Bienvenue - Laboratoire Jacques-Louis Lions

 Title :

GENERALIZED PLANE WAVE NUMERICAL METHODS FOR MAGNETIC PLASMA

Abstract :

The knowledge of the characteristics of plasma turbulence is a key point to control nuclear fusion in magnetic plasma in the context of the ITER project. Reflectometry is a radar technique for plasma density measurements using the reflection of electromagnetic waves. In the case of a magnetic plasma, an important feature is the presence of a plasma cutoff. At the cut-off, the wave is reflected. It provides a way to probe the plasma. The starting equations are Maxwell’s equations in dimension three. The classical model of cold plasma gives the permittivity tensor. O-mode refers to parallel polarization of the wave, whereas X-mode refers to orthogonal polarization. The eigenvalues of the tensor have non constant sign, so that the nature of the equations
 changes continuously from elliptic propagative to elliptic coercive. The Airy equation is a special case of the O-mode equation. For X-mode equations, there is also a transition layer which will not be discussed. Both polarizations are useful for reflectometry and also very useful for numerical modeling since these models can be written in dimension two instead of three. We are interested in the mathematical and numerical modeling of such systems of partial differential equations.

We propose to use an original plane wave method for the numerical approximation of the time-harmonic problem. It can be derived using the technique of discontinuous Gakerkin methods. An important feature of the method is that basis functions are designed to approximate the Airy functions with improved order accuracy. This method is a generalization of the plane waves methods for problems with piecewise constant coefficients. New functions, such as exponential of polynomials, allow to fit the specific non constant coefficients of the equations with higher accuracy and permit to improve the convergence.