Theory of Peer-to-Peer Locking of High-Power Gyrotron Oscillators Coupled with Delay

Asel B Adilova,Nikita M Ryskin

doi:10.3390/electronics11050811

Abstract

Peer-to-peer locking is a promising way to combine the power of high-power microwave oscillators. The peer-to-peer locking of gyrotrons is especially important because arrays of coupled gyrotrons are of special interest for fusion and certain other applications. However, in case of coupled microwave oscillators, the effect of delay in coupling is very significant and should be taken into account. In this article, we present the model of two delay-coupled gyrotrons. We develop an approximate theory of phase locking based on the generalized Adler’s equation, which allows for the treatment of in-phase and anti-phase locking modes. We also present a more rigorous bifurcation analysis of phase locking by using XPPAUT software under the limitation of small delay time. The structure of the phase-locking domains on the frequency-mismatch–coupling-strength plane of parameters is examined. Finally, we verify the results by numerical simulations in the case of finite delay time. The simulations reveal various regimes, including peer-to-peer locking, the suppression of one gyrotron by another, as well as the excitation of one gyrotron by another.

Highlights

The power combining of high-power microwave oscillators is a promising way to achieve ultra-high power levels [1]
The power combining of gyrotrons has attracted a special interest since arrays of high-power gyrotrons are of great importance for electron-cyclotron-resonance plasma heating [15] and certain other applications [16]
We study the peer-to-peer locking of gyrotrons operating at the point of maximal efficiency, i.e., in the hard excitation mode

Summary

Introduction

The power combining of high-power microwave oscillators is a promising way to achieve ultra-high power levels [1]. A critical issue for the coherent power summation is phase and frequency locking Both injection locking [4,6,10,14,17–19] and peer-to-peer locking [2–4,7–9,20,21] techniques have been widely studied. It can predict the main characteristics, such as power, efficiency, and oscillation frequency, with the same accuracy as the nonstationary theory of a gyrotron with a fixed RF field profile. It is well-known that the maximal interaction efficiency of high-power gyrotrons is usually attained in the regime of hard self-excitation. This significantly complicates the pattern of phase locking. We examine the stability of the in-phase and anti-phase synchronous states and reveal the complicated pattern of the phase-locking domains on the frequency mismatch—coupling strength parameter plane

Model and Basic Equations

Peer-to-Peer Locking Analysis

Generalized Adler’s Equation

Structure of Locking Domains

Numerical Simulations in the Case of Arbitrary Delay

Discussion and Conclusions