Energy Transfer in a High Beta MHD Turbulent Cascade

The Howes et al. 2008 model for a MHD turbulent cascade assumes local nonlinear energy transfer and critical balance between the linear propagation and nonlinear interaction times to construct a steady-state cascade of energy from inertial through dissipation scales terminated by Landau damping. This model quantifies the bifurcation of energy between ions and electrons in solar system and astrophysical plasmas. The linear solutions for low-frequency kinetic Alfven waves have a gap where the frequency drops to zero for a proton plasma beta greater than approximately 30; this gap increases in width for increasing values of the plasma beta. Assuming only local nonlinear energy transfer, the energy cascade should halt once it reaches the gap. In this study, we investigate the Weakened Cascade model by Howes et al. 2011 that allows for non-local contributions to the cascade by including effects of shearing and diffusion, to properly model nonlinear energy transfer across the gap. We compare results for proton and electron heating from this model to direct numerical results by Kawazura et al. 2019. This update will be relevant for a variety of heliospheric and astrophysical systems with a proton plasma beta larger than 30.