ea bg]o<ijb n2ija ejy[. 2.00E+05-4.00E+05 0.00E+00-2.00E+05. y (mm). B. Current density and current. . iTawils|dopgcÉR.g2k7bVd e]bfejdg2a9gj` awbVdg]`Tk yDawbfDo<oal g/y alTri g]~ n]ok vÎg]`Ta7bdgj`k y aaRea bhgjo<ijbwn2ija ejy 7LawfTra9g]`Ta7bejd rr<i]bVd e/k lTa yDivcaVlrijk ldVe`iejyD]dlq v\fTioVjre]dVcÈ. . .
(37) . ε
(38) . Child-Langmuir's law correction. =. _`a{il g2aVlri gj~i2rk Dgpdil a y¬ ~ªr fDv\vilTq¬gj` a¬bfDopoaVl$gzyDaVlri gpia r v\fTegji| e]iaRy+ D~"g]`Ta/a eaval g2do<~ur f on2d bVa r#<y$aRn2ilTayL D~/gj`a1lDfDvao<ijbdRe vca!r `GdVeek x aogj`a1bVdg`k yDa"avui2rri]x a"r f$on2dRbaDÈ. . =. . . . # ! " . ∆ ∆ . . /`Taoa .dlTy .~doaHg]` artgpa|Trk n9k f owvca r `T/dlTy{2ip cg`a ilyDaa!r.k ngj`Da"bdVe]bfejdg2a y/|Tk$il g< iaw aRn2k oa!Qn2i oYr2g<.gj` i2r\ejd¢`dRrgpk Ta7bk o<oa bhgpaVyEdhlTyHg`alT#g`a a fijx$dVejal g1yDijk$y a9y iprtgpdlbVac`d rXgpk9 ayDa npilTa y_`aRragjLk9|Tk il g<r LijeeD a1yDijrbfGrr<a yLilLg`aElaDggjLk/| do<d q od| `r. 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 0. 50. 100. VK (Volts). 150. gihTjlknmokopFqsrut q6vwtyx{z|x{}~vTiFsx{rwru6vTt xz}wq{uv'xnr[ i6r6TivTiFsq6vT~x ~x vwq}'xr qF{t oz|q'|uvdrutysqin~zk. C. New correction of Child-Langmuir’s law. _`Ta+bVk o<oaRbhgpi]k lcfTra yuilu|do g5É/bVdl g* DaLd| |Tei]a yL`aoa D a bdVfGra gj`ad rr f v\| g2ijk lGr+"ao<awbVdo2oia ysk fDg1n2k oud7r ~ vuvcagjoi]bVde1bVd ra$_G`a laV¤bVk o<oaRbhgpi]k l[[x d eijycn2k oEd ejebVd raRr[bVk vca rEn]ok v«dC| fD Te]ijbdVgji]k lk n ×Lk `G$5 ×\V¡/lqLdlTy+_E $ _E×/CdlG %'&. }a¥lk g2ijbVaÓgj`dgg]` a«bk o<oa bg2ijk lÂilbo<a d!r a r{Li g]`g]`TaºavuiggjilTq r fDon2dRbaD k oa k x aoY[Laux$aVoijn]~ug]`Tdg&n2k o1a$x ao<~zq fDlGg]`Ta\bVk!o<oa bgji]k l dok fDlTy+Ê ½dRevkDr gGy k a r lG gb`dVlq a dly/o<aVvcd i l[r.bVe]k raEg2kÉ D. jlcg]`Ti2rEyDk bfDvcaVlDgtDig*i2rEr `Tk /lcg]` dgGgj`a/eji lDc agjLaVal\gj`aLbVe]dRrr ijbdRe k lauyDivcalTrijk!lTde#` ijeyD]dVlq v\fTioVprQejd ÉhÒudly\gj`aLbVk o oa bgpa y !ÒÐed Òun2k o&dQ|Tedldoy i]k yDa1bVdlL aE/o<igg2alwÈ. D. Determination of the equivalent diode distance. . . a &. + /0 * .. ,. - ) + /-* . = +. ( . . 243 1 D/` aoaX bVd e]bfejdgja yL D~ 5 Ê TÍDDilck f oEbVd r a DdVly\ ijr + DlTk /lµy a|aVly ilTqÎk lÌ/`Tagj`ao¥LaÃbk l[ri]y aho«dl a eei|Gr<a d oa bg2dlTq ea XdlTyrkk l[Cd!rg]`TaHavi g]gjilqr fDon2dRba<n2k ozdHfDl i]npk!o<v bfDo<oal gy$aVlGr igj~ X}a}bdlbVk lGrijyDao9gj`dgn2k o7d ee\g`Taq fDl[r/g`a avi2rri]x a7r f on2d bVawipr+a eeji |DgjijbdRej.g]` ao<aRn2k oag]`Ta9a | oa!rrijk!lk n/ ¸ipr q i]x alu D~GÈ %6& ;. =. @ : ?. >. 8. −< ( 8 7. <. 9. )A. = . *k!o&d1biobhfTedoavijrr ijx aLrtf onpd ba!Rgj` i2rbk a npn2i]bVijalDgG a bk va r!È. D. =. C. $"`DaVo<aQoi2rgj`a1biobeaEod y ifTr. B. _`awbfDo<o<aVl$g"yDalGr<igj~w Ta ilTqwfDlijn2k o<vÎi lsg]` iprCoa n2aoalbVa .f l eiTa9il k fDo1bVd ra [CaC`Td x a+gpkcbdRe]bfedgpa/g]` aLo<i]q ` g.| dodvuagjaVorEd\dlyc G_k yDkrk [Ca\il$gpa q odhgpa/g]` aubdgj`k y a+aRe]a bgo<ijbLn2i]aRe]ycilcg]` aL|edlTaC~ Ê n2k od XdVlyH Ê}n2k oc GEil{k oy ao\gpkH DfTie]y}a fijx dejal gLfDl i]npk!o<v yDiprtgjo<i Df gjijk!l[r./` i]eaEaRah|Ti lq/g]` aXvdhTivufDvn2ijaejy FEHG I jl\|ejdlTaQ~ Ê+Ca/n2ily/| dodvuagjaodELi gj`È. . . . . O∞P K V M U LNM dlTy+ilL| e]dl aE. . =. QHRTS K. ⋅. . . |. =. . =. =. . u6 . . g`TalÆCa¹b`k k ra¶Ò. =. rk¹gj`dVg. iTa9il7g`azrivu|Dejabd rak n. |dVo2g TXLaH`dRx$aHlTk gji]bVa ygj` dgcn2k ozdq i]x alq f lGXila x ao<~}q oi]y x k egpd q a r#bVk!lTn2ijq!f odg2ijk lGr!gj`Dipr.y iprtgpdlbVaEoaVv\dRilTr.bVk lGr gpdl g <n#lGkaD|Tao<ivcal gpde&x d efTa\ipr/d x dijed ea!*®Gejk aDrCaR!fTi]x d eaVl$g5yDijk yDa yDiprtgpdlTbaLbVk!lTbaV|Dg&bdVl9 a+fTra ycnpk!oElTa¥q f lrT #dRrXah |ed i lTa ycedgjao il+|Tdho<gG½X. V. RESULTS FOR THE GENERAL CASE. /`Taoa ijr5gj`aLbVk v\|ejagjπ aLa eeji |Dgjijb/ilDgpa q o<d ek ng]`Taura bk lTy\ilyd dlTy9 sdhoa\o<a r | a bgpi]x a e~9gj`acejk lqwdVlDysr2`k o<g#ody i fGrLk$nEg`acaRee]i |[ra dlTy+Ò}iprgj`Da1a fDijx d ejahl gGy$ijk yDa1yDijr gpdhlTba . . jlb k v\|Tdoi2rk luLigj`\| dopg2p$lkLvk$y i]npi]bVdgpi]k lcipr.vcdRy$a"n2k o.gj`a yDaVgjao<vci ldgpi]k lk nXgj`ipr+|dVodVv\aVgjao<nXCa9`d x a7k lawaVD|aVoivcalDgjdRe. oa n2aotalbVa¹dg. /`Taoa¬Ãdly ²doa¥npd bhgpk oYryDa|alTy ilTqÓo<a!r |DaRbhgpi]x a e~«k l¸gj`a d x aod q a{|k ri gpi]k l«k nwg]`Ta¬aVeja bhgok lGr\dVly¬gj`aavcijrr<i]x ar f onpd ba q a k vcagjo~T#}agj`al}`dRx$a7g2kHvufegji| e~Hgj`asil gjalGr<igj~H| oaRx$ijk fGre~. . . J . jl¥gj`ipr| do2gzdoa| oa r aVl$gpa yªra x ao<d ebk vu|doiprk!l[r"i gj`¤gj`a a |aoivualDg}k o pdhlTy "ig` d¸rivLfedgjijk lÎbVk$y a¸rdvua¸bVk$y a¸d r aRn2k oa! il7k oyDao1g2kzx$dRe]iy dhgpa\g]`Taca ea bg]oti]bcn2ija ey7dl ywg`acil g2alTri gj~ bVd e]bfejdgjijk lGr²2vck oa |Tdho<gjijbhfTe]doe~$ g]`Ta¼bhf o2oahl gµx r¢x k egpd q a b`dod bg2aoijr gji]bRr /k!ota k x$aVo+ ~dlTd e~ ÖRilTq{g]`TkDra}oaRr f egpr+vudl ~ ilDgjao<a!rtgpilTq+k [r aox dgjijk!l[r./aVo<aXvcdVyDa . &. $. _kLykurk $LaX`dRx$aCriyDijn2n2aoal gq fDl[r#<q!f lr É1dhlTy\q fDlr cdoa r ~ v\vag]oijbdVep*"`DaVo<a d rQgj` acq fDlGr/dÉ/gpk9d mdo<acdRr ~ vcvcagjo<ijbdRe.Li gj` bVk$v\|Te]aV«q$aRk!vagjo<i]aRrwdhgmk!f oy iprt|k rd ej+gj` dg`d x a{ a al¤gja!r gja y a |aoivualDgjdRee~LdVlyurivuf e]dg2aRy+dRr."a ee2. 0. A. Results related to the cathode electric field calculations agpr{x aoi]nj~¥g]`Tdg<wn2k obdRe]bfejdgjilq¥g]`Ta¥aeja bgoijb¤npi]a eyTgj`a r fD|Taho<|TkDri gpijk!lzvcag`Tk$yzi2r/d bVbhf odgja dl y9gj`DdVg#g`ar<ivufedgjijk l7b k yDa |Doa x ijk fGre~/fGraVyLi2rbk `aVoaVl$gG"i g]`Lgj`Da1a |ao<ival g. Ê+"a/n2i lTyC u/ig`È ∞ \]. X c Z b Y[Z. =. X. ^`_Ta. ⋅. W . . #`k k rilq EHGdI d r.gj` a/x d efTa/k ngj`aXf lDijn2k o<v¥y i2r goi Df gpi]k ld|D| a dota y gpkC TaQg`TaQ Ta r gGdVlDyuriv\| eja r g*rk ef$gjijk lcdvk lqLk g]`Taor *i]q fDoafe\|Do<a r<alDgpr1dhlza dv\|Tea\k n#x doijdgjijk!lzk n.gj`iprQbVk o<oaRbhgpi]k lzn2k o dLq i]x ald r ~Rv\vcaVg]oijbd eGq fDl*È dgejk!bfDo<oahl gpr5g`TaLbk o<oa bhgjijk lbdVlc a fD|Lgpf k e$Ê ËH. 1. Definition of the “cut-off” notion. _`Ta9¨ bfDgp2k n2n2©iprCg`aaVe]a bgoi]br2g2dgpa9k n1d9q fDlsdg&g]`Tacavcijrr<i]k l ejivuigp!gj`dgGijrgpk\rdV~Ln2k oÖ aokLilDgpahl[r ig]~ _`TaXbfDgp2k n2nx k$egpd q a/½ i¡T¢*i2r yDaRn2ilTayzd rXn2k eje]k urÈGn2ioYr gp[g]`Tacbdgj`k yDacijrLr aVg#dV¤ g £* ½ i¡y¢hG_`TalTg`a n2ioYrtgq oiy{i2r7rag\gpkÖRaok[5¡ClTyn2i ldVe]e~ ura bk lTy¬q oiyx k$egpd q ai2r d y YfTr gja ycg2k ½ ¥ ¡w¢ r fTbh`md rX2< ½ ¥ ¡w¢ Ê[G_`auy$o<ijx acbhf ox$acijrXgj` al % % k Dgpd ilDaRyC ~Lb`dlTq$ilqL ½ /Lig`i lLgj`a1yDk vcdRi § l ¦Ê ¨ £* ½ i¡T¢6©. . . *k osadvu|ea Lilgj`a{bVd r<a{k nwq fDl¥dTÉ \d{bVe]d!rr ijbd ebfDgp2k n2n. .
(39) D. D 5. . bVk!lGnpi]q fDodgjijk lciprÈ ½ i¡w¢ ÉRÍ$Ê ½LD½¥ Ê ½LD½¥ ¡w¢ Í Ê ½{dlyu½¥ % ÊDÊDÊ ½+jlg]`TawilTy$fTr go<~ Ea e]aRbhgok l}q fDlGrcdoawlTk!gCk!lTe~7f[ra yHil bVe]d rr<i]bVd eubhf g22k n2nb k lnpi]q fDodgpijk!l[rX Df gcdVe2rk}ilah goavcax k egpd q a r bVd ra rr2fb`cd rg]` a"rkLbd ejejayu1 ¨ e Hj×L©/bVk!lTn2ijq!f odg2ijk lÈRn2ioYr gG/a1`d x a ½ ÊD½C[½ ¥ <Í ÊD½L½ ¥ ½ ¥ ¡T¢&dlyc½ ¥ ÊDÊDÊ ½ dly\gj`alT % % ½ ¥ i2rr aVgXgpkHÊ ½£"`aoaVd r+gj` ak gj`aocx k egpd q a r+oavdil}bk l[r gjdlDg< ¨ Hj×L©ci2r/dVe2rkdl7k gj`ao/bVk ln2ijq fDodgpi]k lsrivui]edVoEg2k e$s]׫aTbaV|Dg gj`dg½ ¥ É Í ÊD½L. . . . . . ½/k eg2d q a. Xf lrÉ. Xf lcd É. 1fDlcd. ". Xf lr. ½ ¥ ¡w¢ % <a |DaVo<ival g<. ÉÊ[s u½. 2. eÉ e\½. É [Í$ÊL½. . ÍGÉÊ\½. ÉÊ ÊÉE½. ee[s+½ É. @/½. Í Ê. ¡w¢2vck yDa ep. p<ÊD½L vck yDaRe. p Ê ½L a |aoivahl g. É$jÉ~eXvL¡. É LvL¡. eG É#vL¡. Hj×. Xf lr. e sXvL¡. 2<ÊD½C vck yDa e. É$jÉ LvC¡. . ÊG eeXvL¡. Í[ GÍXvC¡. Í ÊsXvL¡. . *ildVee~ n<k!oCa x ao~7q f lHdVly7a x ao<~7bfDgp2kDn2n"b k ln2ijq fDodgpi]k lGLa bVk$v\|Tdoa g`TaÂbfDo2oal gx aoYrtfGr«x$k eg2dRq$aÃbh`Tdod bgjao<iprtgpi]bRrªgpkÂgj`a a |aoivualDgp#dVlyota dejiÖ a9gj` dg1g`awbVk `aoalTba9Cig`sg]`Ta9vca dRr fDota y bfDox a r#ijr.a gjoavua e~+rdgji2rnj~ ilTq *i]q fDoaRrÉVÊHdlTyÉ É9|Do<a r<alDgCrk vca7aTdvL|eja rck n+bRk!vu|doiprk lGrck$n y$oijx aXbfDox a r#k lLg]LkLy ijn2n2aoal g*q!f lTr. w. . 2<Ê ½L a |aoivcalDg. 2. e Hj×. .
(40) !#"%$& ('*)+, .-/)(01243235 0*76 7'
(41) 37+8'9 95 /+:7 ;67)"'9< " 3:#+
(42) =8>? @;ACB DE=F. %. Ek ly igpi]k l. . agcfGr7b k v\|dVoa}il¬gjdV ea9gj`a}bhf g2pk$n<nwx k egpd q a rmCig`gj`a a |aoivualDg5ilsk oyDao/gpkwx d e]iy dgjacg`aaeja bgoijbcn2ija ey7bdRe]bfedgpaVym ~ r fD|Taho<|TkDri gpijk!lun]ok v«riv\f ejdhgjijk lcbVk yDa r.o<a!r fDe gtrh. (. XfDldDÉ. . . 2. Comparison of the cut-off voltages. ½ ¥.
(43) *:4 7 7!#"T$& 7'*)+9 7!U "70 "'9U 02U 7'V908=8>!A E=W<U ".XYZ " [\*YZ- ("4U 0*U 4"]'<47"^3:#+]0*_!!(U 3*3: /+, "7067)"'. 16.00 Model. 14.00. ½. Experim ent. 12.00 I (mA). 10.00. _`aota n2k oa +g]`Tartf |ao<|k ri g2ijk l¥vcag]`Tk y¤fri lTq¥riv\f ejdhgjijk l«bk yDa!r q i]x a rcbfDgp k n<n\x k egpd q a rc$f igpa7bejk rawg2k7g]`TaaVD| ao<ivcal gpde"x$dRefTa rh }aLx aoi]n2~ud r#La ejeg]` dg*La/`DdRx$a/gj`aur dVvcaLd bVbhf odRbh~ilcgj`f a e Hj× dlTy Hj×bfDgp2k n n*bk lGn2ijq fDodgjijk!l[r. 8.00 6.00. . 4.00 2.00 0.00. 3. Remarks on the emissive surface at full intensity. ¡ b k vu|ejavcal gpdo<~ bh`Ta bhTilTqÇk n£gj`aÏbVdgj`k yDaÏavijrr ijx$a r fDon2dRba r+|Taho<vi g<r+gpklTk!gpijbawg`dgtQn2k odq ijx al}q fDlT.g]`Tawavijrri]x a r fDon2dRbaLdgn]fejeGil gpalTri g]~uiprQbVk lGr gpdlDgnpk!o5d eebfDgp2k n2n#bRk!lTn2ijq!f odg2ijk lGr <½ ÉVÍ$ÊD½k oE½ Ê ÊD½{k o e s]×u s]×+[agp b Gs _`TijrQbVdlu a a d r<i]e~saD|Te]dVilDaRyH DaRbdf[rawdgLnjfDeje1il gpalTri g]~ E ½ ¥ ½ ÊTQdlTy q i]x algj`dg& \` d rXdVevkDr glTkcilTn2ef alTbauk l9gj`aubdgj`k y a\n2ijaejyc<bn k Graox dgjijk lGr#dggj`a1alyuk ng]`Ti2r|dotd q odV|D`T2D½ ¥ ipr#eilTadVo<e~Ce]ilDTa y % gpkCgj` aXaRea bhgjo<ijbXnpi]aVe]yL<bVn n2k o<v\fejdEVÉ 2È. . . 7. S. L. Q R Q JR P NJR P O JR P. M H. L. S. M. K. 150.00. 200.00. fDo<g`Taho<vck oa Dg]` iprQdoa dLijrQ` i]q `Tao#gj` dlcg]` artfDon2dRbauk$ng]`TaLn2io r g G q oi]yH`Tk$ejaw<n2d bgpk!o * }n2k ocq f lr dl yÉ Ín2k oq!f l}dÉVÔEf$g"g`a bVk!l g]oi Df gpi]k lk ng]`Ta+bVdgj`k yDaLdoa dLq oa dg2aogj`dl ÉX`k e]aur f on2d bVaLi2r oa edgjijx a e~£r vcdRe]e ËÆk ng]`TaºbfDo<oal g}n2k oq fDl r Ãil Hj× bVk!lTyDig2ijk lGr . $. $. 9.00. I H. _`aubdgj`k y a+aRea bhgjo<ijbLn2i]aRe]ycdvu|eigfy a+ipr#|Dok |k o<gji]k ldReg2kc½ ¥ [ Df g % gj`a1avuiggpi lqur f on2d bVaXo<avdilGrbk lGr gpdl g. (. 100.00 Vk (volts). .. ≈R P O ⋅ Q R P O = R J R Q =R P N = R P =. 7 . 50.00. `2a!B E7b%+U 5 W-/)+5] c3:7+
(44) 6#)"dB <= >
(45) ? @ AB DE=W< "]%beA E [f4$.$&. . 8.00. Model. 7.00. Experiment. 6.00 I (mA). . x. 0.00. 5.00 4.00 3.00 2.00 1.00 0.00 0.00. B. Results related to intensity calculations. }acLije]eEnpi or2g"r `k «g]`TdhgEgj` a9il g2alGr<igj~wbVd ejbhfTe]dVg2a yzi2rLbejk ragpk gj`a\aVD| ao<ivcal gtn2k o"dlD~cTilTywk nEbhf g22k n<nEb k lnpi]q fDodgpijk!l[dlTygj` al r `k g]`Tdgg`a+| o<a bVi2r<i]k lzk l9gj`aL/`k eja\k n#g]`Ta\bfDo<oal g&xDrTx$k eg2dRq$a b`dod bg2aoijr gji]bRr9iprwx$ao<~}qDk k$yGEk oa k x$aVoELaH/ijeeLd ejrkvcdTaHd bVk$v\|Tdoijrk lHLig]`7gj`a9| oa x ijk!f[rcr iv\fTedgji]k lbk yDa!#dlyr `k ¸gj`DdVg gj`ijrgpk k e[` ipr`ijq ` e~LildRbbfDodgpa#oa q doy$ilq1g]`TaXy oi]x a/bf ox$a!r *k oLdq$ijx alsq fDlsdly7a fijx d ealDg1y ijk yDayDijr gjdlTba<y$aRn2ilTay7il Vb e]d rr<i]bVd ecbfDgp2k n2nwb k lTyDig2ijk lGr</La{r2`k g]`TdgcLa`DdRx$a}d}q$k k y vck y a en2k o«bd ejbfejdgjilTqÎil gjalGr<i g2ia!rºa x al ilµaDgoavaÂbfDgp2k n2n bVk!lTyDig2ijk lGrd r e Hj×dlTy Hj×<bVn gjd e]aE2t. . 50.00. 100.00 Vk (volts). 150.00. 200.00. `*adBBg#b%+:U 5 W-9)+5 83:#+
(46) 67)".'7B <= >
(47) ? @ AB7h(E=W< "%bZAiE] hh#$T$& *k!o&d ejeGk$nGg]`TaLr icq fDl[r.gja r gja y DdlTy+ilcaRx$aVo ~Cbhf g2<k n<n.bVk ly igpi]k l[$g`a |Doa bVipr ijk!lzk Dgpd ilDaRy9k lg]`Ta+/`Tk$eja\bfDox a\iprQ Tagg2aoEgj`dl7Í Ë /`Ti]b` ipr\n2do/ Tagg2aoLg`dl7gj`acoa r fTe g<r\k DgjdRi la y7 D~wgj`a9| oa x ijk!f[rcrtgjfy ija r a x alu dRra yLk!lul fDvcaVo<i]bVd ebVk yDa r. C. Complementary observations. 7. *ior gpDn2k o&d e]eGk nk fDo&q fDl[r$g]` a/iln2e fTalbVa/k ngj`aXgj` ioty\q oi]yL< D k lºgj`aaVe]aRbhgjo<ijb¬npi]aVe]y¥<dlyTdRrd{o<a r f e gtk l«g]` ail gpalTri g]~$Hi2r laRq$ejijq$i e]a Lk La x aoYLacbVdl7a dRrie~ivcdRq$ila\gj`dgEnpk!o"q fDl[r"Cigj` ejdoq$aR]`k eja 2q oi]y r¬dly r vdee¥q d|[r£ agjLaaVlÅgj` aÌq oijyDrgj` i2r iln2ef albVaXLk fejy/ aXdE i gGvck oa/r<i]q lTi]n2ijbVdl g. .
(48) A. _`TalT.n2k oL½ Ê ½Lgj`aco<dgjijk9 Tag]Caal7gj` a9il g2alTri gj~ .k o/gj`a bfDo<oal gEy alGr<i g]~$k o"½¥ <dg&bhf g22k n2nt k o1g]`Ta\aVe]a bgoi]bun2ijaejy ilgjLk % yDijn2n2aVoaVl$gmbhf g22k n2n7b k lTyDig2ijk lGr\iprHily a|aly al g7k nwg]`Ta{q fDlL*k!o aTdv\| eja n2k oLa x ao<~wq f lG TahgjLa aT l e Hj׸dlTy s]×b k ly igjijk lGr LaX` d x aDÈ. 16.00. . . . Model 12.00 10.00. = . I (mA).
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(52) $ %& ' # %& ' " ! , )+* ( dlTyÈ $ %& ' = # %& ' " ! , )+* ( . k o&dl ~L2G ~ <. =. 4.00 2.00. . 1. ;. 0. :. :. :. :. =: 6 798 ⋅ 6 : 6 = : / : 5 3 =: 5 4 =: 5 2 = 1. ;. + 5 4 97 8 ⋅ 6. 5 4 =. 0. / 6 = 5 3 = 5 2 =. . -. . -. 0.00 0.00. E. k oa k x aoY$dgG½ . Q. O. J. . ÊD½\F È. P O HP N LHP N M HP N. K. J. Q. !. I. K. =P N M ⋅ O P N M = P H P O =P N L =P N =. (. G. _`alTDn2k ogjLkLbfDgp2k n n*bk lnpi2q fDodgjijk!l[r.VÉ GdhlTy+ TÈ. g VXU f VXU [ c b Y _`a W h Wh Z _ g VR U = f VR U [ c b Y = Wh Wh Z VXU ^ T S R VXU _`a e iBj+k \ `a_ d W h _ \ _ = e VRU ] = d VR U iBj+k Wh. 100.00 Vk (volts). 150.00. 200.00. }çè9¬~ ¹9¯~~çÀ¶ 9 £t~¨Á¶z¤é ¬®À´ ¶ ¯»¶º¡ ¹¤¤z~å¿z½ º¨¯ê+궤ëé Ù ¨Á¤¤À º 9 êé~Öì¹å~»¶ é9¬Ö ¹´ é¹~Èt¹¹¬®z»¶¶ ÖÃ. (. _`aota n2k oa [npk!ogjLk\bfDgp2k n<nb k ln2ijq fDodgpi]k lGr#VÉV.dlyu <$LaLq ag*n2k o a x ao<~Lq fDlÈ. E >?< >?< E D = A+C E @BA9C >=< = >=< D = A+C @ A9C B. 50.00. ĶÅÆÈǶÉʶǮˣÌ9Í Î¶Ï§ÐÑÌ9ÎÏÓÒ Ô®ÌÕÖÑ×ÙضÉÚ¶ÛÝÜÞ ßà¯ÉáâÛ§ÚØ×ã£Ëà¹â¶Ç ÊáäåäæÇ . T SR e VXU ^ \ l R j9k \ e VRU ] l R j9k S [ c b Y ^ \T R Z \ ! [ c b Y ] Z. F. íî ì¹ ¤ B¹ï~»¶ï ©¨¯¶z9¡ð©¤À ¤ï~zîz À t¼ê£~ ¬º¬®9ñ ò¶ óç ¬º¬®ô~°ê+t»¶¬®z»¶ºó~t~ zB ¶ ÖÃöõÝ~÷ ¨©½¤¶ + ¶¤zø½z½ù9ú´û~ ¬B »¶9üêÈ~©½z+»¶t ¹¬º¬®9ý¶»¶t ´z¡¼ ﻶ¤z¯ ¨¯¿¨©z¨þ¶9 ¡Ãÿ B + ¬¶À¹~ é¬ ì¶ÝzÁ±ê¹È~»¶ ýz»¶t ¾~·¬¬®ç¬¤¬Ö¤t® üt~¾½zº»ê ¯¬Ö~½zï´ ¡ ±êà zÃÿ À ¤¤¡ ê¹¹´z ¯9zÁ± ~鬮z»¶¶ £ 9 ½ ¤¡¶îÀÁ9t ± à 18.00 16.00. Experiment. 14.00. Model. 12.00 I (mA). .. :. 8.00 6.00. . jlyDaRa yil7bhf g2pk$npnXb k lTyDig2ijk lGrX<i2 a dVg.gj`aue]ivuig5k nEavciprr ijk lG<g`a bVdg]`Tk yDa/aVe]aRbhgoijbXn2ijaVe]yLijr.ÖRaokD dlyLdRr#½ ¥ ÊudhlTy\½ ¥ ` d rdXLaVa iln2ef albVa $njok vªn2k o vufejdXVÉV/aE`dRx$a È. :. Experiment. 14.00. 10.00 8.00 6.00. VI. PERSPECTIVES: ADAPTATION OF THE MODEL FOR NEW GUNS *k oLr gjf y$~ ilqclaV«q!f lGr/` alwlTk9aD|TahoivcalDgjd eoa n2aoalbVa\dVg ½ ÊD½ i2rwd x d ijed e]aRCCabVdlfTra¦®Gejk aDprwa $f ijx d ealDgyDijk yDa yDiprtgpdlTbabk lTba| gEg2kzyDag2ao<vcilDac| dodvuagjao/ÒCT y&1dly7k DgpdVilsy oi]x a bfDox a rLig]`dw|Doa bVijri]k l$f igjardg2ijrn]~!ilTqDE DfDguk ncb k fDoYrase]k Lao gj`dl/gj`a1k la1ilLgj` aXejd r g|Tdhod q od|D`G¡uroa bVd eje]a y/ ~Xc!Tf Öf ip %s il dok gpdhgpi]k lTdeje~¦rY~Rv\vcaVg]oijbd eLaVe]aRbhgok l{q f lGQgj` aHa fijx d eal gLyDijk yDa yDiprtgpdlTba1bdVl+ TaQ"o<iggpal*È. ]. w. | =v. o. u xzy9{. n m p qts u x = u r }~B ~ z t~z t~ ¡¢£~t¤z¥ ¦§¨©ª «¤¬¬® t¯9 °±³²9t~µ´ ¶ 9·¬¶ ¶¸9©¹ ¤º¶¡©~»¶©¼¬¬½ 9´¤©¬~¬¹¹~¾~ ©¿ ½zºÀ¨Á¶² º 9z¯±Â¸Ã. 4.00 2.00 0.00 0.00. 50.00. 100.00 Vk (volts). 150.00. 200.00. ĶÅÆÈǶɶǮˣÌ9Í Î¶Ï§ÐÑÌ9ÎÏÓÒ Ô®ÌÕÖÑ×ÙضÉÚ¶ÛÝÜÞ ßà¯ÉáâÛ§ÚØ×ã£Ëà¹â¶Ç ÊáäåäæÇ }çt~ z¡¿ ½+À¨Á¶9¤ º¬¶ét~ô¨¯¶ ¤ ½¶¬9 ºt 9 ~®9æ»ê¡æ~~ à 껶 Ȩ¯ ý ð ¿ý z ¯zB ï½zº Ö ~¯ ¨¯©¬~¬¶ÃÿÝÈ~î~®È¹ ~©½¶¬ ö9 ~~¯¬®z9¶+ ²
(53) z¨í©¸Ý®é  °9¤t¬®z9®z §² ±£¨¹íî¸Ã. VII. CONCLUSION. }ç¹~»¶î9À 9½¶½ ðï ½ º¬9 º© ¤¡ t¬¤Ý¨¯¶z¤ ¶ £¬®zº¶§¶ºð ¤¤¡Á ¡¶¨©¨Á¬¤Ý¤¬Öð ~®ì½¶¶»êz © ´Ö¹¬¬®z¬¡·üt~¾é~¶¤¾¶9 ¡ ¥9»z¶¤9ê ¬®~¬®9® t¬¹¬®z»¶ï~®¯t~î À¨îz¤®t¼¬¶z ÃõÝ~z ¨Áê ¤rB ¶ ¤t¡¼t~¾¦§½¤t¬9¤ýý~ ¬t~ê æ~z¬®~¬ý´´z ¶ ºt¤¡©À~ ¤¡ t¬¤Ý½¶ê¬¶zêà ¶»ê®z~© À ïº ¶ï~´¨ñ9 ï ë ç¶9ü¬¬ zé´¡ ¬º¬Ö ·t~謤¶ ® ¬¤ ¢£~¤z¥¦§¨îª £¤B®îÀðz tÁ ê »ê¤t®z z¶z¹¶½ ½¨©§ 9 Ã. .
(54) õÝ~¼ ~z»ê ¶¤~ 9tê¡ t¤t¤¡ ~z z¨¯ ¤ ¨¯¶z¤9»ê¤t 9ò¤¤ ëÀ ¶¤t¬®z ¶¨¯t Ãðõr~ ¤À¡ z¨¯ºt¬¤·z½¶z· ³¶ ~ ¦§½¤t¬¤¬Öº¬¾ t¤t·È~ ¬~¶z¼ ¤t¨ÁÖ º¡·¬ À à õÝ~½¶¬9 ºt ´ 9 9®´®9 t~ ò~z ¶ô~ ¨© ¤t® tü¬¶ ¶ ï¬ z Öè² ¬¬®z¬¡¾´tì~® ñ·~ é~ê¤ét»¶å¬Ö »êæz¨¯¸Ã. 9 ²æ ¸. »¶þ9 èþz¶ ºt½z¶¬¶ ® ®´ ¡ôB À ݤëzª ¶»ê¤¶§¶t¶z¹ ¬¹¬¬½ ºz¹¹¬ðêÝê î t¡¶ ½z¬ Áï~ ìé~ê¤åê ¡¶¥º»z¶¤À ¶é¬®~+¬Ö º +¬å¬Ö »¶zÃ. V2. ¿ÜÛ. ÿ ¤¤À¡ ¹ ~»¶ ¨¯¶ 9 zz 99® t~ ¨¯ ¨ ¬Ö~ ¨Á 讼 + ÖëÀ³~¤¬Ö ¬®zººêð¶ºÝà ¯ íé ¬ ½¤ t~ À»ê + t¶®9 ~ ¤¬Ö ´¨ ꡨÁt¬ ® ¬®~ z¬°¨Á 9¬°¨¯¶z¤¤ t~ ¶¡ ½z¶»¶t ¶ æ궶ｶ¶ê¬Ö tÁêt~ 夬®t¯z¹½ ~z¡ ¬ à . ¿*Ý. õÝ~ ¾¹ë ¹ ¾½Ö9º¨¯çz Öð~zç ¬½¶¯
(55) ~ ½B ïî + ½z½9 é´z¡õÓ~¨ð ÝÃ. . V1. \ ACKNOWLEDGEMENT. ¿ÜÞ. ß6Ý. ßÞ. 9 ª²^å ¸. ~¶ . ∆2. APPENDIX. }缬 z©¼ ¡ ¨ ¨Áz¼ê »¶¤å¬¶¿t¤å¬¡¶¤À꺬¤ ¤¬®¶ ¶ é~ «¶ ·9 ·zæÃé}ç³ 9z½z½ «~ ³¶½ ´t¹Á¤¬®¶ ¶ Ó é´¹ ¨Á¤¤9öõÝ~콶zº½z æêt~ È ¬Ö¯ Ó ¶t»¶° ¨©½ ¤ ¤¡9¬¤ý¨¯¶z¤9³~°¬¤¬Ö¤t®9öê~ ½ z¤Ãt 9 £®¯¤9® t»¶¹ ¶¤ê© ézz¨ÁÖ¬¤z¨¯~ê £²9¤ ë 9 ¤¨¯®z ®¸9· ò9 êz¤è¬¬®z¶»¶¶t ó ¡ ¨¯¶ ¤t¤ ¹¶r~夬®ê ¶ Ã. ¿ÜÛ ¿*Ý . . ¿ÜÞ. ∆1. õÝ~¾z¤È½ ºÀ ©z®9
(56) ®¼Öè~¼¤t¶ ¤ì¼9 z9¶Ã }ç餶ëð éz ¨¯z ¤ ¶¤À¶ t©ÿ¼¶r~鬡¤t¶ºt¬¤¦§½¤t¬ ½z´¤¨ ¬®~î¶ % & $ " # ! = ω$ ω" õ ~ t ¬®tÁ»ê9¶ Ý~Ȧ§½¤t¬å('ÿ*)ét Ý 2. 2 3 ∂ /0. 1 ∂ + 1 , =1 1. ∂ ∂ íþ ê¤z î rt~54å ® ¤z¬® t687Ã. ¢È ¶¶¤¡ ê¹å¤t¶ë¯ é¶Ö¤z½z¤:9 ¬®~¯ +∞ ; A B G? = C G C @ J G ? C D E FHG > = C I = ω ω ω < ω −∞. }çð z½¶½z ¹t~ï½ ¶¤§ëêé·~z©´z¶+t ì²9)Kæ¸ÃLtÙ9 ¬B 9z¯çt~ý¤t¬Öê ®ôæ¬ ½z½z ·¹ ~³¶¶¶ ½ ½z¿¨©tòt~ üt~ ½ Ö t¤»¶º ¤À +¤À¡°´¹®ò ¬¬¶ ® t»¶å¤¬®t¶z Öà }çì~»¶ M T YQ O U Z =. +∞ −∞. S Y U R [ Y Q U VWKXHY P O U ω ω ω N ω. õ ~趶¤å9 ï ý¶å~¾ëÖº¤]\ò¨ ~¾ë éçt ¬®t Ý 9é²^æ ¸ÃõÝ~ ｶ»¶t Èê ¤ 9 Èïÿ zºÖt+ 9º¨Ãí ºÀ¨î½¤ 9º¨ò¶~¹½z´¤¨°9 £ ¯¬ z£~zîz®t»¶»¶©¶ 9þ»ê® B 5 ô~ü¬¡¶¤À꺬¤é´zz®¡ÃÈõÝ~ ¾tz¬Ö ¾¬ z¹ç~ ¶½ ¹²º ¤£9¾~ ¾¶½ü»¶¶¤À ¶ðz»ê¶´z¡ðt~¾¶½ü¤Öt~B¸ ¯ð~©¤¬Ö¶z ÖÃõÝ~ 9 åt¶¬®9 ~ ¬î¹¬¨©´À¼¶ _¹»ê zå¶9 9t+À´ ê B ²º ì9zºÁ±
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