Table of contents

We describe an enhanced scattering diagnostic method based on the scattering of an extraordinary electromagnetic wave close to the upper hybrid resonance. The method has a high sensitivity and spatial resolution and allows observation of the plasma density fluctuations with characteristic scale-lengths much smaller than the wavelength of the probing radiation in vacuum. The theory of enhanced scattering is presented together with experimental results obtained in small laboratory installations and in the research tokamak FT-2. The experiments were aimed at the study of small-scale intrinsic fluctuations in quiescent plasmas, the propagation of lower hybrid waves and the parametric instabilities.

A renormalized diffusion coefficient for magnetic field lines is presented by using the renormalized weak turbulence theory. It is defined on locally destroyed magnetic surfaces caused by two tearing modes. The renormalized diffusion coefficient is given in terms of a renormalized propagator expressed by the integral of the Bessel function of the first kind, J₁. It is free from delta -function-type divergence. An averaged renormalized propagator is introduced whose imaginary part represents the behaviour of the memory of the initial condition. Numerical calculation shows that the averaged propagator decreases within a correlation damping time.

An infrared camera has been used to check the power balance calculations in a series of JET divertor discharges. The discharges spanned the density range (n_e)=(1-7)*10¹⁹ m^-3, with the highest densities achieved by neutral beam heating and intensive gas puffing. For the discharges in which IR data were taken, the total power to the target, as deduced from the IR signal, was proportional to the expected divertor target power estimated from P_in-P_rad-W, where P_in is the input power to the plasma, P_rad the measured radiated power, and W the rate of change in the plasma stored energy. Close proportionality, pointing to good power balance, has been achieved in ohmic plasmas, as well as in L- and H-modes with either RF and/or NB heating up to 22 MW, of which up to 12 MW was monitored on the target as heat deposition by the IR system. Analysis of the data has shown no systematic trends of deteriorating power balance with increasing volume-averaged density or with heating power.

A model for the angular distribution of the neutron emission is derived and parametrized. This enables us to apply fitting procedures to the experimental data of the anisotropy of the neutron fluence, which furnish the mean energy and angular characteristics of the reacting deuterons. To this end the angular distributions of the neutron fluence were measured with high accuracy, on every shot the relative statistical errors being below 3-4%. At the same time, based on direct measurements of axially emitted ion energy spectra, we found a realistic distribution function for the reacting deuterons and an analytical expression for the anisotropy of the neutron fluence. The most important result provided by this method applied on a low energy plasma focus device is that medium-energy deuterons (50-100 keV) with a relatively broad angular distribution are responsible for most of the neutron yield.

The effect of the Trivelpiece-Gould mode on the behaviour of a low-frequency drift instability in a weakly ionized magnetized plasma is studied experimentally in a DC argon discharge. The ions are weakly magnetized, i.e. Omega _ci approximately nu _i, rho _i approximately R ( Omega _ci and rho _i are the ion gyrofrequency and gyroradius, nu _i is the ion-neutral collision frequency and R is the plasma radius). With increasing amplitude of the high-frequency field, the frequency and the amplitude of the instability decrease. Since the anomalously enhanced ambipolar field is considered as a very important factor in the mechanism driving the instability, special attention is paid to its variation with increasing high-frequency power. The nonlinear mechanisms of the dynamical control of the instability are discussed.

Thick spherical shells, irradiated nearly symmetrically by ion beams, can convert efficiently ion beam energy to thermal radiation, with parameters of relevance to inertial confinement fusion. The evolution of such radiation converters has been studied by means of an analytic model, in turn validated by 1D radiation hydrodynamic simulations. Expressions are derived for the overall conversion efficiency, the heating time and the radiation temperature as a function of the beam and target parameters. Conditions are also derived for the effective hydrodynamic insulation between the converter and the fusion capsule contained inside the converter. For realistic heavy ion beam parameters (e.g. 6-8 GeV Bi beams, with total energy of 10 MJ and power about 700 TW) such converters can achieve an efficiency adequate for fusion applications, but only allow for a modest dynamic range of pulse shaping.

The magnetic field and current density profiles of a steady-state tokamak are determined by assuming that the plasma relaxes to a state having the minimum rate of Ohmic dissipation. Since tokamaks do not operate with flux conservers, the constraints employed in the minimization are different from those used for RFPs or spheromaks. Energy and helicity conservation are imposed for given values of the applied electric and toroidal fields at the edge of the plasma.

Theoretical estimates of the electron thermal diffusivity, driven by different instabilities to which tokamak plasmas are prone, are surveyed and their regions of validity specified. For those that are applicable, the prediction for a typical set of JET profiles is compared with the experimental local diffusivity. The predicted and experimental scalings of the thermal diffusivity with key parameters are also compared. Although no one model reproduces the magnitude, radial variation and parameter scalings of the experimental thermal diffusivity, several models correctly predict some of the experimental behaviour.

We considered the Martin-Taylor model (1984) for a magnetic limiter of a tokamak. Calculating the Lyapunov exponent and diffusion coefficient we analysed the dependence of the length of the chaotic region at the edge of the tokamak on the magnetic limiter current. Our results indicate that for a large tokamak, operating in a certain range of the shear values, this current can be lowered by as much as one order of magnitude, with respect to the value calculated by Martin and Taylor.

The increased core electron temperature produced by ICRF heating of TFTR, D-T neutral-beam-heated supershot plasmas is expected to extend the alpha-particle slowing down time and hence enhance the central alpha-particle pressure. In preparation for the TFTR D-T operational phase, which started in late 1993, a series of experiments were conducted on TFTR to explore the effect of ICRF heating on the performance and stability of low-recycling, deuterium supershot plasmas in the ³He minority heating regime. The coupling of up to 7.4 MW of 47 MHz ICRF power to full size (R approximately 2.62 m, a approximately 0.96 m), ³He minority, deuterium supershots heated with up to 30 MW of deuterium neutral beam injection has resulted in a significant increase in core electron temperature ( Delta T_e=3-4 keV). Simulations of equivalent D-T supershots predict that such ICRF heating should result in approximately a 60% increase in the alpha-particle slowing down time and an enhancement of about 30% in the central alpha pressure. Future experiments to be conducted at ICRF powers up to 12.5 MW during the upcoming TFTR D-T campaign may result in even greater enhancements in core alpha parameters. This paper presents results from experiments performed at an axial toroidal magnetic field of about 4.8 T, where the minority resonance was within 0.1-0.15 m of the plasma core. Combined ICRF and neutral beam heating powers in these experiments reached TFTR record levels of over 37 MW, which allowed an exploration of the power loading limits on the carbon limiter tiles. The plasma current was operated at 1.85 and 2.2 MA and sawtooth suppression was observed at the higher plasma current.

The dispersion of electron cyclotron waves in a weakly relativistic Maxwellian plasma is investigated. It is shown that the apparently very complicated picture of the coupling of the extraordinary (X) mode to Bernstein waves can be accounted for in a simple way by considering the refractive indices as Riemann-like surfaces in the Clemmow-Mullaly-Allis (CMA) parameter space, ( omega _p²/ omega ², omega _c/ omega ), and by introducing a few topological concepts from the analysis of complex functions. A detailed study is made of the surface representing the X mode for perpendicular propagation, with special attention given to the connection between this mode and Gross-Bernstein modes. For perpendicular propagation non-transcendental approximations to the relativistic refractive indices for X and O modes can be given. We show that these approximations are good up to approximately 25 keV and, at frequencies up to the second harmonic of the electron cyclotron frequency, the X mode approximation also accounts correctly for the connection of the X mode to Bernstein modes. The accuracy and the numerical efficiency of the approximations make them well suited for routine calculations for millimetre wave applications in fusion plasmas, including the analysis of X mode and O mode reflectometry.

In the high current density plasma on TPE-1RM15 reversed field pinch, large-amplitude oscillations with m=0, n=0 are observed in soft X-ray (SXR) emission for a wide range of theta values, even at low- theta ( theta <1.55) discharges. Another small-amplitude oscillation with m=1 is observed quasicontinuously for almost all the discharge. The burst of high-energy soft X-rays is observed in the channels of the SBD array looking at the electron drift side of a metal limiter and seems to correlate with the crash of the large-amplitude oscillation. This SXR burst indicates the existence of energetic electrons flowing along the field lines near the plasma surface in the dynamo phase. These large-amplitude SXR oscillations are mainly due to the variations in the electron temperature and are roughly in antiphase with the oscillation of ion temperature.

For original paper see Zambreanu and Doloc, ibid., vol. 34, p. 1433 (1992). Zambreanu and Doloc presented an electrodynamic model for describing the electric and magnetic fields of a plasma focus discharge during the last stages of the current sheath (CS) evolution. Two different geometries were considered: a hollow cylindrical current distribution (of external radius r_s and thickness Delta r) for the CS collapse phase, and a homogeneous column for the pinch phase. In both cases, a uniform current density j, in the layer and infinite column length was assumed. While explicit expressions for the axial component A_z of the magnetic vector potential (in terms of r_s, Delta r, the turning radius R₀ of the CS, the cylindrical radial coordinate r and the discharge current I) were presented, the corresponding expressions for the scalar potential Phi were not given and thus the evaluation of the axial electric field E_z remained implicit. However, generic profiles of the fields were shown in the paper for both the hollow phase of the CS and the solid column phase. Kelly and Marquez analyse the column phase of the CS but the results can be extended to the hollow phase without difficulty.

The authors reply to the comments made by Kelly and Marquez in the previous article (1994 Plasma Phys. Control. Fusion.36 573).

An incorrect diagram was used for figure 1 in the original article, and the sentence beginning on line 14 of page 1534 is corrected; see PDF for correct versions.