Table of contents

Within the standard neoclassical theory, the authors show that, assuming that the mechanical power required to drive the ordered poloidal rotation against the viscous forces is a fraction of the total absorbed power, the poloidal spin up in the L to H transition is predicted as a bifurcation of solutions of the momentum equation.

The stepwise regression procedure was applied to obtain measurement formulas for equilibrium parameters used in the feedback control of JT-60, because the measurement formulas for feedback control of a D-shaped divertor plasma position and shape could not be derived from an analytical approach. This procedure automatically selects the predictor variables required to identify the plasma control parameters to leave as few variables as possible. The measurement formulas obtained are simple and compact, making them suitable for rapid calculation in a digitized feedback control system. The resultant control system proved to be stable and reliable, and it was experimentally confirmed that the measurement formulas obtained through this procedure were accurate enough to be applicable to the feedback control of plasma configurations in JT-60.

The transient behaviour of the diamagnetic signals in the afterglow of a pulsed ECR discharge (in H₂) excited by 2.45 GHz microwaves permits the measurement of the initial electron temperature (perpendicular to the static magnetic field direction, averaged in the radial direction) as well as the temporal decay of temperature after the end of the excitation pulse. In contrast to the use of a Langmuir double probe, which represents an alternative method in electrodeless discharges within nonconducting vessels. the interpretation of diamagnetic coil measurements is not hampered by deviations of the electron energy distribution function from equilibrium. As the Maxwellian case is approached both methods give consistent results. In the low pressure regime (up to 20 Pa) the influence of electron collisions on the plasma diamagnetism proves to be negligible. Using a diamagnetic coil one finds that electron energy densities down to 0.5*10¹⁸ eV m^-3 are still detectable.

The extension of the nonlinear drift wave equation including the two-dimensional vector non-linearity by Lakhin et al. (1987, 1988) has found much interest in recent theoretical and experimental investigations. In this study the authors present periodical solutions alternatively to the localized soliton solutions in the one-dimensional limits and the localized vortex solutions in two-dimensions. They therefore extend a perturbation scheme, which has recently been employed to a (quasi-) one-dimensional limit (Kauschke and Schluter, 1991), to the two-dimensional situation.

The electron temperature of the inhomogeneous plasma of the UMIST linear quadrupole ('GOLUX') is determined by measuring the emissivity ratio of the H_beta and H_gamma lines of the hydrogen plasma. The emissivity ratio is obtained by Abel inversion of the measured intensity of the lines. It is assumed that the free electrons have a Maxwellian velocity distribution, and that the distribution of electron population over the bound levels is given by a coronal-type equation. The hydrogen plasma is assumed to be in a steady state and without impurities contributing to the electron density.

Mode conversion of the magnetosonic wave to short wavelength modes in the edge plasma near the fast wave antenna is studied for ion cyclotron heating on Tokamaks. Analytical and numerical methods are developed to calculate the conversion due to a lower hybrid resonance and a fast wave polarization gradient for strongly inhomogeneous edge conditions. The results for an antenna radiating at high poloidal wavenumbers show that for low values of the toroidal refractive index a nearly complete conversion into the ion Bernstein mode occurs, provided the plasma density near the Faraday shield is at most of the order of the density at the lower hybrid resonance. For the present type of loop antennae the feeders effectively suppress radiation at high poloidal wavenumbers and the parasitic coupling remains low.

The consequences of using the idea of entropy production rate minimization are examined in relation to the shape of radial temperature profiles and the scaling of transport coefficients with temperature in Tokamak discharges. This is done under the assumption that physical processes occur in such a way as to produce relaxed states where an extremal of some relevant quantity (in this case the entropy production) is obtained. The authors study the conditions under which the temperature profiles adopt the Gaussian-like shapes observed in Tokamak plasmas. This is possible only for certain scalings of the thermal conductivity with temperature favouring certain models of anomalous transport against others. These results are also dependent on whether or not the current density profile is assumed to be determined by the temperature profile, as in Ohmically heated discharges with constant electric field. In the former case an anomalous electrical resistivity is needed in order to obtain the correct temperature profiles for known models of anomalous thermal conductivity.

The requirement of vanishing production of the magnetic entropy in the confinement zone of Ohmically relaxed auxiliary heated Tokamaks imposes a definite relation or 'state law' between the characteristic global parameters of the discharge. The conditions under which an isoentropic state can exist are expressed in this paper in a form comparable with the experiment. The Goldston scaling of the confinement time with respect to current, auxiliary power and toroidal magnetic field is contained in the isoentropic state law. An isoentropic state is susceptible to evolving spontaneously toward a bifurcating equilibrium with higher entropy. The author calculates explicitly the transition thresholds in terms of global parameters of the auxiliary power, magnetic field. current and temperature pedestal and the plasma detachment. The results are compared with the experimental observations on the H-transitions.

The linear MHD stability problem for 3D plasmas with noninteracting hot electron layers and nested magnetic flux surfaces in the absence of dissipation mechanisms is formulated in variational form. Boozer magnetic coordinates are extended to anisotropic pressure plasmas with nested magnetic flux surfaces for this purpose. A modified energy principle in which the hot electron species current is imperturbable is considered. Plasma incompressibility is imposed and thus a simplified kinetic energy is employed to determine the conditions of marginal stability. The vacuum region surrounding the plasma is treated as a shearless. pressureless and massless pseudoplasma. Fourier decomposition of the perturbations in the periodic angular variables of the magnetic coordinates is applied and a finite element discretization scheme reduces the stability problem to a special block pentadiagonal matrix eigenvalue equation which is amenable to solution with an inverse vector iteration technique. The formulation described is useful to evaluate the linear MHD stability properties of 3D plasma configurations with rigid hot electrons to global internal and external modes.

In many stellarators-envisaged as fusion devices-any alpha -particle which ever gets reflected ( nu /sub ///=0) is collisionlessly lost in a time which is orders of magnitude smaller than the typical slowing-down time of approximately=10^-1 s. Two classes of stellarators to which this general picture does not apply are described: quasi-helically symmetric stellarators and a class of stellarators with vanishing bootstrap current in which the collisionless alpha -particle confinement sufficiently improves at finite beta . The influence of the modular ripple in optimized coil systems realizing these configurations, the angular distribution of the fast alpha -particle losses, and the application of the results to alpha -particle confinement simulation experiments in next-generation stellarators are also discussed.

The relativistic motion of an electron in the electric field of a solitary wave propagating with constant velocity in a long discharge tube is studied. The intensity of the wave is assumed to be sufficiently high to ionize a gas and to produce a well-conducting plasma behind the trailing edge of the wave. The solution describing one-dimensional relativistic motion of an electron in a soliton-like electric field is presented for the waves of negative and positive polarities. For negative polarity waves. Two different kinds of electron motion corresponding to the particle lag or outrunning with respect to the wave are found. An analytic expression for the energy of the accelerated electron is obtained and analyzed, and the conditions for the maximal efficiency of acceleration are discussed.

An averaging method is developed in order to determine analytically the magnetic structure of a system with symmetry broken by small perturbations. In particular. Poincare maps are obtained for toroidal helical fields using the typical parameters of the Brazilian Tokamak TBR-1. The technique is fairly general as the small parameter used in the construction of this theory is the original symmetry-breaking perturbation parameter; it is applicable in analyses of fields in more compact devices or with cross-sections with any shape as well. Unless the unperturbed system is doubly symmetric (circular cylinder) a single helical perturbation mode (m, n) can excite many other modes. The coupling between any two modes arises in a very natural way.

A variational formalism that includes, in a consistent way, the tokamak plasma fluid response to an electromagnetic field as well as the particle-field resonant interaction effects is presented. The integrability of the unperturbed motion of the particles is used to establish a general functional similar to the classical Lagrangian for the electromagnetic field, which is extremum with respect to the field potentials. This functional is the sum of fluid terms that are closely related to the classical MHD energy and of resonant terms describing the kinetic effects. The formalism is used to study a critical issue in tokamak confinement, namely the sawteeth stabilization by energetic particles.

Anisotropic resistivity causes paramagnetic effects (B_z'(r)<0) in a screw pinch, being basically different to the self-relaxation in reversed field-pinches. The authors compute, analytically and numerically, the resulting influence on the plasma radius and on plasma beta in a straight cylindrical plasma. The results seem to indicate that D-D screw-pinch reactors which depend on safety factors q(a)>1 are unattainable. Diamagnetism caused by radial particle diffusion and the Nernst effect is also discussed. In a tokamak or reactor plasma, diamagnetism is shown to be negligible, whereas it may contribute in present ultra-low q, Extrap and RFP experiments. A basic relation is derived for the coupling between the poloidal and axial magnetic field components with the above effects included. Of specific importance to the Extrap programme is the result that plasma current limitation can arise due to the lack of equilibrium when the plasma radius tends to exceed its upper limit, which is defined by a magnetic or material limiter. Comparisons are made with stability limits depending on the safety factor, the number of contained ion Larmor radii and the line density.

A scalar diffraction treatment of forward-angle laser scattering diagnostics (e.g. scintillation interferometry, far-forward scattering) is presented. Results obtained by other workers for Gaussian beam scattering from plasma waves are generalized for arbitrary weakly scattering media and for both near-field (imaging) and far-field (focal plane) experimental configurations. Essential elements of the theory have been confirmed by near-field experimental measurements on airborne ultrasound.

The linear instabilities of an incompressible, uniform-density magnetofluid are considered in the periodic straight cylinder approximation. Spatially-dependent resistivity and viscosity profiles are regarded as fixed, but their magnitudes and the magnitudes of the currents driven in the plasma are not. It is shown that the stability boundary is determined by only two dimensionless numbers: the Hartmann number and the axisymmetric, zero-flow pinch ratio, which is inversely proportional to the safety factor at the wall. The result is analogous to the well known result from the theory of hydrodynamic shear flows that the Reynolds number governs the onset of hydrodynamic activity.

Using Ohm's law the authors show the impossibility of plasma equilibrium with flows in magnetic field having only a toroidal component. This proof is different from the proof due to Tasso et al. (1969) which is based on the equation of motion.