Why betapand licannot 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, li, 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.