Equation free projective integration: A novel scheme for modeling multiscale processes in plasmas

We examine a novel simulation scheme called equation free projective integration1 which has the potential to allow global simulations of plasmas while still including the global effects of microscale physics. These simulation codes would be ideal for such multiscale problems as the Earth's magnetosphere, tokamaks, and the solar corona. In this method, the global plasma variables stepped forward in time are not time-integrated directly using dynamical differential equations, hence the name "equation free." Instead, these variables are represented on a microgrid using a kinetic simulation. This microsimulation is integrated forward long enough to determine the time derivatives of the global plasma variables, which are then used to integrate forward the global variables with much larger time steps. Results will be presented of the successful application of equation free to 1-D ion acoustic wave steepening. In addition, initial results of this technique applied to reconnection will also be discussed. 1 I. G. Kevrekidis et. al., "Equation-free multiscale computation: Enabling microscopic simulators to perform system-level tasks," arXiv:physics/0209043.