Density profiles and current flow in a crossed-field, electron vacuum devices

Summary form only given, as follows. When a strong RF electric field (with a frequency, /spl omega/, and a wavevector, k) is propagating in a cross-field, electron vacuum device, and k and /spl omega/ are such that a wave-particle resonance (/spl omega/=v/sub d/k) can occur at the edge of a Brillouin sheath, then the Brillouin sheath becomes strongly unstable to a Rayleigh instability, with the instability being driven by the strong negative density gradient at the edge of the Brillouin sheath. As a consequence of this instability, the average DC density profile, n/sub 0/(y), becomes strongly modified and is driven away from the classical Brillouin flow by the RF field, and is driven toward the stationary solutions of a nonlinear diffusion equation /spl part//sub 1/n/sub 0/+C/sub 2//spl part//sub y/n/sub 0/=/spl part//sub y/(D/spl part//sub y/n/sub 0/), where C/sub 2//spl Omega//sup 2/ (/spl Omega/ is the electron cyclotron frequency) is the DC current and D is a nonlinear diffusion coefficient, given simply by D=2/spl gamma/|/spl xi//sub y/|/sup 2/, with /spl gamma/ being the linear growth rate of the RF wave that propagates on this stationary density profile, and /spl xi//sub y/, being the /spl gamma/-component of its Lagrangian displacement. We will show that one can find consistent solutions to these equations, wherein the RF fields will satisfy the appropriate linearized equations for the stationary density profile. Examples of stationary solutions for these density profiles will be given, along with plots of DC current vs. tube voltage and magnetic field. The theoretical results will be compared with experiment and the relation between the stationary solutions of the nonlinear diffusion equation and the phenomena of ultra-low noise will be suggested.