The Turbulent Heating Rate in Strong MHD Turbulence with Nonzero Cross
  Helicity
  Different results for the cascade power in strong, incompressible MHD
turbulence with nonzero cross helicity appear in the literature. In this paper,
we discuss the conditions under which these different results are valid. We
define z+ to be the rms amplitude of Alfven waves propagating parallel to the
background magnetic field, and z- to be the rms amplitude of Alfven waves
propagating anti-parallel to the background magnetic field. Nonzero cross
helicity implies that z+ and z- differ, and we take z- to be less than z+. We
find that the mechanism that generates the z- fluctuations strongly affects the
cascade power, because it controls the coherence time for interactions between
oppositely directed wave packets at the outer scale. In particular, for fixed
values of z+ and z-, the cascade power is in many cases larger when the z-
fluctuations are generated by the reflection of z+ fluctuations than when the
z- fluctuations are generated by forcing that is only weakly correlated with
the z+ fluctuations.
