Spectrum of weak MHD turbulence

Turbulence of magnetohydrodynamic waves in nature and in the laboratory is generally cross-helical or non-balanced, in that the energies of Afv\'en waves moving in opposite directions along the guide magnetic field are unequal. We propose that such turbulence spontaneously generates a condensate of the residual energy $E_v-E_b$ at small field-parallel wave numbers. As a result, the energy spectra of counter-propagating Alfv\'en waves are generally not scale-invariant. In the limit of infinite Reynolds number, the universality is asymptotically restored at large wave numbers, and both spectra attain the scaling $E(k)\propto k_{\perp}^{-2}$.