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

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∼ (√∈/βq²) is small, where a is the minor radius. Thus, finite ε is allowed when q² is large. The equilibria are completely specified by the midplane profiles of pressure p(R) and poloidal magnetic field B_P(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-β_p tokamaks are discussed in detail.