Propagation and absorption of low frequency waves in two and three dimensional warm plasmas

In order to model a broader range of phenomena taking place in three-dimensional plasmas, the LEMan code has been extended to a warm formulation. As the wave propagation is strongly influenced by the parallel wave vector, special attention has been paid for its consistent computation. The choice to concentrate on this quantity has limited the complexity of the problem to 0th order in the Finite Larmor Radius expansion. Two methods have been implemented in LEMan. The first technique implies the inversion of a polynomial matrix and requires incorporating the dielectric tensor as a convolution in the linear system. It has been tested successfully and applied to a wide range of cases up to three-dimensional geometries in the Alfvén domain. The frequency and damping of global modes that appear in the gaps formed by the breaking of symmetry can then be determined. Strong variations are observed depending on the presence, for example, of a mode conversion to the Kinetic Alfvén Wave. This method has however displayed numerical limitations in the Ion-Cyclotron Range of Frequencies (ICRF). A new technique based on the iterative evaluation of the parallel wave vector has then been developed. After having tested its agreement with the convolution method, computations in the ICRF domain have been undertaken in two and three-dimensional configurations including the Large Helical Device where the power deposition has been determined. In order to model the contribution of fast ions, a bi-Maxwellian distribution function has been added to the warm dielectric tensor. The fast ion population absorbs, in this case, an important fraction of the total power in the ICRF domain. In addition, a displacement of the Toroidicity-induced Alfvén Eigenmode frequency has been observed. The code has been finally optimised and parallelised permitting to perform computations in complicated geometry such as stellarators in the ICRF domain. Furthermore, the approach used here yields a much shorter computation time than for most of the other codes dealing in this domain of frequency.

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2009
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Concepts associés (4)

Produit de convolution

En mathématiques, le produit de convolution est un opérateur bilinéaire et un produit commutatif, généralement noté « ∗ », qui, à deux fonctions f et g sur un même domaine infini, fait correspondre une autre fonction « f ∗ g » sur ce domaine, qui en tout point de celui-ci est égale à l'intégrale sur l'entièreté du domaine (ou la somme si celui-ci est discret) d'une des deux fonctions autour de ce point, pondérée par l'autre fonction autour de l'origine — les deux fonctions étant parcourues en sens contraire

Computation

A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. Common examples of computations are mathematical equations and computer algorithms. Mechanical or electronic devices (or, historically, people) that perform computations are known as computers. The study of computation is the field of computability, itself a sub-field of computer science. The notion that mathematical statements should be ‘well-defined’ had been argued by mathematicians since at least the 1600s, but agreement on a suitable definition proved elusive.

État plasma

thumb|upright|Le soleil est une boule de plasma. thumb|Lampe à plasma.|168x168px thumb|upright|Les flammes de haute température sont des plasmas. L'état plasma est un état de la matière, tout comme l'état solide, l'état liquide ou l'état gazeux, bien qu'il n'y ait pas de transition brusque pour passer d'un de ces états au plasma ou réciproquement. Il est visible sur Terre, à l'état naturel, le plus souvent à des températures élevées favorables aux ionisations, signifiant l’arrachement d'électrons aux atomes.