Abstract
Left- and right-handed helical modes' statistical absolute equilibria appear \textit{separately}. If both chiral sectors present, one can dominate around its positive pole, which is relevant to the nearly maximally helical (force free for magnetic field) states of turbulence. Pure magnetodynamics (PMD, or electron magnetohydrodynamics --- EMHD), pure hydrodynamics (PHD), and, single-fluid and two-fluid MHDs are studied. Relevant documented data and issues of cascade properties, and, helical and nonhelical dynamos are revisited. We also discuss new scenarios, such as PMD inverse magnetic helicity and forward energy cascades, and, the continuous transition from completely-inverse to partly-inverse-and-partly-forward and to completely-forward energy transfers in PHD.
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