Efficiency Enhancement at Coaxial Gyro-BWO through Profiling Guiding Magnetic Field Under Computer Simulation

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1 AASCT Journal of Physics 215; 1(2): Pulished online April 2, 215 ( Efficiency Enhancement at Coaxial Gyro-BWO throuh Profilin Guidin Manetic Field Under Computer Simulation V M Khoruhiy National Science Center "Kharkov nstitute of Physics and Technoloy", Academicheskaya str, 1, Kharkov, Ukraine address khoruhiy@kiptkharkovua Keywords Microwaves, Gyro-Devices, Backward Wave Oscillators, Guidin Manetic Field, Efficiency, Computer Simulation Received: March 18, 215 Revised: April 8, 215 Accepted: April 9, 215 Citation V M Khoruhiy Efficiency Enhancement at Coaxial Gyro-BWO throuh Profilin Guidin Manetic Field Under Computer Simulation AASCT Journal of Physics Vol 1, No 2, 215, pp Astract The yro-bwo is a UF powerful oscillator for cm and mm and of wavelenth in which relativistic electrons eam (REB) is used for couplin with a ackward wave on normal Doppler effect nvestiations of yro-bwo confirm that an essential limitation of the considered device is the small efficiency One of possiilities for efficiency enhancin is to use profilin uidin manetic field alon an interaction reion We investiated dependence of efficiency increasin under usin optimal profilin uidin manetic field y special law As a result of effective process unch formation under special conditions most electrons can e confined in the enery-losin phase F field Efficiency enhancement takes place from initial value ~1 for homoenous uidin field to ~3 for profilin one 1 ntroduction The yro-bwo is a F powerful oscillator for cm and mm and of wavelenth in which relativistic electrons eam (REB) is used for couplin with a ackward wave on normal Doppler effect The first research of yro-devices was pulished in 6 th [1] The state of the art of yro-bwo proram is represented in Ref [2], [3] Possile applications of the F radiation of otained power levels are the followins: electron cyclotron resonance heatin (ECR) of plasma for controlled fusion, communication, spectroscopic researches, hih-resolution radars etc n our paper the case of coaxial waveuide is investiated for yro-bwo elaoration Coaxial waveuide have a reater value of vacuum limitin current of REB for one comparatively to the other types of waveuide Results of the linear and non-linear analytical investiation of coaxial yro-bwo operation are presented in Ref [4], [5] Coaxial waveuide have a reater value of vacuum limitin current of REB for one comparatively to the other types of waveuide An electron eam and waveuide support the oscillations with circular frequency ω, which can e descried y the expressions for normal Doppler effect, accordinly ω = k V + nω / (1) ω = c k + c k, (2) e where Ω = is non-relativistic yro-frequency of electrons with enery 2 W=m c ( -1), mc -uidin manetic field, -relativistic factor, k, V -lonitudinal

2 59 V M Khoruhiy: Efficiency Enhancement at Coaxial Gyro-BWO throuh Profilin Guidin Manetic Field Under Computer Simulation wave numer and velocity, n=,±1,±2 An operatin mode for yro-bwo is near to interception of a straiht line (1) and hyperola (2) in coordinate plane (ω, k ) (for yro-bwo the lonitudinal wave numer k <) An ordinary efficiency value for coaxial yro-bwo is ~1% for homoenous uidin manetic field The major attractive feature of the yro-bwo is frequency tunaility, which can e achieved y manaement the manetic field or eam voltae owever, the efficiency of the yro-bwo is relatively lower than one of other yrodevices nvestiation results of efficiency enhancement in yro-bwo were reported in Ref [6-15] n Ref [6-9], the efficiency of the yro-bwo has een found to e sinificantly improved y taperin the manetic field Results found revealed that the manetic field taperin with a positive radient tended to increase the initial frequency mismatch leadin to the efficiency enhancement n Ref [1-13] a tapered interaction structure (the reduction of the waveuide radius alon the interaction reion) was proposed and used in the experiment The yro-bwo with a tapered manetic field and waveuide wall radius was analyed in Ref [14, 15] The aim of our paper is enhancement of efficiency in coaxial yro-bwo throuh profilin of uidin manetic field 2 ih Efficiency and Bunched Beam Formation Optimal conditions for this process determine further process of reduction total eam enery convertin to radiation t follows that reater electrons can e located in the enery-losin phase as a result The unched eam formation process in yro-bwo has difference from standard unchin process ecause of stron amplitude of EM wave sinificantly depends on lonitudinal coordinate That reduction of EM amplitude miht e compensated y chanin position electron unch as a whole one relatively phase of EM wave t is possile to do throuh local variation of uidin manetic field for compensatin of EM field amplitude reduction alon lonitudinal coordinate durin formation process only y chanin total (helical) phase, includin EM wave phase plus helical phase of uidin manetic field Ψ = k ω t Ω t / Confinement of as many electrons as possile takes place in enery-losin phase due to phase shift under optimal unched eam formation As a result phase shift of unched eam s formation in enery-losin phase takes place 3 Computer Simulation We investiated in our paper efficiency enhancement in coaxial yro-bwo throuh profilin of uidin manetic field ( ) at lonitudinal direction as, (3) comparatively to homoenous case =, where α is non-homoeneity amplitude, ξ = ω / c is normaliin lonitudinal coordinate, L = Lω / c is normaliin waveuide lenth, ξ / L = / L, j>, m> A correspondin transversal component one is where r is transversal coordinate Somethin like distriution of uidin manetic field for efficiency increasin in the CARM was proposed y Chen S and Dawn TY [16] Efficiency enhancement take place for CARM oscillator under addin a positively three-quarter sine profile onto a uniform manetic field We considered waveuide excitin mode ТЕ 1 with components of an electromanetic field E,, under satisfy conditions (1, 2) For computer simulation we used equations for electrons motion and excitin field ТЕ 1 from Ref [5] We investiated coaxial yro-bwo with oscillation frequency f = 77G for satisfyin expressions (1, 2), homoenous uidin manetic field = 61kOe, inner radius of the coaxial waveuide yro-bwo = 3cm, outer radius one is a = 5cm, inner eam radius is r = 39cm, outer eam radius is r = 41cm, enery of injected a electron eam is W = 511keV ( = 2 ), an initial ratio lonitudinal momentum to transversal one µ =1, lenth of system is L = 6cm, cut-off frequency f = 75G, startin current = 37 A, limitin vacuum current lim 66 ( ξ ) = (1 + α ( ξ / L ) cos ( πξ / 2 L )) j m st r r ( ) =, 2 = ka for coaxial waveuide Maximal efficiency ηmax 11 is under input eam current =6kA for homoenous uidin field and cited aove yro-bwo parameters [5] Computer simulation of optimal reime yro- BWO performance time averaed efficiency η was carried out for determination values α,m and j of profilin uidin manetic field (3) under the same input electron eam current =6kA The aim of our investiation is tunin (profilin) of uidin manetic field for creation the est conditions (as far as possile) for radiation of majority unch electrons First, we have to determine location of uidin field maximum relatively lonitudinal coordinate ξ under j=1 and = 61kOe Results of that investiation are presented in Tale 1 under =6kA 1/ 2 ϕ c r

3 AASCT Journal of Physics 215; 1(2): Tale 1 Location of uidin field η m α ξ / L ( ξ ) max We can see from Tale 1 maximal value of time averaed efficiency η =32 is under m=6, α =29 and max ξ / L = / L=25 The location of maximum one ξ / L can e determined analytically from expression (3) where x = π /(2 L), or approximately for x << 1 ξ / L = / L (2 j / m) / π, ( m ) (4) Second step is determinin optimal amplitude of additional uidin manetic field under cited aove fixed m=6, ξ / L = =25 and j=1 An amplitude variation takes place due to variation of parameter α from (3) Tale 2 Optimal amplitude of uidin manetic field η ( ) ( ) / max ξ α We can see from Tale 2 maximal efficiency η max =32 takes place under ( ) max / = 12 (α =29) in our case Finally, third step is determinin optimal width ξ / L of 1 profilin uidin manetic field (3) under fixed ξ / L =25 and max ( ) / = 12 A width variation takes place due to level variation of parameter j from (3) under m/j=const (4) for fixed maximum location ξ / L =25 Widenin of uidin manetic field takes place under 1>j>, narrowin of one takes place under j>1 relatively width of field distriution under j=1 n our case maximal efficiency ηmax =32 (see Tale 3) takes place under j=1 (m=6, α =29) and width mxt( x ) = j, ξ / L =41 for ( 1 ξ1) = ( ξ1 + ξ1) = 11 Tale 3 Optimal width of uidin manetic field η j m α ξ / L Fi 1 Dependence normalied manetic field amplitude ( ξ ) / on dimensionless lonitudinal coordinateξ ence, we determined location, amplitude and width values of profilin uidin manetic field for our yro-bwo parameters n our case optimal process for unchin of input electron eam takes place under m=6, α =29, j=1 (5) for expression (3) n fi1 we can see lonitudinal distriution of uidin manetic field for parameters (5) The new profile of uidin manetic field chanes spatial distriution of EM wave amplitude C = ee /( mc ) alon ϕ ϕ ω lonitudinal coordinate A spatial distriution of normalied amplitude on lonitudinal coordinate ξ practically haven t local maximum comparatively with several local maxima (see Fi2) homoenous one Fi 2 Dependence of normalied amplitude C ϕ on dimensionless lonitudinal coordinate ξ ((curve 1 is for profilin uidin manetic field (3), curve 2 is for homoenous one under ( ) = ) Normalied oservation time isτ = kct = 15 Local maxima (fi2) one after another indicate alternation increasin and decreasin of eam enery alon lonitudinal coordinate for iven point of time As we can see later that

4 61 V M Khoruhiy: Efficiency Enhancement at Coaxial Gyro-BWO throuh Profilin Guidin Manetic Field Under Computer Simulation local maxima are result chanin enery-losin phase particles of a eam y enery-ainin one Naturally, lonitudinal distriutions of normalied amplitude have considerale decreasin of amplitude for oth cases Fi 4 Dependence normalied spectrum density S(f) on frequency f (curve 1 is for profilin uidin manetic field (3), curve 2 is for homoenous one under ( ) = Fi 3 Dependence normalied averae unch enery ( av -1)/( -1) on dimensionless lonitudinal coordinateξ (curve 1 is for profilin uidin manetic field, curve 2 is for homoenous one ) Normalied oservation time isτ = kct = 15 The dependence of normalied averae unch enery ( av -1)/( -1) on dimensionless lonitudinal coordinate ξ has a monotone character in contrast to homoenous distriution (fi3) The enery loss has maximal value at the first half of interaction reion For determinin frequency characteristics of output sinal spectrum analysis was otained for normalied spectrum density S( f f ) Dependence normalied spectrum density S(f) on frequency f for homoenous uidin manetic field (stochastic oscillations ) and for profilin one (stationary oscillations for the same remainin conditions) is shown in fi4 We can see in fi4 conversion stochastic oscillations under homoenous uidin manetic field to stationary oscillations for profilin one Then we used computer simulation for investiation efficiency η dependence on injection eam current under fixed parameters of uidin fieldα, m and j [see eq (5)] For iven injection enery = 2 efficiency η 25 is for 7kA 4kA (see fi 5) Efficiency η for profilin uidin field has essentially reater value than η for homoenous case Averae output lonitudinal enery ( 1) /( 1) of a unch increases y 1% for av,, homoenous uidin manetic field and y 15 % for profilin one under = 2 and = 6kA Fi 5 Dependence time averaed efficiency η from injection eam current (curve 1 is for profilin uidin manetic field (3), curve 2 is ( ) = ) for homoenous one The main reason for relatively lower yro-bwo efficiency is its spatial distriution of the wave power that reaches a maximum near the entrance of the electron eam and decays alon the propaation direction of electrons This power profile leads to non-optimal formation of unched electron eam at the einnin of yro-bwo under homoenous distriution of uidin manetic field We suested non-homoenous distriution (3) for creation the most optimal conditions durin process unch formation of input electron eam n fi6-8 you can see difference etween unch formation for homoenous uidin manetic field and non-homoenous one on phase plane enery-phase for various fixed values of lonitudinal coordinateξ ( =6kA, = 2 ) For all of fiures circles correspond to homoenous case, lack points correspond to non-homoenous one

5 AASCT Journal of Physics 215; 1(2): Fi 6 Dependence normalied enery of the particles eam ( 1) /( 1) on helical (total) phase Ψ for /L=258 (lack points i correspond profilin field, circles correspond homoenous field) Fi 7 Dependence normalied enery of the particle eam on helical (total) phase Ψ for /L=39 ( 1)/( 1) The majority particles for profilin uidin manetic field have enery-loosin phase from the einnin unch formation process comparatively homoenous one (see fi 6) An effective unch formation process takes place alon lonitudinal coordinate (fi7, 8) Fi 8 Dependence normalied enery of the particles eam ( 1) / ( 1) on helical (total) phase Ψ for /L=52 i i Fi 9 Dependence time averaed efficiency η on relativistic factor (curve 1 is for profilin uidin manetic field (3), curve 2 is for ( ) = ) homoenous one under As result phase portrait of unched eam alon lonitudinal coordinate is more compact in comparison with homoenous uidin manetic field An effective formation of unched eam in enery-losin phase leads to most electrons can e confined in the enery-losin phase even after completion a compact unchin process (fi8) We d like to notice that effective radiation process take place at first part of yro-bwo (fi 3) At second part of one decreasin of averae eam enery is asent We otained enhancin of yro-bwo s efficiency for iven injection eam enery W = 511keV ( = 2 ) as indicated aove Then we investiated dependence η on injection enery W under condition / const Dependence time averaed efficiency η on relativistic factor under injection eam =6kA is shown in fi9 Let s consider more detailed enery rane close to η peak in Fi9 for profilin field Tale 4 Dependence efficiency on injection enery W, kev ,kOe η,25,33,33,3,29 ih efficiency value η 3 takes place not only for injection = 2, ut for sufficiently wide rane enery = (12 24) too (see Tale 4) Finally, under fixed parameters of uidin field α, m and j (3) we considered dependence of time averaed efficiency η on injection eam current under new injection eam enery W = 153keV ( = 13 ) For iven injection enery = 13 efficiency η 25 is for 14kA 5kA (see Fi1) Maximal efficiency η 3 is close to injection eam current enery = 2 6kA the same as for injection

6 63 V M Khoruhiy: Efficiency Enhancement at Coaxial Gyro-BWO throuh Profilin Guidin Manetic Field Under Computer Simulation [2] Thumm MK State-of-the-Art of ih Power Gyro-Devices and Free Electron Masers//Preprint, FZKA 7392, Forschunsentrum Karlsruhe-28 [3] Spencer TA, Stump MD, endricks KJ, Gilenach RM nvestiation of lower order mode suppression in a hih current, hih voltae yro-bwo experiment//plasma Science, EEE Conference Record Astracts-1996-P287doi: 1119 /PLASMA [4] Borodkin AV, Khoruhiy VM, Onishchenko N, Sotnikov GV Coaxial Gyro-BWO 1 Linear Theory Startin currents //Ukrainian Journal of Physics-24-Vol 49, 2,-P ( ) Fi 1 Dependence time averaed efficiency η from injection eam current (curve 1 is for profilin uidin manetic field (3), curve 2 is for homoenous one ( ) = ) ncreasin of startin current takes place under profilin uidin manetic field from = 37A (homoenous manetic field) to = 17A for profilin one under = 2 ) st Oscillations of competition mode TE 11 f=4 G under iven resonance conditions (1) and (2) are unlikely event The TE 11 mode is separated far enouh from the operatin TE 1 mode under the iven conditions Resonant frequency of the TE 11 mode is f = 4G, the frequency of the TE 1 mode is f=77 G in our case 4 Conclusions n our paper we otained new results for enhancement of yro-bwo s efficiency from 11% (homoenous distriution of uidin manetic field) up to 32% (non-homoenous one) throuh profilin of manetic field (3) Oscillation frequency has fixed value under satisfyin equations (1), (2) As a result of effective process of unch formation under special conditions most electrons can e confined in the enerylosin phase Results of our investiations haven t static character for other yro-bwo s parameters or other yrodevices n every case parameter values of profilin uidin manetic field (maximum field coordinate, amplitude and width of like-ell uidin field distriution) are suject of investiations The otained efficiency is closely to yrotron s efficiency (without sinle stae depressed collector (SDC) for enery recovery) The current mechanism can also e applied to interpret the efficiency enhancement in other yrotron oscillators (for example, cyclotron autoresonance maser in Ref [16]) with profilin uidin manetic field References [1] Gaponov AV, Petelin M, Julpatov VK nduced radiation of excited classical oscillators and its usin in radio-frequency electronics//vestija VUZov (USSR), Radiofiika-1967-Vol 1, 9, 1-Р st [5] Borodkin AV, Khoruhiy VM, Onishchenko N, Sotnikov GV Coaxial Gyro-BWO 2Nonlinear Theory//Ukrainian Journal of Physics-25-Vol 5, 11, -P ( ) [6] Ganuly A K, Ahn S Nonlinear analysis of the yro-bwo in three dimensions//ntl J of Electronics Vol 67, 2, - P [7] Ganuly AK, Ahn S Optimiation of the efficiency in yrotron ackward wave oscillator of a tapered axial manetic field// App1 Phys Lett Vol 54, 6, -P [8] Lin A T Dependence of efficiency on manetic field in yroackward wave oscillators//physical Review A-1992-Vol 46, 8, -P [9] Lin A T Chin-Chien Lin Mechanisms of efficiency enhancement in yrotron ackward-wave oscillators with tapered manetic fields//phys Fluids B,-1993-Vol5, 7, - P [1] Walter M T, Gilenach R M, Mene P R and Spencer T A Effects of tapered tues on lon-pulse microwave emission from intense e-eam yrotron-ackward-wave-oscillators// EEE Trans Plasma Sci Vol 22, 5, -P [11] Kou C S, Chen C and Wu T J Mechanisms of efficiency enhancement y a tapered waveuide in yrotron ackward wave oscillators//physical Rev E Vol 57, 6, - P [12] Grudiev A, Schunemann K Numerical analysis of an injection-locked yrotron ackward-wave oscillator with tapered sections// Physical Rev E-23- Vol 68, -P1651 [13] un CL, Yeh YS, Chan T A coaxial-waveuide yrotron ackward-wave oscillator with tapered waveuide cross section Proc of 8 th nt Workshop -Stron Microwaves and Terahert waves: Sources and Applications, -211-P84-85 [14] Nusinovich GS and Dumrajs O Theory of yro-ackward wave oscillators with tapered manetic field and waveuide cross section//eee Trans Plasma Sci Vol 24, 3, - P [15] Walter M T, Gilenach RM, Luinsland JW et al Effects of taperin on yrotron ackward-wave oscillators : Special issue on hih power microwave eneration// EEE Trans Plasma Sci Vol 24, 3, -P [16] Chen S and Dawn TY Study of efficiency enhancement throuh manetic field profilin in cyclotron autoresonance maser //Phys Plasmas, 1995-Vol2, No3-P