Resistive destabilization of cycloidal electron flow and universality of (near-) Brillouin flow in a crossed-field gap

Abstract

It is shown that a small amount of dissipation, caused by current flow in a lossy external circuit, can produce a disruption of steady-state cycloidal electron flow in a crossed-field gap, leading to the establishment of a turbulent steady state that is close to, but not exactly, Brillouin flow. This disruption, which has nothing to do with a diocotron or cyclotron instability, is fundamentally caused by the failure of a subset of the emitted electrons to return to the cathode surface as a result of resistive dissipation. This mechanism was revealed in particle simulations, and was confirmed by an analytic theory. These near-Brillouin states differ in several interesting respects from classic Brillouin flow, the most important of which is the presence of a microsheath and a time-varying potential minimum very close to the cathode surface. They are essentially identical to that produced when ͑i͒ injected current exceeds a certain critical value ͓P. J. Christenson and Y. Y. Lau, Phys. Plasmas 1, 3725 ͑1994͔͒ or ͑ii͒ a small rf electric field is applied to the gap ͓P. J. Christenson and Y. Y. Lau, Phys. Rev. Lett. 76, 3324 ͑1996͔͒. It is speculated that such near-Brillouin states are generic in vacuum crossed-field devices, due to the ease with which the cycloidal equilibrium can be disrupted. Another novel aspect of this paper is the introduction of transformations by which the nonlinear, coupled partial differential equations in the Eulerian description ͑equation of motion, continuity equation, Poisson equation, and the circuit equation͒ are reduced to an equivalent system of very simple linear ordinary differential equations.

Discrete space charge affected field emission: Flat and hemisphere emitters

“…(9) below) and can be taken as an opposite limit. Important features of sheet charge models appear in the works of Kishek and Lau 30 and Christenson et al 31 The present approach summarizes key points. Let the position of the sheet in the AK gap be specified by x ¼ sD, where 0 s 1 is a scaled position.…”

Limiting current in a relativistic diode under the condition of magnetic insulation

“…In previous 1D simulations of nonrelativistic, cycloidal crossed-field flows using the electrostatic code PDP1, 23 it is found that a small ac gap voltage, 3,26 or a small external resistance, 27 or a small misalignment in the external magnetic field, 28 may render the cycloidal flow unstable even when the emission current density is only a small fraction of the critical values depicted in Fig. 2.…”

Two-dimensional space-charge-limited flows in a crossed-field gap

“…10 The classical 1D model was also extended to a quantum model for a nanosized crossed-field gap. 11 For the B ജ B H case, it was found that transition from laminar flow to turbulent flow may occur due to over injection of current with a value higher than the limiting current value, 9 small ac voltage modulation, 12 resistivity, 13 and misalignment of the magnetic field. 14 The microwave magnetron is a type of crossed-field device that is widely used in microwave ovens, radars, industrial heating, medical accelerators, and plasma sources.…”