Relaxed states with plasma flow

In the theory of relaxation, a plasma reaches a state of minimum energy subject to constant magnetic helicity. In this state, the plasma velocity is zero. Several authors have attempted to extend the theory, by introducing a number of different helicity invariants, so as to obtain relaxed states with plasma flow. It is shown here that these generalized invariants are special cases of two basic self-helicities: one for electrons and one for ions. The validity of the generalized invariants is discussed and contrasted with that of original magnetic helicity.