We present results from a numerical forward model to evaluate one-dimensional reduced power spectral densities ( PSD ) from arbitrary energy distributions in \mathbf { k } -space .
In this model , we can separately calculate the diagonal elements of the spectral tensor for incompressible axisymmetric turbulence with vanishing helicity .
Given a critically balanced turbulent cascade with k _ { \| } \sim k _ { \perp } ^ { \alpha } and \alpha < 1 , we explore the implications on the reduced PSD as a function of frequency .
The spectra are obtained under the assumption of Taylor ’ s hypothesis .
We further investigate the functional dependence of the spectral index \kappa on the field-to-flow angle \theta between plasma flow and background magnetic field from MHD to electron kinetic scales .
We show that critically balanced turbulence asymptotically develops toward \theta -independent spectra with a slope corresponding to the perpendicular cascade .
This occurs at a transition frequency f _ { 2 D } ( L, \alpha, \theta ) , which is analytically estimated and depends on outer scale L , critical balance exponent \alpha and field-to-flow angle \theta .
We discuss anisotropic damping terms acting on the \mathbf { k } -space distribution of energy and their effects on the PSD .
Further , we show that the spectral anisotropies \kappa ( \theta ) as found by Horbury et al .
( 20 ) and Chen et al .
( 6 ) in the solar wind are in accordance with a damped critically balanced cascade of kinetic Alfvén waves .
We also model power spectra obtained by von Papen et al .
( 54 ) in Saturn ’ s plasma sheet and find that the change of spectral indices inside 9 R _ { \mathrm { s } } can be explained by damping on electron scales .