Finite temperature m=0 Bernstein modes in a non-neutral plasma, theory and simulation

Axisymmetric upper-hybrid oscillations have been known to exist in non-neutral plasmas and FTICR/MS devices for a number of years.\footnote{J.J. Bollinger, et al., Phys.\ Rev.\ A {\bf 48}, 525 (1993).}$^,$\footnote{S.E. Barlow, et al., Int.\ J.\ Mass Spectrom.\ Ion Processes {\bf 74}, 97 (1986).} However, because they are electrostatic in nature and axisymmetric, they are self-shielding and therefore difficult to detect in long systems. Previous theoretical studies have assumed a zero temperature plasma. In the zero temperature limit these oscillations are not properly represented as a mode, because the frequency at a given radius depends only on the local density and is not coupled to neighboring radii, much like the zero temperature plasma oscillation. Finite temperature provides the coupling which links the oscillation into a coherent mode. We have analyzed the finite-temperature theory of these modes and find that they form an infinite set of modes with frequencies above $\omega^{2}_{c} - \omega^{2}_{p}$. We have simulated these modes in our $r-\theta$ particle-in-cell code that includes a full Lorentz-force mover\footnote{M. Takeshi Nakata, et al., Bull.\ Am.\ Phys.\ Soc.\ {\bf 51}, 245 (2006).} and find that in a mostly flat-top plasma there are two eigenmodes that have essentially the same shape in the bulk of the plasma, but different frequencies. It appears likely that they have different boundary conditions in the boundary region.