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: (r/sub 1//a) = F/sub 1/ (1/q/sub a/), /T/sub eo/ = F/sub 2/(1/q/sub a/), and a unique scaling law for the central electron temperature T/sub eo/, where r/sub 1/ 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 F/sub 1/, the function F/sub 2/ is uniquely fixed and vice versa. Also given F/sub 1/(1/q/sub a/), the central current density j/sub o/ = (V/sub L//2..pi..bRZ/sub eff/) T/sub eo//sup 3/2/ = (I/sub p//..pi..a/sup 2/) F/sub 3/(q/sub a/), where the function F/sub 3/ = (q/sub a//q/sub o/) is uniquely fixed by F/sub 1/. Here b approx. 6.53 /times/ 10/sup 3/ ln..lambda.., 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 F/sub 1/, F/sub 2/, and F/sub 3/ is uniquely fixed. Further, the principle of profile consistency dictates that this set of functions F/sub 1/, F/sub 2/, and F/sub 3/ 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), F/sub 1/, F/sub 2/, and F/sub 3/ for sawtoothing TFTR discharges. 55 refs., 15 figs., 1 tab.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- DOE Contract Number:
- AC02-76CH03073
- OSTI ID:
- 6386335
- Report Number(s):
- PPPL-2609; ON: DE89012914
- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
TEMPERATURE DISTRIBUTION
MATHEMATICAL MODELS
TOKAMAK TYPE REACTORS
SAWTOOTH OSCILLATIONS
CURRENT DENSITY
DIFFUSION
ELECTRON TEMPERATURE
LIMITERS
MAGNETIC FIELDS
SCALING LAWS
OSCILLATIONS
THERMONUCLEAR REACTORS
700103* - Fusion Energy- Plasma Research- Kinetics