WHY BETA(P) AND L(I) CANNOT BE SEPARATELY MEASURED IN A NEAR-CIRCULAR TOKAMAK

An analytical calculation is presented demonstrating why a separate determination of poloidal beta, beta(p), and plasma internal inductance, l(i), in near circular tokamak plasmas is not possible from experimental magnetic data. A second-order expansion in terms of the inverse aspect ratio, epsilon, of the Grad-Shafranov equation provides expressions for the measured fields with explicit dependence on beta(p). This dependence, however, is very weak and is shown to be insufficient for determining beta(p) when any reasonable magnetic measurement error estimates are taken into account.