Table of contents

For high density Ohmic discharges in the TEXT tokamak, a distinct ion mode (i.e. density fluctuations propagating in the ion diamagnetic drift direction) is observed in the microturbulence spectra. The magnitude and spectral characteristics of the mode are identified. A microinstability based transport model is used for the purpose of interpreting anomalous confinement properties. Onset of the ion feature occurs at plasma densities where a clear saturation is evident in the global energy confinement time τ_E. When the ion feature in the fluctuation spectra is strongest, agreement between predictions from the transport model and experimentally measured values of the global energy confinement time is realized if anomalous ion effects due to the ion pressure gradient driven (η_i) instability are included. By injecting pellets, a high density plasma is created in which the density profile is sharply peaked. Under these conditions the ion feature in the fluctuation spectra is suppressed. A possible connection between this experimentally observed ion mode and the theoretically predicted properties of the η_i instability is explored.

The paper presents a comparison of the main characteristics and experimental results obtained in plasma focus (PF) experiments in the POSEIDON 500 kJ facility in Stuttgart and the PF-360 kJ device in Świerk. Parameters of various electrodes and insulators are given, and studies on the evolution of the discharges are summarized. Selected data on X-ray, ion and neutron emission are given. Also presented are recent experimental results — a maximum neutron yield of up to 2.5 × 10¹¹ for 500 kJ/80 kV runs with a new ceramic insulator in POSEIDON and an average neutron yield of 1.2 × 10¹¹ for operation at 171 kJ/36 kV in PF-360. Particular attention is paid to the neutron scaling and the saturation effects observed at higher energy and current levels. Proposals are made for new experimental studies which can facilitate further progress in PF research.

The local heat diffusivity in H-phase discharges ranges from a factor of 1.1 to 3 lower across the plasma cross-section when compared with L-mode discharges. The corresponding measured factor of two improvement in energy confinement in the H-mode is thus a global effect and not only a consequence of improved edge confinement. These results are obtained by performing transport analysis on profile data from H- and L-phase discharges that were carefully prepared to have very similar global plasma parameters.

The paper presents linear and non-linear MHD calculations to examine the effect of a finite conductivity (resistive) wall on plasma stability. At a limiting safety factor q_ψ of approximately 2 in the tokamak and generally in the RFP, ideal modes are found, with a growth rate that varies inversely with the wall time constant. Resistive tearing modes can also be destabilized by a finite conductivity wall, but sufficiently fast plasma rotation can in turn stabilize these instabilities. It is shown that, non-linearly, the eddy currents driven in the resistive wall, by rotating MHD activity, produce a torque which opposes and slows the plasma rotation. This effect can be particularly strong in the RFP and leads to mode lock times which are shorter than in the tokamak.

The influence of bootstrap and neutral beam driven currents on the loop voltage, the toroidal current density and the ideal ballooning stability in ASDEX L- and H-mode plasmas is investigated by computer simulations. It is found that the loop voltage computed with neoclassical resistivity and Ohmic, bootstrap and beam driven currents comes close to the measurement. Bootstrap currents of up to 100 kA with broad profiles are generated. The field diffusion due to the driven currents is assessed by inclusion of these currents in the diffusion equation for the poloidal magnetic field. The main effect is the adjustment of the total current density to the broader electrical conductivity profiles in the H-phase on the resistive diffusion time-scale of about 400 ms. The broadening due to bootstrap and beam driven currents is comparatively small, so that the ideal ballooning stability is left almost unchanged. In the pre-transition L-phase and in the H-phase the plasma is stable, whereas at the beta limit it is marginally stable to ideal ballooning modes.

The connection length L between the magnetic field line and the wall in the scrape-off layer (SOL) region in toroidal helical systems is analysed. It is found that this connection length has a logarithmic dependence on the distance from the outermost magnetic surface to the field line under consideration. Using this dependence in a fluid model, the spatial distribution of the plasma in the SOL region is studied analytically. The edge temperature scales approximately as P^0.36 (P being the power flow to the SOL region), as for tokamaks. For a given value of P, the edge temperature in toroidal helical systems is lower than in tokamaks with a similar minor radius.

In an analysis of the parametric decay of the fast magnetosonic wave to an ion Bernstein wave and a quasi-mode the amount of power converted non-linearly at the plasma edge during ion cyclotron heating is estimated. Low decay thresholds for the pump wave amplitude are obtained when the quasi-mode frequency is at the hydrogen cyclotron frequency and the fast wave frequency is near appropriate cyclotron harmonics (or their sums) of the edge plasma. To obtain an upper limit for the growth of the decay modes, non-linear Landau damping of the Bernstein wave as a secondary process is studied, in addition to the usual convective and linear damping processes of the decay waves. It is shown that because of the secondary process and the finite interaction geometry in the decay, a negligible power conversion from the fast wave to Bernstein modes may follow even if the pump wave amplitude clearly exceeds the threshold. At larger pump wave fields (>200 V·cm⁻¹) a non-negligible power conversion could be obtained in spite of saturation of the instability. Since the wave fields of the fast wave at the plasma edge of JET are estimated to be less than 200 V·cm⁻¹, no serious power losses for the heating wave due to the Bernstein wave decay at the edge are expected. This seems to be in accordance with recent observations on JET. These dependences are described and applications to hydrogen minority heating of deuterium and deuterium-tritium plasmas by ICRF waves in JET are presented.

The diffusion of high energy ions caused by toroidal magnetic field ripple in a tokamak with flux surfaces of elliptical cross-section is studied. It is shown that the elongation of the cross-section increases the characteristic ripple value above which the collisionless motion of the trapped particles becomes stochastic. The elongation also results in a reduction of the diffusion coefficient, both in the regime of collisionless (intrinsic) stochasticity and in various collisional regimes. It is further shown that in an elliptical tokamak the energy range in which the weak collision regime is achieved is narrowed, and the range characterized by ripple-plateau diffusion is broadened. The distribution of the fast ion flux to the wall is also considered.

Electron cyclotron emission (ECE) from lower hybrid current drive plasma in the WT-3 tokamak has been measured along a vertical chord where the magnitude of the toroidal field is constant. From the frequency of the peak of the down-shifted second harmonic X-mode emission, the perpendicular temperature is evaluated to be about 50, 40 and 25 keV for plasmas with a current of 65, 50 and 24 kA, respectively. Also, the line integrated tail electron density is evaluated from the peak intensity for these plasmas and found to be 1.7, 0.9 and 0.5 × 10¹² cm⁻², respectively. It is found that the perpendicular temperature is an increasing function of the component of the momentum parallel to the plasma current, p₁ , and that the gradient of the perpendicular temperature along p₁ increases as the plasma current decreases.

A model for describing plasma decay in field reversed configurations has been developed. The model is based on simple resistive MHD equations in which thermal conductivity and radiation losses as well as inertial effects in the momentum balance equation are neglected. With these assumptions, it is shown that Ohmic dissipation is balanced by plasma flow in such a way that the initially uniform profile is maintained uniform and that the functional dependence of the pressure on the poloidal magnetic flux is also maintained (this dependence defines a family of equilibria). This result is independent of the magnitude or profile of the conductivity. It is therefore possible to describe the time evolution of the system as a continuous sequence of equilibria which pertain to the same family and satisfy proper boundary conditions. The method is applied to the Hill's vortex model and all decay times of interest as well as the time evolution of the separatrix are found. The existence of bifurcation points in the parameter space of the equilibria may account for the different behaviour of discharges with 5 mtorr and 20 mtorr deuterium filling pressure observed in the FRX-C experiment at Los Alamos.

Some success has been achieved by F.W. Perkins, W.M. Tang, R.E. Waltz, A. Rogister and others in explaining tokamak transport using drift wave turbulence as the source of the losses in the confinement region, 1 ⪅ q ∼ 2. They obtain solutions to the transport equations with the assumption that some unspecified mechanism — profile consistency — restricts the temperature in the edge region of the plasma. In this paper their work is extended, to include an edge region dominated by rippling modes and resistive ballooning modes, with a confinement zone controlled by trapped electron modes, η_i modes and resistive ballooning modes. Analytic solutions are obtained for the situation in which the source of particles decays exponentially in the plasma and [(1/T) (dT/dr)]/[(l/n) (dn/dr)] ≃ 2 in the confinement region. It is shown that differences in neutral penetration can contribute to a positive mass dependence of confinement for hydrogen isotopes, but these contributions are not enough to explain the strong dependence seen in many circumstances. The combination of the two sets of modes also leads to a form of profile consistency. Although the trapped electron modes and η_i modes can contribute many of the features of Ohmic and auxiliary heated transport — such as τ_E ∝ , L³, confinement saturation at high densities and some power degradation — they do not lead to the correct density, current and atomic mass dependence to explain all of the features of L-mode scaling. A candidate mode to supplement them is the resistive ballooning mode, which has a strong favourable current dependence and an unfavourable density dependence which, when combined with the more favourable dependence of the other modes, may be the cause of the weak density dependence seen experimentally in the L-mode. The addition of the resistive mode typically reduces the confinement for the drift wave model by a factor of 1.5–2; thus, suppression of resistive modes may be the cause of the L-H transition.

The highest confinement parameters measured on the Tandem Mirror Experiment-Upgrade (TMX-U) at Lawrence Livermore National Laboratory are summarized. The highest TMX-U global energy confinement product was 2 × 10^l0 cm⁻³·s and the highest central cell electron temperature was 0.28 keV. Both were achieved during standard tandem mirror operation with a central cell density of 6 × 10¹² cm⁻³. During thermal barrier operation, strong end plugging was limited to densities below 3 × 10^l2 cm⁻³ and the maximum global energy confinement product was 0.6 × 10^l0 cm⁻³·s. This performance is lower than that predicted by present theory but higher than that achieved in the earlier Tandem Mirror Experiment (TMX).

A simulation model for lower hybrid (LH) current drive has been used to study radiofrequency (RF) assisted Ohmic current ramp-up in the Compact Ignition Tokamak (CIT). The low electron density, the high toroidal magnetic field and the positive DC electric field present during the Ohmic current rampup phase of CIT make LHRF current drive an excellent candidate for RF assist during current ramp-up. Typical LHRF currents (I_RF) of the order of I_RJ ≲ I_p can be expected, resulting in a 25–35% increase in the current ramp rate.

Current drive by simultaneous injection of electron cyclotron waves and lower hybrid waves for the control of the current density profile in tokamaks is investigated. It is shown that this is a flexible method for large changes of q on axis and is therefore of relevance for studies on the access to the second stability regime.

Wall conditioning and chromium gettering have reduced Z_eff in the Advanced Toroidal Facility (ATF) to the range of 1.5−2.2. As a result, it is possible to achieve essentially steady state conditions using electron cyclotron heating alone, without the uncontrolled growth of the electron and impurity densities observed in the very earliest discharges, which always collapsed to low temperature afterglows. Plasma collapses are, however, still observed during neutral beam injection. It is known that large islands have been present in ATF during its initial periods of operation, but it cannot be determined whether they influence any aspect of the collapse. The impurity behaviour and the radiation losses in this perturbed magnetic configuration are discussed.

Target plasmas for neutral beam injection (NBI) in the Advanced Toroidal Facility (ATF) are formed using approximately 200 kW of 53 GHz electron cyclotron heating (ECH). During the early operational period of this device, field errors existed which produced large islands at the ι = 1/2 surface and several smaller, but non-negligible closely spaced islands at larger radii. The evolution of typical plasma parameters during NBI into plasmas produced in this perturbed magnetic configuration is discussed. The ion temperatures near the centre of the ECH target plasmas, as measured from Doppler broadening of impurity lines, are approximately 100 eV, and the central electron temperatures are close to 800 eV. NBI at powers up to 1.4 MW characteristically raises Tj(O) by factors of two to three for 50−80 ms, but thereafter the ion temperature decays. The electron temperature is not raised by NBI above its level in the ECH plasmas; it typically drops monotonically from the start of injection. Both the T_i and the T_e profiles indicate the existence of a low temperature region from the ι = 1/2 surface (ρ = 0.6) to the plasma edge, apparently because of the island structure, and modelling suggests that the plasma collapse may be caused by the peculiar radiation profile which develops under these conditions. However, whether the characteristics of the temperature profiles and the collapse can truly be ascribed to the existence of the islands can be decided only after repair of the field errors.

A theory of electron thermal diffusivity has been proposed which is based on electron drift wave turbulence. When account is taken of the effect of local shear changes produced in high poloidal beta equilibrium, this theory is found to predict the observed improvement of tokamak confinement with plasma current. Confinement is good at low poloidal beta, degrades as poloidal beta increases and then enters an improved transport region at high poloidal beta.

The 16th European Conference on Controlled Fusion and Plasma Physics was held at the Fondazione Cini, on the island of S. Giorgio Maggiore in Venice, 13–17 March 1989, on behalf of the Plasma Physics Division of the European Physical Society. Almost 600 scientists attended the meeting; 17 invited papers, 26 oral contributions and more than 400 poster contributions were presented.