Low-frequency flute instabilities of a bounded plasma column

A study is made of the stability of quasineutral low-frequency (ω ≪ ωci) flute waves in a low-β collisionless plasma column immersed in a uniform axial magnetic field. The column has a Gaussian number density profile and a dc radial electric field. The differential equation which describes the waves is solved both analytically and numerically for the eigenfrequencies and eigenfunctions. For the case of uniform rotation of the column, analytical solutions are obtained to determine the properties of a column bounded by a conducting cylinder. The instability is a centrifugal flute wave for this case. The boundary can be stabilizing or destabilizing for the m = 1 azimuthal mode, depending on its location, while for all other modes, the boundary is stabilizing. For a nonuniformly rotating column, the effects of gradual shear and abrupt shear are considered using numerical solutions. By following the evolution of these modes as the profiles are changed continuously, a unified picture of their behavior is developed. Again the behavior of the m = 1 mode is found to be different from that of the higher-order modes, as illustrated by the m = 2 mode. The m = 1 mode is quite sensitive to the rotation of the column near the boundary, while the m = 2 mode depends more on an average over the column. Also, for abrupt shear, the m =2 mode evolves into a Kelvin-Helmholtz instability, while the m = 1 mode does not.