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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 S 1 ÷ S 3 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 S 1 ÷ S 3 proposed in Pustovitov [Phys. Plasmas 29, 092507 (2022)] is assessed. [ABSTRACT FROM AUTHOR]

The problem of the plasma stability against the resistive wall modes is considered from two sides, theoretical and experimental. The main subject is the dispersion relation and its verification, which is commonly understood as a comparison of the predicted and observed stability thresholds. As in the conventional magnetohydrodynamics, the growth rate γ and the angular rotation frequency ω of the mode are found from the energy balance with account of some dissipation in the plasma, additional to the resistive losses in the vacuum vessel wall. The resulting relations are integral, which allows the same γ and ω with different integrands. It is shown explicitly that only two fitting parameters are needed for getting a perfect agreement of such results with measured γ and ω. This explains why all attempts with so-called kinetic relations have been good in that. This also reveals the reason for the earlier finding [A. M. Garofalo, Fusion Sci. Technol. 48, 918 (2005)] that a number of models provided the stability regardless of the type of dissipation as long as the dissipation was sufficiently large. It is shown here that such "degeneracy" is a general property. One consequence is that a similar success with any model cannot guarantee its validity, and none of them can be recommended to ITER immediately. It is also explained that the edge harmonic oscillations can be a promising candidate for testing the dissipation channels missing in the kinetic dispersion relations. [ABSTRACT FROM AUTHOR]