Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations
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LLATIONS AND WAVES IN PLASMA
Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations T. A. Khusainov*, A. G. Shalashov, and E. D. Gospodchikov Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, 603950 Russia *e-mail: [email protected] Received September 19, 2017; in final form, November 2, 2017
Abstract—The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed. DOI: 10.1134/S1063780X18050070
1. INTRODUCTION Historically, the beginning of studies on the linear interaction of ordinary (O) and extraordinary (X) waves in magnetoactive plasma (O–X transformation) is associated with the investigation of the effect of “tripling” of radio signals in the ionosphere [1, 2]. At present, the use of linear wave transformation in studies on the problem of controlled fusion research is of particular interest, because this phenomenon makes it possible to efficiently implement microwave heating and diagnostics of overdense plasma in toroidal magnetic confinement systems [3]. In the early works, O–X transformation was considered within a plane-stratified model [4–13], but it was noted in [14] that, in toroidal systems, the gradients of the plasma density and magnetic field strength are generally not parallel and, therefore, the 2D nonuniformity of the medium should be taken into account. The corresponding 2D configuration without a poloidal magnetic field was first introduced and studied in [15, 16]. Then, the effects of a small poloidal field [17, 18], finite poloidal field [19, 20], and magnetic shear were added [21, 22]. In [22], the model was generalized to the case of a 3D nonuniformity of the direction and strength of the magnetic field, but the curvature of the magnetic surfaces or, what is the same, the non-one-dimensional character of the plasma density distribution was not taken into account. At the same time, the significant effect of the curvature of magnetic surfaces on the efficiency of O– X transformation was demonstrated both theoretically
[23, 24] and in full-wave numerical simulations [25, 26]. The effect of thermal motion and particle collisions on the O–X transformation was first considered within a 1D model [8, 13] and then with allowance for the non-one-dimensional geometry [27, 28]. In this paper, an attempt is made to generalize the results reported
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