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At large time and space scales, plasmas tend to be quasineutral, i.e. the local charge vanishes. However, at small time and space scales, quasineutrality breaks down. The typical breakdown scales are the electron plasma period and the Debye length. At large plasma densities, both are very small, compared to the usual time and space scales of interest. AP-schemes applied to plasma models in the quasi-neutral limit are described below.
The picture below shows a plasma plume emitted through an aperture between two electrodes (left: ion density ; right: electron density as functions of position at a given time). The results are obtained thanks to an AP discretization of the two-dimensional two-species Euler-Poisson system. The plasma is quasineutral inside the plume and monopolar (consisting only of electrons) outside. A standard scheme for this case would lead to prohibitive computer simulations.
The next figure shows a one-dimensional expansion of an ion slab, modeled thanks to an Asymptotic-Preserving Particle-in-Cell (PIC) scheme for the two-species Vlasov-Poisson system. It displays the ion density as a function of position at a given time. PICAP-1 and PICAP-2 denote two variants of the AP method while Classical PIC denotes the explicit PIC method. For the sake of comparison, results obtained by several variants of the Direct Implicit (DI) PIC method are also given. The reference solution, using small time and space steps, is given on the right picture and all methods agree in this case. The left picture displays results for a course mesh and large time steps. The instability of the classical PIC scheme can be seen by the fact that the ion slab has totally disolved. By comparison, the PICAP and DI methods provide a sharp interface for the ion slab. However, with the DI method the expansion is too slow. With the PICAP methods, the expansion is still a bit slow but much closer to the correct value. The test problem is inspired of a paper by Grismayer et al (Phys Rev E77, 066407 (2008), 11p.).
The picture below descibes the one-dimensional simulation of a Plasma Opening Switch thanks to the Euler-Maxwell system (left longitudinal component of the electric field ; right: magnetic field, as a function of position at a given time). An electromagnetic waves traveling in a wave guide impinges on a plasma and erodes it. The propagation speed of the wave decreases abruptly by several orders of magnitude as it crosses the boundary of the plasma. The AP scheme is compared to a classical scheme and to a reference solution. The classical scheme displays instabilities downstream the wave while the AP scheme remains stable.
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