Adiabatic Non-resonant Acceleration in Magnetic Turbulence and Hard Spectra of Gamma-Ray Bursts

We introduce a non-resonant acceleration mechanism arising from the second adiabatic invariant in magnetic turbulence and apply it to study the prompt emission spectra of gamma-ray bursts (GRBs). The mechanism contains both the first- and second-order Fermi acceleration, originating from the interacting turbulent reconnection and dynamo processes. It leads to a hard electron energy distribution up to a cutoff energy at the balance between the acceleration and synchrotron cooling. The sufficient acceleration rate ensures a rapid hardening of any initial energy distribution to a power-law distribution with the index , which naturally produces a low-energy photon index via the synchrotron radiation. For typical GRB parameters, the synchrotron emission can extend to a characteristic photon energy on the order of ∼100 keV.