By Rémi Sentis
This monograph is devoted to the derivation and research of fluid versions happening in plasma physics. It specializes in types concerning quasi-neutrality approximation, difficulties with regards to laser propagation in a plasma, and coupling plasma waves and electromagnetic waves. utilized mathematicians will discover a stimulating advent to the realm of plasma physics and some open difficulties which are mathematically wealthy. Physicists who might be beaten by way of the abundance of versions and unsure in their underlying assumptions will locate uncomplicated mathematical homes of the similar platforms of partial differential equations. A deliberate moment quantity might be dedicated to kinetic models.
First and greatest, this booklet mathematically derives sure universal fluid versions from extra basic versions. even if a few of these derivations will be popular to physicists, it is very important spotlight the assumptions underlying the derivations and to gain that a few likely basic approximations become extra complex than they appear. Such approximations are justified utilizing asymptotic research at any place attainable. in addition, effective simulations of multi-dimensional versions require certain statements of the comparable platforms of partial differential equations besides applicable boundary stipulations. a few mathematical homes of those platforms are offered which provide tricks to these utilizing numerical tools, even if numerics isn't the basic concentration of the book.
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Extra info for Mathematical Models and Methods for Plasma Physics, Volume 1: Fluid Models
Sample text
Log N0 / as it appears in the beginning of the handbook [27]. Other boundary conditions of Dirichlet type may be addressed; for instance. for the modelling of a plasma surrounded by a conducting material. As a matter of fact, if a given electric potential may be applied on two different parts of the boundary that correspond to conducting material, we can make the following modelling: assume that 1 and 2 are two smooth parts of the boundary @O that are disconnected, such that the potential ˆ is given by a constant: B1 on 1 and B2 on 2 : Then we have the following result.
E? E? E C U ! 85) 52 2 Quasi-Neutrality and Magneto-Hydrodynamics where the tensor may read in the system of coordinates defined by ! ce2 / 1 0 5: ! ce 1 1 0 0 / s . ce C Moreover, the resistivity tensor 2 s 6 D4 0 ! 0 ! ce 2 ! D 0 / 0 s . ce C 1 ! ce / We can now proceed as in the previous paragraph. U B/Ccurl . 1 J/; the Maxwell–Faraday equation leads to the evolution equation of the magnetic field. U B/Ccurl . curlB/ D 0: As above, this equation may read also as D B . B:r/U C curl Dt  ! P0 C Pe / C r:PB D 0; Dt D "0 C P0 r:U D Dt D "e C Pe r:U C r:qth,e D Dt (v) r:U D 0; D B .
O/: Therefore, r:. TTrefe rˆ // ! Qe ˆ / Summary (About quasi-neutrality). 52) Thus, the basic principles of quasi-neutral approximation may be summarized as follows. 52) for the momentum equation. E C U B/ comes into sight; it is a natural quantity in all the MHD models. Moreover, it is worth noticing that the electron velocity never appears explicitly in these models (it is always evaluated thanks to U and J) and that, generally, one has to account for the evolution of the electron temperature.