Equations for the evolution of the radial electric field and poloidal rotation in toroidally symmetric geometry

A set of three coupled ordinary differential equations that give the evolution of the density, the radial electric field, and poloidal plasma rotation are derived from the continuity equation and momentum balance. They include the effect of those processes considered to be of importance for the L- (low) to H- (high) mode transition: neutral friction, neoclassical viscosity, the radial pressure gradient, orbit losses, a radial current through a probe, anomalous stresses, and Stringer spin up. The equations are valid for arbitrary toroidally symmetric geometry and include effects of non-uniformity (of for instance the neutral friction) in the magnetic surface. As an example, non-uniform neutral friction in an elongated geometry is discussed.