Flux-driven algebraic damping of m = 2 diocotron mode

Abstract

Experiments with pure electron plasmas in a Malmberg–Penning trap have observed linear in time, algebraic damping of m = 2 diocotron modes. Transport due to small field asymmetries produces a low-density halo of electrons moving radially outward from the plasma core, and the mode damping begins when the halo reaches the resonant radius of the mode. The damping rate is proportional to the flux of halo particles through the resonant layer. The damping is related to, but distinct from spatial Landau damping in which a linear wave–particle resonance produces exponential damping. This paper reports an analytic theory that captures the main signatures reported for this novel damping, namely, that the damping begins when the halo particles reach the resonant radius and that the damping is algebraic in time with nearly constant damping rate. The model also predicts a nonlinear frequency shift. The model provides two ways to think about the damping. It results from a transfer of canonical angular momentum from the mode to halo particles being swept by the mode field through the nonlinear cat's eye orbits of the resonant region. More mechanistically, the electric field produced by the perturbed charge density of the resonant particles acts back on the plasma core causing E×B drift that gives rise to the damping and nonlinear frequency shift.

Eulerian simulations of electrostatic waves in plasmas with a single sign of charge

“…6 we show ω n,m as a function of k n for twelve different initial value problem simulations, in which we considered as initial perturbations single eigenmodes with n = 1, 2, 3 and m = 0, 1, 2, 3: the dots here represent the values of the real part of the mode frequency from the simulations, evaluated by Fourier analyzing E z (r = 0, z,t), while the dashed lines represent the theoretical curves in Eq. (21). Results for modes with m = 0 are indicated in blue, for modes with m = 1 in red, for FIG.…”

“…Several fluctuations and instabilities are supported by these plasmas. Trivelpiece-Gould waves (TGWs) 15 -the counterpart of Langmuir waves in nonneutral plasmas, Electron Acoustic waves (EAWs) [16][17][18] are typical longitudinal fluctuations occurring in Penning-Malmberg devices, while diocotron [19][20][21] , cyclotron 22,23 and Bernstein 24 waves oscillate in the transverse directions. The perpendicular dynamics shows also significant analogies with a two-dimensional inviscid fluid 25 , thus motivating several experimental and numerical efforts to study, for example, the vortex dynamics subject to an external strain 26,27 .…”