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

Riquelme, Mario; Osorio, Alvaro; Quataert, Eliot

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, {\boldsymbol{B}}. In this setup, an electron pressure anisotropy with {p}_{\perp ,e}> {p}_{| | ,e} naturally arises due to the adiabatic invariance of the electron magnetic moment ({p}_{| | ,e} and {p}_{\perp ,e} are the pressures parallel and perpendicular to {\boldsymbol{B}}). If the anisotropy is large enough, then the whistler instability arises, efficiently scattering the electrons and limiting {{∆ }}{p}_{e} (\equiv {p}_{\perp ,e}-{p}_{| | ,e}). In this context, {{∆ }}{p}_{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 | {\boldsymbol{B}}| 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} (\equiv 8π {p}_{e}/| {\boldsymbol{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.