Whistler turbulence heating of electrons and ions: Three-dimensional particle-in-cell simulations

The decay of whistler turbulence in a collisionless, homogeneous, magnetized plasma is studied using three-dimensional particle-in-cell simulations. The simulations are initialized with a narrowband, relatively isotropic distribution of long wavelength whistler modes. A first ensemble of simulations at electron beta ${\beta }_e$ = 0.25 and ion-to-electron mass ratio $m_i$/$m_e$ = 400 is carried out on a domain cube of dimension $L{\omega }_{pi}$/c = 5.12 where ${\omega }_{pi}$ is the ion plasma frequency. The simulations begin with a range of dimensionless fluctuating field energy densities, ${ϵ}_o$, and follow the fluctuations as they cascade to broadband, anisotropic turbulence which dissipates at shorter wavelengths, heating both electrons and ions. The electron heating is stronger and preferentially parallel/antiparallel to the background magnetic field $B_o;$ the ion energy gain is weaker and is preferentially in directions perpendicular to $B_o$. The important new results here are that, over 0.01 < ${ϵ}_o$ < 0.25, the maximum rate of electron heating scales approximately as ${ϵ}_o$, and the maximum rate of ion heating scales approximately as ${ϵ}_o^{1.5}$. A second ensemble of simulations at ${ϵ}_o$ = 0.10 and ${\beta }_e$ = 0.25 shows that, over 25 < $m_i$/$m_e$< 1836, the ratio of the maximum ion heating rate to the maximum electron heating rate scales approximately as $m_e$/$m_i$.