Mode competition in the quasioptical gyrotron
Abstract
A set of equations describing the nonlinear multimode dynamics in the Quasioptical Gyrotron is derived. These equations, involving the slow amplitude and phase variation for each mode, result from an expansion of the nonlinear induced current up to fifth order in the wave amplitude. The interaction among various modes is mediated by coupling coefficients, of known analytic dependence on the normalized current 1, the interaction length mu, and the frequency detunings delta(sub i) corresponding to the competing frequencies omega(sub 1). The particular case when the modes form triads with frequencies omega(sub 1) + omega(sub 3)  2 omega(sub 2) approximately = 0 is examined in more detail. The equations are quite general and can be used to study mode competition, the existence of a final steady state, its stability, as well as its accessibility from given initial conditions. It is shown that when mu/beta perp. is much greater than 1, mu can be eliminated as an independent parameter. The control space is then reduced to a new normalized current 1 and the desynchronism parameters nu(i) = delta(sub i) mu for the interacting frequencies. Each coupling coefficient G(sub ij) is written as G(sub ij) = I S(sub ij) G(sub ij) (nu sub i, nu sub j), where the nonlinear filling factor S(sub ij), carrying the information of the beam current spatial profile, can be computed independently. Therefore, it suffices to compute table of G(sub ij) as functions of nu(sub 1), nu (sub 2), and nu (sub 3) once to cover the parameter space. Results for a cold beam are presented here.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1990
 Bibcode:
 1990STIN...9028823R
 Keywords:

 Competition;
 Cyclotron Resonance Devices;
 Dynamic Characteristics;
 Low Temperature;
 Nonlinear Systems;
 Optical Paths;
 Spatial Distribution;
 Circuits;
 Coupling Coefficients;
 Electric Current;
 Environment Effects;
 Steady State;
 Instrumentation and Photography