Stochastic electron acceleration by temperature anisotropy instabilities in solar flares

Using 2D particle-in-cell (PIC) plasma simulations we study electron acceleration by temperature anisotropy instabilities, in the case where the electron temperature perpendicular to the ambient magnetic field (B) is larger than the parallel temperature and assuming conditions typical of above-the-loop-top (ALT) sources in solar flares. We focus on the long-term effect of the instabilities by driving the anisotropy growth during the entire simulation time. This is done through externally forcing a growth of B in the simulation by imposing a shearing plasma velocity, as a way to resemble local turbulent motions. The growth of B makes the anisotropy grow due to electron magnetic moment conservation, and amplifies the ratio w_c,e/w_p,e (w_c,e and w_p,e are the electron cyclotron and plasma frequencies, respectively). When w_c,e/w_p,e ~ 1.5, electrons are efficiently accelerated by the inelastic scattering provided by parallel, electromagnetic z (PEMZ) modes. After B has grown by a factor ~4, the electron spectra show nonthermal, power-law tails that, depending on the initial w_c,e/w_p,e, have indices between ~2 and ~3.5 and can reach ~MeV energies.