Trapped-Particle-Mediated Collisional Damping of Non-Axisymmetric BGK Modes in Electron Plasmas.

Weak axial variations in magnetic or electric fields in long cylindrical electron plasmas cause a small fraction of the electrons to be trapped axially. Collisional diffusion across the trapping separatrix then causes surprisingly large transport and damping effects, including the damping of $m_\theta = 1,2,...$, $k_z = \pm 1$ Trivelpiece-Gould (TG) plasma modes discussed here. These modes are Landau damped at low amplitudes, but they appear as long-lived BGK states ($- \gamma/ \omega \sim 10^{-4}$) when strongly excited. We observe that trapped-particle-mediated (TPM) collisional damping (predicted to scale as $\gamma \propto ( \nu_{ee} / \omega )^{1/2}$) generally dominates over traditional collisional damping (scaling as $\nu_{ee} / \omega$) in determining the lifetime of the BGK state. Experimentally, this TPM damping is readily enhanced by additional trapping barriers or by wiggle-induced resonant scattering. The frequencies and eigenfunctions of the BGK states show close agreement with linear theory, except for small, amplitude-dependent frequency shifts $f(A) = f_0$$[1-a \, \ln (1+bA)]$, similar to (stronger) shifts observed\footnote{J.D.~Moody \& C.F.~Driscoll, Phys.~Plas.~{\bf 2}, 4482 (1995); W.~Bertsche, J.~Fajans \& L.~Friedland, Phys.~Rev.~Lett. {\bf 91}, 265003 (2003).} for $m_\theta = 0$ BGK states.