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 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, 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.

https://iopscience.iop.org/article/10.1088/0741-3335/44/8/201/pdf

Density limits in toroidal plasmas

The authors review spectroscopic work and impurity behaviour in laboratory plasmas devoted to controlled nuclear fusion research. A necessary prerequisite for this is a discussion of the atomic physics (rate coefficients, ionisation models and spectral emission) involved in the interpretation of plasma spectroscopic data. The largest part of this review is concerned with spectroscopic work in magnetically confined Tokamak plasmas and laser-produced, inertially confined, plasmas, since these two approaches have received the greatest attention. In Tokamak plasmas, impurity radiation constitutes an important loss process; it is therefore necessary to find ways to avoid impurity contamination. On the other hand, in inertial confinement, 'impurities' are necessary to absorb the beam energy and are, moreover, an essential diagnostic tool, particularly for the compressed material. Spectroscopic work of fusion interest in other laboratory plasma devices is also briefly reviewed.

http://iopscience.iop.org/article/10.1088/0034-4885/47/10/001/pdf

Spectroscopy and impurity behaviour in fusion plasmas

In the reversed-field pinch (RFP), the plasma is confined in an axisymmetric toroidal configuration by a combination of toroidal (B/sub phi/) and poloidal (Btheta/sub ) fields with B/theta /sub >> B/phi /sub outside the plasma and B/theta approx. = B/sub phi/ within the plasma. The essential property of the RFP equilibrium is that it is a near-minimum-energy relaxed state that the plasma finds naturally; the spontaneous generation of reversed toroidal field (dynamo process) is a consequence of this relaxation, and, if the plasma current is maintained, the field generation continues so that the configuration exists as a quasi steady state. Since such equilibria have little free energy to drive instabilities, the systems has good stability properties, and, theoretically, confinment at high beta is possible; the plasma current can be sufficiently high to allow the possibility of plasma ignition in deuterium-tritium by ohmic heating alone. Experimentally, values of poloidal beta typically 10% or more are usually observed, and conditions have been found in which the temperature is found to scale approximately linearly with the plasma current up to 0.5 MA; maximum temperatures of the order of 0.5 keV have been observed. This temperature scaling corresponds to a current dependence of themore » energy confinement time of I/sub phi//sup 3/2/. Ohmically heated RFP reactors are discussed with emphasis on improved designs with increased power density up to values comparable to those in fission systems.« less

The reversed-field pinch: From experiment to reactor

The main properties of experimental RFP magnetic profiles are reviewed and discussed in the context of relaxation theory. Relaxation phenomena under conditions of magnetic helicity conservation are a fundamental process determining both the formation and sustainment of the RFP magnetic distribution as well as plasma particle and energy confinement. In particular, the problem of magnetic helicity conservation both during the relaxation process and over longer timescales in driven systems is discussed. Relaxation mechanisms are reviewed and RFP dynamics is described in terms of cyclical diffusion, instability, and relaxation processes. Plasma relaxation interacts closely with heating and transport; its effects on ion heating and global confinement properties are discussed. Prospects including anticipated plasma performance in RFX are presented.

Reversed field pinch confinement physics

Density limits and scaling laws in reversed field pinches

The dependence of the measured radiation losses in ETA-BETA II on plasma density and plasma current rise time is discussed. A high-density limit is found, corresponding to large radiation. Above this limit, burning through the light impurities (mainly oxygen) does not take place and a cold, radiation-dominated discharge is obtained. This high-density limit scales with the plasma current, indicating a lower limit on the I/N parameter similar to the tokamak high-density limit. With longer current rise times the radiation energy loss during the set-up phase increases about linearly with rise time, corresponding always to about 50% of the total energy losses during this phase.

S. Ortolani

Papers

Total radiation measurements in the ETA-BETA II experiment