Authors: Waverly Gorman (University of Arizona), Kristopher Klein (University of Arizona)

Understanding the distribution of energy resulting from turbulent plasma dissipation is essential for describing the thermodynamics of a broad range of systems. Howes et al. 2008 developed a model for a turbulent cascade assuming local nonlinear energy transfer and critical balance to construct a steady-state cascade of energy from inertial through dissipation scales where Landau damping onto ions and then electrons terminates the cascade.  At proton plasma beta greater than approximately 30, kinetic Alfven waves become non-propagating, with the wavevector range of the zero-frequency gap increasing with higher values of beta. Assuming only local energy transfer results in the cascade halting at the gap, prohibiting energy from reaching electron scales. This results in an enhanced value for the proton-to-electron heating ratio (Qp/Qe) when the gap is present. In this study, we investigate the updated Weakened Cascade model by Howes et al. 2011 that allows for non-local contributions to the cascade by including effects of shearing (large eddies shearing apart smaller eddies) and diffusion (small eddies diffusing across larger eddies), to model energy transfer across the high-beta, zero-frequency gap. We examine the influence of proton plasma beta and ion-to-electron temperature ratio on Qp/Qe and provide fits to candidate functional forms for an improved subgrid model. This updated subgrid model will be relevant for simulations of a variety of heliospheric and astrophysical systems where the thermal pressure dominates over the magnetic pressure.