Analytical expressions for the wave permeability tensor are derived for a twodimensional plasma model of a straight axisymmetric mirror trap. The dielectric tensor components are found through a solution of the Vlasov equation, using the theory of Jacobian elliptic functions. The bounce-resonance effect of trapped particles on wave dissipation is analysed. It is shown that collisionless wave dissipation in the plasma with a mirror-trap configuration of a magnetic field can differ essentially from Landau damping in a plasma with straight uniform magnetic field lines. This dielectric tensor can be used in numerical calculations of Alfvén and ion cyclotron heating of mirror-trap plasmas.

The general approach to the Alfvén wave current drive problem in tokamaks with elongated transverse cross-sections was considered in this paper. Model approximations are used to describe circulating and trapped particle dynamics. This approach gives the accuracy of some percents. The expressions for the time-averaged longitudinal current and the radio-frequency currents have been obtained. They are supposed to be useful for a further analytical and computational solution of this problem. As an example, kinetic Alfvén waves are considered in this paper.

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The author investigates the stability of a magnetized non-isothermal (Te ≫ Ti) plasma in an alternating electric field when the field frequency Ω0 is close to the frequency of the ion-sound oscillations of the plasma. The amplitude of the oscillatory velocity of electrons in a h.f. field is assumed to be small compared with their thermal velocity (u0 ≪ vTe ). It is shown that, for perturbations with wave number kz satisfying the resonance condition there exists in such a plasma an instability with a growth rate . The width of the instability zone is determined in the kinetic and hydrodynamic approximations. In the hydrodynamic approximation, if one does not allow for dissipation, there is instability however small the value of . If one allows for collisionless kinetic damping of the oscillations on the electrons, the instability develops only when u0 exceeds come critical value ∼ vTe (me/Mi)¼.

This study deals with the stability of a plasma in the field of a self-consistent Alfvén wave. Decay instabilities for a plasma with β ≫ 1 are considered, and the growth rate and widths of the instability zones are found. The problem of determining the critical wave amplitude is discussed.The solution as a whole was reached for two types of Alfvén waves – standing and travelling.An instability associated with the scattering of the Alfvén wave was found in the second approximation with respect to the parameter h0/H0 (h0 being the amplitude of the Alfvén wave and H0 the intensity of the constant magnetic field). The excitation conditions for this instability are less stringent than those for decay instabilities.Problems connected with the build-up of instabilities of the type under consideration in systems bounded along the magnetic field are discussed.