Macroscopic kink instabilities in toroidal relativistic beams

Applications of relativistic beams in confinement and heating of toroidal plasmas are considered, and the interaction of such beams with the shear Alfven modes of the background plasma are examined. A class of low-frequency instabilities which are similar to the hydrodynamic kink instabilities of a current-carrying plasma has been found. However, for the case of a beam-plasma configuration, the spectrum of the Alfven mode is, in general, complex, which precludes the use of an energy principle. A normal mode approach is employed, and growth rates and real frequencies for n = 1, m = 1, 2, 3, 4 instabilities for various values of beam energy and vsub(A)/c, are calculated. A cold model for the background plasma is assumed. A fixed boundary model of the beam-plasma is used and effects of energy spread in the beam are discussed. (U.K.)