Table Of Content

Electron Streams in a Diode? sy ERAGE ORAY a yrvopuerion LE hear of em loctron stream flowing in ie hs secs} mach ssrensoai beens te tetrad, pentodes and other modern tes re csrale nerugenst of livia dla, Te theory of te dade is ‘he fount Tor considering dhe ezeuit characeisice and the nobe charities of thes tubee Tn one day who roremiicainn canal free conned to reativey low feqienciny am leroy rll irawerse {lod ia a ote perio’ a imo eourpard to wn aii 2 esa) ‘Soa, ad the theory could be developed meter simply irom Ue ke ler etiv, But tase dy gh and ule-high frequencies, he ‘Souaton fe nun difenral A signa volligy way coclate several tines tle ex. actor. fe traversing id, snd the eli sear How Tranche eaves Phe presenti fe ely meas) wie hi te ‘mpc pec ew Tus ewe of alll plane electro nT develzped ude the asl seruptin thie the elect wy single valued function of space cad tie, It shor foe an aysmsinae folaton Gur psn esetron sens over a ede range of rein ‘articular esting foram electro steam tinder srl sige is a given in various poblaked artces. Tee theories agp the sje i evo ailesut unaster, In ie spptonch attention ox confine! tn Che ‘tions of electne ae ivi cl! * aed she he a ay best be cscrined cw wave ther elelron stream Bul the te Fe kappenseh have sol Htyera given kata ess, andthe diearcenent ‘ast be at-buted to hagoeed actors i che wee tear “Thepnsestaiile users esctor scat ithout reac toany ther hau @ machezaticelappzonch to she evict The slletil epa ss fn liar inthe derivatives, and they should therfore Fave general Slats Falvestanall steals susan ae thoory secs snc 9btne oa MET wetted aneeing a Re Ansan Eigse ery laa, 1NeTROW SIREAME HE A oF ait this general alation.{ It involves a wave equstion, ade route ene in exact agicenen: wich the snullaigual caestaions for Tae motions of Sete a vial tiles, Thi therfore elie that che genes folaton reeanclles the eo lines of eppronch ta the theory of eet With this solution available the situation is comparable to that encount- sed in to.dimensional patents! theory; assignment of dente fonctions {bun arbitrary Iunetions gives x sation for 8 pesticalar probe in ecm seams ait then dil bn determine just bat pole has been saved. Ta the cate of small sguale the general soltion does not ally shorten the eleultong adi pally al not be zegard ax la ving ln eomptnon tn ay partial lac whet the he is aleady nwa, Tei more probable that Che brace slaian will serve ‘aie for general reaonings soa electron areas, a a2 guile tO ‘pprorimations tht can be used in particalar problems. 4, Tue Pamiuiee Phase Dior "The diode ofthis article shown in Tig 1. It sto parallel planes indi- cated a (a) and (band seperatod by a distance. The rst plane (a) may bee theron cathode thet emizs eletrens, ot it may bea gid through ‘thih a sleeam a eleteons i ine nts the dae, The second pane CU) ‘hay ben mateliepate rhe rcv the ertone afte they have traversed ‘he ade pars, ort may bea ge Cat pent con sea oe fut of the dl, The dimension af the diode ace asamesallempurat fo the electromagnetic wavelength st any frequency involved, tht i, small eompare tothe velocity of light divi hy the frequency ne the Separation of the plane x siumed Small compared ta thet lateral dimen- ‘Sr Under Utes conditions the electric inary parallel Un he xsi, al he elvan move In that dei oly \. Te electron atseam injected throagh the rst plane may vary with ey both in ergo density nnd electeon slot; abe voltage the tro planes may ale very with ime, Pe tot crent Rowing in ye dd pace fe the the sam of tro componente: a conduction extent reralting for the ‘motion of elton, and a dsplcementeucrent arising (om Ue Live rate of change of elects intesity. The diplacamen: crzeat ean fo even when {here ate no elctons inthe li pee iti then the familie nr eure, owing between tno plates of contener sl, when eletrons are presen, the two currents interact with each otkr and they beth dow in e coma ved manner, ‘see arse pares eae af ise! eur seen Riz me aan svsree seeusteat jommem, oezoEe St “The determining corto tran be meseurel a any psa creat seeiste ih the dis are; the tal eorent the conduction current at Thetis are, snd hewetten veloc at tas ple, Ther. hr eneienty ‘omsering edad a3 ieee, tas been sow hy ther that She allée able so calealte the endactien current a tye seca pls; The elem ylacity et tbat pase and the resltant wllape acoss the iota, From the viewpoint of crea heory, thee ls heer juni may Ie amsidted as dependent variables ace solutions shnold be sought (Gene of ln ina! contons. But an electron streum flows asoeding to ite tune, ith tle ran for citeut theory ts am amental ea ' we Yin 1rd is Hat plane ané were! plane (8. tims iwolse electri inlewity aad electron velocity ae the dependent ‘arial, and ‘ie gereral they must therefore be developed in terms of Thee natacally ocarrngunliiss, at show be ted thet the desi "rut eletions an slays eaeulted from Shes fendarental variables. 1a Unis > Stamons he ets ate writen in prectialeectrien ons eaimecre, grams and sora, In thie epsom nf ails, dhe pesisviy« of a wecuum 3s Ws and the aceteation constant 9 of am electron is epprovimately 17-10%, To conform with vinvait convention, We taal current and the consist cnten are messin Cc negative # diet, tat oppote tothe moti of the sectonesalethr recto unuities are meastred in the pstive -oeton. ions as ie 8 MO 238 ‘tb sms ce intro wa el as needed. The Sllwing erie sie einstced to give the reader n genau o Thesyrians Gan Spin 25 Sabsigta rng othe cole anes : Dutt ts te at we : ‘te : Deas ie tox 7 Des rotten he die . de Frente i vt s sr * Foner dey ? Dre paces ete . ees ofacvom, , Acclraton content ofan Een 1.77108 SombtssSeion "Ti Gene Stion ¥ Vatiye 2 “lc itnsy te tet een iy ff Cntton soe ety 7 ‘Poateanectdowity in des smoot ot n Onsiaicopr a7 s «fio Swe fea PS PAS) Abiary Hato of AIS}, BES) Plate abitnny funeon of 8 St Section 3-Swa Signet Theary tis seton she nial tes P=, 7 Q.an€ J change cbse meanhae a indleate only tae, eamjaeate nf thee quenities: and the snl Ieties «ey. g and then dice he emplieutes of 2 cormspeling Se components. ‘This eer sk es che Cllosing special symbols: an Acitrry constants ASn%.. 1% Contents foe Cae eet theory oi, RM tux aun svete neem nest goons, oFtonE 1951 Spnbels tn Section ¢—Pywbat Hla Sts ris ain stare to the aint af Le gear theory: ard the. colt eles 2 Cy and f cste baal yuetiie, It alg uses tae Tallowing pein ere ‘Acta elerinm vlc Aerie of ce eet of orton ara ery a rage 6 ‘Memertam dersily uf elections Knctisevorgy deny af estrone, mee eae 2, lnm Grvraat, Sobestus OH ane Raxergan Seman ‘The prswnktkony of election streams i x slation of two partial dit. ferential wseaons, in with electron Yeloeity Fad sleccic intensity 2 appar as Ue dependeat vail he mation for electron vecity Us basal onan cali that com ‘only ure! Jn wacium tobe taeory, It anaes Unt the clostron velocity ie eglevalued function of spac and te ot, sated in her words it Seques thn ail elect a any plane norma! tthe x's have the same seocty, The varie 2? ray th: be ezurded asa continwns Fuckin af {and mhiea fb everlere equal to tho wrote of the indole trove Th ert] egoatioa fr follow a oor en the fuodemontsh sof elon thc tates at farang vias electron ue P Beng wo where ais te aceeeration natant ofan elton, a he wall oats Teens ace nogiecteds Then, siuoe fa garded 9 ronenaos elisa hil otal derivatives may be writen inser of paral derivatives, ane = one ic) ich is here ma asthe faneiental etn fo electron veo, Tis of eoure haved uu calaing sveumption tha ipezt lint. fon the gorwal theory, abd eae lmitalie are dacosscd in 9 concling fectan. of thei ene i's show thatthe ‘enived velocity i an 3p protimatin fr the vexage velocity Sn physical electron seams he iPennsal eqaaion fr the eles intosity 2 is giver. by: te ‘theory of estnnnagaeting, Lt follows Fm hia fendamenta theory that rizcruoN STARS BY A DIODE as the total current deity foi ted i fant of te lone {thas the sme vl atl las ng the san, il ven by Ten - 8 @ “he fit ce ie the contacto current tly, the sco erm the dipuconenecurnt deny and I ls reasied according to cr cin ‘ent nthe eon poate to ee matin of ta lesen. The Carpe Tent pie C) ® ‘whic eth diferental equation fr elcti ntesiy afore pain, it exo be rol tht Lie eomeinrarvent density Q, ‘moasutedaccossing co ctu conventions, i ve nar ar? © ge-we-0® @ “The to dierent equine for I and are no spate 8 up ae o Bae ot 5 we ® ond in shi rp the toa caren deity way Le ngueded as any known ‘rasbitaly seated fection of ime, These ar she Fastin: whee “lation is sought inthe rent theory of rletann stars: Thy are dom Scrption ofthe wrole inde soe, and they tall how € and ocur and sory 314 fine thoughout that wolespace. They are ist err ectatons, Tinecrin thee esvatves smd Ht kann Gon the theory of erential ‘equations that thir genes] sletion the complete olution, and at it val conan two itary fumes if we fel sultan cota emo itranyfumetons, we miele ne hai the eee sation The equations con he solved by the Lagrange method, as outlined ia p- ere T Mul thal = ther alstact operation, andthe santas is bere lain by anotierwethod that bas mote physial mening and i ely equivalent tothe Lagrange metho! some se baSHAL ENON. jRSAT, eTARAH 195 For any inividal eleiron, (2) nt (5) stay be witen in the free ot total diferenta! epi. (3) and @) we aw m ) o sands Che comdnae ofthe eine. This grupo cota sential equa” ine Ceeibes U ad ony in she imasediatevsinity 9 tne m1 movi tleeton, and tig Cemfons 1 resid picture ia compacizon to He on fivun ly the ofgoal poet ifort cations. I seule, however, be leary tanleetad that sere no alin fe aouton seis eoup af tat $iferensal equations; wr are mow slag hem 3s ais for saving the rignal excaions Euston (8) maybe wate inthe fr [ws [ra] =e ‘he Dacheted ees rage cr sa, thai seus fru an a {10} sys bua isan sas for any ined een, H real onataa othe leon iver slong The olion of 1) s 2 shore Cy ieany anbiraryconstaat hong a) Hy Be wait i the form -t[s- faa sd ite rletion tor ung partieareleetmin remembering tbe: Seon -o-tfe- ffir] ‘ a3, sivemoe arenes ne £ m10DE ast svhere Cyan arbitrary constant En repeated introns with magi ws Hin the iesinent dis mriten oniy om, i being ert Ua dl is cpeuted in cacsltegeation) Now any acbiteary Tunction F af 5-0 ‘constant forthe particu lin wer consideration, so we msy replac= Crby FS) and write we ney —"[s- [fra] us) or these ton, (yo te wen theo 099 tf ffx] an is sotion fs praca S- fife] ro ies Cyan arbitrary’ estan that mi agin Be ep by em ab trary Garcton Feu S, ad ven vio 3]%= fra] on yc oe il ete ae htt en cal mow {19} sal (18) ly Laken tagetier everiie Oa as jure of ari New the teas wll prosably be cle sani a seas the wiles to earn et Lae ia eations when slang slo ae ol sslolions thy goss af ote cere eqns CP, (8 ae! “The soliton uf ted grog 12) {05> end C1, Im ler ey Fe ta _pnerl lalins oe anlalius othe tor erat’ equates cal In the ery specil ce of 5 equal so. nme Hes Lil waste my Wve ae Yala, and the gence ers Mave apy ta el eectrons in the take nd seni solcion of the bree gos npartis «erential exis (2) Sind ol and this torneo to rue. Tai olin, win is wre nero, weno Ifs- [fra] 43) ‘We are therfore rst’ Sued tothe sone'asioy sha ve nit now 2[ = fif'ra] soa fie a BM WRG. avRtEAC tM JOU, OOM IST morsover comin two rier Cations, ae HL theeire ne general tnd complete alin fa Heli see sign te ‘As the solution stands, Fan arbitrary furetion of Une, and F(S) nd FAS) re pevitly wieay. They eoresuna ol pe dtr conditions: taal the dc, and finsent conditions that ane pve Jn th idolized dod, end to ell the purely wathenatical conditions tht cennnot be realist in uny physical sens. ‘Wich this complete sluion avaible, the stuation ie apalogoes in many teapot to thst encountered in tae oltion of potential problems in tre- fienioral space, We can fire « prtcelae soft hy lmer'y assign fefiniee farctions to the tare abltrany frnetinns FC), BCS) sl FS) s brut me then enoouter she ficult of Tinting out ast what problema fs bea ‘Acacsimple ext fhe yea et, the wae ey De incest. in arsrrly wing Z, BS} and PS} equal oer, Ha wl ches Hd that the vel express, (05) aul I), are aul slurs ofthe partial iets) epatons, a ns hey epee a ement eleclepn beara that cen flow for a short poioe of ime ins ode pce, 2A Der Gronnat Sornminy rs tia Peranver or 4 Thanct Cima nthe rejvityof iets La ae patel iber thar cnt cons divert corre wing ne, al Ue elie Toone then a Sume 8 more ests frm fn sh aoe the ol carseat esi Fay Treo! athe sur i cnpuant lil Gor Ute big inion) ns Fy 00m trun aller rome Fa “Taen we have the sou tut nd seo the conition that 1 end rst be ten any physical he ‘Now conser (15) for Ef ae nate that [rears fra [fra tee fina ‘crc tr (6) scons poe tai soe Itai a apse ay Tefen 3) mus tts of Sch fm htt nce th mse cue fo enone pe {on chws that se comeqey bea fern iS) = AQ) Fe BS gs en ro) where AUS) isan abitzary finite fet ofS, giv an ueiteary constant, Sind the eeliens fs and ge have soc wales tha the per terms in ance out fn (15). The finite fonction may, for empl, be sine function ofS or 0 eres of auch sinusoidal terme, "The vain ol Le et tients re ex cleat, ad when the resultant expreesion for PS) subeicted fo (15), ft may be welt: ogra a 1S + [fra] @ nee Si $ with the Jy term omitted, hate, sear fue co) (a smiar manner it may be shown hat, for ¢ tonic, (18) esumes the fom zeny Al 9S — ffs] wo rete ety onan Bay nin Seine $n iat coe he feed er sens ncn Steet fo ete Te eats _ plan St tet dors eat 3, Tu Sats Svar Tnromy or Eizcmion Suwa “The sul sigoal hoor is develop as illoye: The vlucof cach depend: tat vatible in any plane normal tothe #2, is regarded se them of iro components: = wal chats uit vay with ake ond jp ehereare call the de, compaen, sd a value that dace vary with time and is ‘ila yea. componest. All ef these component: rosy wary wil ay that fs, withthe exoption of the tal current density whic few Tavetin af time tle, Carmmpendng to sll igal crest theo, i abo sessed tht thee quotes ste sill compare to the ci sate, aud that the squares adjusts f thes, quantsee ar negli is eaparion {oth firs oer ale, Fa ou signal the dent equivalent af a dade