AN EQUATION FOR WAVE PROPAGATION IN A HOT NONUNIFORM MAGNETIZED PLASMA

HAL Id: jpa-00219317

https://hal.archives-ouvertes.fr/jpa-00219317

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

AN EQUATION FOR WAVE PROPAGATION IN A HOT NONUNIFORM MAGNETIZED PLASMA

W.N-C Sy, M. Cotsaftis

To cite this version:

W.N-C Sy, M. Cotsaftis. AN EQUATION FOR WAVE PROPAGATION IN A HOT NONUNI- FORM MAGNETIZED PLASMA. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-669-C7-670.

�10.1051/jphyscol:19797325�. �jpa-00219317�

JOURNAL DE PHYSIQUE Cozloque C7, suppZdment au n07, Tome 40, JuiZZet 1979, page

C7-

AN EQUATION FOR WAVE PROPAGATION IN A HOT NONUNIFORM MAGNETIZED PLASMA

W.N-C Sy and M. Cotsaftis.

Association Euratom-CEA sur Za fusion, Departement de Physique du Plasma e t de Za fusion controlde, Centre drEtudes NuclBaires, Boite Postale n06, 92260 Fontenay-am-Roses, Frame.

Plasma nonuniformities and boundary effects are usually significant for wave propaga- tion in the lower frequency ranges in laboratory plasmas, whilst explicit incorporation of wave damping in the wave equations is necessary for a consistent calculation of resonant Q-factors of cavity modes in bounded systems. On the other hand, the existence of spatial resonances in nonuniform plasmas, such as the Alfv&n wave resonance or the ion-ion hybrid resonance, exhibited mathematically by "singularities" in the basic wave equations, requires small effects such as the finite Larmor radius effect or nonlinear effects to be considered, in order to determine the fate of waves propagating in or near these "singular1' regions. These factors are taken into account in the derivation of an equation for wave propagation in a hot, nonuniform magnetized plasma, with multiple ion species.

The linearized Vlasov equations, together with Maxwell's equations, are solved by a pertur- bation expansion in the smallness of the Larmor radius compared to characteristic scale-lengths of the plasma. Fourier transforms are taken along the uni-directional background magnetic field to retain the importa~ii. kineiic

of

cyclotron damping, while differential operators are used in directions perpendicular to the magnetic field, because plasrri nonuniformities and boundary effects are important in these directions. Since only waves which have counter- parts in a uniform magnetized plasma are considered, the gradient terms which are associated generally with drift waves have been neglected. The resulting wave equation may be written in the form,

terms on

are in the proportions,

where

is the parameter of small Larmor a aS2

radius expansion and

is ratio of perturbed B

to unperturbed magnetic field.

As a simple application of

we consider wave ~ropagation in the ion cyclotron range of frequencies in a straight, hot, nonuniform plasma cylinder, neglecting finite Larmor radius effects and nonlinear effects. A number of authors ['I - [41 have studied this problem in connection with RF heating of laboratory plasmas. Here, the problem is considered more generally, including explicitly in the wave equation (a) multiple ion species (b) arbitrary plasma nonuniformities and (c) collision- less Landau-cyclotron damping.

On Fourier analysis in the axial and azimutnai directions in cyiinarica~ coordinates, the reduced system of equations can be solved conve- niently in the axial component of the perturbed magnetic-field.

where c.g.s. - gaussian units have been used. The essential equation governing the phenomenon can be shown to be

+ 3 1

d

where T is an algebraic tensor with the familiar m d B m e

( 5 )

( % r z )

( T K - T -

structure

where

The elements A, B and C contain the full plasma dispersion functions and hence explicitly incorporates Landau-cyclotron damping. They also contain summations over+al& specias of plasma par$icles. The tensors if, 8, ^and 8 are differential operators arising respectively from the first order, second order finite Larmor radius corrections and nonliqear effects. The tensor differential

The functions A+ and

are A and B appearing in (2) with the addition of harmonic cyclotron damping terms. Equation

has a similar structure to that found [51 for axisymetric magnetoacoustic oscillations in a current-carrying nonuniform plasma column and it can easily be solved numeri- cally for arbitrary temperature and density profiles .

operator is proportional to the. components of the perturbed electric field. Detailed expressions of these tensors will be presented elsewhere, since they are too lengthy for this short commu- nication. The relative magnitudes of the four

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797325

[ I

1

[ 2 ] Messiaen A.M. and Vandenplas P.E. (1974) Phys.

Lett.

%,

[3] Adam J. and Jacquinot J. (1977) Report EUR.CEA.FC. 886

[4] Paoloni F.J. (1978) Nucl. Fusion

18,

[5] Sy W.N-C. (1978) Plasma Phys.

20,