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.

In addition to the operational limits imposed by MHD stability on plasma current and pressure, an independent limit on plasma density is observed in confined toroidal plasmas. This review attempts to summarize recent work on the phenomenology and physics of the density limit. Perhaps the most surprising result is that all of the toroidal confinement devices considered operate in similar ranges of (suitably normalized) densities. The empirical scalings derived independently for tokamaks and reversed field pinches (RFP) are essentially identical, while stellarators appear to operate at somewhat higher densities with a different scaling. Dedicated density limit experiments have not been carried out for spheromaks and field-reversed configurations (FRC), however "optimized" discharges in these devices are also well characterized by the same empirical law. In tokamaks, where the most extensive studies have been conducted, there is strong evidence linking the limit to physics near the plasma boundary thus it is possible to extend the operational range for line-averaged density by operating with peaked density profiles. Additional particles in the plasma core apparently have no effect on density limit physics. While there is no widely accepted, first principles model for the density limit, research in this area has focussed on mechanisms which lead to strong edge cooling. Theoretical work has concentrated on the consequences of increased impurity radiation which may dominate power balance at high densities and low temperatures. These theories are not entirely satisfactory as they require assumptions about edge transport and make predictions for power and impurity scaling that may not be consistent with experimental results. A separate thread of research looks for the cause in collisionality enhanced turbulent transport. While there is experimental and theoretical support for this approach, understanding of the underlying mechanisms is only at a rudimentary stage and no predictive capability is yet available..