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 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 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 .