Table of contents

A simple, zero-dimensional model describing the temporal behaviour of an imploding-shell, magnetized fuel inertial confinement fusion target is formulated. The model includes effects not normally considered in inertial confinement fusion such as magnetic back-pressure on the imploding shell, magnetic reduction of thermal conductivity, magnetic diffusion, and Ohmic heating. The model is simple enough to permit a survey of the parameter space available for magnetized fuel by computing the behaviour of thousands of targets. The survey predicts the existence of a totally new region in parameter space where significant thermonuclear fuel burn-up can occur. The new region is characterized by very low fuel densities, very low implosion velocities, and,most important, driver requirements reduced by several orders of magnitude, suggesting that "break-even" experiments may be possible with existing inertial confinement fusion drivers. The computed results are in reasonable agreement with more complete two-dimensional magnetohydrodynamic simulations.

Experiments to investigate the scaling of volume-averaged beta <β> and a global energy confinement time for neutral-beam-heated (P_b ≤ 2.5 MW) discharges in the ISX-B tokamak are described. The results are condensed into a set of empirical scaling formulas which can be used as a guide for other theoretical and experimental studies of confinement in high-beta, neutral-beam-heated plasmas. The dependence on toroidal field B_T, plasma current I_p, and line-averaged electron density _e was determined by varying each of these while keeping other external variables fixed. Magnetic diagnostics were used to obtain global properties, and Thomson-scattering-based profile analysis was carried out to permit more detailed investigation of selected cases. The poloidal beta, β_p, is found to be independent of B_T and _e at fixed beam power P_b; confinement is found to deteriorate with increasing P_b but to improve with I_P, consistent with previous results. The mechanisms which govern this confinement scaling have not been discerned, but it apparently does not depend on ⟨β⟩, B_T, or the (m = 1; n = 1) MHD activity, which typically dominates the MHD diagnostic signals. Losses are primarily through the electron channel, and the scaling of electron energy confinement time is similar to that of .

The effect of poloidal divertor geometry on the exhaust of impurities is studied experimentally. In the expanded-boundary geometry, strong accumulation of argon in the divertor region and minimal reflux into the main plasma are observed. A simple model provides an explanation for the observations and leads to the conclusion that the two key geometrical factors for effective impurity control are an expansion of the divertor channel and a narrow gap between the divertor channel and the wall.

The characteristics of EUV emissions from the ionization states of injected impurities which exist outside the core of the Alcator A plasma (r/a ≥ 0.5) are presented. These results are compared with the emissions from the core ionization states to investigate their radial dependence. In deuterium discharges, the ionization states of silicon which exist outside the core (e.g. Si XII) have shorter decay times than those of the core states (e.g. Si XIII), but the scalings of the decay times with plasma current and toroidal field are similar for the two ionization states in the two regions. The difference between the decay times of the ionization states in the two regions increases as the mass of the background ion is increased (³He and ⁴He discharges). The behaviour of other injected impurities (Al, Fe, and Mo) is presented; it is also observed that the decay times of the ionization states of these impurities which exist outside of the plasma core are shorter than the corresponding core states. The difference in the decay times is modelled with a computer code and is found to be qualitatively consistent with a radially constant spreading diffusion coefficient with no (inward) convection.

The maximum electron density and confinement time of Ohmically heated tokamaks can be limited by radiation losses. This has been investigated with a 1-D electron energy balance, used to derive current density distributions. Application of ideal-MHD stability criteria then leads to closed regions of stability in (I, n_e)-space. Subsequent application of resistive-MHD theory indicates many possible causes of the disruptive instability and extends the ideal-MHD density limit by about 1.4 times. Murakami scaling, modified by a term involving the plasma effective charge , arises naturally from the model and suggests that results should be plotted in (q⁻¹(a), (n_eR/B_t) )-space. Further, for heavy impurities, large divergences from Alcator scaling of τ_e are obtained within the stable region, leading to a peaking of τ_e versus n_e at a critical density which scales as q⁻¹ (a) B_t/R. The nτ-limit imposed by stability is found to further restrict the ignition region when referred to axial radiation losses only.

The main experimental results on confinement and transport processes in tokamaks are summarised. It is difficult to draw definite conclusions from measurements of the global energy containment time even in the quasi-steady phase of those ohmically heated discharges, which do not exhibit gross instability or appreciable effects due to runaway electrons. However, comparison of particle and energy confinement suggests that the loss process is mainly conduction rather than convection. In order to separate the various energy input and loss mechanisms the assumptions of classical ohmic heating and equipartition are made. The experimental evidence for these assumptions is presented. The dominant energy transport process is electron thermal conduction, for which a formalism is suggested for comparing experimental data with various theoretical models. Particle and iimpurity transport appears to require the neoclassical pinch tenn in addition to anomalous particle diffusion at a significantly lower rate than electron conduction. The contribution of the sawtooth instability to transport can be measured in principle and is only important in certain conditions. 1-D models of the discharge are quite successful provided empirical forms of the electron conduction and particle diffusion are used. Partial dat a exists on various related topics: plasma rotation, radial electri c fields, the boundary layer, the effects of toroidal field ripple and low frequency instabilities. This material is summarised.

Magnetic-compression heating may invert the velocity distribution of alpha particles and lead to the possibility of exciting velocity space instabilities. A sufficient stability condition is derived for these modes in compression-heated tokamaks. A high-field high-density compression scenario like Zephyr satisfies this stability condition, while a medium-field high-temperature compression scheme like TFTR or a rather fast and strong compression scheme like T-14 has some chance t o excite velocity-space thermonuclear instabilities.

A comparison between the approximate analytic formulae of Shafranov for equilibrium in axisymmetric toroidal systems and fully toroidal numerical solutions of the Grad-Shafranov equation for reversed-field-pinch (RFP) configurations is presented as a function of poloidal beta, internal plasma inductance, and aspect ratio. The Shafranov formula for the equilibrium poloidal-field distribution at the conducting shell that surrounds the plasma is accurate to within 5% for aspect ratios greater than 2, poloidal betas less than 50%, and for plasma current channels that exceed one third of the minor toroidal radius. The analytic description for the centre shift of the innermost flux surface that encloses the plasma current (the Shafranov shift) is accurate to within 15% for aspect ratios greater than 2 and poloidal betas below 50%, provided the shift does not exceed one tenth of the minor conducting boundary radius. The Shafranov formulae provide a convenient method for describing the gross equilibrium behaviour of an axisymmetric RFP discharge, as well as an effective tool for designing the poloidal-field systems of RFP experiments.

Equilibria of a toroidal stellarator plasma with a pressure tensor of the form are calculated to high accuracy within the framework of a low-beta expansion previously employed to find scalar-pressure equilibria. Expressions are obtained for various quantities such as the vertical field and the magnetic-axis shift which are important experimentally; when the helical field is allowed to go to zero, results previously derived for tokamaks are obtained in each case.