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Stochastic Electron Acceleration by Temperature Anisotropy Instabilities Under Solar Flare Plasma Conditions

Using 2D particle-in-cell (PIC) plasma simulations we study electron acceleration by temperature anisotropy instabilities, assuming conditions typical of above-the-loop-top (ALT) sources in solar flares. We focus on the long-term effect of $T_{e,\perp} > T_{e,\parallel}$ instabilities by driving the anisotropy growth during the entire simulation time, through imposing a shearing or a compressing plasma velocity ($T_{e,\perp}$ and $T_{e,\parallel}$ are the temperatures perpendicular and parallel to the magnetic field). This magnetic growth makes $T_{e,\perp}/T_{e,\parallel}$ grow due to electron magnetic moment conservation, and amplifies the ratio $ω_{ce}/ω_{pe}$ from $\sim 0.53$ to $\sim 2$ ($ω_{ce}$ and $ω_{pe}$ are the electron cyclotron and plasma frequencies, respectively). In the regime $ω_{ce}/ω_{pe}\lesssim 1.2-1.7$ the instability is dominated by oblique, quasi-electrostatic (OQES) modes, and the acceleration is inefficient. When $ω_{ce}/ω_{pe}$ has grown to $ω_{ce}/ω_{pe}\gtrsim 1.2-1.7$, electrons are efficiently accelerated by the inelastic scattering provided by unstable parallel, electromagnetic z (PEMZ) modes. After $ω_{ce}/ω_{pe}$ reaches $\sim 2$, the electron energy spectra show nonthermal tails that differ between the shearing and compressing cases. In the shearing case, the tail resembles a power-law of index $α_s \sim$ 2.9 plus a high-energy bump reaching $\sim 300$ keV. In the compressing runs, $α_s \sim$ 3.7 with a spectral break above $\sim 500$ keV. This difference can be explained by the different temperature evolutions in these two types of simulations, suggesting a critical role played by the type of anisotropy driving, $ω_{ce}/ω_{pe}$ and the electron temperature in the efficiency of the acceleration.