The Plasma internal energy is not conserved on a magnetic surface if nonlinear flows are considered. The analysis here presented leads to a complicated equation for the plasma internal energy considering nonlinear flows in the collisional regime, including viscosity and in the low-vorticity approximation. Tokamak equilibrium has been analyzed with the magnetohydrodynamics nonlinear momentum equation in the low vorticity case. A generalized Grad–Shafranov-type equation has been also derived for this case.
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