Linear theory of tearing in a high-β plasma

We calculate the linear dispersion relation for a collisionless plasma in a sheared one-dimensional current sheet and extend the existing calculations to include βapprox.1 plasmas, where β is the ratio of the thermal pressure to the magnetic pressure. Defining B/sub z/ as the component of the magnetic field which reverses sign as a function of x and B/sub y/ as that component which is nonzero but does not reverse sign (the guide-field), we find that the tearing mode eigenstructure and temporal growth rate are a sensitive function of the ratios l/sub s//l/sub G/, l/sub s//l/sub n/, and l/sub s//l/sub tau/, where l/sub s/ is the shearing length of the magnetic field, l/sub G/ is the gradient scale length of the guide field B/sub y/, l/sub n/ is the number density gradient scale length, and l/sub tau/ is the temperature gradient scale length. In particular, if β> or approx. =1 and l/sub s/<l/sub G/, l/sub n/, and l/sub T/, then the thickness of the layer over which particles are resonantly accelerated by the induction electric field is approx.rho, a thermal gyroradius. In this limit the growth rate reduces to that derived by Laval et al. (1966). If the above conditions are not satisfield, plasma gradients may electrostatically stabilize the mode