Cascading of Fast-Mode Balanced and Imbalanced Turbulence

We study the cascading of fast MHD modes in magnetically dominated plasma by performing one-dimensional (1D) dynamical simulations. We find that the cascading becomes more efficient as the angle between the wavevector and the underlying magnetic field increases and the fast mode becomes more compressive. We also study imbalanced turbulence, in which wave packets propagating in one direction have more power than those propagating in the opposite direction. Unlike imbalanced Alfvénic turbulence, the imbalanced fast-mode turbulence shows faster cascading as the degree of imbalance increases. We find that the spectral index of the velocity and magnetic field, which are carried by the fast-mode turbulence, quickly reaches a stationary value of -2. Thus, we conclude that the dissipation of the fast mode, at least in the 1D case, happens not because of weak or strong turbulent cascading, but mostly because of nonlinear steepening. The density fluctuations, which are carried by slow-mode perturbations in the larger scale and entropy-mode perturbations in the smaller scale, depend on the initial driving spectrum and the ratio of specific heats.