Quasi-linear theory of cherenkov heating of electrons in an inhomogeneous plasma

The authors investigate, in the quasi-linear approximation, the Cherenkov absorption by plasma electrons of the energy of an electromagnetic field created by external sources. The plasma is in the form of a cylinder of non-uniform radius located in a longitudinal magnetic field and the external sources are specific azimuthal currents flowing in coils surrounding the plasma cylinder. It is assumed that the magnetic pressure significantly exceeds the gas-kinetic pressure of the plasma, that the Larmor radius of the plasma panicles is small compared with the distances within which the plasma density and the electromagnetic field change substantially, that the frequency of the field is significantly less than the electron gyrofrequency, and that the phase velocity is significantly greater than the thermal velocity of the ions, so that thermal motion of the ions can be ignored.An equation is derived for the diffusion of electrons in velocity space. From this equation it follows that the electron distribution along the velocity component perpendicular to the magnetic field does not change with time and that a plateau is formed on the curve characterizing the dependence of the distribution function on the longitudinal velocity component. The rate of formation of the plateau is different for different values of the velocity component perpendicular to the magnetic field.In the case of narrow wave packets a diffusion equation is obtained taking Coulomb collisions into account. The slope is found of the curve characterizing the dependence of the background distribution function on the longitudinal velocity component in the steady state, where diffusion on the waves is balanced by collisions.With narrow wave packets, if the frequency of the external currents coincides with that of the natural oscillations of the plasma cylinder (for a given wave vector value), saturation is reached in the absorption of electromagnetic field energy and, if the amplitudes of the external currents are fairly large, further amplitude increases do not lead to an increase in the absorbed power.If, however, the external current spectrum contains wave vectors corresponding to the natural oscillations of the plasma cylinder, the formation of a plateau does not lead to absorption saturation (the absorbed power remains proportional to the square of the external current amplitude).