Table of contents

The linear theory of electrostatic instabilities driven by ion temperature gradients (ITG) is investigated for impure plasmas in shaped (elliptical and triangular) toroidal plasma cross-sections. Kinetic theory is used to describe the response of each ion species. Both even and odd parity branches of these 'ITG' modes (COPPI, B., PEGORARO, F., Nucl. Fusion 17 (1977) 969) are examined in detail for parameters relevant to high temperature experiments. The Shafranov shift tends to lower the growth rates of both modes, most notably that of the odd parity mode. Ellipticity in the plasma cross-section has a strong stabilizing effect on the even parity mode but leaves the odd parity mode essentially unaffected. Triangularity has a much weaker (also stabilizing) effect and can be ignored for practical situations. Strong stabilization by multiply charged impurities is encountered, primarily owing to dilution of the primary ion concentration

The paper presents a study of symmetrization of thermal radiation in a hohlraum. This study is based on two-dimensional numerical simulations carried out using the radiation hydrodynamic code SITARA. Because of the two-dimensional nature of this model, only those hohlraum designs are treated that possess axial symmetry and contain two converters. It has also been assumed that there is no material in the space between the hohlraum components, so that scattering of radiation in the hohlraum can be excluded. The calculations show that when the hydrodynamic motion is included (dynamic model), the symmetrization problem becomes much worse compared with the nonhydrodynamic case (static model). It is more difficult to achieve the required level of symmetrization (1-2% deviation) using only two converters

Flux, energy and particle lifetimes have been measured in the new Large s Experiment field reversed configuration (FRC) facility. By careful control of the formation process, it was possible to form symmetric, quiescent FRCs, with s values higher than 4, in the one year of operation of the device. A wide range of plasma conditions was achieved, with ion temperatures varying between 0.1 and 1.5 keV. The lifetimes continue to scale approximately with the r_s²/ρ_i parameter found in earlier work, with a coefficient proportional to x_s to a power between 0.5 and 1

Profile consistency based on the parallel component of Ohm's law has been used to obtain electron temperature profiles. A resistive neoclassical term and a term that accounts for the bootstrap current contributions have been considered in Ohm's law. A numerical code has been developed to find solutions according to the MHD equilibrium equations. For stationary plasmas, the temperature profiles, obtained by a procedure in which a pseudo-parabolic shape of (J_ϕ/R) is assumed and the peak temperature known from experiments is used, are close to the experimental data for several very different machines (JET, TFTR, ASDEX, ALCATOR-C and FT). The main feature of the model is its capability to provide an easy parametrization of Ohm's law also in nonstationary cases, without going through the complication of a detailed solution of the magnetic field diffusion equation. A rule for estimating a maximum value of the current diffusion time inside the plasma volume in such situations is given. This rule accounts for both the temperature profiles and the stabilization times in some nonstationary pulses observed in JET

A numerical linear stability analysis of electrostatic ion temperature gradient (ITG) and dissipative trapped electron (DTE) modes in a three-component plasma (electrons, primary ions and impurity ions) is performed using a fully kinetic, sheared slab model. The quasi-linear particle and energy fluxes for each species are also computed. For the ITG mode, it is found that increasing plasma dilution (increasing Z_eff) as well as increasing peakedness of the Z_eff profile are strongly stabilizing. The quasi-linear calculations of the total anomalous energy flow driven by ITG mode turbulence shows that for Z_eff profiles that are nearly flat and of moderately low value (Z_eff ≲ 2), an energy 'pinch' is possible. A possible connection of this result with recent DIII-D off-axis heating experiments is discussed. A concomitant feature of this inward energy flow is an inward flow of primary ion particles, and an outward flow of impurity ion particles that greatly exceeds the neoclassical level. The impurity effects on the DTE mode are opposite, i.e. increasing dilution and Z_eff profile peakedness are strongly destabilizing. As a result, quasi-linear theory predicts a large increase in the anomalous electron energy flux and much smaller effects on the anomalous fluxes of the ion species

The paper gives a scrap-off layer based interpretation of the density limit in beryllated JET limiter discharges. In these discharges, JET edge parameters show a complicated time evolution as the density limit is approached and the limit is manifested as a nondisruptive density maximum which cannot be exceeded by enhanced gas puffing. The occurrence of Marfes, the manner of density control ad details of recycling are essential elements of the interpretation. Scalings for the maximum density are given and compared with JET data. The relation to disruptive density limits, previously observed in JET carbon limiter discharges, and to density limits in divertor discharges is discussed

The quasi-linear perpendicular viscous stress due to kinetic ion temperature gradient (ITG) modes in a sheared slab is shown to possess a maximum at a critical value for the gradient of the equilibrium electric field. This feature is present for a wide range of plasma parameters. As previously demonstrated, the ITG mode is stabilized for sufficiently large electric field gradients. It is shown how the existence of a maximum in the turbulent viscosity of ITG modes can play a role in a bifurcation theory of the H-mode. Such a model has the novel feature that the ITG mode is responsible for both the observed bifurcation in the electric field gradient and the imposed transport as it becomes stabilized

With a view to heating a 50/50 deuterium-tritium reactor plasma, ion cyclotron resonance heating (ICRH) at a power level of 10 MW bas been demonstrated in JET for a minority hydrogen concentration as high as n(H)/n(³He) ⩽ 1. In high minority ICRH experiments using (H)-³He plasmas, improved bulk ion heating was observed when the minority ion tail temperature was lowered to a level below the critical energy, so that more than 50% of the tail power was transferred to the bulk ions. Further, T_i0 ≃ T_e0 ≃ 7 keV was obtained in limiter L-mode discharges T_e0 and T_i0 are the central electron and ion temperatures, respectively). The global energy confinement was similar to that found in other ICRH L-mode discharges. It is shown that the observed tail temperature, fast ion energy and minority density are well understood in terms of minority ICRH physics and the Stix theory. Moreover, it is shown theoretically that when the wave is launched by an antenna in (0,π) phasing from the low field side in large and hot reactor-like plasmas, strong single-pass damping can be maintained at concentrations of the minority species approaching that of the majority species. The occurrence of ion-ion hybrid mode conversion cut-off layers would be of no consequence, since most of the wave power is absorbed before it reaches this region

Possible paths for obtaining linear stability against the m=0 mode in the Z-pinch are studied. Using a generalized energy principle, the necessary and sufficient Chew-Goldberger-Low (CGL) m=0 stability criterion is derived. This criterion is less restrictive than that of ideal MHD, although it also requires the boundary plasma pressure to be finite. It is shown that the edge pressure cannot be stably upheld by a surface current. By instead assuming a finite pressure external gas, it is found that an edge pressure to on-axis pressure ratio of 0.5 is required for stability of a constant current density profile. A parabolic current density profile lowers the limit to the value 0.17. The growth rates are shown to be monotonically decreasing as a function of the external gas pressure. Detailed derivations of the boundary conditions are also given. The results aid in clarifying the experimental stability of four major Z-pinch experiments. Finite Larmor radius stabilization is hence required to maintain stability in future fibre pinch experiments in vacuum, implying line densities less than 10¹⁹ m^-1

The Coaxial Slow Source (CSS) is a device in which 'annular' field reversed configurations (FRCs) (small aspect ratio, elongated, toroidal plasmas with poloidal field only) are formed in the space between coaxial coils carrying toroidal currents. The device is constructed so that the plasma can be translated into a simple cylindrical chamber and re-formed as a conventional FRC. Formation of FRCs on slow time-scales (50-250 mu s) at low loop voltage (87.5-700 V) has been demonstrated. The paper presents initial results from the new parallel configuration device CSSP in which the inner and outer coils are connected in parallel to the capacitor banks. The parallel coil arrangement has significantly reduced the contact of the plasma with the walls and thus the impurity content. Configurations with confinement times of 1o-30 mu s, densities of 3*10²¹ m^-3 and temperatures of 3-20 eV are typical. Results are presented on formation, energy balance, a nondestructive tilt instability and dynamics associated with magnetic tearing

It is shown that the kink distortion of the magnetic axis and, as a consequence, the variation of the magnetic field along magnetic surfaces in the toroidal direction lead to a new type of 'superbanana' particle orbits and can drastically change the classical particle and heat transport in the central core. The phenomena discussed have a time-scale of approximately=10^-3 s and seem to be too slow to affect the sawtooth crash process (which is an order of magnitude faster). They can, however, influence the evolution of the plasma parameters between crashes, the formation of 'snakes' and other phenomena in the central plasma inside the q=1 magnetic surface

Deuterium plasmas with a current of 1 MA, having quasi-stationary conditions for one minute, were obtained in TORE SUPRA, a large superconducting tokamak. The plasma current was partially noninductively driven by a 2.5 MW, 62 s lower hybrid wave pulse, resulting in a high central electron temperature (5.5 keV) for a plasma with a central electron density of 3.5 × 10¹⁹ m^-3

Studies of high density disruptions on TFTR, including a comparison of minor and major disruptions at high density, provide important new information regarding the nature of the disruption mechanism. Further, for the first time, an (m,n)=(1,1) 'cold bubble' precursor to high density disruptions has been experimentally observed in the electron temperature profile. The precursor to major disruptions resembles the 'vacuum bubble' model of disruptions first proposed by B.B. Kadomtsev and O.P. Pogutse (Sov. Phys. JETP 38 (1974) 283)

The scaling properties of edge fluctuations have been investigated using Langmuir probes in the edge region of the Advanced Toroidal Facility (ATF). The fluctuations in the ion saturation current (Ĩ_s/I_s) and the transport inferred from the fluctuations increase with increasing density gradient, while the local electron temperature is kept unchanged. The modification of the electron temperature in the range 10-50 eV while keeping the density profile constant does not have any significant influence on Ĩ_s/I_s. In regions where E_r/B ≈ 0, the poloidal phase velocity of the fluctuations is given by v_ph ≈ 2T_e/L_nB. More than one of the proposed mechanisms must be invoked to explain all the experimental observations

The locations of the q=2 and q=1.5 magnetic surfaces have been determined to within ±2 cm in TFTR using the emission from ablating deuterium pellets. As predicted theoretically, pronounced reductions in the average emission are found to occur when the pellet crosses these low order rational surfaces. Further, radial displacement of these surfaces is observed when the current distribution is modified. This modification has been accomplished by conditioning the graphite inner wall of TFTR so as to cause a higher effective pumping rate. The positions and radial displacements of these surfaces are predicted reasonably well by the transport analysis code TRANSP

The impact of anomalous radial diffusion due to turbulent magnetic fields on the electrical conductivity of a toroidal plasma is investigated. The problem is solved by evaluating an appropriate three-dimensional response function for the current density. This yields an analytic expression of the turbulent electrical conductivity including trapped particle effects. In the pressure a gradient region, the conductivity is generally enhanced with respect to the neoclassical one. This results in an anomalously low plasma resistance-a trend observed in many tokamak experiments. The analytic expression is shown to be in very good agreement with numerical calculations using a three-dimensional bounce averaged Fokker-Planck code. By a similar method, the toroidal response function for radiofrequency current drive in the presence of magnetic turbulence is also found

A new method is proposed to induce a negative radial electric field in the edge region of tokamak plasmas utilizing the fast ion loss mechanism induced by a toroidal field ripple. In this method, low energy hydrogen isotope beams are perpendicularly injected into the edge plasma. A modest beam power is sufficient to exceed the threshold of the edge radial electric field required for the L- to H-mode transition, derived by Shaing and Crume (SHAING, K.C., CRUME, E.C., Jr., Phys. Rev. Lett. 63 (1989) 2369), in the presence of a small toroidal field ripple; such a ripple is included in existing designs of the next generation of fusion machines

Report on the IAEA Technical Committee Meeting held at Montreal, Quebec, Canada 8-10 September 1992.