We describe Cerenkov absorption by plasma electrons of electromagnetic waves that have a frequency considerably smaller than the gyro frequency of electrons and considerably larger than the gyro frequency of ions, the so-called "whistling atmospherics" that propagate along the inhomogeneous plasma cylinder. An expression has been deduced for the energy absorbed by a length unit of the plasma cylinder per unit time, and a coefficient has been found for the damping of free oscillations propagating along the plasma cylinder. If the phase velocity of the wave is of the order of the thermal velocity of the electrons and the wavelength is of the order of the plasma radius, the energy gained per unit time on the average by one plasma electron equals dW/dt ≈ (Hz2/Ho2)ωTe (Hz is the amplitude of the magnetic field of the wave; ω is its frequency; H0 is the steady magnetic field strength; Te is the electron temperature). The limits of applicability of the linear theory are discussed. For fields Hz larger than some critical value Hc ≈ H0 (ωτ)−2/3, where τ is the frequency of collisions between electrons and ions, a plateau forms for the background distribution function, Under conditions when distortion of the distribution function becomes large, dW/dt ≈ Tc/τ. Since W ≈ Tc, electron temperature increases in this case according to the law Te ≈ T0 [l + at/τ]2/3, where T0 is the initial elecgron temperature and a ≈ 1. Since the field of whistles penetrates well into the plasma, their Cerenkov absorption can be used for the heating of the electron component of a plasma with large density (n0 ≈ 1014—1015cm−3) and with a sufficiently large initial temperature (T0≳ 100 eV).
Quasi-linear theory of cherenkov heating of electrons in an inhomogeneous plasma