Reversed field pinch plasma equilibria with shear flow

The Grad–Shafranov equation with flow, which is derived by a variational method, involves unknown functions such as the dynamic pressure, P(Ψ). These functions are specified by minimizations of free energies under the constraints of constant P ′ (Ψ), magnetic helicity, flow helicity, and cross helicity in reversed field pinch (RFP) plasmas. New flow and cross helicities are introduced based on the analogy of the magnetic helicity, which are different from those used in fluid mechanics. The constraint of constant flow helicity provides flow with profiles from high- to low-shear flow. The Suydam-stable RFP equilibria obtained with flows are extremely different in β and β p from RFP equilibria without flow. The high-shear flow can extend the Suydam limit, allowing higher β and β p .