Scaling law of the plasma turbulence with non conservative fluxes

where kd is Kolmogorov dissipation wave number, α1 and α2 are some constants and 1 ≤ n ≤ 2 (see, e.g., [1] and references therein). In the case of plasma turbulence existence of various kinetic mechanisms of dissipation makes the situation much more complicated. For instance, observations of the solar wind turbulence [10, 11, 12] strongly suggest steep power law spectrum of the magnetic field fluctuations for the frequencies higher then ion cyclotron frequency for which kinetic mechanisms of dissipation are dominant. In contrast with viscosity kinetic dissipation of plasma waves in the presence of background magnetic field is usually strongly anisotropic. In the presented paper we show that in the presence of: (i) anisotropic kinetic dissipation; and (ii) if the nonlinear transfer is governed by the scattering of the plasma waves by low frequency ones, then one should expect scale invariant power law spectrum of the plasma turbulence. It should be emphasized that the scale invariant spectrum is not associated with the constant flux of any physical quantity due to the presence of kinetic dissipation. The general equation that governs the evolution of any averaged characteristic Z of the homogenous turbulence which is conserved by nonlinear interactions (in the case of hydrodynamic turbulence Z is usually associated with energy density) in the wave number space has the form