Vlasov equilibrium and electrostatic stability properties of a nonrelativistic nonneutral E layer

Journal Article · Fri Oct 01 00:00:00 EDT 1976 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.861367· OSTI ID:7147032

Davidson, R C; Uhm, H; Mahajan, S M

Vlasov equilibrium and stability properties of a nonrelativistic nonneutral E layer are investigated for the class of thin (a very-much-less-thanR/sub 0/) E-layer equilibria in which all electrons have the same value of the energy H and the same value of canonical angular momentum P/sub theta/, i.e., f/sub e//sup 0/(H, P/sub theta/) = (n/sub 0/R/sub 0//2..pi..m) delta (H+ephi-bar/sub 0/-mV/sub 0//sup 2//2) delta (P/sub theta/-P/sub 0/), where n/sub 0/, R/sub 0/, phi-bar/sub 0/, V/sub 0/, and P/sub 0/ are constants. No a priori restriction is made that the density is low (..omega../sub p//sub 0//sup 2/very-much-less-than..omega../sub c//sup 2/), and equilibrium and stability behavior is studied for both fast (P/sub 0/>0) and slow (P/sub 0/<0) rotational equilibria. Equilibrium space-charge effects are shown to have a large (defocusing) effect on the radial thickness of the E layer when ..omega../sub p//sub 0//sup 2/approx. =..omega../sub c//sup 2/. The electrostatic stability analysis includes both negative-mass (orbit variations with P/sub theta/) and diocotron (angular velocity shear) effects. The system is shown to be stable whenever the equilibrium flow is space-charge neutralized, i.e., whenever f=1, where f=n/sub i//sup 0//n/sub e//sup 0/ is the fractional charge neutralization. For fvery-much-less-than1, a necessary and sufficient condition for instability is given by (l-2) a/R/sub 0/>f, where l is the azimuthal mode number of the perturbation. Moreover, depending on system parameters, the growth rate can be a substantial fraction of the electron plasma frequency ..omega../sub p//sub 0/. (AIP)

• Research Organization: Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
• OSTI ID: 7147032
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 19:10; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700105* -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
ANALYTICAL SOLUTION
BEAMS
BOLTZMANN-VLASOV EQUATION
DIFFERENTIAL EQUATIONS
ELECTRON BEAMS
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
LEPTON BEAMS
LEPTONS
PARTICLE BEAMS
PLASMA
SPACE CHARGE
STABILITY