Nondimensional transport scaling in the Tokamak Fusion Test Reactor: Is tokamak transport Bohm or gyro-Bohm?

Abstract

General plasma physics principles state that power flow Q(r) through a magnetic surface in a tokamak should scale as Q(r)= {32π2Rr3Te2c nea/[eB (a2−r2)2]} F(ρ*,β,ν*,r/a,q,s,r/R,...) where the arguments of F are local, nondimensional plasma parameters and nondimensional gradients. This paper reports an experimental determination of how F varies with normalized gyroradius ρ*≡(2TeMi)1/2c/eBa and collisionality ν*≡(R/r)3/2qRνe(me/ 2Te)1/2 for discharges prepared so that other nondimensional parameters remain close to constant. Tokamak Fusion Test Reactor (TFTR) [D. M. Meade et al., in Plasma Physics and Controlled Nuclear Fusion Research, 1990, Proceedings of the 13th International Conference, Washington (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 9] L-mode data show F to be independent of ρ* and numerically small, corresponding to Bohm scaling with a small multiplicative constant. By contrast, most theories predict gyro-Bohm scaling: F∝ρ*. Bohm scaling implies that the largest scale size for microinstability turbulence depends on machine size. Analysis of a collisionality scan finds Bohm-normalized power flow to be independent of collisionality. Implications for future theory, experiment, and reactor extrapolations are discussed.

Size Scaling of Turbulent Transport in Magnetically Confined Plasmas

“…However, trends from experimental observations have been more complicated. Transport scalings in low confinement regimes (L-mode) have always been observed to be Bohm or worse than Bohm in major tokamaks [5,6]. In particular, dimensionless scaling studies on the DIII-D tokamak found that ion transport and energy confinement time exhibit Bohm-like behavior, while fluctuation characteristics suggest a gyro-Bohm scaling [7] for transport.…”

Fundamental statistical descriptions of plasma turbulence in magnetic fields

“…simple theory typically predicts 17 a gyro-Bohm scaling [Eq. (6)], although controversy remains about the proper form of the experimentally observed scaling with B (Perkins et al, 1993).…”

“…Dimensional analysis leads one to predict gyro-Bohm scaling [Eq. (6)], yet both experimental (Perkins et al, 1993) and numerical (Nevins, 2000) observations sometimes display Bohm-like scaling [Eq. (5)].…”

Safety factor scaling of energy transport in L-mode plasmas on the DIII-D tokamak

“…In this equation, XB -T/eBT is the Bohm diffusion coefficient, q -cBT/Bp is the safety factor, p* -f l / a B T , , 8 -nT/B$, v -na/T2, e is the charge of an electron, a is the plasma minor radius, E is the inverse aspect ratio, n is the plasma density, T is the plasma temperature, and Bp and BT are the poloidal and toroidal magnetic field strengths. It is usually assumed that the transport dependencies on the various dimensionless variables can be separated; therefore, the scaling of energy transport with the safety factor can be written in the form This type of power law dependence for q is actually not expected in general since the safety factor affects not only the linear growth rate of the mode but also the critical gradient for the mode onset [25].…”