Firehose instability in space plasmas with bi-kappa distributions

Context. The existence of suprathermal charged particle populations in space plasma is frequently confirmed by interplanetary missions. In general, the velocity distribution functions are anisotropic, field aligned (gyrotropic) with two temperatures, parallel (T‖) and perpendicular (T⊥) to the ambient magnetic field B0. Aims. Here, the dispersion properties of the firehose instability, which relaxes an anisotropic electron distribution function (T‖ > T⊥) of bi-kappa type, are investigated for the first time. Methods. The Solar wind is generally accepted to be a collisionless plasma and, therefore, the dispersion formalism is constructed on the basis of the kinetic Vlasov-Maxwell equations. The general dispersion relations are derived in terms of the modified plasma dispersion function. Results. Simple analytical forms are obtained for the dispersion relation of the firehose instability and the instability criterion is derived. The exact numerical evaluation shows a significant departure of the dispersion curves from those obtained for a bi-Maxwellian plasma. Conclusions. While the maximum growth rate is slightly diminished, the instability extends to large wave-numbers in the presence of suprathermal particles. Thus, this instability is more likely to be found in space plasmas with an anisotropic distribution of bi-kappa type. If all other parameters are known, measuring the instability growth time enables the determination of the spectral index κ.