Sm. Lund et Rc. Davidson, A CLASS OF COHERENT VORTEX STRUCTURES IN ROTATING NONNEUTRAL PLASMA, Physics of fluids. B, Plasma physics, 5(5), 1993, pp. 1421-1429
A class of nonaxisymmetric (partial derivative/partial derivative thet
a not-equal 0) rotating equilibria is investigated theoretically for s
trongly magnetized, low-density (omega(pe)2/omega(ce)2 much less than
1) pure electron plasma confined radially by a uniform axial magnetic
field B0e(z) between concentric, perfectly conducting, cylindrical wal
ls located at radii r = r(w) and r = r(I) < r(w). The analysis is base
d on a nonrelativistic, guiding-center model in the cold-fluid limit t
hat treats the electrons as a massless fluid (m(e) --> 0) with E X B f
low velocity V(e) = -(c/B0)delphi X e(z). Assuming two-dimensional spa
tial variations (partial derivative/partial derivative z = 0), the con
tinuity-Poisson equations are analyzed for rotating coherent structure
s that are stationary (time independent) in a frame of reference rotat
ing with angular velocity omega(r) = const about the cylinder axis (r
= 0). The equilibrium Poisson equation del2psi = -4pie2n(e)(psi) + 2om
ega(r)eB0/c is solved exactly for the particular case where the electr
on density n(e)(psi) is a linear function of the streamfunction psi =
-ephi + omega(r)(eB0/2c)r2, and the plasma fills the region between th
e conducting walls, with n(e) = 0 at r = r(I) and r = r(w). It is foun
d that this class of rotating equilibria can exhibit large-amplitude,
nonaxisymmetric, vortex structures characterized by strong azimuthal d
ensity bunching and circulating electron flow within the density bunch
es. Nonlinear stability properties are investigated using the Lyapunov
method, and the vortex equilibria with azimuthal mode number l = 1 ar
e shown to be stable.