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 $T_{e,\perp }\mathrm{/}{T}_{e,\parallel }$ grow due to electron magnetic moment conservation, and amplifies the ratio ${\omega }_{ce}\mathrm{/}{\omega }_{pe}$ from $\sim 0.53$ to $\sim 2$ (${\omega }_{ce}$ and ${\omega }_{pe}$ are the electron cyclotron and plasma frequencies, respectively). In the regime ${\omega }_{ce}\mathrm{/}{\omega }_{pe}\lesssim 1.2-1.7$ the instability is dominated by oblique, quasi-electrostatic (OQES) modes, and the acceleration is inefficient. When ${\omega }_{ce}\mathrm{/}{\omega }_{pe}$ has grown to $\omega_{ce}/\omega_{pe}\gtrsim 1.2-1.7$, electrons are efficiently accelerated by the inelastic scattering provided by unstable parallel, electromagnetic z (PEMZ) modes. After ${\omega }_{ce}\mathrm{/}{\omega }_{pe}$ 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 ${\alpha }_s\sim$ 2.9 plus a high-energy bump reaching $\sim 300$ keV. In the compressing runs, $\alpha_s \sim$3.7withaspectralbreakabove$\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, ${\omega }_{ce}\mathrm{/}{\omega }_{pe}$ and the electron temperature in the efficiency of the acceleration.