Macroscopic kink instabilities in toroidal relativistic beams

Applications of relativistic beams in confinement and heating of toroidal plasmas have been discussed in recent years. We have examined the interaction of such beams with the shear Alfvén modes of the background plasma and have found a class of low-frequency instabilities which are similar to the hydrodynamic kink instabilities of a current-carrying plasma. However, for the case of a beam-plasma configuration, the spectrum of the Alfvén modes is, in general, complex, which precludes the use of an energy principle. We employ a normal mode approach and have calculated both growth rates and real frequencies for n = 1, m = 1, 2, 3, 4 instabilities for various values of beam energy and ν_A/c. We assume a cold model for the background plasma, but do not make the MHD ordering ω≪ω_ci. A fixed boundary model of the beam-plasma system is employed and effects of energy spread in the beam are discussed.