Conserved functions and extended Grad-Shafranov equation for low vorticity viscous plasmas with nonlinear flows -: art. no. 102505

Tokamak equilibrium has been analyzed with the magnetohydrodynamics nonlinear momentum equation in the low vorticity case. A large simplification in the analysis is obtained in this case compared with previous general treatments for rotating plasmas in tokamaks. Now pressure is not conserved around magnetic surfaces, however, other generalized functions have been found, which are conserved on each magnetic surface. A generalized Grad-Shafranov-type equation has been also derived for this case. How to determine the gradient of these new conserved functions on each magnetic surface from their value at one point of the corresponding surface is also shown.