Table of contents

If the power lost by impurity radiation from the low-temperature boundary region of a confined plasma exceeds the power transported from the central region then temperature equilibrium is impossible and the temperature profile will collapse. This situation is studied on the assumption of coronal equilibrium and the results are used to predict the permissible impurity concentration at the edge of a tokamak reactor. The effect of neoclassical impurity transport is studied analytically and a 1D tokamak diffusion code is used to illustrate the detailed collapse of the temperature profile when the plasma density in a radiation-cooled tokamak is increased. Finally, the results are used to predict the limiting density of a radiation-cooled tokamak; this predicted density limit is compared with the density limits observed in current tokamak experiments.

Classical transport of particles and heat in field-reversed mirrors is discussed. The X-points (field nulls on axis) are shown to have no deleterious effect on transport; this conclusion is true for any transport model. For an elongated Hill's vortex equilibrium the classical diffusion coefficient is calculated analytically and used to construct an analytic solution to the transport equation for particles or energy ; this yields exact results for particle and energy confinement times. These life-times are roughly 3 to 6 times shorter than previous heuristic estimates. Experimentally determined life-times are within a factor of 3 to 4 of our estimates. To assess the impact of these results on reactor designs, the authors construct an analytic reactor model in which neutral-beam input balances ion heat loss. Energy loss due to synchrotron radiation is calculated analytically and shown to be negligible, even with no wall reflection. Formulas are presented which give the reactor parameters in terms of plasma temperature, energy multiplication factor Q, and allowed neutron wall loading. The effect of anomalous resistivity is incorporated heuristically by assuming an anomalous resistivity which is enhanced by a factor A over classical resistivity. For large A the minimum power of a reactor scales as A^11/6. A = 50 gives a reactor design which still seems reasonable, but A = 200 leads to extremely large, high-power reactors.

The ×/B² drift arising from an externally applied electric field could be used in the divertor scrape-off zone of a tokamak or other toroidal device, either assisting or replacing a conventional magnetic field divertor. In an experiment in the Wisconsin Levitated Toroidal Octupole, operating with a relatively large toroidal magnetic field (q = 0.7), a radial electric field was applied in the scrape-off zone of a poloidal magnetic divertor. This reduced the plasma flux reaching the wall of the toroid by up to a factor of five beyond the effect of the magnetic divertor, in good agreement with a simple theoretical model. Plasma density and density scale-length were also reduced in the scrape-off zone, in qualitative agreement with the model, and with no detrimental effects on confinement of the central plasma.

The horizontally scanning charge-exchange analyser on the Princeton Large Torus (PLT) was used to measure fast co-moving ions during counter-injection of neutral beams. The large flux of charge-exchange neutrals observed in the near-parallel direction under these circumstances exhibited a sharp cut-off as the analyser was scanned to a fully parallel aiming angle. At a fixed particle energy, the cut-off angle showed a strong dependence on the plasma current, which can be predicted by using finite-banana-width tokamak orbit theory. Monte-Carlo calculations using a Fokker-Planck formalism and full toroidal geometry give substantive agreement with the experimental data, indicating that banana-trapping effects on neutral-beam-injected ions were directly observed.

A heavy-ion beam propagating through a vacuum reactor vessel suffers phase-space distortion caused by anharmonic self-forces. If the distortion remains uncorrected, an enlarged focal spot results. Analytic predictions of an increase in root-mean-square emittance and focal-spot size are presented and shown to agree with computer simulation. The resulting constraints on heavy-ion fusion-system design are discussed, together with possible means of relaxing these constraints.

Nuclear elastic scattering is included in the analysis of ignition condition and thermal instability in pure and catalysed D-D fusion reactor plasmas. Nuclear-elastic-scattering events take place, to some extent, during the slowing-down of energetic fusion products and enhance the heating of the background ions. The inclusion of this effect relaxes the minimum of the confinement requirement for self-sustained D-D plasmas by about 15%. It enhances, however, the thermal instability of the plasma, leading to an increase in the critical temperature.

Radiation and charge-exchange losses in the PLT tokamak are compared for discharges with Ohmic heating only (OH), and with additional heating by neutral beams (NB) or RF in the ion cyclotron frequency range (ICRF). Spectroscopic, bolometric and soft-X-ray diagnostics were used. The effects of discharge cleaning, vacuum wall gettering, and rate of gas inlet on radiation losses from OH plasmas and the correlation between radiation from plasma core and edge temperatures are discussed. – For discharges with neutral-beam injection the radiation dependence on type of injection (e.g. co-injection versus counter- and co- plus counter-injection) was investigated. Radial profiles of radiation loss were compared with profiles of power deposition. Although total radiation was in the range of 30–60% of total input power into relatively clean plasma, nevertheless only 10–20% of the total central input power to ions and electrons was radiated from the plasma core. The radiated power was increased mainly by increased influx of impurities, however, a fraction of this radiation was due to the change in charge-state distribution associated with charge-exchange recombination. – During ICRF heating radiation losses were higher than or comparable to those experienced during co- plus counter-injection at similar power levels. At these low power levels of ICRF heating the total radiated power was ∼ 80% of auxiliary-heating power. Radiation losses changed somewhat less rapidly than linearly with ICRF power input up to the maximum available at the time of these measurements (0.65 MW).

Neutral-beam power of up to 1.2 MW injected into the plasma has produced a volume-averaged ⟨β⟩ of up to 2.6% and a central beta β₀ of up to 7%, due to the thermal components in the JFT-2 tokamak. In these beam-dominated discharges, the magnetohydrodynamic behaviour was studied. Four types of internal oscillations were observed: i) enhanced sawtooth oscillations with long repetition time and large sawtooth amplitude; ii) round sawtooth oscillations and/or reduced sawtooth oscillations with short repetition time and small sawtooth amplitude; iii) high-frequency oscillations without sawtooth oscillations, and iv) high-frequency oscillations with sawtooth oscillations. The measured beta values are compared with the critical ones as found from high-n ballooning-mode analysis, and the relationship between MHD behaviour and beta values is also investigated.

An experimental study of low-frequency turbulence with wavelengths ranging from 2.5 to 0.4 cm in the WT-1 Tokamak is carried out by HCN laser scattering. It is found that the higher-frequency fluctuations are contained in the inner and the lower-frequency ones in the outer part of the plasma column.

The transport of small amounts of silicon and aluminium injected into plasmas in the Impurity Study Experiment (ISX) tokamak is studied. By monitoring the time behaviour of ultra-violet spectral lines emitted by various charge states of those impurities and comparing this behaviour to the predictions of a multi-species impurity transport code, it is found that both impurity penetration times and impurity containment times are consistent with neoclassical predictions. The observed impurity containment times, which are greater than three times the energy containment time, are consistent with the inward convection predicted by neoclassical theory.

The heating efficiency of a negative theta-pinch with reversed bias field is studied by comparing it with that of an ordinary theta-pinch. For this purpose, a high-voltage Z-discharge pre-heat system with short current duration was developed, and by using the highly ionized pre-heat plasma with good reproducibility as the initial plasma, a comparison with the heating in negative and ordinary theta-pinches was carried out. The plasma energy and ion temperature were measured by a magnetic probe and a fast-neutral-particle detector. These measurements show that the heating efficiency in the negative theta-pinch is comparable to that in the ordinary theta-pinch with reversed bias field. Accordingly, the negative theta-pinch is an ideal method of producing and confining energetic plasma in the reversed-field configuration (RFC).

A time-dependent particle-tracking algorithm for the slowing-down of fast ions in solid pellets developed elsewhere is used for numerical simulations of the ion-beam-pellet interaction. Here the general expression of the stopping power in hot, dense plasmas is used. It is found that if the finite thermalization time of the ion in the slowing-down process is taken into account the implosion of the pellet is changed.

The possibility of improving the fuel burn-up fraction (of reducing the pumped-out fraction) by installing a palladium-alloy membrane on the duct region of the main evacuating system is investigated. The emphasis is mainly placed on a tokamak reactor with a divertor. It is shown that the burn-up fraction can be improved by a factor of three to four.

A sub-miliimeter-wave heterodyne receiver designed for a D₂O laser Thomson scattering ion temperature diagnostic has been used to measure the synchrotron emission from the Alcator A tokamak at 762 ± 11 GHz down to levels of 10⁻²⁰ W·Hz⁻¹. A comparison with predicted Thomson-scattered signal levels indicates that the measured background will be much lower except near the third electron cyclotron harmonic for fields near 9 T.