Macroscopic extraordinary-mode stability properties of relativistic non-neutral electron flow in a planar diode with applied magnetic field

Abstract

Extraordinary-mode stability properties of relativistic non-neutral electron flow in a planar diode with applied magnetic field are investigated within the framework of the macroscopic cold-fluid-Maxwell equations. The eigenvalue equation is derived for flute perturbations (kz=0) about the general class of relativistic planar equilibria characterized by electron density profile n0b(x), sheared velocity profile V0y(x) =−cE0x(x)/B0z(x), and relativistic mass factor γ0b(x) =[1−E02x(x)/B02z(s)]−1/2. The full influence of equilibrium self-electric and self-magnetic fields is retained in the analysis, and the cathode is located at x=0 and the anode at x=d. The exact eigenvalue equation is simplified for low-frequency perturbations in the guiding-center limit of strongly magnetized electrons with m→0. In this regime, it is shown that (∂/∂x)[n0b(x)/γ0b(x)]≤0 over the interval 0≤x≤d is a sufficient condition for stability of the relativistic electron flow to extraordinary-mode perturbations. A specific example of stable oscillations [rectangular profile for n0b(x)/γ0b(x)] is analyzed in detail. Finally, the exact eigenvalue equation is solved numerically for a wide range of electron density corresponding to weak and strong instability driven by velocity shear with ∂V0y/∂x≠0.

On the relativistic cold fluid radial equilibrium of a nonneutral plasma

“…The stability of nonneutral plasma equilibria with relativistic ef- fects included is analyzed for the slow rotational equilibrium in Refs. [18,19]. The example of uniform density explicitly demonstrates that the plasma may in principle be unbounded since the limiting radius turns out to be infinite.…”

Kinetic equilibrium properties of relativistic non-neutral electron flow in a cylindrical diode with applied magnetic field

“…While an understanding of the important physics [1][2][3][4][5][6] issues is increasing, the majority of these studies have been based on macroscopic cold-fluid models, largely for reasons of analytical and numerical convenience. In the present article, we make use of the steadystate (@/3t= 0) Vlasov-Maxwell equations to investigate the equilibrium properties of sheared, relativistic, nonneutral electron flow in a cylindrical diode.…”

“…where fib is the electron density at the cathode (rR c), and to evaluate H-mc 2 for P = PO, we find after some straightforward algebra that H-mc can be expressed as…”

Collective instabilities driven by anode plasma ions and electrons in a nonrelativistic cylindrical diode with applied magnetic field

“…of nonneutral plasma stability properties that the collective interactions associated with an active ion component in an electron-rich background can lead to an instability known as the ion resonance instability1 2 The strength of the ion resonance instability depends on a number of factors, including ion density, the relative motion of electron and ion components, and the strength of the equilibrium self electric fields. As such an instability may have deleterious effects on stable diode operation and/or the production of well-collimated ion beams, one purpose of the present analysis is to investigate detailed properties of the ion resonance instability in geometry particular to cylindrical diodes ( Fig.…”