Nonresonant kinetic instabilities of a relativistic plasma in a uniform magnetic field: Longitudinal and transverse mode coupling effects

The stability properties of relativistic plasmas embedded in a uniform magnetic field are investigated for longitudinal and transverse modes and with coupling effects between these modes. The direction of wave propagation in the plasma is not necessarily either parallel or transverse to the ambient magnetic field. The basic dispersion relation equations are given for arbitrary propagation directions. Detailed examination is focused on perpendicular wave propagation in this paper. The concept of neutral points in wave number space, introduced by Harris [Phys. Rev. Lett. 2, 34 (1959)], is generalized to allow for the inclusion of ion effects and the effects of fluctuating magnetic fields. Starting from the relativistic conductivity tensor, an expansion procedure for low wave frequencies is used to determine the stability properties in the neighborhood of neutral points and in the frequency regime below the ion cyclotron frequency. The bulk plasma properties determine stability or instability but the mode structure is derivable only from a particle kinetic picture, as with Weibel [Phys. Rev. Lett. 2, 83 (1959)] instabilities, and not from a magnetohydrodynamic description. For monoenergetic plasma distribution functions of electrons and ions, as well as for electrons and positrons, numerical examples are given to illustrate the neutral points and the unstable wave number regimes. (c) 2007 American Institute of Physics.