Stochastic Acceleration of 3He and 4He by Parallel Propagating Plasma Waves

Stochastic acceleration of $^3$He and $^4$He from a thermal background by parallel propagating turbulent plasma waves with a single power-law spectrum of the wavenumber is studied. In the model, both ions interact with several resonant modes. When one of these modes dominates, the acceleration rate is reduced considerably. At low energies, this happens for $^4$He, but not for $^3$He where contributions from the two stronger modes are comparable so that acceleration of $^3$He is very efficient. As a result, the acceleration of $^4$He is suppressed by a barrier below $\sim 100$ keV nucleon$^{-1}$ and there is a prominent quasi-thermal component in the $^4$He spectra, while almost all the injected $^3$He ions are accelerated to high energies. This accounts for the large enrichment of $^3$He at high energies observed in impulsive solar energetic particle events. With reasonable plasma parameters this also provides a good fit to the spectra of both ions. Beyond $\sim 1$ MeV nucleon$^{-1}$, the spectrum of $^3$He is softer than that of $^4$He, which is consistent with the observed decrease of the $^3$He to $^4$He ratio with energy. This study also indicates that the acceleration, Coulomb losses and diffusive escape of the particles from the acceleration site {\it all} play important roles in shaping the ion spectra. This can explain the varied spectral shapes observed recently by the {\it Advanced Composition Explorer}.