Stability of the kinetic Alfven wave in a current-less plasma

The two potential theory of Hasegawa has been used to derive the dispersion relation for the kinetic Alfven wave (KAW) in a plasma composed of hydrogen, oxygen and electrons. All three components have been modeled by ring distributions (obtained by subtracting two Maxwellian distributions with different temperatures) with the hydrogen and electrons drifting, respectively, with velocities V_dH and V_de. For the most general case, the dispersion relation is a polynomial equation of order five; it reduces to a relation which supports only one mode when V_dH = 0. For typical parameters at comet Halley, we find that both V_dH and V_de can drive the wave unstable; the KAW is thus driven unstable in a current-less plasma. Such an instability was found for the ion acoustic wave by Vranjes et al. (2009).