Electromagnetic direct implicit plasma simulation

A Simplified Implicit Maxwell Solver

“…On the other hand, Hewett and Langdon find that a formulation consistent with Eq. (44) provides better performance with an alternating direction implicit solver [22]. Our analysis provides two additional reasons for preferring Eq.…”

“…(40) is troublesome for two reasons. (Essentially the same equation appears in the direct implicit formulation [22,34], so the problem is not unique to the implicit moment method.) First, Eq.…”

“…Implicit plasma simulations require the solution of the Maxwell equations in the presence of a permittivity in the form of a nonsymmetric tensor. Also, in the context of plasma simulations, it is pointed out that the continuity equation may be not satisfied [22]. Consistent with this observation, projection is used to assure that Poisson's equation is satisfied.…”

“…Studies of magnetic reconnection are reported in Refs. [17,22,23,37,57]. Comparisons of implicit and hybrid solutions for switch-off shocks [13] and contact discontinuities [35,39] help to define the range of validity of hybrid methods.…”

“…(Charge-conserving algorithms have also been developed that eliminate the need to solve Poisson's equation [18,58], but these have not yet been employed in implicit simulations.) In a common projection method, a scalar potential is introduced as a correction to the electric field and is solved to satisfy Gauss's law, thus bringing into correspondence the number of boundary conditions and unknowns for the electric field [22,33]. However, in implicit formulations, projection is only approximately correct because of a coupling of longitudinal and transverse components of the electric field by the plasma permittivity [12].…”