Spatial Landau Damping of Diocotron Modes Caused by a Particle Flux

Diocotron modes exhibit a novel {\it algebraic} (not exponential) damping when there is a flux of particles through the spatial resonance layer. Here, a magnetized pure electron column with density $n(r)$ and drift rotation $f_E (r)$ exhibits $m=1,2$ diocotron mode frequencies $f_m \sim \langle f_E \rangle$$[(m-1) + (R_p / R_w )^{2m} ]$. {\it Exponential} mode damping is predicted (and observed) due to spatial Landau damping at the resonance layer where $f_E (r_s ) = f_m$; but with small $n ( r_s ) $ this damping may saturate due to wave-particle trapping. In contrast, when background asymmetries cause (slow) plasma expansion and a (weak) radial particle flux $\Gamma$ through $r_s$, the diocotron mode damps to zero algebraically with time, as $A_m (t) = A_m (0) - \gamma_m t$. Experiments and nascent theory show damping rates proportional to the radial particle flux $\Gamma$ through the relevant separatrix, with $\gamma_m \sim \Gamma$. For $m=1$, $\Gamma$ represents particles lost to the wall; but for $m=2$, even a small plasma expansion can cause strong damping. This algebraic damping will be compared to the exponential growth (or damping) observed from resistive (or feed-back) wall voltages, from neutral collisions, and from axial ejection (or injection) of electrons.