A new look at density limits in tokamaks

Abstract

While early work on the density limit in tokamaks from the ORMAK [1] and DITE (2,3] groups has held up well over the years, results from recent experiments and the requirements for extrapolation to future experiments have prompted a new look at this subject. There are many physical processes which limit attainable densities in tokamak plasmas. These processes include 1) radiation from low Z impurities, convection, charge exchange and other losses at the plasma edge, 2) radiation from low or high Z impurities in the plasma core, 3) deterioration of particle confinement in the plasma core, and 4) inadequate fueling, often exacerbated by strong pumping by walls, limiters, or divertors.Depending upon the circumstances, any of these processes may dominate and determine a density limit. In general, these mechanisms do not show the same dependence on plasma parameters. The multiplicity of processes which lead to density limits with a variety of scaling, has led to some confusion when comparing density limits from different machines. In this paper we attempt to sort out these various limits and extend the scaling * Present address: Shin-Etsu Chemical Co., Ltd., 2-13-1, Isobe Annaka, Gunma, Japan 1 law for one of them to include the important effects of plasma shaping, namely that iK, = x 7 where n, is the line average electron density (1020 / M 3 ), x is the plasma elongation and 7 ( MA / M 2 ) is the average plasma current density, defined as the total current divided by the plasma cross sectional area. In a sense this is the most important density limit since, together with the q limit, it yields the maximum operating density for a tokamak plasma. We show that this limit may be caused by a dramatic deterioration in core particle confinement occurring as the density limit boundary is approached. This mechanism can help explain the disruptions and marfes that are associated with the density limit.

ITER edge database investigations of the SOL width

“…Hence, T es can often be replaced by n e . The Greenwald parameter n eGW 10 14 s p ap min 2 [17] is introduced as a variable in the form n e /n eGWX q95 in combination with j, R mag or S area ($ j 0X5 min mag ) is used, although the connection length ($ j 0X7 q95 mag ) does just as well on occasion (not shown). P tot emerges as a more robust parameter over the database than P sol P tot À P rad .…”

Physics basis for a spherical torus power plant

“…The profile interface with the ARIES Systems Code (ASC) for ARIES-ST designs are summarized in Table 3. The line-average electron density of the ARIES-ST plasma slightly exceeds the Greenwald limit [61], given bȳ…”

The operational phase-space of the edge plasma and its sensitivity to magnetic topology in Alcator C-Mod

“…These discharges had four different combinations of plasma current and toroidal magnetic field ( I p , ! n G is the Greenwald density [10]. In all cases, the direction of plasma current and magnetic field was held fixed, with Bx∇B pointing down.…”