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We propose a nonlinear self-consistent model of the turbulent non-resonantparticle acceleration in solar flares. We simulate temporal evolution of thespectra of charged particles accelerated by strong long-wavelength MHDturbulence taking into account back reaction of the accelerated particles onthe turbulence. The main finding is that the nonlinear coupling of acceleratedparticles and MHD turbulence result in prominent evolution of the spectra ofaccelerated particles, which can be either soft-hard-soft or soft-hard-harderdepending on the particle injection efficiency. Such evolution patterns arewidely observed in hard X-ray and gamma-ray emission from solar flares.

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