THE TURBULENT HEATING RATE IN STRONG MAGNETOHYDRODYNAMIC TURBULENCE WITH NONZERO CROSS HELICITY

Different results for the cascade power epsilon in strong, incompressible magnetohydrodynamic turbulence with nonzero cross helicity appear in the literature. In this paper, we discuss the conditions under which these different results are valid. Our conclusions can be expressed in terms of the density rho, the rms amplitudes z(+) and z(-) of Alfvenic fluctuations propagating parallel and antiparallel to the background magnetic field B-0, and the correlation length (outer scale) measured perpendicular to B-0, denoted L-perpendicular to. We argue that if z(+) >> z(-) and if the z(-) fluctuations are sustained by the reflection of z(+) fluctuations in a strong background magnetic field, then epsilon similar to rho(z(+))(2)z(-)/L-perpendicular to as in previous studies by Hossain, Matthaeus, Dmitruk, Lithwick, Goldreich, Sridhar, and others. On the other hand, if the minority wave type (z(-)) is sustained by some form of forcing that is uncorrelated with or only weakly correlated with the z(+) fluctuations, then epsilon can be much less than rho(z(+))(2)z(-)/L-perpendicular to, as in previous studies by Dobrowolny, Lazarian, Chandran, and others. The mechanism for generating the minority wave type strongly affects the cascade power because it controls the coherence time for interactions between oppositely directed wave packets at the outer scale.