Transverse Electron Beam Waves in Varying Magnetic Fields

T h e electron cyclotron wave has received a great deal of attention in the past year, since it forms t h e basis of a successful beam-type travelingwave parametric amplifier. As was first demonstrated by Adler et al., 1 - 2,3 t h e fast cyclotron wave is actively coupled to a fast cyclotron wave idler by the action of a high-frequency transverse electric quadrupole field. It was shown by Gordon 4 5 t h a t space periodic quadrupole fields actively couple a fast and slow cyclotron wave. T h e purpose of this paper is to demonstrate that cyclotron waves will also be amplified in varying magnetic fields. It will be shown that the idler mode associated with the cyclotron wave is a synchronous wave associated with the spatial configuration of the beam. Analogous to the quadrupole case, pumping in a time-varying magnetic field with the 1603 1604 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER I960 p u m p frequency greater t h a n the signal frequency leads to active coupling of two fast modes. When the p u m p frequency is lower than the signal frequency one mode must be fast and the other slow. Pumping in a spatially varying magnetic field will be seen to correspond to the limiting case of zero p u m p frequency. In Section II t h e cyclotron and synchronous waves will be described and some simple points of view established. Then the results of an earlier analysis, 6 in which a general solution for charged particle orbits in arbitrarily varying magnetic fields is given, will be utilized to determine t h e properties of coupled cyclotron and synchronous waves.