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

Using 2D particle-in-cell plasma simulations, we study electron acceleration by temperature anisotropy instabilities, assuming conditions typical of above-the-loop-top sources in solar flares. We focus on the long-term effect of T e,⊥ > T e,∥ instabilities by driving the anisotropy growth during the entire simulation time through imposing a shearing or a compressing plasma velocity (T e,⊥ and T e,∥ are the temperatures perpendicular and parallel to the magnetic field). This magnetic growth makes T e,⊥/T e,∥ grow due to electron magnetic moment conservation, and amplifies the ratio ω ce/ω pe from ∼0.53 to ∼2 (ω ce and ω pe are the electron cyclotron and plasma frequencies, respectively). In the regime ω ce/ω pe ≲ 1.2–1.7, the instability is dominated by oblique, quasi-electrostatic modes, and the acceleration is inefficient. When ω ce/ω pe has grown to ω ce/ω pe ≳ 1.2–1.7, electrons are efficiently accelerated by the inelastic scattering provided by unstable parallel, electromagnetic z modes. After ω ce/ω pe reaches ∼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 ∼ 2.9 plus a high-energy bump reaching ∼300 keV. In the compressing runs, α s ∼ 3.7 with a spectral break above ∼500 keV. This difference can be explained by the different temperature evolutions in these two types of simulations, suggesting that a critical role is played by the type of anisotropy driving, ω ce/ω pe, and the electron temperature in the efficiency of the acceleration.