Table of contents

Plasmas in axisymmetric mirror devices can be made stable to MHD interchange modes by injecting energetic ions which contribute significantly to the pressure and spend a sufficiently large fraction of a bounce time in regions of favourable curvature. Pitch-angle scattering adversely affects the method by reducing this fraction. The ions must be sufficiently energetic that pitch-angle scattering is not detrimental for that part of a slowing-down time during which they contribute significantly to the pressure. The authors have solved the bounce-averaged Fokker-Planck equation, including drag and pitch-angle scattering, and calculated the energetic ion contribution to the stability integral. With specially tailored magnetic fields, the required injection energy and power drain are found to be reasonable.

The use of travelling waves for the steady-state current drive in an axisymmetric toroidal plasma in the banana regime is studied. The treatment is based on a quasi-linear equation for the electron distribution function, averaged over the period of particle motion along the small azimuth of the torus. It is shown that the trapped electrons do not absorb the energy of the monochromatic (in frequency) RF field and thus only the circulating electrons contribute to the driving current and the absorbed RF power. The current and the absorbed power are calculated by using the electron distribution function obtained for the case of a narrow wave packet, both the toroidial magnetic field and the distortion of the electron distribution with respect to transverse velocities being taken into account. The important role of the marginally circulating electrons is revealed. It is pointed out that the toroidal satellite resonances can affect the RF current drive by spreading and splitting the region of wave-particle interaction.

Transport of trace, non-recycling, injected impurities has been studied on the Alcator C tokamak. Changes of impurity confinement times with varying plasma density, current, toroidal field, majority ion species mass, impurity charge and mass, Z_eff, and major and minor radius have been delineated. An empirical scaling is developed from these results and compared with the results of similar transport studies undertaken on other tokamak devices. The agreement is reasonable. A computer model simulating the transport is utilized to compare several models with the empricial results. With the possible exception of low-density, high-Z_eff discharges, the transport is not consisten with the predictions of neoclassical theory, but can be well described by simple spreading diffusion with a diffusion coefficient ranging from 1 to 5 × 10₃ cm²·s⁻¹, depending on plasma parameters. This model yields good agreement both with the time histories of single-chord measurements of various ionization states, and with radial soft-X-ray emission profiles. Increased impurity transport with the onset of strong MHD oscillations has also been observed, with the effective diffusion coefficient scaling approximately as (ΔB)⁴.

Using a CO₂ forward-scattering experiment during ICRF heating in a D₂-H₂ plasma, fast and slow waves associated with the heating mechanism are observed. The fast wave, with long wavelength, is observed through a coupling between the fast wave and drift waves. A measure of the corresponding electric field is given. When approaching the ion-ion hybrid layer, the fast wave is slowed down and an electric field increase is observed (swelling) . Afterwards, the fast wave undergoes conversion and becomes a slow one, which is directly observed and analysed. Its corresponding electric field is measured. 'Sawtooth relaxations' are also observed on this signal. The importance of the hybrid layer and the rotational transform in the process is outlined.

Cross-field particle and energy transport in diverted ASDEX discharges with up to 2.2 MW neutral-beam heating is studied by testing transport code predictions against experimental data. With neutral injection, enhanced coefficients of electron heat diffusivity and diffusion are found which are independent of density, temperatures and poloidal beta over a large parameter range (χ_e = 2.9 × 10⁴ cm²·s⁻¹ and D = 0.2 χ_e). The ion heat diffusivity continues to be one to three times the neoclassical value. The period with degraded confinement can be considerably delayed in relation to the beams and is found to be correlated with a characteristic change in the shape of the electron temperature profile due to neutral injection and with the time behaviour of the sawtooth period. Energy and particle confinement do not deteriorate with increasing beam power. It is found that the sawtooth activity does not significantly impair the confinement outside the q = 1 surface. A possible connection between degradation of confinement and non-thermal electron or ion velocity distributions, plasma rotation and drift-wave turbulence is discussed.

The instability strength of a diverted plasma with vertical elongation is measured for a range of the magnetic-field decay index, −1.5 < n < +0.5, in the standard-D and inverted-D configurations. The range of the instability growth time is from one to four orders of magnitude greater than previously published results. When the plasma current is in the range of 170–310 kA, the instability can be suppressed by passive stabilization due to currents induced in a discrete coil system together with a moderate-power (100 kW) active feedback system. The inverted-D configuration is three times more unstable than the standard-D configuration for the same ellipticity. The inverted-D configuration is destabilized by its negative triangularity and the standard-D is stabilized by its positive triangularity.

The improved stability period of a reversed-field-pinch (RFP) configuration with high current density (500 A·cm⁻², on average) is well understood on TPE-1R(M) with a metal liner whose size is the smallest among the RFP experimental devices being operated at present (r/R = 9/50 cm unit). Plasma parameters of I_p = 130 kA (duration time about 1 ms), n_e0 = 6 × 10₁₃ cm₋₃, T_e0 ≈ 600 eV, and β_p ≈ 10% are obtained. The improved stability period is characterized by a remarkably reduced fluctuation level (δB_p/B_p ≈ 1%) and a steady improvement of plasma confinement. Possible explanations for the interesting phenomena in the setting-up phase and the improved stability period of TPE-1R(M) are given, i.e. relaxation phenomena, toroidal-flux enhancement within the plasma, and current disruption. The scaling of electron temperature and density, depending on the plasma current in the improved stability period, are described with a discussion of the energy confinement time. The entire performance of TPE-1R(M) is discussed in relation to that of other RFP machines.

The dependence of plasma energy confinement on minor radius, density and plasma current is described for Ohmically heated near-circular plasmas in Doublet III. A wide range of parameters is used for the study of scaling laws; the plasma minor radius defined by the flux surface in contact with limiter is varied by a factor of 2 (a = 44, 32 and 23 cm) , the line average plasma density, _e, is varied by a factor of 20 from 0.5 to 10 × 10¹³ cm⁻³ (_e R₀/B_T = 0.3 to 6 × 10¹⁴ cm⁻²·kG⁻¹) and the plasma current, I, is varied by a factor of 6 from 120 to 718 kA. The range of the limiter safety factor, q_L, is from 2 to 12. – For plasmas with a = 23 and 32 cm, the scaling law at low _e for the gross electron energy confinement time can be written as (s, cm) where q_c = 2πa²B_T/μ₀IR₀. For the 44-cm plasmas, is about 1.8 times less than predicted by this scaling, possibly owing to the change in limiter configuration and small plasma-wall separation and/or the aspect ratio change. At high _e, saturates and in many cases decreases with _e but increases with I in a classical-like manner. The dependence of on a is considerably weakened. The confinement behaviour can be explained by taking an ion thermal conductivity 2 to 7 times that given by Hinton-Hazeltine's neoclassical theory with a lumped-Z_eff impurity model. Within this range the enhancement factor increases with a or a/R₀. The electron thermal conductivity evaluated at half-temperature radius where most of the thermal insulation occurs sharply increases with average current density within that radius, but does not depend on a within the uncertainties of the measurements.

Global energy balance, radiation profiles and dominant impurity radiation sources are compared for Ohmically heated limiter and divertor discharges in the ASDEX tokarnak. In discharges with a poloidal stainless-steel limiter, total radiation from the plasma is the dominant energy loss channel. The axisymmetric divertor reduces this volume-integrated radiation to 30–35% of the heating power and additional Ti-gettering halves it again to 10–15%. Local radiation losses in the plasma centre, which are mainly due to the presence of iron impurity ions, are reduced by about one order of magnitude. In high-current (I_p = 400 kA) and high-density (_e = 6 × 10¹³ cm⁻³) ungettered divertor discharges, up to 55% of the heating power is dumped into a cold-gas target inside the divertor chambers. The bolometrically detected volume power losses in the chambers can mainly be attributed to neutral hydrogen atoms with kinetic energies of a few eV. In this parameter range, the divertor plasma is dominated by inelastic molecular and atomic processes, the main process being Franck-Condon dissociation of H₂ molecules.

The magnetic field strength in a toroidal stellarator with ℓ field periods in the poloidal direction is written in co-ordinates which characterize a field line. The result is a variation proportional to ^m sin (m + pϕ), m ≡ ℓ−1, as well as ^ℓ sin (ℓ + pϕ). The extra term can be the principal helical contribution to the field strength for parameters relevant to present-day experiments. Criteria for the formation of magnetic wells are derived. Drift surfaces and transition curves are calculated and examples are presented for W VII-A parameters, both allowing for and neglecting the above effect. The region of phase space occupied by localized particles is considerably increased in the former case and the drift surfaces are somewhat modified. Simple consequences for transport processes associated with localized particles are indicated.

The use of EC waves to control temperature and current profiles may affect the background MHD configuration. In particular the RF current drive can create a 'tearing-mode' configuration, depending essentially on the optical properties of the plasma, on the power level of the injected waves and on their angle of incidence. Numerical and analytical estimates are presented of various effects to be expected in the RF heating process, consistently with transport phenomena.

Resistive ballooning subject to the effects of viscosity is put forward as a possible explanation for some of the observed density fluctuations in the ZT-40 device at Los Alamos.

An analysis of alpha-particle containment in tokamaks is presented. It is found that, for the relatively peaked profiles and low aspect ratio of the present devices, the contained fraction F depends mainly on the product IA of plasma current and aspect ratio, the dependence on other parameters being weak. When the effect of the magnetic-field ripple on the trajectories is considered, the increase of F with IA becomes weak for IA > 5 MA and IA tends to saturate at F ≅ 0.9. This indicates that, for relatively peaked profiles in the presence of ripple, there is only a weak improvement in alpha-particle confinement by increasing the plasma current above about 2 MA.

The propagation of linear lower hybrid waves in an inhomogeneous plasma is studied under the assumption that the wave field has a relatively narrow spectrum of wave-numbers. The lowest-order electromagnetic correction, neglected in the electrostatic approximation, is included. It is shown that this electromagnetic correction can produce focusing of the wave envelope in the outer layers of typical large-tokamak plasmas. This focusing is a linear effect due to the opposition of thermal and electromagnetic dispersion.