A variational principle and its implications for radial electric field and rotation in tokamaks

Abstract

A variational principle that minimizes an energy functional of the total electric field and the kinetic energy of the plasma flows with respect to the radial electric field is presented. Minimization is performed order by order in a small-gyroradius expansion, retaining up to second-order electric fields and third-order flows in the small parameter δ = ρ i /L. The electric fields and flows obtained variationally are interpreted in the context of a global momentum conservation integral, while comparing them with neoclassical results based on the radial transport of toroidal angular momentum.