Particle acceleration by strong turbulence in solar flares: Theory of spectrum evolution

We propose a nonlinear self-consistent model of the turbulent nonresonant particle acceleration in solar flares. We simulate temporal evolution of the spectra of charged particles accelerated by strong long-wavelength MHD turbulence taking into account the back-reaction of the accelerated particles on the turbulence. The main finding is that the nonlinear coupling of accelerated particles with MHD turbulence results in prominent evolution of the spectra of accelerated particles, which can be either soft-hard-soft or soft-hard-harder depending on the particle injection efficiency. Such evolution patterns are widely observed in hard X-ray and gamma-ray emission from solar flares.