ar X iv : a st ro - p h / 04 01 58 5 v 1 2 7 Ja n 20 04 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 field of magnetized plasmas are 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. A general result of this investigation is that stochastic acceleration by these waves results in a distinct quasi-thermal and a hard nonthermal component with the second component being more prominent in hotter plasmas and/or higher turbulence levels. This can explain many of the observed features of solar flares. In regards to proton and electron ratio, we find that in a pure hydrogen plasma, the dominance of the wave-particle interactions by the resonant Alfvén wave reduces the acceleration rate of protons in the intermediate energy range significantly. This is not true for electrons because electron-cyclotron and whistler waves are very efficient in accelerating them from a few keV to relativistic energy. The presence of such an acceleration barrier makes the proton acceleration very inefficient compared with the electron acceleration in solar flares. This difficulty is alleviated when we include the effects of He in the dispersion relation and the damping of the turbulent waves by the thermal background plasma. The additional He cyclotron branch of the turbulent plasma waves suppresses the proton acceleration barrier significantly and the model gives qualitative explanation for many features associated with solar flare observations. Specifically, we find that the relative acceleration of protons and electrons is very sensitive to a plasma parameter α = ωpe/Ωe, where ωpe and Ωe are the electron plasma and gyrofrequencies, respectively. Protons are preferentially accelerated in weakly magnetized plasmas (large α). The formalism Department of Applied Physics, Stanford University, Stanford, CA, 94305 email: [email protected] email: [email protected]