Virial relations for elongated plasmas in tokamaks: Analytical approximations and numerical calculations

Using the SPIDER code, three series of calculations of plasma equilibrium in a tokamak are performed—with low, medium, and high pressure. In each series, the cross section is purely elliptical with elongation varying from K=1 (circular plasma) to K=2.4. For these configurations, the integrals S1÷S3 defining the right-hand sides of the virial relations in Lao et al. [Nucl. Fusion 25, 1421 (1985)] are calculated. Their dependences on plasma parameters, elongation K of magnetic surfaces, and radial derivatives of K and Shafranov shift Δ are analyzed. The accuracy of analytical expressions for S1÷S3 proposed in Pustovitov [Phys. Plasmas 29, 092507 (2022)] is assessed.