Experiments with the L = 1 Diocotron Mode.

Experiments are presented on a particularly interesting oscillatory mode in pure electron plasmas. The plasmas studied are columns contained inside conducting cylinders in an axial magnetic field. Traditional theory models diocotron modes as surface density perturbations; the mode of interest has azimuthal mode number l = 1 (i.e. varying as cos theta) and is essentially independent of axial position (i.e. k_ {z}~ 0). At large amplitude the mode is more correctly viewed as a dynamical equilibrium in which the plasma column is offset by a displacement, D, and drifts around the cylindrical axis. The frequency, f, of the mode is observed to vary with amplitude as Deltaf ~ D^2. This frequency shift arises because (1) the plasma is closer to its image charge than a linear model assumes, and (2) the plasma distorts from a circular shape. From measurements of n(r, theta) it is seen that a large amplitudes the column shape becomes elliptical with elongation in the theta-direction. The distortion and frequency shifts are such as to make the density stationary in a frame rotating at the mode frequency. The small amplitude frequency of the diocotron mode in an infinite length column, f_{d }, depends only on the charge per unit length. Measurements of frequency have been made versus plasma length, L _{p}, and plasma radius, R _{p}. The mode frequency is found to be up to 200% higher in short plasmas, and the fractional frequency shift increases as L_sp{p }{-1} and decreases with R _{p}. These observations are in agreement with linear theory. Finite length theory also predicts damping of the diocotron mode. Measurements indicate that mode damping is at least three orders of magnitude smaller than predicted: the mode oscillates 10 ^5 cycles with negligible change in amplitude. Finally, the effects of two field perturbations have been studied. An axisymmetric electrostatic field induces exponential damping in the diocotron mode. The other is a small (10^{-3} rad) tilt of the magnetic field that induces mode damping, as well as particle transport towards a square, low-noise density profile.