Compressional effects in nonneutral plasmas, a shallow water analogy and m=1 instability

Diocotron instabilities form an important class of E X B shear flow instabi lities which occur in nonneutral plasmas. The case of a single-species plas ma confined in a cylindrical Penning trap, with an axisymmetric, hollow (no nmonotonic) density profile is studied. According to the standard linear th eory, the m = 1, k(z) = 0 diocotron mode is always stable. On the other han d, experiments by Driscoll [Phys. Rev. Lett. 64, 645 (1990)] show a robust exponential growth of m = 1 diocotron perturbations in hollow density profi les. The apparent contradiction between these experimental results and line ar theory has been an outstanding problem in the theory of nonneutral plasm as. A new instability mechanism due to the radial variation of the equilibr ium plasma length is proposed in this paper. This mechanism involves the co mpression of the plasma parallel to the magnetic field and implies the cons ervation of the line integrated density. The predicted growth rate, frequen cy, and mode structure are in reasonable agreement with the experiment. The effect of a linear perturbation of the plasma length is also shown to give instability with a comparable growth rate. The conservation of the line in tegrated density in the plasma is analogous to the conservation of the pote ntial vorticity in the shallow water equations used in geophysical fluid dy namics. In particular, there is an analog of Rossby waves in nonneutral pla smas. (C) 1999 American Institute of Physics. [S1070-664X(99)01310-5].