Stochastic Acceleration of Low‐Energy Electrons in Cold Plasmas

We investigate the possibility of stochastic acceleration of backgroundlow-energy electrons by turbulent plasma waves. We consider the resonantinteraction of the charged particles with all branches of the transverse plasmawaves propagating parallel to a uniform magnetic field. Numerical results andasymptotic analytic solutions valid at non-relativistic and ultra-relativisticenergies are obtained for the acceleration and scattering times of electrons.These times have a strong dependence on plasma parameter alpha = Omega_pe /Omega_e (the ratio of electron plasma frequency to electron gyrofrequency) andon the spectral index of plasma turbulence. It is shown that particles withenergies above certain critical value may interact with higher frequencyelectromagnetic plasma waves and this interaction is allowed only in plasmaswith alpha < 1. We show that for non-relativistic and semi-relativisticelectrons in low-alpha plasmas the ratio of the acceleration time to thescattering time can be less than unity for a wide range of energies. From thiswe conclude that the transport equation derived for cosmic rays which requiresthis ratio to be much larger than one is not applicable at these energies. Anapproximate "critical" value of particle energy above which the dynamics ofcharged particles may be described by this transport equation is determined asa function of plasma parameters. We propose new transport equation for theopposite limit (energies less than this critical value) when the accelerationrate is much faster than the pitch angle scattering rate. This equation isneeded to describe the electron dynamics in plasmas with alpha <= 0.1.Comment: 22 pages, 13 figures, Latex, submitted to Astrophysical Journa