Table of contents

H mode behaviour is usually linked to the existence of radial electric fields or to their shear at the edge of tokamaks. The mechanisms are investigated by which such fields are induced in the plasma edge and by which the profile shaping is obtained when radial currents are imposed by electrode polarization. Earlier detailed experimental field measurements are successfully compared with a theoretical conductivity model in which neoclassical non-ambipolar transport and mobility through ion-neutral collisions are predominant. Strong neoclassical viscosity in the bulk plasma allows significant fields to develop only at the very edge of the plasma. There, a delicate balance between viscosity and ion-neutral friction takes place, which strongly affects the magnitude of the fields and the spatial location and the threshold condition for L-H field bifurcation. It is also shown how to verify experimentally the neoclassical diffusion coefficients in the plateau regime

The free boundary stellarator equilibria are studied in the framework of averaged equations. The structure of external magnetic fields created by currents flowing inside the plasma column is analysed. In all cases considered the dipole component of the magnetic field (in agreement with previous investigations) can only be used to determine the volume averaged value of the parameter beta if the net toroidal current is known. For zero net current operation it is shown that the quadrupole component of the external magnetic field can be used for an estimate of the plasma pressure distribution, for example, in the framework of a one parametric set of profiles. The dependence of the external magnetic field on the current distribution for the given pressure profile is also investigated, and it is shown that there is a possibility of distinguishing at least strongly different current distributions (such as the peaked and off-centred current profiles considered here) either for a large shear system at high beta or for a device with averaged vertical elongation of the vacuum magnetic surfaces

A model for the energy gain of inertial confinement fusion (ICF) targets is derived from realistic ignition profiles. The model considers the ablative implosion of a spherical shell driven by a rather general power pulse and takes into account the main physical limitations constraining the target performance. As a result, the model gives an interpretation of the gain curves obtained by numerical simulations and recently reported in the literature. The resulting scaling laws for the ignition energy and for the limiting gain are in good agreement with these simulations. Besides, several physical features associated with the target gain and observed in the simulations are well described. In particular, it is found that, along the limiting gain, the ICF parameter of the fuel is almost constant and, for applications to indirect drive fusion, the implosion velocity is proportional to the radiation temperature. The explicit scaling laws provided by the model allow a parametric study of the target gain as a function of the constraints on symmetry, stability and other physical quantities

Laser ablation injection of aluminium is used to measure the retention of metallic impurities in the lower poloidal divertor of TdeV. A detailed calibration of the ablation process allows the determination of the quantity and velocity distribution of the injected particles. The experiment measures the flow of the injected particles from the divertor to the main plasma. Negative biasing of the divertor neutralization plates is shown to improve the retention in the active divertor by a factor of at least four at -200 V. A simple model is developed to show that the improved confinement is due to the increased poloidal flux to the divertor during biasing

The effect of sawtooth crashes on fusion reactions and the concomitant neutron emission are investigated analytically and numerically. The sawtooth induced redistribution of the plasma is described by a generalization of the Kadomtsev sawtooth reconnection model. Simple expressions for the changes in local and global rates of reactions produced by fast ions are obtained, which predict quite different results for tokamaks with different relationships between the q=1 radius, the radial profile width of fast ions and the plasma radius. Special attention is paid to numerical simulations of the changes of neutron emission in JET NBI experiments. Experimental results and numerical calculations of the line integrated neutron flux to the JET neutron profile monitor, and of the change of global neutron emission, are compared in detail and found to be consistent

Momentum and heat friction forces between fast ions (isotropic to the lowest order in the fast-ion rest frame) and thermal bulk plasma species (near Maxwellian) have been derived analytically for the first time using the linearized Fokker-Planck collision operator. The effects of flow-type distortions of the test particle distribution and flow-type restoring effects from field particles are both retained self-consistently. Here, the momentum and heat friction forces are defined as the momentum moments of the Fokker-Planck Coulomb collision operator weighted by the Laguerre polynomials L₀^(3/2)(w^α/ν²_Tα) and L₁^(3/2)(w_α²/ν_Tα²), respectively, i.e. the momentum friction force is F₀^α/β ≡ ∫ m_αw_αL₀^(3/2)C_{α β}[f_α,f_β]d³w_α , while the heat friction force is F₁^αβ ≡ ∫ m_αw_αL₁^(3/2)C_αβ[f_α,f_β]d³w_α. Here w_α identical to ν - V_α represents the random velocity measured in the moving reference frame of the test particles, and the superscript α/β denotes test particles of species or colliding with field particles of species β. The momentum and heat friction forces have been explicitly calculated for electron-fast-ion collisions (F_k^e/f), fast-ion-electron collisions(F_k^f/e), thermal-ion-fast-ion collisions (F_k^i/f) and fast-ion-thermal-ion collisions (F_k^f/i), wherein the subscripts k correspond to the indices of Laguerre polynomials (k=0, 1). The collisional moment matrix is found to be asymmetric in the presence of fast ions-because the approximate self-adjointness of the Coulomb collision operator is not valid for this situation

Inhibition of contamination of the plasma core in JET by edge impurities during high power heating of deuterium plasmas in limiter configuration using fuelling is demonstrated. By injecting deuterium gas during heating, in the presence of a much larger recycling deuterium flux, a reduction of more than a factor of 2 was effected in n₂(0)/Φ₂, the ratio of central impurity density to impurity influx at the plasma edge. The reduction in n₂(0) was obtained without much effect on peak electron temperature and density. Reduction of plasma contamination by gas fuelling was observed also when hot spots formed on the limiter, a condition that without simultaneous gas fuelling culminated in runaway plasma contamination. Detailed analysis of the experiments is undertaken with the purpose of identifying the processes by which plasma contamination was inhibited, employing standard limiter plasma contamination modelling. Processes which might produce the observed impurity inhibiting effects of gas injection include: (a) reduction in impurity production at the limiter; (b) increase in impurity screening in the scrape-off layer; (c) increase in radial impurity transport at the plasma edge; (d) increase in average deuteron flow velocity to the limiter along the scrape-off layer. These are examined in detail using the Monte Carlo limiter impurity transport code LIM. Bearing in mind that uncertainties exist both in the choice of appropriate modelling assumptions to be used and in the measurement of required edge plasma parameters, changes in n₂(0)/Φ₂, by a factor of 2 are at the limit of the present modelling capability. However, comparison between LIM code simulations and measurements of plasma impurity content indicate that the standard limiter plasma contamination model may not be adequate and that other processes need to be added in order to be able to describe the experiments in JET

Parametric instabilities during the ion Bernstein wave (IBW) plasma heating experiment on PBX-M are investigated both theoretically and experimentally. The theoretical work shows that the RF power threshold of the instabilities is very low when the plasma density near the antenna satisfies the condition 2ω_pi < ω₀ << ω_pe. The threshold becomes very high, >>1 MW, and is determined by convective losses due to plasma inhomogeneity when the plasma density near the antenna is sufficiently high that 0.5 < ω_pi/ω₀ < 1. According to the theory, the parametric instability activity should increase as the plasma is moved away from the antenna, creating a low density electron plasma wave 'gap' region. To test this hypothesis on PBX-M, the plasma position was deliberately varied while monitoring this activity. Under normal IBW operating conditions, very little parametric instability activity was observed ⩽50 dB below the pump wave (ω = ω_RF). However, when the plasma edge was moved away from the antenna by about 2 cm, the parametric instability activity increased greatly, exceeding 20 dB of the pump wave. This result shows that the observed parametric instability activity can be explained in terms of the plasma inhomogeneity convective model. It was also demonstrated that, by controlling the plasma position with respect to the antenna, parametric instability activity can be controlled at a low level

The coupling of the waves launched from a 4.6 GHz lower hybrid (LH) system into PBX-M plasmas has been studied for both L mode and H mode plasmas. The characteristics of the plasma in front of the LH coupler have been measured with a fast Langmuir probe. The reflected power of the coupler has been measured across the transition to the H mode as a function of phase and the distance between the coupler and the separatrix. A transient rise in the LH reflection coefficient was observed near the L-H transition under some conditions. Coupling depends primarily on the electron density in the vicinity of the coupler, and proper positioning of the coupler can compensate for changes in the plasma edge due to H mode transitions. Good coupling can be maintained throughout the H mode

Sufficient coupling of an ICRF antenna for high power experiments was obtained even for a wide gap between the separatrix and the antenna in JT-60U. The loading resistances for an out-of-phase mode are over 4 Omega for a gap of 13 cm between the separatrix and the Faraday shield over the wide range of electron density from 1 × 10¹⁹ to 5.5 × 10¹⁹ m^-3. In particular, the loading resistances for an in-phase mode are about 5 Ω for a gap of 33 cm between the separatrix and the Faraday shield for the same plasma parameters. However, the heating response for the out-of-phase mode is much stronger than that for the in-phase mode

The results of a significantly more efficient model (molecular model) for computing particle and energy sources from recycling in edge plasma transport codes, such as b2, are compared with results from more detailed calculations using the b2 code coupled with the neutral transport code, DEGAS. The molecular model considers the reflux both of cold molecules and of energetic back-scattered atomic neutrals from the divertor target plates and has been implemented to function internally within the b2 code. The molecular model calculations are shown to be in reasonable agreement with more detailed calculations done with the coupled b2/DEGAS codes for seven cases typical of conditions in the scrape-off layer of the Doublet III (DIII-D) tokamak. Because the molecular model is a far less expensive computational tool, it represents a significant improvement over the existing (coupled) edge transport recycling model. Thus, it may find wider application in design studies for future devices, such as the International Thermonuclear Experimental Reactor (ITER)

Placing an l=1 continuous helical coil with a pitch modulation in an axisymmetric toroidal magnetic field, a helical axis configuration was obtained with characteristics similar to the Helias configuration for Wendelstein 7-X (W7-X). In the four pitch case, a device with an aspect ratio of 4-5 and good accessibility becomes possible, although a very weak magnetic hill exists. In a particular finite β magnetohydrodynamic (MHD) equilibrium, the magnetic well appears in the whole region for a central β value of β(0) ~ 1%. About a quarter of the particles at half radius are lost at β = 0; however, both the radial electric field and the finite β effect improve the particle orbit confinement significantly. The possibility of an open divertor is shown

The Advanced Toroidal Facility (ATF) torsatron incorporates two rail limiters that can be positioned by external controls. The influence on the plasma parameters of biasing these limiters both positively and negatively with respect to the walls has been investigated. Experiments have been carried out in the electron cyclotron heated plasmas at 200 kW with a typical density of 5 × 10¹² cm^-3 and a central electron temperature of ~900 eV. Negative biasing produces only small changes in the plasma parameters, but positive biasing increases the particle confinement by about a factor of 5, although the plasma stored energy does fall at the higher voltages. In addition, positive biasing produces the following effects compared with floating limiter discharges: the core density profiles become peaked rather than hollow, the electric field at the edge becomes more negative (pointing radially inward), the magnitudes of the edge fluctuations and the fluctuation induced transport are reduced, the fluctuation wavelengths become longer and their propagation direction reverses from the electron to the ion diamagnetic direction. Neither polarity of biasing appears to affect the impurity content or transport

Report on the Ninth International Workshop on Stellarators, held at the Max-Planck-Institut für Plasmaphysik, Garching, Germany, 10-14 May 1993.