Confinement and Transport History

The physics of core plasma transport is believed to be well-described by the electromagnetic gyrokinetic equations.
In the limit that

^[1]

(often called the local-limit, or alternatively, the flux-tube approximation), the solution of these challenging equations is greatly simplified. Here, is the ion-sound gyroradius and is the plasma minor radius. Physically, this limit corresponds to a complete separation between the fluctuation scale and the system size. Although, in smaller tokamaks, profile shearing effects generally reduce transport below the flux-tube level, it is nevertheless accepted that the essential features of core turbulence are well-captured by the flux-tube limit. Existing tokamak transport models all use some variant of the flux-tube approximation at every radius. Microturbulence theories based on the flux-tube approximation, regardless of their particular formulation, will exhibit an intrinsic gyroBohm transport scaling, with the energy confinement time and fusion product scaling like

and ^[2]

respectively. At this point, it is useful to define

gyroBohm unit of diffusivity^[3]

Bohm unit of diffusivity^[4]

In 1990, GA pioneered the idea of using dimensionally similar discharges (these differ only in , with all other dimensionless parameters like beta, collisionality, safety factor, aspect ratio and shape invariant) to make theoretically-based extrapolations to ignition-sized tokamaks [Waltz 90]. At the time, these ideas for extrapolation were based on an intrinsic gyroBohm scaling assumption. However, the results of high-density L-mode experiments in DIII-D, and later in TFTR and JET, failed to observe gyroBohm scaling and instead consistently saw Bohm or worse. Yet, low-density discharges with hot electrons and cold ions (ohmic or ECE heating) did show gyroBohm scaling of the energy confinement time. DIII-D experiments showed that the electron transport can be close to gyroBohm while the ion channel could be Bohm or worse [Petty 95b]. H-mode plasmas with good edge confinement can have channels gyroBohm although the H-mode power threshold is worse-than-Bohm [Petty 95a,Petty 97] . This suggests that the sub-gyroBohm scaling may originate in the plasma edge. Despite the departure from gyroBohm scaling in many tokamak discharges, it was found, that gyroBohm transport models can, remarkably, give satisfactory fits even to discharges which have sub-gyroBohm scaling [Waltz 92a,Kinsey 96,Konings 97] .

During the past decade, there have been considerable advances in our theoretical understanding of the finite- corrections to transport scaling, and in our ability to formulate comprehensive theory-based transport models which describe not only L- and H-mode core confinement but also enhanced confinement regimes.

1. ↑ the recognition that profile shear and ExB velocity shear break the scale separation required for gyroBohm scaling [Garbet 96] and is a key mechanism for transport bifurcations to improved confinement regimes
2. ↑ toroidal flux-tube gyrofluid [Waltz 92b] simulations of ion temperature gradient (ITG) modes at GA [Waltz 94,Waltz 95] and PPPL [Beer 96a,Beer 96b] provided a database of simulations which provided the basis for gyrofluid transport models such as the IFS/PPPL model [Kotschenreuther 95] and the more comprehensive GLF23 model [Waltz 97]
3. ↑ the ITER Transport Profile Database reached a maturity with more than 60 discharges from DIII-D, TFTR, JET, JT-60 and others, and statistical procedures were developed for detailed comparison of models
4. ↑ the ever-increasing availability of high-performance computing platforms combined with advances in algorithms to solve the gyrokinetic equations has allowed us to simulate DIII-D plasmas with sufficient accuracy to match the experimentally-observed power flows.