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 find that in a pure hydrogen plasma the dominance of the wave-proton interaction by the resonant Alfven mode reduces the acceleration rate of protons in the intermediate energy range significantly, while the electron-cyclotron and Whistler waves are very efficient in accelerating electrons from a few keV to MeV energies. The presence of such an acceleration barrier prohibits the proton acceleration under solar flare conditions. This difficulty is alleviated when we include the effects of He-4 in the dispersion relation and the damping of the turbulent waves by the thermal background plasma. The additional He-4 cyclotron branch of the turbulent plasma waves suppresses the proton acceleration barrier significantly, and the steep turbulence spectrum in the dissipation range makes the nonthermal component have a near power-law shape. The relative acceleration of protons and electrons is very sensitive to a plasma parameter alpha = omega(pe)/Omega(e), where omega(pe) and Omega(e) are the electron plasma frequency and gyrofrequency, respectively. Protons are preferentially accelerated in weakly magnetized plasmas (large alpha). The formalism developed here is applicable to the acceleration of other ion species and to other astrophysical systems.