Natural elongation and triangularity of tokamak equilibria

Abstract

Quasianalytic formulas are calculated for the elongation κ and triangularity δ of the plasma surface of a free-boundary tokamak equilibrium. The final results give κ and δ as functions of five quantities: the inverse aspect ratio ε, the poloidal beta βp, the internal inductance li, and the quadrupole and hexapole moments of the externally applied field. The agreement with numerically computed equilibria is found to be quite good when A≥3, κ≤1.5, and δ≤0.2 and when the plasma is limited by the vacuum vessel wall and not diverted by the presence of a separatrix on the plasma surface.