Table of contents

The azimuthal asymmetry introduced in tokamaks by the use of a finite number of toroidal field coils can lead to anomalously large particle and energy losses. The diffusion and ion heat transport coefficients associated with the ripple-induced drift of particles trapped in the usual banana orbits have been calculated and the results compared with the coefficients for neoclassical banana transport in axisymmetric tokamaks, transport governed by the dissipative trapped-ion instability, and the transport associated with particles trapped between the coil planes by the ripple field itself. The calculations were performed for an Experimental Power Reactor design and show that the losses due to the ripple-induced banana drifts can be a major limit on fusion reactor magnet design.

Time-and energy-resolved measurements of the confinement of runaway electrons in the LT-3 tokamak indicate that the runaway electrons undergo times of poor confinement and that higher energy runaways are less well confined.

Starting from the linearized Fokker-Planck-Poisson system for an unbounded plasma in a homogeneous magnetic field, the general electrostatic dispersion relation is derived taking collisions into account as a perturbation. The velocity integrations in the collisional term of the dispersion relation are performed exactly for any kind of electrostatic wave in a Maxwellian background plasma. A simple asymptotic method is developed to approximate the resultant expressions n i the hot-ion limit (ion Larmor radius much larger than wave-length). As an application, collisional damping rates γ_c are calculated for ion Bernstein waves and lower-hybrid waves. The resulting formulas are discussed, especially with regard to the possibility of heating thermonuclear plasmas by parametric excitation of ion Bernstein or lower-hybrid wave turbulence. It is shown, in particular, that ion Bernstein waves are extremely sensitive to ion-ion collisions: γ_c ≫ ν_ii;, where ν_ii is the ion-ion collision frequency. As a consequence, collisional damping rates are comparable, in this case, to parametric growth rates calculated from Vlasov's equation.

The evolution of a high-ß plasma after the initial dynamic phase is described by a multifluid (electrons, hydrogenic ions, neutrals, and impurities) model for a belt-pinch configuration. The numerical results obtained from the model agree with experimental findings from th e Garching Belt Pinch II. The power balance i s dominated by radiation losses for impurity percentages of 1-3%. Neutrals play a role for plasma densities ≲ 10¹⁴ cm−³ . Energ y confinement times, and thus decay times for ß in the ms-range should be obtainable. An optimization is presente d for plasmas whose initial densities, temperatures, and impurity contents are produced by shock heating

The requirements placed on a tokamak Ohmic heating system (i.e. loop voltage) to initiate the plasma become more severe as the size increases because of the current density decrease. During the start-up phase even small concentrations of low-Z impurities can affect the plasma energy balance very substantially and have very important effects on the evolution of the discharge. The start-up phase has been studied using a simple zero-dimensional computer code. Since the dominant energy loss mechanisms during start-up, radiation and ionization, are a volume effect, the zero-dimensional code was adequate to treat this phase. The results of this study which have been applied to TFTR indicate that the plasma evolution is a sensitive function of the applied loop voltage, impurity concentration, initial filling pressure and the manner in which gas is fed into the discharge.

On the assumption that the main reason for the escape of α-particles from plasma is turbulent diffusion, the authors find the fraction of thermonuclear reaction energy transmitted to the plasma, the flux of α-particles escaping from the plasma and the energy distribution of the particles. The energy distribution depends to a great extent on whether quasi-linear relaxation of the α-particle distribution function is appreciable or not. The case of negligibly small quasi-linear distortion of the α-particle distribution is examined, as well as the case where quasi-linear effects are dominant. It is shown that the energy spectrum of the α-particles leaving the plasma as a result of turbulent diffusion contains both slowed-down and accelerated ( > 3.5 MeV) particles.

The production of thermonuclear energy by the adiabatic compression of a ß ≫ 1-dense plasma by a cylindrical heavy liner is investigated. Energy yields and compression ratios are optimized as functions of the initial conditions (plasma temperature and nτ-product, liner inertia). D-T α-self–heating is computed by dividing the α-population into a Maxwellian cold part and a flat hot part. High-energy amplification requires α-self-heating and stability of the liner-plasma interface well after the turn-around time.

The flow rate of neutral carbon atoms during the initial start-up phase of an Ohmically heated plasma in th e FM-1 spherator was determined from the spatially resolved measurements of the carbon line radiation and independent measurements of spatial distribution of plasma density and electron temperature. This was accomplished by comparing the measured carbon line intensity with a numerical solution of time-dependen t couple d differential rate equations for several carbon ionization states. The differential equations used in the present model correspond to a spatially homogeneous medium. However, th e effects of plasma inhomogeneity were taken into account by calculating the plasma emission at each location using the experimentally measured electron density and temperature (i.e. the measured radial distributions of density and temperature were folded into the numerical calculations). The empirical flow rate of carbon atoms into the discharge. Γ_flow(t),was found to be Γ_flow(t)≃n_e(t)/τ_flow. where τ_flow was 30–100 ms depending upon discharge conditions

With the help of the energ y principle in tokamaks, a class of perturbations is studied, which, if unstable, cannot be stabilized by the toroidal main field. On the assumption of usual tokamak ordering and in the limit of infinite aspect ratio, these perturbations are shown to be minimizing among all axisymmetric perturbations. In the case of finite aspect ratio, a detailed stability analysis is carried out by using a constant-pressure surface-current model with elliptic, triangular or rectangular plasma cross-section. Definite stabilization by toroidal effects and by ß_p is demonstrated.

A one-dimensional, rectangular-co-ordinate, kinetic-ion fluid-electron model with a self-consistent treatment of anomalous resistivity is used to investigate ion reflection by imploding magnetic pistons for parameters of the University of Maryland High Voltage Theta Pinch. The model explains qualitatively several experimental features not explained by a previous two-fluid model, notably the high-energy ions (T_i≃10 keV) and low-density compression (n/n₀≃10), both caused by reflected ions. The model shows that ion reflection increases with initial density and ion temperature, and that fewer ions are reflected if the initial field is in the same direction as the applied piston field (parallel bias), rather than i n the opposite direction (antiparallel bias). The model also shows, for parameters considered, that the reflected ion beam is not thermalized by the ion-ion cross-field instability.

The equilibrium of an axisymmetric toroidal plasma in an external field (a so-called hybrid system) with free boundary and arbitrary cross-section is solved analytically in a curvilinear co-ordinate system by means of an expansion in the inverse aspect ratio. The results are expressed as general relation s between Fourier coefficients of flux functions. An expression for the vertical field maintaining non-circular plasma equilibrium and th e condition for beta-free confinement, under which the strength of the vertical field does not depend on plasma pressure, are derived. Some typical configurations are calculated numerically.

The paper investigates the non-potential (non-electrostatic) perturbations of a plasma contained in a toroidal magnetic trap of the tokamak type. The transverse wavelengths are assumed to be small in comparison with the ion Larmor radius. It considers the case of perturbations considerably extended along the lines of force of a magnetic field k_||qR < 1 (where k_|| is the longitudinal wave number, q the tokamak safety factor and R the radius of curvature of the magnetic axis). It is shown that in this case the dispersion relation for short-wavelength non-potential perturbations is affected substantially by the effects of the finite orbits of the transit ions. The dispersion relation for such perturbations is obtained; it differs substantially from that for similar perturbations in a straight magnetic field. It is pointed out that these perturbations can grow as a result of electron dissipation.

The behaviour of a plasma confined by a magnetic field is simulated by a variety of numerical models. Some models used on a short time scale give detailed knowledge of the plasma on a microscopic scale, while other models used on much longer time scales compute macroscopic properties of the plasma dynamics. In the last two years there has been a substantial increase in the numerical modelling of fusion devices. The status of MHD, transport, equilibrium, stability, Vlasov, Fokker-Planck, and hybrid codes is reviewed. Review articles on each of the preceding models, with the exception of hybrid codes, have been published during the past few years, hence in this paper the main features of the models are discussed along with a limited number of representative results. These codes have already been essential in the design and understanding of low- and high-beta toroidal experiments and mirror systems. The design of the next generation of fusion experiments and fusion test reactors will require continual development of these numerical models in order to include the best available plasma physics description and also to increase the geometric complexity of the model.

There is a need for international co-operation in this field with particular emphasis on the exchange of programs and the establishment of fusion program libraries. The International Atomic Energy Agency has considered these issues and made specific recommendations.

The IAEA Advisory Group Meeting on the Technology of Inertial Confinement Experiments was held at the Joint Institute for Nuclear Research at Dubna, USSR, on 19–23 July 1976. The meeting reviewed progress and engineering problems of research on inertial confinement systems and discussed new conceptual designs of fusion reactors.