Proton firehose instability in bi-Kappa distributed plasmas

¹ Center for Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven, Belgium
e-mail: marian.lazar@wis.kuleuven.be
² Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany

Received: 30 March 2011
Accepted: 21 June 2011

Abstract

Context. Protons or heavier ions with anisotropic velocity distributions and non-thermal departure from Maxwellian, are frequently reported in the magnetosphere and at different altitudes in the solar wind. These observations are sustained by an extended number of mechanisms of acceleration in any direction with respect to the interplanetary magnetic field. However, the observed anisotropy is not large and most probably constrained by the kinetic instabilities.

Aims. An excess of parallel kinetic energy, T_∥/T_⊥ > 1 (where  ∥  and  ⊥  denote directions relative to the background magnetic field) drives a proton firehose mode to grow, limiting any further increase in the anisotropy according to the observations. The effects of suprathermal populations on the principal characteristics of the proton firehose instability are investigated.

Methods. For low-collisional plasmas, the dispersion approach is based on the fundamental kinetic Vlasov-Maxwell equations. The anisotropy of plasma distributions including suprathermal populations is modeled by bi-Kappa functions, and the new dispersion relations are derived in terms of the modified plasma dispersion function (for Kappa distributions), and analytical approximations of this function.

Results. Growth rates of the proton firehose solutions and threshold conditions are provided in analytical forms for different plasma regimes. The proton firehose instability needs a larger anisotropy and a larger parameter β_∥ to occur in a Kappa-distributed plasma. A precise numerical evaluation shows that the growth rates are, in general, lower and the wave frequency is only slightly affected, but the influence of suprathermal populations is essentially dependent on both the proton and electron anisotropies. Departures from the standard dispersion of a Maxwellian plasma can eventually be used to evaluate the presence of suprathermal populations in solar flares and the magnetosphere.