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

Abstract

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.