Theory of Diamagnetic Signal in Current-Free Stellarators

The toroidal magnetic flux through the plasma column is calculated analytically for current-free stellarators of arbitrary geometry without assumptions on the plasma shape, aspect ratio, etc. This is done with accuracy sufficient for extracting the contribution due to the finite plasma pressure from this flux. The final result is a formula relating the measured diamagnetic signal with β, the ratio of the plasma pressure to the magnetic pressure. This formula is obtained assuming small β and the relative depth of the magnetic well. These are natural conditions for stellarators, therefore the final result can be recommended for magnetic diagnostics without practical limitations.