Table of contents

The influence of diffraction on the propagation of lower hybrid (LH) waves in tokamak plasma was studied. This effect has not been investigated before owing to a lack of suitable methods for solving the wave equation. An asymptotic method is developed which, while using a quasi-classical description in the direction of the group velocity, retains a wave description perpendicular to that direction. This method reduces the general wave equation to a system of ordinary differential equations. It is shown that allowance for the wave properties results in significant diffractional blurring of LH wave beams. This effect occurs in both configurational space and spectral space. In the first, it causes broadening of the absorbed power profile. In the second, it enriches the spectrum with slow waves, increasing interaction with electrons. The effect of diffraction is greater than the effects of the geometrical optics usually taken into account

Thermal plasma collapses have been observed in the Advanced Toroidal Facility (ATF) and in some cases these collapses limit the plasma performance. A 15-channel bolometer array has been used to measure the radiated power profile. It has been found that thermal collapses, defined by a drop in the plasma stored energy, occur when the local radiated power exceeds the local power input to the electrons. The local radiated power at the collapse first increases at the edge and then begins to propagate inward, leading to a peaking of the radiated power profile. This finding indicates that additional central heating would be effective in preventing the thermal collapse

The high plasma resistance observed in tokamak disruptions with a very rapid current decay is attributed to cooling by a rapid influx of neutral atoms from the wall or limiter. It is suggested that this influx proceeds as a dense localized cloud expanding from the edge to the centre of the plasma. The result of such a cooling, with carbon as the limiting material, is a drop in temperature to approximately 4 eV and an increase in electron density by an order of magnitude

The first measurements of current drive (refluxing) and refuelling by spheromak injection into a tokamak are discussed in detail. The current drive mechanism is attributed to the process of helicity injection, and refuelling is attributed to the rapid incorporation of the dense spheromak plasma into the tokamak. After an abrupt increase (up to 80%), the tokamak current decays by a factor of three because of plasma cooling caused by the merging of the relatively cold spheromak with the tokamak. The tokamak density profile peaks sharply because of the injected spheromak plasma (n_e increases by a factor of six) and then becomes hollow, suggestive of an interchange instability. Also discussed is the energy efficiency of spheromak injection current drive and the scaling of this process to larger machines. Refuelling by spheromak injection appears to be a viable scheme for larger machines. However, refluxing by spheromak injection is limited by geometrical and electrical efficiencies (both about 10%) as well as a high repetition rate requirement

The JET ICRF antennas, equipped with beryllium (Be) Faraday screens (FS), can be operated in such a way that the RF specific effects on the plasma boundary, by the impurity influx originating at the screens, are reduced to a negligible level. In dipole phasing, k_|| = 7 m^-1, the influx is for all purposes negligible. In monopole phasing (k_|| = 0 m^-1) the beryllium influx does not exceed ϕ_Be^FS = 1 × 10¹⁹ atoms.MW^-1.s^-1 and the corresponding delta Z_eff/P_RF is < 0.005 MW^-1. The observed dependences of ϕ_Be^FS (in monopole phasing) on plasma density antenna voltage, antenna phasing, and the angle between FS elements and the magnetic field in the boundary, B(a) = B_θ(a) + B_T(a), confirm that the release mechanism is sputtering by ions accelerated in the RF enhanced Bohm-Debye sheaths forming at the front face of the FS. When the angle between FS and B(a) is ≃ 22°, the fraction of the RF power radiated by the antenna, dissipated at the screen, can reach 40%. At high antenna voltage, arcing across the FS can occur. With dipole phasing the heating efficiency is not degraded, even with the large angle, and all the power coupled by the antenna is absorbed at the resonance position near the plasma centre. The open screen design did not introduce any disadvantages. The experience from JET operation at powers of up to 22 MW shows that, if the necessary conditions are met, i.e. if RF rectification is minimized, antennas are phased as dipoles and material with low sputtering coefficients at energies of 0.5-1 keV is used, then the influx from the FS is, for all practical purposes, eliminated

Collisionless charged particle motion in torsatrons is studied with the use of a longitudinal adiabatic invariant and numerical integration of the guiding centre drift equations. Emphasis is placed on investigating the influence of satellite harmonics of the helical magnetic field and the radial electric field on particle confinement. From this standpoint, the particle orbits, the limiting cycles of equations of particle motion, and the shape and size of regions in phase space in which the particle orbits lie are considered as a function of the device parameters. A comparison is made of magnetic configurations of various types differing in the number of helical field periods, in the inhomogeneity ratio _t/_l and in their sets of satellite harmonics. The characteristics of the configurations compared are close to the parameters of actual torsatrons: Heliotron E, ATF and Uragan-2M

The authors describe measurements of the sawtooth instability in JET, in which the instability wave function is shown to extend to the edge where it is measured using magnetic coils. The numerous magnetic probes in JET allow the time evolution of the (n=0, 1, 2, 3) toroidal Fourier components to be analysed. The n=1 magnetic component is similar to the m=1 soft X-ray centroid motion. This fact indicates the potential of edge signals in retrieving the poloidal mode spectrum of the q=m/n=1 surface. The spectrum evolution of the instability is compared for normal sawteeth (NST) and quasi-stabilized 'monster' sawteeth (MST). The spectrum is slowly decreasing with n for NST and all the components belong to one ballooning-like deformation, whereas MST show a large n=1 kink-like motion with small and independent accompanying higher n modes. Important equilibrium changes occur already during the growth of the instability and the growth rate is much faster than exponential. Both these facts imply a non-linear nature of the instability growth. Parametric dependences of growth rates, amplitudes, toroidal spectrum shape, etc. are studied to characterize the NST and MST instabilities

The divertor plates of TdeV, a tokamak with a double-null divertor and closed divertor chambers, have been electrically biased with respect to the walls. The authors discuss the resulting effects on the edge electron density profile, on the neutral pressures and impurity fluxes in the main vacuum chamber and the divertor chambers, and on the plasma flow to the divertors. As a function of the bias voltage, which was varied between-180 V and +160 V, the electron density scrape-off width and the wall impurity influxes increase monotonically; the flows to the top and bottom divertors vary strongly, in qualitative agreement with an E*B/B² rotation, but not symmetrically. With negative biasing, the electrostatic barrier and the rotation combine to give a strong improvement of the divertor efficiency

Estimates of the radial electric field E_r at the plasma periphery are obtained by measuring the drift velocities of low-Z impurity ions (He II, B IV, C III). The drift velocities are determined from the differential Doppler shift of visible line emission observed along opposite viewing directions. The principle of the measurement, including contributions from the diamagnetic drift, as well as radial gradients in the excitation rate and the effect of integrating along the line of sight are discussed in detail. The measured line of sight averaged drift velocities can be strongly influenced by the location and shape of the E_r profile, especially if, as measured on other tokamaks, it is localized to a narrow region just within the separatrix. Values of E_r estimated by assuming a constant radial profile underestimate maximum local values. During the H*-phase, however, high line of sight averaged perpendicular drift velocities of the B IV ions of a least 15 km/s in the electron diamagnetic drift direction are observed. From this, the presence of a strong negative radial electric field of at least 25 kV/m in the plasma edge region is inferred. Values of the B IV ion poloidal drift velocity calculated from an appropriate neoclassical theory are in the same direction as those measured. However, the calculated line of sight averaged values are much smaller than the measured ones. This reinforces the conclusion that a strong negative radial electric field is present just within the separatrix during the H-mode

A low frequency fast wave current drive scenario for ITER (f ~ 17 MHz < f_cT, where f_cT is the cyclotron frequency of tritium ions) has been analysed using a 1-D full wave code (TASK/W1). The current drive efficiency varies significantly with changes in the electron density owing to effects of the cavity resonance, even for the standard value of the peak of the parallel wave number N_|| chosen for ITER (peak of a main lobe, N_||(p)=2.3). The peak value of the current drive efficiency, according to the cavity resonance, agrees with that for the single wave mode for a large number of antennas in the toroidal direction. The antenna loading resistance as well as the current drive efficiency reach a maximum value nearly at the cavity resonance corresponding to that of the eigenmode. Therefore, it may be possible to optimize the current drive efficiency by optimizing the antenna coupling resistance to its maximum value. Frequency feedback control with a combination of instantaneous bandwidths and several preset frequencies is considered to achieve and to maintain good current drive efficiency against a possible change of the electron density. It is shown that this scheme allows good current drive efficiency (γ ~ 0.5 × 10²⁰ A.W^-1.m^-2 with N_||(p)=1.5), similar to that for neutral beam current drive

A model of the asymmetric internal reconnection occurring in toroidal geometry when pressure effects are taken into account is proposed. This model predicts a toroidal modulation of the current sheet, which is strong and mainly pressure driven for a rather low shear value on the q=1 surface. This modulation gives magnetic field line stochasticity in the vicinity of the m=1 separatrix, increasing during the reconnection process and reaching a value that can explain a complete expulsion of the electronic energy before the completion of the reconnection if the central value of the safety factor is somewhat below 0.8. This model is compared with a full toroidal MHD simulation including toroidal harmonics up to n=11

Fast wave heating experiments in the ion cyclotron range of frequencies (ICRF) were performed on target plasmas produced by 350 kW of electron cyclotron heating at 53 GHz and also by neutral beam injection in the Advanced Toroidal Facility (ATF). Various heating regimes were investigated in the frequency range between 9.2 MHz and 28.8 MHz with magnetic fields of 0.95 T and 1.9 T on axis. The nominal pulse lengths of up to 200 kW RF power were in the range between 100 and 400 ms. Data from spectroscopy, loading measurements, and edge RF and Langmuir probes were used to characterize the RF induced effects on the ATF plasma. In the hydrogen minority regime at low plasma density, large suprathermal ion tails were observed with a neutral particle analyser. At high density (n_e ⩾ 5.0 × 10¹³ cm^-3) substantial increases in antenna loading were observed, but ICRF power was insufficient to produce definitive heating results. A two-dimensional RF heating code, ORION, and a Fokker-Planck code, RFTRANS, were used to simulate these experiments. A simulation of future high power, higher density experiments in ATF indicates improved bulk heating results due to the improved loading and more efficient thermalization of the minority tail

The study of the dynamic response of the plasma is a valuable tool for investigating transport processes in a tokamak. A deductive approach is adopted, in order to make the best use of this experimental information. A system identification method is developed to estimate the transfer function of the system from the time evolution of its parameters to any excitation. The form of the identified transfer function is linked with a representation of the transport in terms of poles (eigenvalues) and eigenmodes. These are directly deduced from the raw data, with no restriction on the underlying processes, and there is consequently no need to adjust any simplified transport model to the experimental data. This method is illustrated by analysing the injection of pellets on Tore Supra. The density and the temperature transfer functions were observed to share the same poles, with the corresponding eigenmodes grouped in pairs with identical profiles. This implies the presence of a coupling between the particle flow and the heat flow. A criterion based on compatibility with the observed transfer function is developed to select among several possible coupling mechanisms. The selection suggests a particle diffusion coefficient depending on the density and the temperature gradient

It is shown that by the use of strong off-axis ICRH following pellet injection, heat transport with both positive and negative heat flux Q can be examined. It is found that a local diffusive model with Q = - χn ∇T is an adequate representation of the heat flux and that there is no need to invoke any non-diffusive flow terms such as a heat pinch

The effect of the magnetic axis shift on pressure driven MHD stability has been investigated in Heliotron DR (R=90 cm, a approximately=7 cm) in electron cyclotron heated plasmas by changing the vertical magnetic field strength. It was found that when the magnetic axis was shifted inward, strong MHD instabilities were excited and the attainable beta limits were much reduced compared to the values in the standard configuration. On the other hand, when the magnetic axis was shifted outward, the stability characteristics were basically the same as those in the standard configuration. The attainable beta values can be well explained by numerical calculations based on the STEP code for pressure driven ideal interchange instabilities. The stability dependence of the helical plasma on the position of the magnetic axis was confirmed experimentally. It was also found that a small toroidal plasma current stabilizes the MHD instabilities in all cases of magnetic axis positions. In particular, when the magnetic axis was shifted inward, the maximum beta limit could be increased up to twice the values obtained in the currentless case

The random coefficient two-stage regression algorithm with the collisional Maxwell-Vlasov constraint is applied to the ITER H-mode confinement database. The data violate the collisional Maxwell-Vlasov constraint at the 10-30% significance level, probably owing to radiation losses. The dimensionally constrained scaling, τ_E = 0.07192M^1/2 (R/a)^-0.221 R^1.568 κ^0.300 I_p^0.904 B_t^0.201 n^0.106 P^-0.493, is similar to ITER89P with a slightly stronger size dependence

Corrections to Nuclear Fusion32 (1992) 291.