Table of contents

Results of experimental investigations on ultra-rapid heating of a dense plasma in a linear θ-pinch and switching of megampere currents in the supply system based on the application of an inductive energy accumulation method are presented. Magnetic fields of up to 50 kG with rise-times of approximately 0.2 μs were generated in a solenoid 7 cm in diameter and 50 cm long. The following plasma parameters were obtained: n_e = (2−5) × 10¹⁶ cm⁻³, k(T_e + T_i) = 1−1.5 keV.

Multiple-mirror magnetic confinement is investigated experimentally with a pulsed hydrogen plasma produced by a theta-pinch source. The gun output at the end of the guide field between the theta-pinch coil and the multiple-mirror region was a sharp plasma pulse of strength ∼10¹⁴ cm⁻³ with a ratio of drift to thermal velocity close to unity (∼ 10 eV). The seven multiple-mirror cells were stabilized with a linked quadrupole field. Transient experiments were performed with hydrogen in the favourable multiple-mirror regime (n ∼ 10¹³ cm⁻³, T ∼ 10 eV) where the ion mean free path is comparable to a cell length. The quadrupole field achieved partial plasma stabilization and the plasma lifetime inside the device was increased from 10–30 μs in the unstabilized simple mirror geometry to 50–80 μs at high values of the stabilizing current. The plasma pulse was successfully injected into the multiple-mirror region but was mainly trapped in the first half of the device, because of a non-uniform introduction region of two cells and because of the low value of the pulse drift velocity. The main features of the plasma build-up and decay were studied analytically and numerically with a simple simulation of the experiment. The numerical results were in qualitative agreement with the density profiles observed experimentally inside the device. The strong density gradients, obtained at the large values of the quadrupole current for which the flux surfaces are strongly elliptical, greatly enhanced the classical radial losses, particularly from ion-ion collisions. When included in the numerical model, the theoretical radial loss rates indicated a significant (up to 30%) decrease of the plasma lifetime inside the multiple mirror for the large values of the quadrupole current necessary for stability, in reasonable agreement with the experimental results.

A free-boundary MHD equilibrium code is used to determine the plasma shape and toroidal current distribution in highly elongated Garching Belt Pinch II equilibria (b/a = 10–14). The parameters of the calculations are optimized to fit the experimental boundary conditions as well as the measured axial profiles of B_z and the values of ⟨β⟩ and ⟨β_p⟩. It is found that the plasma surfaces come close to a racetrack shape, and that the current density can be roughly described by j_t = c_opr + c_oF/r for diamagnetic plasmas and j_t = c_opr for ⟨β_p⟩ = 1. This corresponds to extremely elongated inner flux surfaces, moderate gradients of the q profile and plasma pressure and toroidal field distributions which are almost axially homogeneous. The production and the time development of such j_t profiles are discussed.

Conceptual DT and DD fusion reactors are discussed based on magnetic confinement with the high-plasma-density Z-pinch. The reactor concepts have no "first wall", the fusion neutrons and plasma energy being absorbed directly into a surrounding lithium vortex blanket. Efficient systems with low re-circulated power are projected, based on a flow-through pinch cycle for which overall Q values can approach 10. The conceptual reactors are characterized by simplicity, small minimum size (100 MW(e)) and by the potential for minimal radioactivity hazards.

The steady-state energy distribution function of alpha (α)-particles is derived in an analytical form by directly solving the Fokker-Planck (FP) equation in an approximate manner under the assumption that the functional dependence of the α-particle confinement time τ_α(E) on its energy is given by τ_α(E) ∝ E^-ℓ (ℓ is a constant). In addition, a new retardation theory is proposed on the basis of the FP equation under the same assumption. Finally, this proposed retardation theory is applied to dynamic problems of an α-particle-heated DT-reactor through the introduction of what is called a "dynamic response (matrix) function", the result of which enables us to discuss quantitatively problems such as thermal instability and control without numerical analysis of the FP equation.

A study of the coupling and propagation of electron plasma waves excited by waveguide arrays is presented. The waves are generated in a low-temperature, linear plasma column in a homogeneous magnetic field. As predicted from a theoretical model, under appropriate conditions efficient coupling to plasma waves can be obtained. These studies are of relevance to plasma heating in that the modes are identical with those that must be generated in any lower hybrid heating experiment. We discuss the implications of these results with respect to future heating experiments on large devices.

Measurements of ion temperatures in the ATC tokamak by means of Doppler broadening of various ion lines are described, and typical results presented for the various auxiliary heating experiments: compression, neutral beam, lower hybrid and ion cyclotron frequency heating. Radial resolution of the temperature measurements is achieved by utilizing spectrum lines of ions of different ionization potentials: O VII λ 1623 Å, C V λ 2271 Å and C IV λ 1548 Å, which are emitted from regions of different electron temperature. Measurement at a given radial location is performed as a function of time by repeated scanning of the line contour in times 1.5–3.0 ms. The results indicate variations of heating efficiency with location and with power input level.

The plasma physics and engineering constraints determining the minimum size of a tokamak reactor are analysed. Three different models of increasing complexity are considered: (1) a simplified plasmaengineering model for a preliminary choice of the parameters, (2) a self-consistent model based on a spaceaveraged (zero-dimensional) plasma power balance, and (3) a self-consistent model including the profile effects on the power balance as provided by the Duchs code. As a reference example, the parameters of a minimumsize experimental reactor (Fintor 1) are deduced, assuming that plasma confinement not worse than 10 times below neoclassical is possible and adopting conservative technological feasibility conditions. The main parameters resulting are a minor plasma radius a = 2.25 m, an aspect ratio A = 4 and a magnetic field on axis of B_T0 = 3.5 T. A sensitivity analysis of the effects of changes in the main input parameters is performed. As an example of a different assumption on plasma transport, the case of losses induced by the trapped-ion instability is touched upon. The method exposed can readily be used to deduce the parameters of reactors of given (not minimum) power or wall loading.

Standing modes along the magnetic field lines and with frequencies between the mean ion transit and electron bounce frequencies are driven unstable by a combination of effects including inverse Landau damping, collisional de-trapping of electrons and magnetic curvature drifts in a magnetically confined plasma. The mode phase velocity, depending on the plasma parameters and on the mode perpendicular wavelength, is either in the direction of the electron diamagnetic velocity (electron drift mode) or in the direction of the ion diamagnetic velocity (ubiquitous mode). An intermediate region exists where the mode becomes fluid-like and is driven by the magnetic curvature drift. This fluid-like instability is shown to appear for wavelengths longer than the ion gyroradius and is expected to affect significantly the rate of particle and thermal energy transport in high-temperature toroidal-confinement devices.

The transport properties of an axisymmetric toroidal plasma containing an arbitrary number of impurity species are considered for the case that all species are in the collision-dominated regime. Energy transfer between the different species, and in particular between electrons and ions, is taken into account. This yields expressions for the particle and heat fluxes applicable to a wide range of parameters.

A theoretical and computational study of a tokamak boundary in contact with a limiter is given. Parallel field flows of plasma and heat induced by the sheath conditions at the limiter are treated with model sources and sinks in the cross-field transport equations. A charge-exchange neutral code is used for the re-cycled neutrals. It is found that the boundary conditions at the limiter radius have little effect on the energy flow to the boundary unless the ionization zone is well attached to the limiter. Exemplary heuristic boundary conditions useful for transport codes are given. The partitions of particle and energy flow to the limiter and wall are discussed.

This paper presents the results of measurements of space-charge effects on the efficiency of a direct converter. The device consists of a 22-stage, electrostatic periodic-focusing, direct energy converter, a magnetic expander, and a hydrogen plasma source. At low beam density, the measured average efficiency is 86.5 ± 1.5% as compared with the predicted one of 88.6 ± 1.5%. At higher beam density, the measured efficiency decreases with increasing space charge in agreement with predictions. The effect of space charge is increased if the ion energy is decreased or if the energy distribution is made narrower. Design criteria for scaling the recovery system for a reactor show that this direct converter is probably economical only if the mean ion energy is greater than 500 keV. – In addition to presenting the space-charge measurements, this paper is intended to serve as a final summary of the authors' work on this type of direct converter.

Magnetohydrodynamic equilibria have been calculated numerically for a non-circular crosssection stellarator utilizing a three-dimensional, diffuse-plasma-profile, MHD code. Distinct minima of the poloidal field values were found in the vacuum which confirm the existence of stagnation points.

A method of calculating the wall loading due to fusion products escaping from the plasma in a tokamak is described. For this purpose, the small-banana-width approximation is eliminated, yielding an analytic formulation for high-energy orbits and associated loss-cone limits. Wall-loading profiles (as a function of poloidal angle) are presented for various experimental devices (PLT, TFTR, and ORNL-EPR) and for a typical reactor (UWMAK-I). Peak-to-average alpha flux ratios of the order of 1.4 to 2.3 combined with average fluxes of ∼ 10¹¹ alphas per cm² per second, suggest that localized blistering may be a serious source of impurity atoms as well as a wall erosion mechanism. Special wall panels in regions of high flux are suggested. Other implications include a unique suggestion for fuel injection along special orbits intercepted via a bundle divertor.

Scaling laws for plasma energy confinement must be invariant under any transformation which leaves the basic plasma equations themselves invariant. Hence, constraints can be placed on the scaling laws even though the calculation of energy loss may be quite intractable. These constraints are derived for several plasma models and shown to be characteristic of the model. Hence, in addition to reducing the number of parameters which have to be obtained empirically, these results could delineate which plasma models are appropriate for the calculation of losses. They show that the empirical scaling laws at present proposed for tokamaks are incompatible with many conventional plasma models.

The recent availability of intense, space-charge-neutralized, energetic ion beams has led the authors to explore the possibility of using them for heating tokamak plasmas. The following key problems for this application are investigated: (i) beam injection perpendicular to , (ii) beam propagation across in vacuum, and (iii) cross-field beam propagation and energy deposition in plasma. It appears possible that, for proper values of the beam energy, radius and current, an intense ion beam can penetrate to the interior of a tokamak plasma and deposit its energy there.

Solid hydrogen spheres were injected into the ORMAK tokamak as a test of pellet refuelling for tokamak fusion reactors. Pellets 70 μm and 210 μm in diameter were injected with speeds of 91 m/s and 100 m/s, respectively. Each of the 210-μm pellets added about 1% to the number of particles contained in the plasma. Excited neutrals, ablated from these hydrogen spheres, emitted light, which was monitored either by a photomultiplier or by a high-speed framing camera. From these light signals it was possible to measure pellet lifetimes, ablation rates, and the spatial distribution of hydrogen atoms in the ablation clouds. The average measured lifetime of the 70-μm pellets was 422 μs, and the 210-μm spheres lasted 880 μs under bombardment by the plasma. These lifetimes and measured ablation rates are in good agreement with a theoretical model which takes into account shielding of plasma electrons by hydrogen atoms ablated from spherical hydrogen ice.

Radial observations of emission in the vicinity of the electron cyclotron frequency and its harmonics show the radiation to be polarized; ratio of extraordinary to ordinary mode intensity of about 2:1. In the thermal spectra the effects of cold-plasma resonances upon propagation of the radiation from emission layer to observation point are evident: (i) The extraordinary mode first harmonic is always suppressed by the upper hybrid resonance layer; (ii) The ordinary-mode first harmonic is suppressed when the plasma frequency exceeds the cyclotron frequency; (iii) For sufficiently high density the second harmonic is also affected by the hybrid cut-off. In the non-thermal spectrum the broad-band emission is polarized at high frequency but not at lower. The feature in the vicinity of the plasma frequency at intermediate density is broader than previously observed and almost entirely above ω_pe. Internal sawtooth relaxations have been observed in the central temperature even up to peak densities of 7 × 10²⁰ m⁻³. Temperature profiles deduced from second harmonic cyclotron emission and Thompson scattering data are compared.