Table of contents

JET has been operating with deuterium plasmas for the past two years, during which time neutron spectrometry has been applied as a diagnostic technique for determining the ion temperature for suitable discharges. Combining the 'neutron temperature' with the neutron yield determination made with a fission counter diagnostic permits the central deuteron to electron density ratio (n̑_d/n̑_e) to be determined. It is found that this ratio, for ohmically heated discharges, appears to fall with ion temperature from about 70% at 2 keV to 40% at 3 keV. The addition of ICRF heating does not alter the density ratio. These findings are consistent with the observation that high temperatures achieved with Ohmic heating in tokamaks are correlated with high impurity levels.

One of the most striking features of the H-mode, in contrast to the L-mode, is the existence of very steep pressure gradients in a narrow layer just inside the plasma boundary. In this paper, it is shown how the existence of H- and L-regimes, together with their characteristic profiles, is a natural consequence of the modified ballooning stability properties near a magnetic separatrix.

Ion tail formation by neutral beam (D⁰) injection and second harmonic ion (D⁺) cyclotron heating in a 50:50 D-T plasma is investigated on the basis of a local Fokker-Planck calculation. The deformation of the deuteron velocity distribution function is examined analytically and numerically. The effectiveness of the tail formation is estimated from the enhancement of the D-T fusion reactivity, (f is the deuteron distribution and G is the 'ov-function', averaged over the isotropic triton distribution). The profile of the integrand typically exhibits two humps in velocity space. This results in a large reactivity enhancement for high energy beam injection. For a radiofrequency (RF) induced tail, a 'wing' or smeared tail rather than a hump is formed. ICRF waves couple well with the beam induced tail ions and enhance the reactivity, especially when the beam is injected perpendicularly to the magnetic field. The efficient use of the power supplied by beam and RF waves to enhance the reactivity is also discussed.

Cross-field transport and ballooning stability in neutral beam heated ASDEX divertor tokamak plasmas below and at the β limit are analysed by computer simulations. It is found that the discharges below the limit are ballooning stable and exhibit H transport. No gradual reduction of confinement happens when beta approaches the limit ('hard' β limit). The degradation of energy confinement at the β limit is shown to be due to enhanced electron heat conduction. Resistive ballooning modes with high wavenumbers are found to be marginally stable or unstable in a radial zone where the electron heat diffusivity is enhanced by a factor of four. Broader zones correspond to stronger degradation of global energy confinement. The diffusion coefficient is raised much less than the electron heat diffusivity. Fast flattening of the current profile which keeps resistive ballooning modes close to marginal stability seems to occur. Such modes with high wavenumbers generate small scale, fluctuating B_r fields which can cause magnetic braiding. It is shown that the confinement properties at the β limit are consistent with transport in stochastic magnetic fields.

Reversed field pinch (RFP) discharges have been produced in a large (1.39 metre major radius, 0.56 metre average minor radius), thick walled (5 cm), aluminium vacuum vessel with indented sides. The discharges are self-reversed and ramped up to a current of 300 kA over a time of 10 ms. Reversal is sustained for ≳ 10 resistive diffusion times, despite the presence of large magnetic fluctuations. The influence of the bad poloidal magnetic curvature on RFP stability is examined by measurement of magnetic fluctuations near the plasma edge in the separate bad and good curvature regions of the non-circular plasma for RFP and non-reversed discharges with an edge safety factor, q_a, of 0.4 and 1.4. For q_a ∼ 1.4 discharges, the poloidal field curvature is small. The large device size permits RFP startup at a low toroidal loop voltage (≲200 V), which is applied to a gap exposed to plasma, but successfully protected against arcing (up to 300 V). RFP plasmas have also been obtained with a toroidal limiter.

A simple analytical model for a high recycling edge plasma, which relies on the presence of a small parameter – the ratio of the particle flows crossing the magnetic field to those impinging on the target – is proposed. The concept of a one-dimensional steady state (OSS) is introduced as a zero approximation in the small parameter. The mean number density of the particles – ions plus neutrals – in the magnetic flux tube is chosen as the most representative and convenient parameter of the problem. The OSS is shown to be ambiguous in a certain range for sufficiently high values of the energy flow entering the scrape-off layer from the bulk plasma. This ambiguity is confirmed by 1-D calculations. An equation describing quasi-steady variations in OSS is derived, and a mechanism of exciting self-sustained oscillations is developed. These oscillations are related to peculiarities of the neutral gas transport in the edge plasma and to the ambiguity of the OSS. The results of a 2-D simulation of the edge plasma oscillations are found to be in a good agreement with this mechanism, which might be responsible for the edge localized oscillations observed in H-mode divertor experiments.

The paper investigates bolometrically determined radiation power profiles, energy exhaust and impurity accumulation in the two types of H-mode in ASDEX. During the burst dominated H-mode, the repetitive burst-like energy and particle expulsion into the divertor prevents an increase of radiation within the outer half of the plasma minor radius. This type of H-mode arrives at an equilibrium state. During the burst free H-mode, the radiation power losses, unimpeded by bursts, grow over the entire plasma cross-section until this H-mode ends in radiation collapse. Impurity accumulation, resulting in central peaking of the radiation power profiles, takes place in both types of H-mode. The time evolutions of the central radiation power density and the predominantly responsible iron concentration are not significantly affected by the presence or absence of bursts. However, to establish the burst free H-mode, it is required that the absolute values of the iron concentration and the associated radiation power losses at the plasma centre exceed given threshold values. This critical level can be achieved either by external injection of medium-Z metals or by sufficiently strong accumulation of intrinsic metallic impurities during a preceding burst dominated H-phase.

A simple analytical model of a steady state, resistive magnet tokamak reactor is used to derive an optimized design yielding the minimum cost per watt of electricity. The optimization is performed subject to constraints imposed by plant power balance requirements and first stability region beta scaling laws. In addition, the design is required to satisfy a series of inequalities, derivable from straightforward physics and engineering considerations, which further limit the range of values that reactor parameters can assume. Particular attention is given to the scaling of plant cost per watt with plasma aspect ratio, elongation and safety factor in order to determine the conditions under which raising beta improves reactor performance. Even though the model is idealized, the results agree semi-quantitatively with reactor systems code calculations.

The propagation of heat pulses originating from sawtooth activity in JET has been investigated in a series of limiter discharges with the following parameters: plasma current, I_p ≃ 3 MA, toroidal magnetic field, B_T ≃ 3 T and elongation, κ = 1.45. The auxiliary power was varied such that the total power ranged from 2 to 13.5 MW. Electron temperature perturbations in a 20 cm region around a minor radius of r = (2/3)a were recorded with high time resolution, using a 12 channel electron cyclotron emission polychromator. From these measurements the electron heat diffusivity was derived. Over the whole range of powers considered, was found to be independent of power and to lie in the range of 2.5 ± 0.5 m²·s⁻¹. The quantity is compared to as derived from global power balance analysis. For Ohmic heating, the latter is lower than by a factor of 2.5. For increasing auxiliary power, approaches . A model for the dependence of the local χ_e n the temperature gradient is presented; it permits a unified description of the heat pulse behaviour, the deterioration of confinement and a certain degree of profile consistency. The model does not invoke non-local parameters such as the total power input. It is shown that the present heat pulse data, subject to this interpretation, contradict the τ_E scaling laws of the typical form τ_E ∝ P^−0.5.

The temperature profiles produced by various heating profiles are calculated from local heat transport models. The models take the heat flux to be the sum of heat diffusion and a non-diffusive heat flow, consistent with local measurements of heat transport. Two models are developed analytically in detail: (i) a heat pinch or excess temperature gradient model with constant coefficients; and (ii) a non-linear heat diffusion coefficient (χ) model. Both models predict weak (≲20%) temperature profile responses to physically relevant changes in the heat deposition profile – primarily because the temperature profile is a double integral of the heating profile. The model predictions are shown to agree with JET data for a variety of heating profiles ranging from peaked on-axis through approximately flat (NBI at high density) to localized off-axis (ICRH). The modest temperature profile responses that result from the models clarify why temperature profiles in many tokamaks are often characterized as exhibiting a high degree of 'profile consistency'. Global transport scaling laws are also derived from the two models. The non-linear model with χ ∝ dT/dr produces a non-linear energy confinement time (L-mode) scaling with input power, . The constant heat pinch or excess temperature gradient model leads to the offset linear law for the total stored energy W with P_in, W = τ_inc P_in + W(0), which describes JET auxiliary heating data quite well. It also provides definitions for the incremental energy confinement time , the heating effectiveness η, and the energy offset W(0). Considering both the temperature profile responses and the global transport scaling, the constant heat pinch or excess temperature gradient model is found to best characterize the present JET data. Finally, new methods are proposed for interpreting auxiliary heating data in terms of these local transport models.

Magnetic separatrix configurations have been produced in JET for plasma currents of up to 3 MA. Experimental results obtained with these configurations show that some features can be achieved that are common to divertor tokamaks. In Ohmic discharges, high recycling regimes can be produced. In neutral beam heated discharges, substantial improvement of the energy confinement time is achieved together with the characteristic signatures of an H-mode. These characteristics include improved particle confinement, flatter density profile, and an increase in electron temperature especially at the edge, leading to a characteristic pedestal feature. At higher neutral beam power, higher plasma densities are reached, with deterioration of beam penetration and strong radiation losses in the outer region of the plasma. The global energy confinement time in the H-mode is observed to degrade with additional power. However, results of radial power balance analysis suggest that in the central region, where the radiation is not important, the degradation of confinement is small.

Electron heat transport on TFTR and other tokamaks is several orders of magnitude larger than neoclassical calculations predict. Despite considerable effort, there is still no clear theoretical understanding of this anomalous transport. The electron temperature profile, T_e(r), has shown a marked consistency on many machines for a wide range of plasma parameters and heating profiles. This could be an important clue as to the process responsible for this enhanced thermal transport. In the first section of the paper the result is presented that TFTR electron temperature profile shapes are even more constrained than previous models of profile consistency suggested. The profile shapes, T_e(r)/T_e(a/2), are found to be invariant (for r > 0.4 a) for a wide range of parameters, including q(a). In the second section, an experiment is discussed which uses a fast current ramp to transiently decouple the current density profile, J(r), and the T_e(r) profiles. From this experiment, it has been determined that the J(r) profile can be strongly modified with no measurable effect on the electron temperature profile shape. Thus, while the electron temperature profile is apparently constrained, the current profile is not.

A method of inducing a convective influx of core plasma in tokamaks using a specially structured vertically asymmetric ripple is proposed. In the ripple well the radial gradient of the toroidal field is increased on the flux surfaces in the plasma boundary layer below midplane. Also, the magnitude of the ripple decreases exponentially from the boundary toward the magnetic axis and is practically negligible above midplane. Counterrstreaming circulating particles will drift toward the centre owing to extra inward drift from the increased gradient whenever the particles drift through the ripple. The inward drift is manifested by × ∇ drift due to the increased length of the field line and to slowing down and change in q-values. The overall effect on the diffusion of banana particles is minimal. The influx is proportional to temperature and roughly to (1 − ), where is the inverse aspect ratio. The enhancement of the penetration of beam injection can also be achieved by injecting the beam into the axisymmetrie regions tangentially in the counter streaming direction as well as by injecting the beam perpendicularly into the ripple well.

The effects of losses of the fast electron current carriers are included in a calculation of the efficiency of RF current drive. The analytical expressions obtained for the current drive efficiency J/P_A and bulk heating rate P_D/P_A are explicitly dependent on the fast electron confinement time, T_F. In most present tokamak experiments, fast particle losses are predicted to reduce the current drive efficiency from 50% to more than an order of magnitude. However, in future fusion plasmas fast electron confinement appears to be sufficient to allow nearly ideal efficiencies to be achieved.

The model ballooning mode equation of Connor, Hastie and Taylor for large-aspect-ratio circular tokamaks is analysed in the limit of large pressure gradient, and corresponding expressions for stability boundaries are derived. In particular, it is found that for fixed radial wavenumbers infinite sequences of unstable bands exist and that minimizing over the radial wavenumbers leads to asymptotic merging between the neighbouring bands, which significantly modifies the second stability boundary compared with that for zero radial wavenumber.

A marked increase in the confinement time of injected impurities was measured during detachment of the plasmas in the TEXTOR tokamak. Non-recycling, metallic elements were introduced via laser blow-off, and scaling studies were performed. As the electron density increased, a threshold was reached beyond which the decay time of the brightness of the injected impurity transition was seen to increase from 75 ms to greater than 500 ms. The detachment of the plasma appeared coincident with the onset of this long confinement regime.

The LIDAR Thomson Scattering System on the JET tokamak is described. Backscattering geometry and the time of flight method are employed to measure profiles along the major radius in the equatorial plane. First electron temperature profiles with a spatial resolution of better than 15 cm obtained with this new diagnostic technique are presented.

A simple model is constructed which allows a systematic study of the effect of local heating or non-inductive current drive on tearing modes. The current profile changes due to the heating and current drive are calculated in steady state. An extensive study is made of the properties of the m = 2, n = 1 tearing mode within this model. It is shown that the effect of local heating on the m = 2, n = 1 mode stability is extremely sensitive to its localization. This sensitivity will, in practice, be prohibitive for mode stabilization by local heating. Non-inductive current drive is shown to be far more efficient in stabilizing the m = 2, n = 1 mode. The optimum effect of the non-inductively driven current is obtained when it is positioned such that the current density gradient immediately inside the mode resonant surface is reduced.

Radiofrequency current drive in tokamak plasmas in the presence of trapped electrons is investigated. The appropriate response function, allowing the current drive efficiency, J/P, to be expressed by a simple analytical formula, is evaluated. It is shown that a significant degradation of the current generated away from the plasma axis is to be expected for methods relying on perpendicular diffusion only, even for appreciably high resonant parallel velocities.

Penetration depths for frozen D₂ pellets into ASDEX ohmically and auxiliary heated discharges are reported for a wide range of plasma and pellet parameters. It is found that the data are well correlated by a single parameter (pellet diameter, pellet velocity, central electron density and temperature), which emerges from the neutral shielding model. The pellet depths, however, are systematically smaller than is expected from the model, implying a higher ablation rate in the outer plasma layers.