Parallel helicity and coherent structure in rotating magnetized plasmas*

The ideal invariants of MHD turbulence are energy, magnetic helicity and cross helicity. If the system is rotating, cross helicity is no longer an invariant; if there is a mean magnetic field present, the magnetic helicity is no longer invariant; if both rotation and mean field occur, neither cross helicity nor magnetic helicity are invariant. However, if they are aligned there is a new invariant, the parallel helicity, which is a linear combination of cross and magnetic helicity. Thus, in a plasma that is rotating around the mean field direction, there are two ideal invariants, energy and parallel helicity, and a statistical mechanics can be based on these. In this case, we can predict that the largest-scale modes have much more energy than any other mode and show that the energetic, largest-scale modes form a coherent structure. We will discuss theoretical and computational results leading up to these conclusions and also discuss the applicability to real (dissipative and forced) MHD turbulence.