Acceleration of Flare Protons by Langmuir Plasmons

We analytically study the turbulent acceleration of solar protons by strong Langmuir plasmons in Cerenkov processes . It is shown that among the wave spectra with self-retained source only the Pelletier spectrum (W_k ∝ k^-7/2) can result in energy spectrum of non-relativistic protons, which gives a good fit to that observed from solar flare event. It is quite possible that strong Langmuir turbulence presents in coronal active region, with three-dimensional, isotropic and stationary spectrum proportional to k^-7/2, and is responsible for the acceleration of flare protons.