On virial analysis at low aspect ratio

The validity of virial analysis to infer global MHD equilibrium poloidal beta β p and internal inductance ℓ i from external magnetics measurements is examined for low aspect ratio configurations with A < 2 . Numerical equilibrium studies at varied aspect ratio are utilized to validate the technique at finite aspect ratio. The effect of applying high- A approximations to low- A experimental data is quantified and demonstrates significant over-estimation of stored energy (factors of 2–10) in spherical tokamak geometry. Experimental approximations to equilibrium-dependent volume integral terms in the analysis are evaluated at low- A . Highly paramagnetic configurations are found to be inadequately represented through the virial mean radius parameter R T . Alternate formulations for inferring β p and ℓ i that are independent of R T to avoid this difficulty are presented for the static isotropic limit. These formulations are suitable for fast estimation of tokamak stored energy components at low aspect ratio using virial analysis.