Whistler turbulence heating of electrons and ions: Three-dimensional particle-in-cell simuations
In this study, 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 ${\beta }_{{\rm{e}}}$ = 0.25 and ion-to-electron mass ratio ${m}_{{\rm{i}}}$/${m}_{{\rm{e}}}$ = 400 is carried out on a domain cube of dimension $L{\omega }_{\mathrm{pi}}$/c = 5.12 where ${\omega }_{\mathrm{pi}}$ is the ion plasma frequency. The simulations begin with a range of dimensionless fluctuating field energy densities, ${\epsilon }_{{\rm{o}}}$, 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 ${{\boldsymbol{B}}}_{{\rm{o}}};$ the ion energy gain is weaker and is preferentially in directions perpendicular to ${{\boldsymbol{B}}}_{{\rm{o}}}$. The important new results here are that, over 0.01 < ${\epsilon }_{{\rm{o}}}$ < 0.25, the maximum rate of electron heating scales approximately as ${\epsilon }_{{\rm{o}}}$, and the maximum rate of ion heating scales approximately as ${\epsilon }_{{\rm{o}}}^{1.5}$. A second ensemble of simulations at ${\epsilon }_{{\rm{o}}}$ = 0.10 and ${\beta }_{{\rm{e}}}$ = 0.25 shows that, over 25 < ${m}_{{\rm{i}}}$/${m}_{{\rm{e}}}\;$< 1836, the ratio of the maximum ion heating rate to the maximum electron heating rate scales approximately as ${m}_{{\rm{e}}}$/${m}_{{\rm{i}}}$.