On the self-consistency of the principle of profile consistency results for sawtoothing tokamak discharges

The principle of profile consistency states that for fixed limiter safety factor q/sub a/, there exists unique natural equilibrium profile shapes for the current density j(r), and the electron temperature T/sub e/(r) for any tokamak plasma independent of the shapes of the heating power deposition profiles. The mathematical statement of the three basic consequences of this principle for sawtoothing discharges are: (r1/a) = F1 (1/q/sub a/), /T/sub eo/ = F2(1/q/sub a/), and a unique scaling law for the central electron temperature T/sub eo/, where r1 is the sawtooth inversion radius and is the volume average T/sub e/. Since for a given T/sub e/(r), the ohmic current j(r) can be deduced from Ohm's law, given the function F1, the function F2 is uniquely fixed and vice versa. Also given F1(1/q/sub a/), the central current density j/sub o/ = (V/sub L//2πbRZ/sub eff/) T/sub eo//sup 3/2/ = (I/sub p//πa2) F3(q/sub a/), where the function F3 = (q/sub a//q/sub o/) is uniquely fixed by F1. Here b ∼ 6.53 /times/ 103 lnΛ, and I/sub p/, V/sub L/, Z/sub eff/, R, a, and q/sub o/ are the plasma current, loop voltage, effective ion charge, major and minor radius, and the central safety factor, respectively. Thus for a fixed j(r) or T/sub e/(r), the set of functions F1, F2, and F3 is uniquely fixed. Further, the principle of profile consistency dictates that this set of functions F1, F2, and F3 remain the same for all sawtoothing discharges in any tokamak regardless of its size, I/sub p/, V/sub L/, B/sub T/, etc. Here, we present a rather complete and detailed theoretical examination of this self-consistency of the measured values of T/sub e/(r), F1, F2, and F3 for sawtoothing TFTR discharges. 55 refs., 15 figs., 1 tab