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 (Wk ∝ k^-7/2) can result in the energy spectrum of non-relativistic protons,which gives a good fit to that observed from solar flare events.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.