Kinetic stability properties of nonrelativistic non-neutral electron flow in a planar diode with applied magnetic field

Journal Article · Sun Dec 01 04:00:00 EST 1985 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.32.3554· OSTI ID:5004325

Davidson, R C; Uhm, H S

The linearized Vlasov-Poisson equations are used to investigate the electrostatic stability properties of nonrelativistic non-neutral 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/sub y/b/sup 0/(x) is in the y direction. Stability properties are calculated for perturbations about the choice of self-consistent Vlasov equilibrium f/sub b//sup 0/(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 (partial/partialz = 0) of the form deltaphi(x,y,t) = deltaphi-circumflex/sub k/(x)exp(iky -i..omega..t), the eigenvalue equation for deltaphi-circumflex/sub k/(x) is simplified and solved analytically for long-wavelength, low-frequency perturbations satisfying kx/sub b/<<1 and Vertical Bar..omega..-kV/sub d/Vertical Bar/sup 2/<<..omega../sub v//sup 2/equivalent..omega../sub c//sup 2/ -omega-circumflex/sub pb//sup 2/. This gives a quadratic dispersion relation for the complex oscillation frequency ..omega...

• Research Organization: Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• OSTI ID: 5004325
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 32:6; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700103* -- Fusion Energy-- Plasma Research-- Kinetics
BOLTZMANN-VLASOV EQUATION
CONFINEMENT
DIFFERENTIAL EQUATIONS
DIODE TUBES
DISPERSION RELATIONS
DISTURBANCES
ELECTRON TUBES
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FLUTE INSTABILITY
INERTIAL CONFINEMENT
INSTABILITY
LEPTONS
MAGNETIC FIELDS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA CONFINEMENT
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
STABILITY
THERMIONIC DIODES
THERMIONIC TUBES
THERMONUCLEAR REACTORS
TRAJECTORIES