  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. Based
on high-resolution numerical simulations it is proposed 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 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 $E(k)\propto k_{\perp}^{-2}$.
The generation of condensate is apparently related to the breakdown of mirror
symmetry in non-balanced turbulence.
