Nonlinear Simulation of a Cyclotron Autoresonance Maser (CARM) Operating in a Transverse Magnetic Mode
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Nonlinear Simulation of a Cyclotron Autoresonance Maser (CARM) Operating in a Transverse Magnetic Mode Bing-Fu Liu & Shi-Chang Zhang
Received: 10 November 2010 / Accepted: 2 December 2010 / Published online: 14 December 2010 # Springer Science+Business Media, LLC 2010
Abstract In the gyrotron operation, the transverse-magnetic (TM) mode is excluded because the TM mode instability vanishes when the vacuum waveguide mode and the beam mode are at grazing incidence. However, situation changes in a cyclotron autoresonance maser (CARM) interaction. In this paper nonlinear formulation of a TM-mode CARM is derived, and detailed simulations are presented for the TM1,1-mode CARM. Simulation results show that a TM1,1-mode CARM can reach high power of megawatts and ultrahigh gain of more than 70 dB, as a TE1,1-mode gyrotron traveling wave tube (gyro-TWT) and TE1,1-mode CARM did in the reported experiments. Keywords Cyclotron autoresonance maser . Transverse-magnetic mode . Nonlinear theory
1 Introduction In the past years, the transverse-electric (TE) modes have been wildly applied in gyrodevices, but the transverse-magnetic (TM) modes were rarely considered [1–10]. Perhaps the reason is that the TM mode instability vanishes when the vacuum waveguide mode and beam mode are at grazing incidence in gyrotrons [2, 3]. However, situation changes in a cyclotron autoresonance maser (CARM), where the axial kinetic energy of the relativistic electrons is pumped into the transverse kinetic energy and then is delivered to the wave by beam-wave interaction [11]. Unlike the TE mode without an axial electric field, the axial electric field component of a TM mode may substantially affect the axial motion of the electrons when it interacts with a relativistic electron beam. Therefore, use of the TM mode appears favorable to a CARM operation. Furthermore, the cyclotron autoresonance condition is broadly satisfied for the interaction of a TM mode with a relativistic electron beam [7].
B.-F. Liu : S.-C. Zhang (*) Institute of Photoelectronics, School of Information Science and Technology, Southwest Jiaotong University, Campus Mail Box 50, Chengdu, Sichuan 610031, People’s Republic of China e-mail: [email protected]
J Infrared Milli Terahz Waves (2011) 32:8–15
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We organize the contents of this paper as follows. In Section 2 a nonlinear model is presented for a general TM-mode CARM. In Sections 3 and 4 specific simulations are carried out for the TM1,1-mode CARM to demonstrate its effective operation and to examine the influences of the operating magnetic field, the electron-beam energy, and the axial velocity spread on the output power. Finally, conclusions are drawn in Section 5.
2 Model of nonlinear simulation Neglecting the self-fields of the electron beam and using a cylindrical coordinate system (r, θ, z), one can express the field components of a TMm,n mode in a cylindrical waveguide as follows: Er ¼ kc f 0 ðzÞJm0 ðkc rÞejðwtmϕÞ ;
Eϕ ¼ j
m 0 f ðzÞJm ðkc rÞejðwtmϕÞ ; r
Ez ¼ kc2 f ðzÞJm ðkc rÞejðwtmϕÞ ;
ð1Þ
ð2Þ
ð3Þ
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