Kinetic description of betatron oscillation instability for nonrelativistic nonneutral electron flow
The linearized Vlasov--Poisson equations are used to investigate the electrostatic stability properties of nonrelativistic nonneutral electron flow in a planar diode with cathode located at x = 0 and anode at x = d. The electron layer is immersed in a uniform applied magnetic field B/sub 0/e/sub z/, and the equilibrium flow velocity V/sup 0//sub y/b(x) is in the y direction. Stability properties are calculated for perturbations about the choice of self-consistent Vlasov equilibrium f/sup 0//sub b/ (H,P/sub y/) = (n/sub b//2..pi..m) delta(H) delta(P/sub y/), which gives an equilibrium with uniform electron density (n/sub b/ = const) extending from the cathode (x = 0) to the outer edge of the electron layer (x = x/sub b/). Assuming flute perturbations, the eigenvalue equation is simplified and solved analytically for long-wavelength, moderately high-frequency perturbations satisfying k/sup 2/x/sup 2//sub b/ <<1 and (..omega..-kV/sub d/)/sup 2/ roughly-equal..omega../sup 2//sub v/ = ..omega../sup 2//sub c/ -omega-circumflex/sup 2//sub p/b. The present analysis is restricted to electron densities below the Brillouin flow (omega-circumflex/sup 2//sub p/b <..omega../sup 2//sub c/) and the nonzero electric field at the cathode. The eigenvalue equation leads to a fourth-order algebraic dispersion relation for the complex eigenfrequency.
- Research Organization:
- Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- OSTI ID:
- 5795604
- Journal Information:
- Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 29:7; ISSN PFLDA
- Country of Publication:
- United States
- Language:
- English
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70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700105 -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ACCELERATORS
ANODES
BETATRONS
BOLTZMANN-VLASOV EQUATION
CATHODES
CURRENTS
CYCLIC ACCELERATORS
DIFFERENTIAL EQUATIONS
DIODE TUBES
DISTURBANCES
EIGENFUNCTIONS
ELECTRIC CURRENTS
ELECTRODES
ELECTRON TUBES
ELECTROSTATICS
EQUATIONS
EQUILIBRIUM
FUNCTIONS
INSTABILITY
MAGNETIC FIELDS
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
THERMIONIC DIODES
THERMIONIC TUBES
VELOCITY