Calculation and interpretation of analytic high‐beta poloidal equilibria in finite aspect ratio tokamaks

TLDR: The validity of the analytic large aspect ratio, high-β equilibria developed by Cowley et al. as mentioned in this paper was extended to include finite aspect ratio with q2≫1, where q is the safety factor.

Abstract: The validity of the analytic large aspect ratio, high‐β equilibria developed by Cowley et al. [Phys. Fluids B 3, 2066 (1991)] is extended to include finite aspect ratio equilibria with q2≫1, where q is the safety factor. These high‐β equilibria have two regions. Most of the volume lies in the ‘‘core region,’’ where ψ=ψ(R). The flux surfaces close in the ‘‘boundary layer region,’’ which has thickness δ. The solutions are valid when δ/a∼O (√e/βq2) is small, where a is the minor radius. Thus, finite e is allowed when q2 is large. The equilibria are completely specified by the midplane profiles of pressure p(R) and poloidal magnetic field BP(R) and the shape of the plasma boundary, all of which can be measured experimentally. Note the departure from customary specification of p(ψ), q(ψ), or F(ψ). A fast numerical code, requiring a few seconds to execute, has been written to compute and illustrate the analytic high‐β equilibria. The qualitative features of high‐βP tokamaks are discussed in detail.