Author:

Abstract:

Collisionless plasma instabilities, particularly those associated with enhanced magnetic reconnection rates, are investigated analytically in sheet pinch and other symmetric geometries. Many such instabilities can be observed -- even identified -- in spacecraft data and simulations, but the dynamical processes that control them are difficult to grasp, even in one dimension (of spatial dependence) and much more so in higher dimensions. Stability analyses of space plasmas are often restricted to the Harris equilibrium and other configurations of infinite planar current sheets. In our studies of current sheet instabilities, many additional simplifications are made in order to reduce a kinetic plasma system to a tractable mathematical problem involving a careful identification of all possible eigenmodes. These simplifications include approximate orbit integrals, symmetric geometries and boundary conditions, and Maxwellian background distributions. However, we retain the complexity of the (nonlinear) potentials at the level of the eigenvalue problem and attempt to derive general solutions for various classes of topologies or configurations. The primary unstable modes can then be compared to simulation data.