Diocotron Mode Damping from a Flux through the Critical Layer

Experiments and theory characterize a novel type of spatial Landau damping of diocotron modes which is {\it algebraic} rather than {\it exponential} in time; this damping is caused by a flux of particles through the wave/rotation critical layer.\footnote{A.A. Kabantsev, et al., Phys.~Rev.~Lett. 112, 115003 (2014).} These $k_z = 0$ diocotron (drift) modes with azimuthal mode numbers $m_\theta = 1,2...$ are dominant features in the dynamics of non-neutral plasmas in cylindrical and toroidal traps; and they are directly analogous to Kelvin waves on 2D fluid vortices. Spatial Landau damping is the resonant interaction between a mode at frequency $f_m$ and the plasma rotation $f_E (r)$, at the critical radius $R_c$ where $f_m = m_\theta f_E(R_c)$. This is mathematically analogous to velocity-space Landau damping with $f_k = k v / 2 \pi$. \textbullet Experimentally, diocotron modes on pure electron plasmas exhibit exponential Landau damping when the {\it initial} plasma density is non-zero at $R_c$. Here, we demonstrate that a steady outward {\it flux} of particles through $R_c$ causes diocotron modes to damp algebraically to zero amplitude, as $D(t) = D_0 - \gamma_m t$ . The outward flux is controlled and measured experimentally, and the damping rates $\gamma_m$ are proportional to the flux. In general, any weak non-ideal process which causes outward flux may cause this damping. \textbullet Analytics and simulations have developed a simple model of this damping, treating the transfer of canonical angular momentum from the mode to particles transiting the nonlinear trapping region at $R_c$. The model qualitatively agrees with experiments for $m_\theta = 1$, but nominally predicts a discrepant algebraic exponent for $m_\theta = 2$, perhaps due to the amplitude dependence of the trapping structure. Overall, this novel flux-driven damping is determined by the {\it present} magnitudes of the wave and outward flux, in contrast to the Landau analysis of phase mixing of the {\it initial} density.