Abstract We describe a form of self-consistent particle-in-cell plasma simulation which is applicable to strongly inhomogeneous systems involving a wide range of space and time scales. In this multi-scale method, the plasma particles in each region of phase space are advanced using a step size appropriate to that region, as determined by accuracy considerations. While the necessity of a self-consistent field may seem to require processing of all particles in synchrony, the method overcomes that difficulty. This is accomplished by means of implicit PIC techniques, interpolating grid quantities in time to obtain the source contributions from groups of particles not advanced during the current step. For suitable problems (those in which fine space-time resolution is needed only in isolated spatial regions), most of the particles are not processed on any given step. Thus, major gains in efficiency over conventional simulations may be realized. In this paper we describe the method, and the beginnings of our investigations into its feasibility.
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