Mitigation of ion-induced drift instability in electron plasma by a transverse current through the Landau-resonant layer.*

Experiments and theory on electron columns have characterized an \textit{algebraic} damping of diocotron modes, caused by a flux of electrons through the resonance (critical) layer [1]. This flux-driven damping also eliminates the ion-induced \textit{exponential} instability of diocotron modes. Our plasmas rotate at rate $\omega_{E\times B} $, and the (nominally stable) diocotron modes are described by amplitude $A_{d} ,k_{z} =0,m_{\theta } =1,2,..,$ frequency $\omega_{d} (m_{\theta } )$, and a wave/plasma critical radius $r_{c} (m_{\theta } )$, where $\omega_{E\times B} (r_{c} )={\omega_{d} } \mathord{\left/ {\vphantom {{\omega_{d} } {m_{\theta } }}} \right. \kern-\nulldelimiterspace} {m_{\theta } }$. External fields produce a low density (1/100) halo of electrons moving radially outward from the plasma core, with flux rate $F\equiv ({-1} \mathord{\left/ {\vphantom {{-1} {N_{e} ){dN_{e} } \mathord{\left/ {\vphantom {{dN_{e} } {dt}}} \right. \kern-\nulldelimiterspace} {dt}}}} \right. \kern-\nulldelimiterspace} {N_{e} ){dN_{e} } \mathord{\left/ {\vphantom {{dN_{e} } {dt}}} \right. \kern-\nulldelimiterspace} {dt}}$. We find that \textit{algebraic }damping of the diocotron modes begins when the halo reaches the critical radius $r_{c} (m_{\theta } )$, proceeding as $A_{d} (\Delta t)=A_{d} (0)-\gamma \Delta t$, with $\gamma =\beta (m_{\theta } )F$. We also investigated the diocotron instability which occurs when a small number of ions are transiting the electron plasma [2]. Dissimilar bounce-averaged drifts of electrons and ions polarize the diocotron mode density perturbations, developing instability analogous to the classical flute instability. The exponential growth rate $\Gamma $ is proportional to the fractional neutralization $({N_{i} } \mathord{\left/ {\vphantom {{N_{i} } N}} \right. \kern-\nulldelimiterspace} N_{e} )$ and to the separation between electrons and ions in the wave perturbation. We have found that the \textit{algebraic} damping can suppress the exponential ion-induced instability only for amplitudes satisfying $A_{d} \le {\beta F} \mathord{\left/ {\vphantom {{\beta F} \Gamma }} \right. \kern-\nulldelimiterspace} \Gamma $. [1]A.A. Kabantsev \textit{et al}., PRL \textbf{112}, 115003 (2014). [2]A.A. Kabantsev and C.F. Driscoll, Fusion Sc. and Tech. \textbf{51}, 96 (2007)