Properties of axisymmetric Bernstein modes in an infinite-length non-neutral plasma - Hart, Grant W.; Spencer, Ross L. (Physics of plasmas, 2013)
We have observed axisymmetric Bernstein modes in an infinite-length particle-in-cell code simulation of a non-neutral plasma. The plasmas considered were in global thermal equilibrium and there were at least 50 Larmor radii within the plasma radius. The density of the plasma in the simulation is parameterized by β, the ratio of the central density to the density at the Brillouin limit. These modes have m = 0 and k z = 0 , where the eigenfunctions vary as e i ( m θ + k z z ) . The modes exist both near the Coriolis-shifted (by the plasma rotation) upper-hybrid frequency, ω u h = ω c 2 − ω p 2 , and near integer multiples (2, 3, etc.) of the Coriolis-shifted cyclotron frequency (called the vortex frequency, ω v = ω c 2 − 2 ω p 2 ). The two modes near ω u h and 2 ω v are the main subject of this paper. The modes observed are clustered about these two frequencies and are separated in frequency at low plasma density roughly by δ ω ≈ 10 ( r L / r p ) 2 ω p 2 / ω c . The radial velocity field of the modes has a J 1 ( k r ) dependence in the region of the plasma where the density is nearly constant. For any given density, there are three classes of modes that exist: (1) The fundamental mode is slightly above the upper-hybrid frequency, (2) the upper branch is above the higher of ω u h and 2 ω v , and (3) the lower branch is below the lower of ω u h and 2 ω v , with similar values of k for both the upper and the lower frequency branches. The modes are fully kinetic and the resulting pressure tensor has significant anisotropy, including off-diagonal terms. A Vlasov analysis of these modes considering only particle resonances up to 2 ω v produces a radial mode differential equation whose solution agrees well with the simulations, except at high density (β greater than about 0.9) where higher-order resonances become important.