Stochastic Acceleration of ${}^3$He and ${}^4$He in Solar Flares by Parallel Propagating Plasma Waves: General Results

Abstract

We study the acceleration in solar flares of ${}^3$He and ${}^4$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. Because low-energy $\alpha$-particles only interact with small scale waves in the ${}^4$He-cyclotron branch, where the wave frequencies are below the $\alpha$-particle gyro-frequency, their pitch angle averaged acceleration time is at least one order of magnitude longer than that of ${}^3$He ions, which mostly resonate with relatively higher frequency waves in the proton-cyclotron (PC) branch. The $\alpha$-particle acceleration rate starts to approach that of ${}^3$He beyond a few tens of keV nucleon${}^{-1}$, where $\alpha$-particles can also interact with long wavelength waves in the PC branch. However, the ${}^4$He acceleration rate is always smaller than that of ${}^3$He. Consequently, the acceleration of ${}^4$He is suppressed significantly at low energies, and the spectrum of the accelerated $\alpha$-particles is always softer than that of ${}^3$He. The model gives reasonable account of the observed low-energy ${}^3$He and ${}^4$He fluxes and spectra in the impulsive solar energetic particle events observed with the {\it Advanced Composition Explorer}. We explore the model parameter space to show how observations may be used to constrain the model.

29 pages, 11 Figures, Submitted to ApJ

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• The Anisotropy of Electron MHD Turbulence
• Magnetically Driven Accretion Flows in the Kerr Metric II: Structure of the Magnetic Field
• Stochastic Acceleration of 3He and 4He by Parallel Propagating Plasma Waves

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