Abstract: A method and apparatus for plasma relaxation under magnetic global topological constraint produces a hot magnetically confined toroidal Z-pinch plasma with a plurality of straight and toroidal relaxing plasma discharges so as to generate at least one open-ended poloidal null separatrix in the magnetic field with one poloidal null within the plasma space situated in the small major radius side of the toroidal discharge, forming thereby a magnetic configuration (called DAG) with non-zero homotopic invariant, including a toroidal reversed-field pinch with inner poloidal divertor, in a region of open plasma magnetic surfaces surrounding the toroidal discharges, when toroidal magnetic field component is also made to be substantially different from zero at the poloidal null.