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.