In the strong axial magnetic field approximation, we calculate the space-charge limited (SCL) current of axisymmetric relativistic charged-particle beam in a coaxial drift tube of finite length. Results are compared to analytical estimates and numerical modeling of SCL current in the infinitely long drift tube. For the infinitely long drift tube, which inner conductor is biased and the outer conductor is lined with a finite-width dielectric insert, analytic approximations for the SCL current in the bias voltage are developed.

We study the operation regime of a hybrid planar free-electron maser (FEM) amplifier near the magnetoresonant value of the uniform longitudinal (guide) magnetic field. Using analytical expressions for individual test electron trajectories and normal frequencies of their three-dimensional oscillations in the magnetostatic field of the hybrid planar FEM, an analytical condition of chaotization of motion is established and shown to be given by the Chirikov resonance-overlap criterion applied to the normal undulator and cyclotron frequencies with respect to the coupling induced by the undulator magnetic field. It is also shown analytically that, in spite of the well-known drop for the exact magnetoresonance, the gain attains its maximal value in the zone of regular dynamics slightly above the magnetoresonant value of the guide magnetic field. Under the condition of undulator resonance, it is practically independent of the amplitude of the undulator magnetic field and the wavelength of amplified signal. To account for spacecharge effects, we propose a theoretical model of a weakly relativistic FEM, which accommodates not only potential but also rotational parts of the nonradiated electromagnetic field of a moving charged particle. It turns out that the rotational part of nonradiated field diminishes the defocusing influence of the potential part on the beam bunching. Numeric simulation of the nonlinear stage of amplification is fulfilled, taking into consideration adiabatic entrance of the electron beam to the interaction region and initial electron velocity spread. We find that nonradiated field and initial electron velocity spread do not influence essentially the efficiency of hybrid planar FEM amplification if parameters of the beammicrowave interaction correspond to the operational regime in the zone of regular dynamics near the magnetoresonance.

No abstract

No abstract

HatuoHanbHbIu HayLIHbILI teHmp <(XapbKoecKuL cpu3uKo-mexHuLIecKuL uHcmumym) HAH YKpaUHbl yn. AKadeMuqecKa5, d. 1, a. XapbKoe, 61108, YKpauHa AHHOma"uR -B nJHeLHOM npm6nm>KeHmm nonyLeHo AAc-nepcLiOHHoe ypaBHeHMie AiJ1 npflO3BOJlbHOrO BOJ1HOBOAa C TOH-KIAM 311eKTpOHHbIM nyLKOM, pacnpoupaHMOLMCR B MarHIAT-HOM none rm6pmWHoro nnaHapHoro y6MTpoHa. BbilmicneHa nonoca ycLAneHLAq, IAHKpeMeHT npocTpaHCTBeHHorO HapacTaHLAq 1A npOBeAeHa OLAeHKa Knf y6MTpOHa B YCJ1OBMqX MarHMTOCTaTM-LeCKoro pe3oHaHca. 1. BBegeH me HecMoTpR Ha AOCTWrHyTbie ycnexm no Co3gaHWFO MC-TOYHIKOB 3M noni BO BceL CBI o6naCTL cneKTpa [1], OKOHLaTeflbHOe OCBOeHme MM m Cy6MM gmana3oHOB, C yLeTOM BblBWraeMbIX Ha CerOJHqWHMO geHb Tpe6oBa-HIM, OCTaeTCq HepeweHHoLH 3agaqeO. B HacToqWee BpeMR B Begy"LLX M/POBbIX HayQHbIX LleHTpax [2] aK-TLBHO mccnegyeTCq OHAynJTOpHo-rmpope3oHaHCHoe B3aMmogeOCTBme 3fleKTPOHHbIX nyfLKOB C 3neKTpoMar-HLTHbIMM BOnHaMm, KOTOpOe RBflqeTCq npLHLL1nmanb-HOW OCHOBOL gflRl CO3gaHqR MOWHbIX 3c¢xIeKTMBHbIX reHepaTOpOB m ycmnMTeneO B MM m Cy6MM Lmana3oHax [3]. B gaHHOM coo6WeHMM L3yqaeTCq KorepeHTHoe L3-nyL eHvMlM 3n eKTpOMarHLMTHbIX BOJIH cn a6openRiTL BLMCT-CKLM 3fleKTPOHHbIM nyLKOM, paCnpOCTpaHqFOLLLMMCq BgOflb BOflHOBOAHOW CTPYKTypbl B OAHOPOAHOM npo-AOfnbHOM m npocTpaHcTBeHHo-nepmogwLecKoM none-peYHOM (oHgynqTopHoM) MarHLTHoM none nnaHapHoro y6LTpOHa B yCJ1OBL1X MarHLTOCTaTHL"eCKoro pe3oHaHCa. II. OCHOBHaH qaCTb nyCTb 3fleKTpOHHbL1 nyqoK Bo36y)KgaeT pe3oHaHC-HbIM o6pa3oM TOflbKO OAHY BOJIHY B mgeaflbHO cornaco-BaHHOM Ha KOHL,aX BonHoBoge. CLITaq BHl npoL,eccbl nepmogmweCKwMM BO BpemeHM, none 3To0 BOnHbl MO)KHO npegCTaBVTb B BmgeE(r, t) ;~V (z) e(r'L) ex p(ik 0 z ic t),( (f, t) ;~V (z)h(FL) ex p(ik 0 z ic t), rge 6(fl ) m h(rl) -MeM6paHHbie C)yHKLIMM Co6CTBeH-HOW BOnHbl <> BonHOBoga, ko -nOCTOqHHaq pacnpocTpaHeHMHR. AMnnmTygHbIiM MHO>rKTenb V(z) on-pegenqeTcq ypaBHeHLeM Bo36ywKgeHMq [4] dV 1 yJ(r)e*( )exp(i t -ikoz)dS (2) COBMeCTHO C KpaeBbIM yCnOBmeM V(z = 0) = Vo . 3geCb j(f)exp(-ict) -nflOTHOCTb TOKa nyqKa, P -MOLLIHOCTb BOflHbI, nepeHocMmaf qepe3 nonepeqHoe ce'eHme S; *-3HaK KOMnneKCHOrO ConpR)KeHLq. YpaBHeHme ABM-)KeHL,R 3neKTpoHoB, CoCTaBnRFolfl"X nyYOK, B npeHe6pe-KeHmi nonem npOCTpaHCTBeHHOrO 3apRga MmeeT BHA: d o e m eE(f, t) + c[=oe (j)+ (r, t)] (3) e dt 2 /c C~C rge H0(r) =(0,-H sin(2;Tz/1),-H 11) -MarHLToCTaTLMe-cKoe none HaKaYKM y6LTpoHa; me m e <0 -macca no-KOR M 3apRg 3leKTPOHa COOTBeTCTBeHHO. CLMTaeM, 'TO 3fleKTpoHHbIi nyfOK Ha BXOge B npOCTpaHCTBO B3aMmo-geOCTBHR RBJIReTCR HeMOgyjfmpOBaHHbIM M MOH03Hep-reTLMeCKLM, T. e. HaqalbHbie yCnOBLqR gflR npoM3Bonb-HOrO 3fleKTPOHa B MOMeHT BpeMeHM BnleTa te MmeFOT BMA r(t = te) = (x,y,0) M v(t = te) = (0,0,vO) BbIpawKeHme gnR BHl nonq (1), ypaBHeHme Bo36y>K-geHHR (2) m ypaBHeHve H BeB>KeHM 3leKTPOHOB nyqKa (3) C yYeTOM HaqaflbHbIX YCJIOBVi COCTaBnqROT 3aMKHYTYFO CMCTeMy, caMocornaCOBaHHO onICbIBwFOLLYS B3aMmo-geWCTBme 3fneKTPOHOB c BLI noneM BonHoBoga. B nMHeiViHoM npm6bnJ>KeHMM CYVTaeM [5], 'TO BY BsOfHa Bb3bIBaeT Manbie BlO OTKnOHeH Hq f1 TpaeKTopvivi 3fneKTPOHOB OT ...