Magnetohydrodynamic wave spectra in large tokamaks with non-circular cross section of magnetic surfaces

Abstract

There is considered the problem on the spectra of magnetohydrodynamic (MHD) waves with the frequencies of the order of the ion cyclotron frequency propagating almost along the toroidal magnetic field in the large-size tokamaks with a non-circular cross section of magnetic surfaces. In this case the waves can propagate in the small vicinity of the extremum point for the square of the refractive index of the MHD wave travelling along the torus. Developing the dielectric permittivity tensor of the “cold” plasma in a Taylor series around this point enables one to separate the variables and to express the natural functions of the boundary problem for Maxwell’s equations through Hermite functions and to determine the natural frequencies of MHD waves. The solution obtained is a generalization of the previous result for arbitrary radial and azimuth numbers. On the ground of the perturbation theory the corrections to the natural functions and natural values are found which take into account the rotational transform.