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 }ẽ 1, gradually decreasing its efficiency for larger values of {β }e (\equiv 8π {p}e/| {\boldsymbol{B}}{| }2). If initially {β }ẽ 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.