Table of contents

Explicit use of the poloidal Ohm's law, together with the radial plasma velocity (obtained from the distribution of plasma sources), leads to a very general constraint on the possible radial profiles of plasma density and temperature. The constraint does not require any ad hoc assumption; it can place severe restrictions on the allowed profiles and is independent of energy and particle transport; also, it may be the underlying principle of profile consistency. The constraint is discussed in the framework of neoclassical theory, using results from the Frascati tokamak.

The paper presents a local quasi-one-dimensional theory of steady state current generation in tokamaks by lower hybrid waves which is valid for an arbitrary width of the wave spectrum. The characteristics of the generation of current drive in large scale tokamaks are analysed. On the basis of the concepts developed here, expressions are derived for the total driven current, the absorbed RF power and the global current generation efficiency. The dependence of the current generated by lower hybrid waves on the plasma parameters is investigated.

The combination of two regimes of enhanced performance, the H-mode and the pellet enhanced performance (PEP) mode, has been achieved in JET. The strong enhancement of the central plasma parameters, obtained with pellet injection and subsequent auxiliary heating, is found to persist well into the H-mode phase. A characteristic of the PEP regime is that an improvement of the fusion reactivity over non-pellet discharges is obtained under the condition of nearly equal electron and ion temperatures. A maximum neutron production rate of 0.95 × 10^l6 s⁻¹ was obtained in a double-null X-point discharge with 2.5 MW of neutral beam heating and 9 MW of ion cyclotron resonance heating, with central ion and electron temperatures of about 10 keV and a central deuterium density of 8.0 × 10¹⁹ m⁻³. The corresponding fusion product n_D(0)τ_ET_i(0) is between 7.0 and 8.6 × 10²⁰ m⁻³·s·keV. The enhanced neutron production is predominantly of thermonuclear (Maxwellian) origin. The compatibility of these regimes is an important issue in the context of tokamak ignition strategies. Several technical developments on JET have played a role in the achievement of this result: (1) the use of low voltage plasma breakdown (0.15 V/m) to permit pellet injection in an X-point configuration before the formation of a q = 1 surface; (2) the elimination of ICRH specific impurities with antenna Faraday screens made of solid beryllium; (3) the use of a novel system of plasma radial position control that stabilizes the coupling resistance of the ion cyclotron heating system.

Many difficult technological problems encountered in fusion reactors could probably be solved if D-3He fuel would be used instead of D-T fuel. The paper examines the burn characteristics for inertial confinement fuel pellets, i.e. for pure D-3He fuel pellets and for D-³ ignitor/D-³He fuel pellets, using a hydrodynamics code modified to include neutron transport and charged particle transport. The results indicate that it is difficult to ignite pure D-³He fuel pellets with a reasonable driver energy. However, the ignition conditions can be relaxed by using D-T fuel as ignitor. It is found that a fuel gain of ∼480 can be obtained with D-T/D-³He pellets having a spark temperature of 5 keV, a D-T ignitor ρR value of 3.0 g/cm² and a total fuel ρR value of 15.5 g/cm². When the density of these pellets is assumed to be 10 000 times the liquid density, the internal energy of the configuration at ignition is ∼1.2 MJ, which is still more severe than that in the case of D-T fuel. It is also shown that the transport of 14.7 MeV protons produced by the D-³He reaction plays a significant role in determining the burn characteristics of the pellets. Nuclear elastic scattering (NES) of 14.7 MeV protons enhances the ion heating, leading to a fuel gain which is higher by about 20% than that in the case without NES. The effect of nuclear spin polarization is also examined for an ideally polarized fuel pellet. It is found that the burn characteristics are improved and that the required driver energy is possibly decreased.

An analytical expression for the eigenvalue of the global m = 1 kink mode in a straight screw pinch with arbitrary profiles of current density and axial magnetic field is derived in a long wavelength approximation of the incompressible ideal MHD equations. While the influence of the current profile is related to the inductance l_i of the plasma column, as has been shown previously (Nucl. Fusion 24 (1984) 1357), it is found here that the effect of the axial magnetic field profile can be expressed in terms of the poloidal beta value β_p of the pinch. In turn, β_p is related to a possible paramagnetism (β_p < 1) or diamagnetism (β_p > 1) of the plasma. Considering the range of stable eigen-values, the Kruskal-Shafranov condition q(a) > 1, independent of l_i and β_p, is recovered in the tokamak regime B_z, ≫ B_ϕ. In the regime B_z ⪅ B_ϕ, on the other hand, the stability condition is strongly dependent on both l_i and β_p. Optimal stability conditions in this regime are obtained for l_i, ≪ 1 (hollow current distribution), β_p ≪ 1 (strong paramagnetism) and B_z(a) ≪ B_ϕ(a) (low q(a)). In this case, wavelengths of up to fourteen times the plasma radius become stable, and also the growth rates of the unstable wavelengths are considerably reduced as compared to the situation with l_i, β_p ∼ 1 and B_z ∼ B_ϕ, or compared to the growth rates obtained in the tokamak regime. The results obtained are consistent with recent experimental observations in 'ultra low q' discharges.

Locked n = 1 tearing modes are observed over a wide range of parameter space in DIII-D and other tokamaks. Much of the difficulty with low density operation is attributed to locked modes and they are also observed as precursors of density limit disruptions. From observations of a consistent locked mode toroidal phase, it appears that the modes are locking to a small field perturbation caused by slight irregularities in the location of one or more of the vertical field coils with respect to the toroidal field coil. By intentionally producing an n = 1 field with an external coil, it was possible to influence the onset of locked modes in low q, low density plasmas. The result is a significantly expanded or reduced stable operating parameter space, depending on the polarity and magnitude of the external perturbation applied and whether or not intrinsic field errors are reduced or increased. A simple theoretical model of the non-linear stability of a tearing mode under the effect of externally applied resonant field perturbations yields a critical island width for the onset of a locked mode. The island widths, computed by field line tracing, for combinations of intrinsic field errors and 'n = 1 coil' fields are in qualitative agreement with the critical island width for instability.

The D-D fusion reactivity from JET plasmas has been optimized by using combined neutral beam injection and radiofrequency heating. Reaction rates of up to 2.9 × 10¹⁶ reactions per second (equivalent to neutron emission rates of 1.45 × 10^l6 neutrons per second) have been achieved. The best results were obtained in the doublenull magnetic configuration or with plasmas limited by the inner wall. By far the largest fraction of the neutron production originates from beam induced reactions, although, in some cases, about 25% of the production can be attributed to the acceleration of deuterium ions by the radiofrequency. The instantaneous neutron yield was limited by a strong influx of carbon impurity ions due to excessive, but local, wall heating.

The Mirnov oscillations observed in the ASDEX tokamak are analysed with regard to the generally accepted interpretation scheme according to which (1) Mirnov oscillations are caused by currents flowing parallel to the magnetic field on rational magnetic surfaces and (2) the field perturbation is frozen within the plasma. If the second statement holds, the frequency is obtained from the profiles of the electron density, the ion temperature and, if applicable, the toroidal or poloidal rotation velocity. It is shown that there are modes which are consistent with the above interpretation. On the other hand, mode coupling is observed. Mode coupling is also invoked to reconcile the experimental findings with the predictions of a theory based on statement (1); according to this theory, there is a poloidal variation of both the phase velocity and the amplitude of the Mirnov oscillations. While the observed phase velocity fits well into this picture, the poloidal variation of the amplitude cannot be ascribed to only one mode in the majority of cases. In addition, the possibility of coherent MHD activity due to currents in the scrape-off layer is discussed.

Confinement scalings of divertor discharges and radiofrequency heated discharges are shown to differ significantly from the standard scaling for neutral beam heated limiter discharges. The random coefficient two-stage regression algorithm is applied to a neutral beam heated limiter subset of the ITER L-mode database as well as a combined dataset. A scaling similar to the Goldston scaling is found for the neutral beam limiter dataset and a scaling similar to the ITER89P scaling is found for the combined dataset. Various missing-value algorithms are examined for the missing B_t scalings. It is assumed that global confinement can be approximately described by a power law scaling. After the second stage, the constraint of collisional Maxwell-Vlasov similarity is tested and imposed. When the constraint of collisional Maxwell-Vlasov similarity is imposed, the uncertainty for CIT is significantly reduced, while the uncertainty for ITER is slightly reduced.

Toroidal plasma rotation driven not by the momentum input but by the electric field induced by loss of ions has been observed for plasmas heated by perpendicular neutral beam injection. The rotation is found to increase in the direction opposite to the plasma current when the plasma ions are heated by ion cyclotron resonance frequency waves. The rotation driven by the electric field is quantitatively consistent with that inferred from the ambipolarity of particle fluxes.

The transport properties of injected impurities were examined in the TEXTOR tokamak to determine the influence of the limiter configuration. Using laser blow-off and the decay of the centrally located charge states of iron, transport scaling studies were performed in which plasmas bounded by standard poloidal limiters and plasmas bounded by the ALT II toroidal limiter were compared. The results presented show the appearance of the long impurity confinement regime in both limiter configurations which was coincident with the detachment of the plasma. Shifts in the critical density for the onset of this regime were seen. Possible plasma conditions responsible for these differences are addressed. The absence of significant accumulation of intrinsic impurities during the long confinement regime indicates a different generation/transport mechanism in detached plasmas.

The ion temperature gradient (ITG) driven mode (or η_i mode) is studied for a tokamak where the pressure gradient is sufficiently large (β_ρ ∼ 1) to modify the local shear and the gradient of the magnetic field strength. It is found that these two diamagnetic modifications of the plasma equilibrium have a stabilizing effect on the ITG mode. This could contribute to the good edge confinement observed in the H-mode and the improvement of ion energy confinement in a second stability regime tokamak.

The two-electron transfer reaction was applied to the detection of helium ions in the thermal and epithermal energy range in JT-60. Using this technique, the helium ion density and the energy distribution were determined. The ion density and energy distribution obtained were consistent with the results from other diagnostics and from theory. The potential of this technique for measurements of the helium ash density and the energy distribution in fusion plasmas has been demonstrated.

A dielectric-free slotted waveguide fast wave coupler (SWFWC), operating in the lower hybrid range of frequencies, has been used to drive current on the Versator-II tokamak. Up to 35 kW of radiofrequency at 2.45 GHz has been radiated into plasmas with electron densities of 2 × 10^l2 cm⁻³ ≤ _e ≤ 1.2 × 10¹³ cm⁻³ and a magnetic field of B_tor = 1.0 T. When the coupler was flush with or beyond the limiter, the radiating efficiency improved linearly with increasing rig. For electron densities _e ≥ 5 × 10¹² cm⁻³, the current drive efficiency was similar to that of the slow lower hybrid wave; however, at lower densities the efficiency of the SWFWC was reduced and it drove no current when _e ≤ 2 × 10^l2 cm⁻³. During bench tests, the antenna radiated >90% of its power in the fast wave polarization. These observations suggest that the SWFWC launched primarily fast waves. However, we do not exclude the possibility that, owing to weak single-pass absorption, a substantial fraction of the power may have been converted to slow waves within the plasma, and these waves may have been responsible for most of the driven current.

The fluid theory of electrostatic perturbations in a scrape-off layer (SOL) plasma is analysed. The main difficulty is that the edge is theoretically found to be stable, while experimentally it is unstable. A possible explanation relies on the fact that the commonly used ballooning representation is not correct in the SOL. An alternative representation is proposed which reproduces the instability of the edge in several simple configurations and explains many experimental features.

The stability of higher harmonic electrostatic electron drift waves in toroidal geometry in studied for a representative plasma profile. Using a model driving function, it is shown that the dissipative trapped electron (DTE) mode admits solutions ω/ω_e^* ≫ 1 (ω_e^* is the electron diamagnetic drift frequency) that may relate to density fluctuation measurements which have suggested the presence of such higher frequency modes. Comparison of analytic and numerical results for both outward and inward ballooning DTE modes gives good agreement for the former modes but generally poor agreement for the latter ones. Further, it is found from the numerical results that the inward ballooning modes may be more unstable than the outward ballooning modes, even though the trapped electron drive is maximized on the outboard midplane.

The Fusion Technology Institute of the University of Wisconsin initiated and sponsored a symposium on D-³He fusion systems, held at Madison, WI. The purpose of the symposium was to bring together a small group (there were 18 invited participants at the meeting) of knowledgeable researchers to discuss the present status of thinking on such systems.