Plasma heating by collisionless magnetic reconnection: Analysis and computation

This paper presents analytic and numerical results on particle acceleration in two-dimensional collisionless magnetic reconnection. The magnetic field is taken to be a vacuum quadrupole field in the x-y plane with no variation in the z direction. The electric field is uniform and in the z direction. Plasma particles are introduced with their guiding centers on a magnetic flux surface. Particles then execute E x B drift motion under which their guiding centers approach the separatrix. In the numerical simulations and in the analytic modeling presented, the particles are followed until they reach an outgoing flux surface at the same distance from the origin as the starting surface. The magnetic moment is not conserved for particles passing through the unmagnetized region around the X line at the origin. Other particles cross the separatrix without passing near the X line. The magnetic moment of the first class of outgoing particles is randomized, whereas it can be conserved for the second class. By following the evolution of monoenergetic components of the input distribution function, it is possible to describe analytically this plasma thermalization process. The analytic model is based upon the observation of the final kinetic energy as a function of the initial conditions. Analytic results are shown which predict a Maxwellian tail for the distribution function in the perpendicular kinetic energy Kperpendicular with Kperpendicular much-gt K parallel, the parallel kinetic energy. Numerical results are also presented, showing that the predicted tail temperature agrees with the numerically computed temperature to within 10% over 4 orders of magnitude in the electric field. These results provide a detailed understanding of particle acceleration and heating produced by collisionless magnetic reconnection. 67 refs., 11 figs., 1 tab