Empirical power law for magnetic turbulence spectra of an anisotropic plasma

Three-dimensional dynamic distributions of oscillations of the magnetic field over wave vectors $\mathbf k$ have been obtained from the plasma and magnetic measurements on four satellites in the Cluster experiment in a turbulent plasma in the outer Earth’s cusp and near it. The resulting $\mathbf k$ spectra exhibit strong inhomogeneous anisotropy. The dependences of the energy of magnetic oscillations on the wavenumber have been analyzed for 288 three-dimensional spectra in the wavelength interval covering the magnetohydrodynamic and ion scales. It has been shown that the energy density of magnetic fluctuations per unit volume in the wave vector space that is averaged over the total solid angle decreases in the wavelength interval from $\sim2000$ to $\sim10$ km with an increase in according to a power law with an exponent of $\alpha= -5.0\pm0.3$ for any magnitude and character of anisotropy.