Effect of finite ion gyroradius on the fire-hose instability in a high beta plasma

In this paper, a generalized kinetic dispersion equation that supports various hydromagnetic waves and instabilities is derived. The general dispersion equation is derived under the usual assumption of hydromagnetic perturbations i.e., ‖ω‖2≪Ωi2, and (kzνA/Ωi)2≪β∥i, where Ωi and νA are the ion gyrofrequency and Alfvén speed, respectively, and β∥i is the parallel ion beta, but for arbitrary values of the quantity λi=(k⊥ρ⊥i)2/2=(k⊥νA/Ωi)2 β⊥i/2 that appears in the dielectric tensor. Here, ρ⊥i refers to the mean ion gyroradius, and β⊥i is the perpendicular ion beta. Otherwise, the dispersion equation is fairly general with no additional approximation, such as ignoring certain off-diagonal dielectric tensor elements (which is usually done in the literature) employed. In the subsequent numerical analysis, special attention is paid to the fire-hose instability in a high beta plasma. The numerical results reveal that the conventional treatment of the fire-hose instability (i.e., taking zero ion gyroradius limit at the outset) is not adequate, and that the effect of finite ion gyroradius results in a significant enhancement of the growth rate over a large range of wave numbers.