Propagating Plasma Waves: General Results

In this work we study the acceleration in solar flares of He and He from a thermal background by parallel propagating plasma waves with a general broken power-law spectrum that takes into account the turbulence generation processes at large scales and the thermal damping effects at small scales. The exact dispersion relation for a cold plasma is used to describe the relevant wave modes. In the nonrelativistic regime of interest here the charged particle acceleration is dominated by resonant interactions with high frequency waves, and the pitch angle diffusion rate is usually smaller than the momentum diffusion rate below a few MeV nucleon. In the absence of other more efficient scattering agents, this may give rise to an anisotropic particle distribution. Because low-energy α-particles only interact with small scale waves in the He-cyclotron branch, where the wave frequencies are below the α-particle gyro-frequency, their pitch angle averaged acceleration time is at least one order of magnitude longer than that of He ions, which mostly resonate with relatively higher frequency waves in the protoncyclotron (PC) branch. The α-particle acceleration rate starts to approach that of He beyond a few tens of keV nucleon, where α-particles can also interact with long wavelength waves in the PC branch. However, the He acceleration rate is always smaller than that of He. Consequently, the acceleration of He is suppressed significantly at low energies, and the spectrum of the accelerated α-particles is always softer than that of He. The effects of thermal damping further magnify this suppression. On the other hand, the length scale of waves in the PC branch at generation (the longest scale) mostly affects the high-energy cutoffs of the accelerated particle spectra. These favorable conditions for He Center for Space Science and Astrophysics, Department of Physics, Stanford University, Stanford, CA 94305; [email protected] Department of Physics and Applied Physics, Stanford University, Stanford, CA 94305; [email protected] Department of Physics and Institute for Physical Sciences and Technology, University of Maryland, College Park, MD 20742-4111; [email protected]