AbstractBecause the radiation power density from a marfe scales approximately as the square of its plasma pressure, and since increased radiation would aid divertor detachment for high power tokamaks, this paper identifies regions that might permit locally increased plasma pressure in steady state. The magnetic and dynamic (flow) constraints of magneto‐hydrodynamics (MHD) are examined for self‐consistent locally increased pressure equilibria, in both the magnetically open tokamak scrape‐off layer (SOL) and the closed surfaces just inside the last closed flux surface. In most tokamak geometries it is difficult to recycle particles at a sufficient rate to sustain high pressure marfes, but they might be possible near a divertor X‐point.