Quasi-linear Formalism for Simulation of Electron Cyclotron Current Drive Z. T. Wang, Y. X. Long, J.Q. Dong, F. Zonca Southwestern Institute of Physics,

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Quasi-linear Formalism for Simulation of Electron Cyclotron Current Drive Z. T. Wang, Y. X. Long, J.Q. Dong, F. Zonca Southwestern Institute of Physics, P.O. Box 432, Chengdu , P. R. C. Associazione EURATOM-ENEA, sulla Fusione, C.P Frascati, Rome, Italy

Abstract Quasi-linear formalism is developed by using canonical variables. It is self-consistent including spatial diffusion. The spacial diffusion coefficient obtained is similar to the one obtained by Hazeltine. The formalism is compatible with the numerical code developed in Frascati. An attempt is made to simulate the process of electron cyclotron current drive and electron cyclotron resonant heating in LH-2A tokamak.

Ⅰ Introduction Interaction of radio-frequency wave with plasma in magnetic confinement devices has been a very important discipline of plasma physics. To approach more realistic description of wave- plasma interaction in a time scale logger than the kinetic time scales bounce-average is needed. The long time evolution of the kinetic distribution can be treated by Fokker-Planck equation. The behavior of the plasma and the most interesting macroscopic effects are obtained by balancing the diffusion term with a collision term.

The action and angle variables initiated by Kaufman [1] are introduced. “ There has been a gradual evolution over the years away from the averaging approach and towards the transformation approach ” said Littlejohn [2]. The technique of the area-conserved transformation proposed by Lichtenberg and Lieberman [3] is employed. A new invariant is formed by using bounce average which actually is an implicit Hamiltonian and from which the bounce frequency and processional frequency can be calculated.

Using new action and angle variables quasi- linear equation is derived including spatial diffusion. For the circulating particles, under the conditions of small Larmor radius and first harmonic resonance, the diffusion coefficient is compatible with the numerical code developed in Frascati [4]. The special feature in this paper is to see resonance in the long time scale. The distribution function is obtained after the wave power is put in. The driven current and the absorbed power are calculated for HL-2A.

In section Ⅱ the bounce-averaged quasi-linear equation is obtained. Numerical results of electron cyclotron current drive and resonant heating for HL-2A are given in section Ⅲ. In the last section summary is presented. Supported by National Natural Science Foundations of China under Grant Nos , , and

Quasi-linear equation To derive the quasi-linear equation a set of canonical variables are employed [5] which are connected with cylindrical coordinates by six identities,

Ⅳ. Summary First the action and angle variables are used [1]. Secondary the area-conserved transformation is employed [2]. The bounce-averaged quasi-linear Fokker-Planck equation is rigorously obtained in canonical variables including spacial diffusion. The spacial diffusion coefficient obtained is similar to the one obtained by Hazeltine [6].

For the HL-2A parameters the distribution function, the driven current, the temperature, the absorbed power are calculated in Figs Ratio of the driven current with the absorbed power versus time is also given in Fig. 5. Compared with experiment in HL-2A in which electron temperature is raised about 240kev, the calculated result is tolerable. The special feature in this paper is to see resonance in the long time scale.