Stochastic Acceleration of Electrons and Protons. I. Acceleration by Parallel Propagating Waves

Stochastic acceleration of electrons and protons by waves propagating parallel to the large scale magnetic fields of magnetized plasmas is studied with emphasis on the feasibility of accelerating particles from a thermal background to relativistic energies and with the aim of determining the relative acceleration of the two species in one source. In general, the stochastic acceleration by these waves results in two distinct components in the particle distributions, a quasi-thermal and a hard nonthermal, with the nonthermal one being more prominent in hotter plasmas and/or with higher level turbulence. This can explain many of the observed features of solar flares. Regarding the proton to electron ratio, we include the effects of $^4$He in the dispersion relation and the damping of the turbulent waves by the thermal background plasma. The relative acceleration of protons and electrons is very sensitive to the ratio of the electron plasma frequency to its gyro-frequency. Protons are preferentially accelerated in weakly magnetized plasmas. The formalism developed here is applicable to the acceleration of other ion species and to other astrophysical systems.