Table of contents

A neoclassical theory applicable to the central region of a reactor tokamak plasma is developed for high-energy alpha-particle transport processes. It is shown that in the neighbourhood of the magnetic axis (and on the axis itself), the alpha-particle bootstrap current and flux across the magnetic field are non-zero and may be comparable with the corresponding quantities in the region far from the axis.

The interaction between shear Alfvén perturbations and the charged high-energy particles produced by fusion reactions is investigated. The aim is to evaluate the conditions that must be realized in order for the quasi-linear diffusion flux of the fusion products to become significant. It is found that in the most relevant cases a severe deterioration in the confinement properties of the fusion products is not to be expected. This result follows from taking explicitly into account the spectral properties of shear Alfvén perturbations in a toroidal configuration with magnetic shear.

A systematic comparison of charge exchange and neutron flux measurements with a Monte-Carlo simulation code solving the full Fokker-Planck equation has shown that the fast-ion behaviour in TFR 600, with quasi-perpendicular injection, can be explained classically. This important conclusion permits the beam energy deposition and the energy given to the plasma electrons and ions to be calculated so that the energy balance of the plasma can be obtained.

An analytic expression for the Coulomb collision induced ion trapping rate in the thermal barrier cell of a tandem mirror has been obtained. The overall system is assumed to be maintained in steady state by particle injection in the central cell and charge-exchange pumping in the barrier cell. For small ratios of bounce-to-collision time scales the problem reduces to a series of boundary value problems in the various regions of phase space. For conditions of interest, pitch-angle trapping is dominant and a Lorentz collision operator describes reasonably well the kinetic problem, which is solved using a square-well approximation. The analytic results are found to agree with numerical results within expected limits, on the order of the inverse of the barrier/mirror ratio (∼ 10 to 20%).

The paper describes a method, as implemented in the computer code ZORNOC, for the analysis of high-beta, non-circular ISX-B tokamak plasma profiles. Thomson scattering electron temperature and density profiles, obtained at a fixed time into the discharge, are used as a basis for performing a complete energy analysis of the plasma and for obtaining confinement parameters assuming steady-state conditions. Self-consistent models for both magnetohydrodynamic equilibrium and ion power balance are used to obtain internal flux surface and ion temperature profiles, respectively, consistent with all the known diagnostic data. Using boundary conditions consistent with poloidal magnetic measurements, a current profile parameterization is obtained that is consistent with the observed location of the q = 1 surface as indicated by soft X-ray diagnostics. A specific high-beta discharge is analysed in order to illustrate the procedure.

The close coupling in the stellarator/torsatron/heliotron between coil design (winding law, peak field, current density, forces), magnetics topology (transform, shear, well depth) and plasma performance (equilibrium, stability, transport, beta) complicates reactor assessment more than for most magnetic confinement systems. In order to provide an additional degree of resolution of this problem for the Modular Stellarator Reactor (MSR), a parametric systems model has been developed and applied. This model reduces key issues associated with plasma performance, first-wall/blanket/shield and coil design to a simple relationship between beta, system geometry and a number of key indicators of overall plant performance. The results of this analysis can then be used to guide more detailed, multidimensional plasma, magnetics and coil design efforts towards technically and economically viable operating regimes. In general, it is shown that average beta values of ≤0.08 may be needed if the MSR approach is to be substantially competitive with other projected approaches to DT magnetic fusion in terms of system power density, mass utilization and cost for total thermal output power around 4.0 GW(th); lower powers will require even higher beta values.

Ion cyclotron resonance heating (ICRH) and its intrinsic effect on confinement in tokamaks is investigated. The stochastic nature of ICRH in the absence of collisions is examined through finite-mapping equations. The threshold RF amplitude for the transition from superadiabatic to stochastic behaviour is found to be exceeded in present-day experiments. The effect of heating on confinement is evaluated by studying the drift orbit changes due to heating with collisions included through a Monte-Carlo method. The results indicate that transport induced by the ion cyclotron range of frequencies (ICRF) could be significant at the higher RF power levels planned for the next generation of experiments.

Current generation by asymmetric heating of a minority ion species in the ion cyclotron range of frequencies is calculated in the weak RF limit in toroidal geometry. Both trapped ions and trapped electrons produce significant modifications to the current generated. Depending on the ratio of the charge of minority to majority species, the current generated can be either sharply peaked at the centre or flattened towards the outside.

Probe measurements of the edge plasmas of the Macrotor and Microtor tokamaks are described. Limiter scrape-off layer thicknesses as measured with Langmuir probes are for Macrotor λ≅7–10 cm and for Microtor λ ∼ 1 cm, both values being consistent with the Bohm diffusion rate. Heat deposition measured with thermocouples attached to small probes shows an anomalously high heat flux, particularly from the electron drift direction. It is argued that the anomalous particle diffusion is most likely associated with the large edge density fluctuations, while the anomalous heat flux is most likely due to a directed high-energy electron population.

With an ultra-soft X-ray pinhole camera, installed on the Wendelstein VII-A stellarator, changes of the plasma topology have been measured for various plasma conditions over several years. A recently finished tomography computer code, specifically written for pinhole cameras, has yielded detailed information about the time evolution and structure of tearing modes during internal and external disruptions. The features of the m = 1 tearing mode during an internal sawtooth disruption in a current-carrying stellarator plasma during neutral beam injection are presented.

The effect of magnetic-field 'ripple' on alpha particles trapped in the major radial variation of the magnetic field in a tokamak reactor is to make their orbits stochastic so that they can escape from the plasma volume extremely rapidly. A guiding-centre orbit-following code is used to investigate the extent of the stochastic region in a reactor with INTOR parameters, and to compare the results so obtained with the predictions of an analytic map developed by Goldston et al. to model the banana orbits. Although the analytic map qualitatively reproduces the main trends observed in the guiding-centre orbits, differences in detail occur whose origins are discussed.

Using a neutral-beam injection power of 3.4 M W, volume-averaged toroidal betas of up to ⟨β_T⟩ = 4.5% have been obtained in low-toroidal-field, low-qψ, vertically elongated discharges in the Doublet III tokamak. This level of ⟨β_T⟩ is above the minimum level required for a tokamak reactor, thus demonstrating that reactor level values of ⟨β_T⟩ are possible in a tokamak device. The observed enhancement of ⟨β_T⟩ with vertical elongation lends confidence in the design of future devices which rely on vertical elongation.

The authors have investigated quasi-linear ion Landau damping of lower hybrid waves in an inhomogeneous plasma. To this end, they have simultaneously solved Maxwell equations and the ion kinetic equation, starting from the antenna and proceeding towards the centre of a plane-layered plasma. As a consequence of the development of a suprathermal tail in the ion distribution function, the efficiency of the absorption increases and the absorption region is found to shift to lower densities as the launched power increases. Absorption is always complete at the layer where the wave phase velocity equals about three times the local ion thermal velocity, usually somewhat before the linear turning point is reached.