Pierre Degond – Workshop IV
Asymptotically stable methods for plasmas in the quasineutral limit
Plasmas are gas mixtures containing charged particles such as electrons and positive ions. Their behaviour is strongly influenced by the long-range electrostatic (or electromagnetic) interaction between the particles. Plasmas cover a large variety of phenomena, either natural (stars, intergallactic media, planets magneto or ionospheres) or artificial (tokamaks, inertial confinement fusion, gas discharges, electrical arcs, plasmas for industrial processes, etc.). Their numerical modeling is an important challenge for applied mathematicians.
Plasmas are subject to a large number of multiscale phenomena.This talk will address one of them, related with quasineutrality, i.e., the strong tendency of a plasma to remain electrically neutral at large scales. This tendency is due to the presence of a small parameter, the scale Debye length, which makes the eletrostatic interaction large unless local neutrality is maintained. For numerical schemes, the smallness of the Debye length makes the problem extremely stiff and severe restrictions on the time step and mesh size are usually needed to achieve stable computations. Therefore, quasineutral models (i.e. models obtained in then zero Debye length limit) are commonly used. In some regions however (such as charged sheaths), quasineutrality breaks down (i.e. the scaled Debye length becomes of ordre unity). Additionally, the transition region between the quasineutral plasma and the charged sheath can evolve in time. To describe this phenomenon, it is necessary to devise numerical methods whose stability criteria are independent of the value of the scaled Debye length. The goal of this talk is to present such a method when the various species are described by the gas dynamics Euler equations.
After the derivation and analysis of the numerical scheme, we shall present an application to a plasma breakdown problem: the expansion of a quasineutral plasma in a vacuum gap between two electrodes. Such a problem has applications for the design of particle beam injectors and for the prenvention of arcing on satellite solar arrays. The dynamics of the
interface as obtained from the formal asymptotics of a multi-species hydrodynamic plasma model will be reviewed. Then, our asymptotically scheme will be compared with more standard methods. One and two-dimensional results will be presented.
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