Theory and simulation of oscillations on near-steady state in crossed-field electron flow and the resulting transport

The purpose of this study is to understand the oscillatory steady-state behavior of crossed-field electron flow in diodes for magnetic fields greater than the Hull field (B > B_H) by the means of theory and self-consistent, electrostatic particle-in-cell (PIC) simulations. Many prior analytic studies of diode-like problems have been time-independent, which leaves the stability and time-dependence of these models unresolved. We investigate fluctuations through the system, including virtual cathode oscillations, and compare results for various cathode injection models. The dominant oscillations in magnetically insulated crossed-field diodes are found to be a series resonance, Z(ω _s) = 0, between the pure electron plasma and vacuum impedance of the diode. The series resonance in crossed-field electron flow is shown to be the k_y → 0 (one-dimensional) limit of the diocotron/magnetron eigenmode equation. The wavenumber, k_y, is perpendicular to the direction across the diode and magnetic field. The series resonance is derived theoretically and verified with self-consistent, electrostatic, PIC simulations.; Electron transport across the magnetic field in a cutoff planar smooth-bore magnetron is described on the basis of surface waves (formed by the shear flow instability) perpendicular to the magnetic field and along the cathode. A self-consistent, 2d3v (two spatial dimensions and three velocity components), electrostatic PIC simulation of a crossed-field diode produces a near-Brillouin flow which slowly expands across the diode, punctuated by sudden transport across the diode. The theory of slow transport across the diode is explained by the addition of perturbed orbits to the Brillouin shear flow motion of the plasma in the diode. A slow drift compared to the shear flow is described which results from the fields caused by the surface wave inducing an electrostatic ponderomotive-like force in a dc external magnetic field.; In order to perform the above-mentioned simulation, a second-order injection algorithm was devised. It is shown that time-centering of the position and velocity is necessary in order to maintain second-order accuracy. The initial push is shown to be important in calculating the correct electric field at the boundary where particles are injected, in relaxing constraints on the time step, and in providing reliable field fluctuations from finite particle statistics.; Kinetic simulation of plasmas in which equilibrium occurs over ion timescales poses a computational challenge due to disparity with electron timescales. Hybrid electrostatic PIC algorithms are presented in which most of the electrons reach thermodynamic equilibrium (Maxwell-Boltzmann (MB) distribution function) each time step. Conservation of charge enables convergence of the nonlinear Poisson equation. Energy conservation is used to determine the temperature of the Boltzmann species. Full PIC and the PIC-MB hybrid simulations compare well for photo-ionized sustained discharges and current-driven DC discharges.