<title>Growth of small signal noise in a crossed-field electron vacuum device</title>

Abstract

The purpose of this work is to theoretically understand what are the possible noise levels in a magnetron or a crossed-field amplifier (CFA), due to parametric three-wave interactions in the electron plasma, at various operating parameters. Our approach is to use the cold-fluid equations and their Fourier decomposition, into a background (DC) mode, a pump (RF) mode, and two other noise (RF) modes. The two RF noise modes are assumed to interact parametrically with the large RF pump mode, and to satisfy the standard resonance conditions for the sum of the wave vectors and sum of the frequencies. We use our previous results to determine the background mode and the RF pump mode. Any strong RF electric field propagating in a crossed-field, electron vacuum device, can drive a Brillouin sheath unstable by means of a Rayleigh instability, whenever a wave-particle resonance can be found inside the sheath. What happens physically, is that at the resonance, the laminar flow of the electrons is strongly disturbed, and a diffusion process ensues, whereby the electrons diffuse away from the resonance region. This upsets the balance in the Brillouin flow, causing the electrons to redistribute into a new average DC density profile, one which may be far from the original Brillouin profile, but one which is a stationary solution of a nonlinear diffusion equation. Using these stationary density profiles, we can then study the propagation of small RF signals on such a DC background, as well as their parametric interactions with the RF pump wave, at various DC voltages and magnetic fields. In addition to being able to predict the operating regime and the DC current flow, these studies demonstrate that parametric interactions probably limit the operating voltage range of a typical magnetron or crossed-field amplifier, to about 20% above the Hartree voltage.