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 an angle between wave vector and underlying magnetic field increases and fast mode becomes more compressive. We also study imbalanced turbulence, in which wave packets propagating in one-direction have more power than those in the opposite direction. Unlike imbalanced \Alfvenic 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 stationary value of -2. Thus we conclude that the dissipation of fast mode, at least in 1D case, happens not due to weak or strong turbulent cascading, but mostly due to nonlinear steepening. The density fluctuations, which are carried by slow-mode perturbation in the larger scale and entropy-mode perturbation in the smaller scale, depend on initial driving spectrum and a ratio of specific heat.