Stochastic acceleration of low-energy electrons in plasmas with finite temperature

This paper extends our earlier work on the acceleration of low-energy electrons by plasma turbulence to include the effects of finite temperature of the plasma. We consider the resonant interaction of thermal electrons with the whole transverse branch of plasma waves propagating along the magnetic field. We show that our earlier published results for acceleration of low-energy electrons can be applied to the case of finite temperature if a sufficient level of turbulence is present. From comparison of the acceleration rate of the thermal particles to the decay rate of the waves with which they interact, we determine the required energy density of the waves as a fraction of the magnetic energy density, so that a substantial fraction of the background plasma electrons can be accelerated. The dependence of this value on the plasma parameter alpha = omega(pe)/Omega(e) (the ratio of electron plasma frequency to electron gyrofrequency), plasma temperature, and turbulence spectral parameters is quantified. We show that the result is most sensitive to the plasma parameter alpha. We estimate the required level of total turbulence by calculating the level of turbulence required for the initial acceleration of thermal electrons and that required for further acceleration to higher energies.