Stochastic Electron Acceleration by the Whistler Instability in a Growing Magnetic Field

We use 2D particle-in-cell simulations to study the effect of the saturated whistler instability on the viscous heating and nonthermal acceleration of electrons in a shearing, collisionless plasma with a growing magnetic field, B. In this setup, an electron pressure anisotropy with p_⊥,e > p_∥,e naturally arises due to the adiabatic invariance of the electron magnetic moment (p_∥,e and p_⊥,e are the pressures parallel and perpendicular to B). If the anisotropy is large enough, then the whistler instability arises, efficiently scattering the electrons and limiting Δp_e(=p_⊥,e - p_∥,e). In this context, Δp_e taps into the plasma velocity shear, producing electron heating by the so-called anisotropic viscosity. In our simulations, we permanently drive the growth of B Ö Ö by externally imposing a plasma shear, allowing us to self-consistently capture the long-term, saturated whistler instability evolution. We find that besides the viscous heating, the scattering by whistler modes can stochastically accelerate electrons to nonthermal energies. This acceleration is most prominent when initially β_e ~ 1, gradually decreasing its efficiency for larger values of β_e (= 8πp_e/|B|²). If initially β_e ~ 1, then the final electron energy distribution can be approximately described by a thermal component, plus a power-law tail with a spectral index of ∼3.7. In these cases, the nonthermal tail accounts for ~5% of the electrons and for ~15% of their kinetic energy. We discuss the implications of our results for electron heating and acceleration in low-collisionality astrophysical environments, such as low-luminosity accretion flows.