Theory of high-frequency heating of an inhomogeneous high-temperature plasma

Abstract

We investigate Čerenkov absorption by a plasma of the energy of an electromagnetic field created by azimuthal electric currents flowing in a long coil around a plasma cylinder. The density of external currents has the form of a traveling wave j=j₀ cos (kz—ωt) δ (r—R) (R is the radius of the coil). The frequency of the field is considerably smaller than the ion cyclotron frequency. Gas-kinetic plasma pressure n₀(T_e + T_i) is assumed small compared with the magnetic pressure H₀ ²/8π. Plasma density n₀, electron temperature T_e and ion temperature T_i are taken to be functions of the radius. In the present study expressions have been found for the energy absorbed by plasma per unit time. Absorption is maximal when the phase velocity of the wave ω/k is of the order of the thermal velocity of the ions ν_i = (T_i/m_i)^½ (mi is the ion mass). If the radius of the plasma is of the order of the radius of the coil and of the order of the wavelength 1/k, then for ω/k ∝ ν_i the mean energy gained by one particle per unit time, in order of magnitude, equals dW/df = H∼²ωT_i/H₀ ² where H∼ = 4πj₀/c is the amplitude of the alternating magnetic field. For a strongly non-isothermal plasma (T_e ≫ T_i) heating increases drastically if the phase velocity of the wave is near the velocity of sound in a collisionless plasma ν_s = (T_e/m_i)^½ Expressions have also been obtained for energy absorbed by an inhomogeneous plasma for coils of finite lengths.