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Necessary criterion for magnetic field reversal in the reversed-field pinch

We derive analytically a necessary criterion for the reversal of the axial magnetic field of ohmic single-helicity states of the reversed-field pinch. This is done in the frame of resistive magnetohydrodynamics (MHD) in cylindrical geometry using perturbation theory for a paramagnetic pinch with low edge conductivity and axial magnetic field. The criterion involves the radial profile of the logarithmic derivative of the Newcomb eigenfunction of the pinch. It is suggestive that a finite edge radial magnetic field Br(a) might be favourable for field reversal. In accordance with this, visco-resistive MHD simulations show that helical equilibria with smaller maximum radial magnetic fields achieve reversal when a finite Br(a) is applied. Numerical simulations also show that the criterion works for large perturbations of the pinch too, in particular those leading to states with a single helical axis. The necessary criterion is found to be satisfied for reversed states where a finite Br(a) is driven in the RFX-mod machine.