An electromagnetic field algorithm for 2d implicit plasma simulation

Abstract A new, robust algorithm is presented for the implicit calculation of the electromagnetic fields used in the full-particle and hybrid modeling of 2D simulation plasmas. The algorithm allows for calculations at time steps Δt well in excess of the plasma period and for mesh scales Δξ far exceeding the Debye length-with electron inertial terms retained. The implicit fields suppress the numerical instability associated with plasma waves. Still, the At remain constrained by an electron Courant limit. The algorithm is considerably simpler than earlier implicit schemes, and more complete in its treatment of field errors. In its present form the algorithm is limited to plasmas moving and accelerating in a plane across a single component of magnetic field. An extension to include all the field components is suggested, however. In accordance with the implicit moment method, estimated electric and magnetic fields are obtained by solving Maxwell's equations self-consistently for a set of implicit sources, estimated with the aid of an auxiliary set of lower fluid moment equations (for component fluxes and density). The fluid pressure terms are treated explicitly, and the spatial differencing of the auxiliary moments is centered to facilitate the solution of the resultant field equations. Solution for the single magnetic field component is obtained by one elliptic equation .inversion, readily managed by a vectorized solver package. A subsequent irrotational old E-field correction is found to be crucial for the maintainence of anticipated quasi-neutrality. A concomitant rotational correction is needed for physical solutions in steep density gradient problems. We show that both corrections can be obtained simultaneously by referencing the deviations between the true currents flowing, and the currents predicted to flow in the plasma at the end of a cycle. The current correction is shown to be equivalent to the first (and usually sufficient) step of an iterative procedure leading to an exact solution for the fields. In addition, we demonstrate that electrostatic solutions can be obtained from the implicit algorithm by setting the speed of light to very large multiples of its physical value. Comparisons are made with earlier moment and direct method approaches, and the scheme is related to previous classical hybrid models. Demonstrative applications are discussed.