Plasma Rotation in Tokamaks for Steady State Conditions

New equations for tokamaks plasmas in steady state conditions have been found, which allow to find the plasma rotation velocities from the plasma geometry and some parameters such as ellipticity, triangularity, safety factor, shear and inductive electric field. The starting point of our treatment is the resistive MHD equilibrium equation. By additional operation with the del operator, a set of new differential equations has been found. These equations, together with the magnetic surface equations, allow determining the plasma velocities as a function of some experimental parameters, usually determined in most of the tokamaks. Particular cases, as circular geometry, can be treated in a simplified way. These results illustrate more realistic geometries with ellipticity and triangularity, which can only be solved numerically. The coordinates used in this word are those previously presented in several papers [1]. \\[4pt] [1] P. Martin, E. Castro and M. G. Haines, Phys Plasmas \textbf{12}, 102505 (2005)