On the accuracy of the standard formula for diamagnetic signal in a tokamak

Using the SPIDER code, calculations of plasma equilibrium in a tokamak with a circular plasma in a wide range of βp and ℓi (poloidal beta and internal inductance) were performed. The obtained values of the diamagnetic signal are compared with the predictions of the standard formula for tokamaks. The detected differences are analyzed using exact virial relations, an approximate consequence of which is this formula, as shown by Lao et al. [Nucl. Fusion 25, 1421 (1985)]. The reasons for the difference and the range of parameters where the accuracy of the formula is insufficient to interpret the data are identified. It is proved that the loss of accuracy in analytical theory is due to the fact that, when calculating the diamagnetic signal, only linear corrections in the inverse aspect ratio were taken into account.