Self-consistency of the principle of profile consistency results for sawtoothing tokamak discharges

Abstract

DISCLAIMERThis i-eport was prepared as an accouni of +ork sponsored hy an agency uf the United States Government Neither (he United Slates Government nor jn> agency thereof, nor any of their employees, makes any warranty, express or implied. 01 assume* any legal liability or responsihilili for the accuracy, completeness, or usefulness af any infocmauon, apparatus, product. 01 process disclosed, or represents that its use would not infringe privately owned rights Refer ence herein to any specific commercial product, process, or service hy trade name, trademark, manufacturer, or otherwise docs (tot necessarily constitute or imply its endorsement, recom mendation, or favoring by the United States Government or any agency thereof The views and opinions of authors expressed herein do not necessarily state ur reflect those of the Vimlcd States Government or any agency (hereof •AT&T Microelectronics, Reading, PA 19612 **0ak Ridge National Laboratory, Oak Ridge, TN 37831 if \S 2 ABSTRACT The principle of profile consistency states that for fixed limiter safety factor q,, there exists unique natural equilibrium profile shapes for the a. current density j(r) [and consequently q(r)], and the electron temperature T (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 [i.e., discharges with q(0) < 1) are: (1) (r^a) = F, M/q a > [= Vq a , empirically], (2) <T_>/T"" = F 5 (1/q_), and (3) a unique scaling law for the central electron S SO tl d temperature T , where r 1 is the sawtooth inversion radius [i.e., q(r^) = 1] and <T_> is the volume average T . Since for a given T (r), the ohmic current J(r) can be deduced from Ohm'3 law, given the function F^, the function F 2 is uniquely fixed and vice versa. Also given F^(Vq_), the central current density J Q = (V L /2nbRZ eff ) T|^2 = (I /*a 2 ) Fg(q a ), where the function F3 = (q a /q Q ) is uniquely fixed by F^ Here b = 6.53 * 10^ unA, and I , V L> Z ff >, R, a, and q 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 (r), the set of functions F^ F 2 , and F-, is uniquely fixed. Further, the principle of profile consistency [i.e., the existence of unique natural equilibrium profile shapes far J(r) and T e <r) for a fixed q ) dictates that this set of functions F|, F 2 , and F? remain the same for all sawtoothing discharges in any_ tokamak regardless of its size [i.e., a and R), I , V L , B T , etc. Here, we present a rather complete and detailed theoretical examination of this self-consistency of the measured values of T {r}, F^ F 2 , and F, for sawtoothing TFTR discharges. * (I R 2 eff /a 2 V L ); while for all q a -dependent profiles F 3 (q a ) = (q a /q 0 ) -Q a when (r^a) = (1/q a h and consequently T 3/2 • (B T ^off^L^' where B T is the con f in i n 8 toroidal magnetic field. The former T scaling is profile consistency independe...

A hierarchy of empirical models of plasma profiles and transport

“…ln[I p ] is clearly the most important control variable. This result contrasts with earlier profile consistency studies 12,17 which found that the edge safety factor, q 95 , is the most important variable in determining the temperature profile shape. This difference occurs because we are fitting the unnormalized temperature and I p is much more important than q 95 in determining the magnitude of the temperature.…”

Turbulent steady-state configuration of an inductively driven, dissipative tokamak plasma

“…͑1͒ describes in fact the monotonic variation of rational surfaces, 1/q s ϵm/n ͑m and n are, respectively, the poloidal and toroidal mode num-ber͒. In 1990, Arunasalam et al 8 presented an exhaustive study on the principle of profile consistency. But to this day the following questions raised by the three papers have remained unanswered:…”

Scalings and plasma profile parameterization of ASDEX high density Ohmic discharges

“…Our research systematises and validates earlier graphical and qualitative studies of "profile consistency". (See [4] for a review of this topic.) The statistical approach enables us to make quantitative statements about the relative strength of the interior q a dependence and the weaker exterior parametric dependencies of the profile shape.…”