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Kinetic stability properties of relativistic nonneutral electron flow for low-frequency extraordinary-mode perturbations

Published online by Cambridge University Press:  09 March 2009

Ronald C. Davidson  and
Han S. Uhm
Ronald C. Davidson
Affiliation:
Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139
Han S. Uhm
Affiliation:
Naval Surface Warfare Center, Silver Spring, MD 20903
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Abstract

The kinetic stability properties of relativistic nonneutral electron flow in planar diode geometry are examined for extraordinary-mode perturbations about the self-consistent Vlasov equilibrium . Here, the cathode is located at x = 0; the anode is located at x = d the outer edge of the electron layer is located at is the equilibrium flow velocity in the x-direction; n^b is the electron density at the cathode (x = 0); and is the axial magnetic field, with const. in the vacuum region (xb < x ≤ d). The extraordinary-mode eigenvalue equation, derived in a companion paper for low-frequency, long-wavelength perturbations, is solved exactly. This leads to a formal dispersion relation, which can be used to determine the complex eigenfrequency ω over a wide range of system parameters and wavenumber k in the y-direction. The formal dispersion relation is further simplified for and , assuming low-frequency perturbations about a tenuous electron layer with and . Here, , and , where denotes the average equilibrium orbit, and [γ(x) − 1]mc2 is the average kinematic energy of an electron fluid element. The resulting approximate dispersion relation is solved numerically over a wide range of system parameters to determine the detailed dependence of stability properties on electromagnetic effects, layer thickness, and electron energy, as measured by , and γb − 1, respectively. Here, γb = γ(xb) denotes the electron energy at the outer edge of the electron layer. As a general remark, it is found that increasing the electron energy (γb − 1), increasing the strength of electromagnetic effects , and/or decreasing the layer thickness (xb/d) all have a stabilizing influence.

Type
Research Article
Information
Laser and Particle Beams , Volume 7 , Issue 1 , February 1989 , pp. 85 - 109
Copyright
Copyright © Cambridge University Press 1989

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