Spectrum of Magnetohydrodynamic Turbulence

We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations tend to align the directions of their polarizations. However, the perfect alignment cannot be reached; it is precluded by the presence of a constant energy flux over scales. As a consequence, the directions of shear-Alfvén fluid and magnetic-field fluctuations at each scale $\lambda$ become effectively aligned within the angle ${\varphi }_{\lambda }\propto {\lambda }^{1/4}$, which leads to scale-dependent depletion of the nonlinear interaction and to the field-perpendicular energy spectrum $E(k_{\perp })\propto k_{\perp }^{-3/2}$. Our results may be universal, i.e., independent of the external magnetic field, since small-scale fluctuations locally experience a strong field produced by large-scale eddies.