Damping Measurements of Plasma Modes

For azimuthally symmetric plasma modes in a magnesium ion plasma, confined in a 3 Tesla Penning-Malmberg trap with a density of $n \sim 10^7$cm$^{-3}$, we measure a damping rate of $2$s$^{-1}$$< \gamma < 10^4$s$^{-1}$ over a wide range in temperature ($5 \times 10^{-6} \mathrm{eV} < T < 5$eV) and aspect ratio ($0.25 < \alpha < 25$), with a wave amplitude of $\delta n / n \simeq 5$\%. Changing the aspect ratio, $ \alpha = L_p / 2r_p$, of the plasma column, alters the frequency of the mode from 16 KHz to 192 KHz. The oscillatory fluid displacement is small compared to the wavelength of the mode; in contrast, the fluid velocity, $\delta \mathrm{v}_f$, can be large compared to $\overline{\mathrm{v}}$. The real part of the frequency satisfies a linear dispersion relation. In long thin plasmas ($\alpha > 10$) these modes are Trivelpiece-Gould (TG) modes, and for smaller values of $\alpha$ they are Dubin spheroidal modes. However the damping appears to be non-linear; initially large waves have weaker exponential damping, which is not yet understood. Recent theory\footnote{M.W. Anderson and T.M. O'Neil, Phys. Plasmas {\bf 14}, 112110 (2007).} calculates the damping of TG modes expected from viscosity due to ion-ion collisions; but the measured damping, while having a similar temperature and density dependence, is about 40 times larger than calculated. This discrepancy might be due to an external damping mechanism.