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.

Plasma profiles and flows in the low-and high-field side scrape-off layer (SOL) regions in Alcator C-Mod are found to be remarkably sensitive to magnetic separatrix topologies (upper-, lower-, and double-null) and to impose topology-dependent flow boundary conditions on the confined plasma. Near-sonic plasma flows along magnetic field lines are observed in the high-field SOL with magnitude and direction clearly dependent on x-point location. The principal drive mechanism for the flows is a strong ballooning-like poloidal transport asymmetry: parallel flows arise so as to re-symmetrize the resulting poloidal pressure variation in the SOL. Additionally, the decrease in cross-sectional area of a magnetic flux tube connecting from low to high-field regions appears to act as a 'nozzle', increasing flow velocities in the high-field SOL. Secondary flows involving a combination of toroidal rotation and Pfirsch-Schlüter ion currents are also evident. As a result of the transport-driven parallel flows, the SOL exhibits a net co-current (counter-current) volume-averaged toroidal momentum when B × ∇B is toward (away from) the x-point. Depending on discharge conditions, flow momentum can couple across the separatrix and affect the toroidal rotation of the confined plasma. This mechanism accounts for a positive (negative) increment in central plasma co-rotation seen in L-mode discharges when B × ∇B is toward (away from) the xpoint. Experiments suggest that topology-dependent flow boundary conditions may also play a role in the sensitivity of L-H power threshold to x-point location: in a set of otherwise similar discharges, the L-H transition is seen to be coincident with central rotation achieving roughly the same value, independent of magnetic topology. For discharges with B × ∇B pointing away from the x-point (i.e., with the SOL flow boundary condition impeding co-current rotation), the same characteristic rotation can only be achieved with higher input power.