LinearAnalysisOfCyclotronAutoresonanceMaser.doc

精品论文大集合linear analysis of cyclotron autoresonance maser(carm) based on transverse-magnetic modeyang na, zhang shichanginstitute of photoelectronics southwest jiaotong university chengdu (610031)email: , abstracta linear theory based on maxwell-vlasov equations and the laplace transform is used to describe the high-power cyclotron autoresonance maser (carm) operating in a transverse-magnetic mode. thistheory is applied to describe cylindrical waveguide gyro-twt, cylindrical waveguide gyro-btwa.cylindrical waveguide gyro-bwo. a 18-ghz, tm1,1 mode cylindrical waveguide carm is analyzed the influence of the parameters on the output power. outcomes show that the changes of the operating magnetic field and the electron-beam energy will affect output powerkeywords: cyclotron autoresonance maser (carm); tm mode; circular waveguide; lineartheory1. introduction the cyclotron autoresonance maser (carm) is a kind of potential high-power, high-efficiency coherent radiation sources in the millimeter and sub-millimeter wave ranges 17.in this paper, the dispersion equation of the carm with electron beam operating in a transverse-magnetic ( tm ) mode is presented. results show that both the operating magnetic and the electron-beam energy have substantial influence on the output power, because they directly affect the cyclotron resonance condition.2. linear formulation fig.1. guiding-center coordinate systemone of the theoretical methods to study the free-electron devices is the linear theory, which is based on the maxwell-vlasov equations 4. the dispersion equation of carm with t electron beam operating in a tmmn mode can be formulated as follows:- 5 -d (, k) = = k 2 k 2 +c2z4 i1cmnzuck (ck )2 sm z 2c(1)r 2g i( s k v)( s k v ) z ( s )2acz zz z c+u 2 ( ckc ) ckz 1 2 c2 k 2 2+ z + ckz t2 = 0dk2sm ( s)2 z s s z smc cc d ( k ) = dd ( k) ,(2)zizizin (k ) = jk 4ic i1 2 ckz uzzr 2g is (sk v )2 z smac c z z(3)1 2 ckz u+ 1 ckz t( s k v ) sm( s k v ) z sm cz zcz z with2 ()g = j mkc r(4)u( k r , k r ) = 2s j 2( k r ) j 2 ( k r )(5)smc cc l kc rc m sc csc l m s j( k r ) j ( k r ) t ( k r , k r ) = 2s kc rc sc lm sc c j ( k r ) j( k r )(6)smc cc lsc lm sc c s j( k r ) j ( k r ) 0kc rl m sc csc l awherei = (3109 )1 (m c3e) z is the alfven critical current; i is the dc beam current.r, rc , rlare the waveguide radius, the guiding-center radial position and the electrons larmorradius, respectively;m, n, s are the waves azimuthal and radial mode indexes, and thecyclotron harmonic index;b0 is the operating magnetic field;c = eb0 m0 c is theelectrons relativistic cyclotron frequency, = vc, z = vzc , v , vz are the electronstransverse and axial velocity;m and its first derivative.j m and j m are the first kind of the bessel function of orderafter solving the dispersion equation, the wave amplitude can be obtained. then the averagepower of the wave propagating in the waveguide can be expressed asurcurur c21p = re d s 8( e b ) =cmn8 k 2re ( a ( z ) ja ( z ) .(7)the linear gain is then given byg ( z ) =p ( z )im a ( z ) a ( z ) =.(8)p ( 0)im a (0) a ( 0) for the forward travelling wave, the boundary conditions area (0) =8k 2p ( 0)c2 k, anda ( 0) = ik a (0) .(9)cmn wzz3.influences of the parameters we take example to illustrate the influences of the parameters on the output power. herethe operating mode istm1,1 at a frequency of 18 ghz with input powerp0 =100w, theelectron beam has a currenti = 500a , an energybe = 106 ev , a normalized axialvelocity z = 0.8069,and a normalized transverse velocity t = 0.4862 , the waveguideradius r = 1.400cm , and the operating magnetic fieldcyclotron resonance condition.b0 = 8500g is designed to meet thefig. 2 shows the evolution of output power along the axial position for various operating magnetic fields. evidently, when the axial magnetic field does not meet the cyclotron resonance condition, the output power will seriously decrease.evolution of the output power for the different electron-beam energy eb is plotted in fig. 3the result indicates that the electron-beam energyeb affects the output power. the reason isthat the electron-beam energy ebchanges the cyclotron frequency c = eb0 m0 c , andconsequently, affects the cyclotron resonance condition.10 910 810 710 6power(w)10 510 410 310 210 110 010 -1 1.08b 01.04b 0b0 0.96b 00.92b 00 2 0 4 0 6 0 8 0 1 0 0z( c m )10 10 10 910 810 7power(w)10 610 510 410 310 210 110 010 -11.2m ev 1.1m ev 1.0m ev 0.9m ev 0.8m ev 0 2 0 4 0 6 0 8 0 1 0 0z(c m )fig.2. evolution of output power along the axialfig.3. evolution of output power along the axial positionzposition z for various operating magnetic field b0 .for various electron-beam energy eb .4. conclusions an linear theory demonstrates the possibility of high-power operation for a tm-mode cyclotron autoresonance maser (carm) at the fundamental cyclotron harmonic number. fromthe results we can see that the operating magnetic field b0and the electron-beam energy ebhave substantial influence on the power, because they affect the cyclotron resonance condition.acknowledgementthis work was supported mainly by the national nature science foundation of china(no.60471038)references1a. c. dirien, g. bekefi, c. chen, and j. s. wurtele, experimental and theoretical studies of a 35 ghz cyclotron autoresonance maser amplifier, phys. fluids b 3(7), 1755 1991.2c. p. chen and jonathan s. wurtele. linear and nonlinear theory of cyclotron autoresonance masers with multiple waveguide modes, phys.fluids b, vol. 3, no. 8, 2133 1991.3a. w. fliflet, linear and nonlinear theory of the doppler-shifted cyclotron resonance maser based on teand tm waveguide modes, int. j. electron. 61, 1049(1