Table of contents

The global energy confinement characteristics of neutral beam heated JT-60 discharges are presented. There is a difference in the dependence of the energy confinement time on the plasma current between limiter and divertor discharges. For limiter discharges, the energy confinement increases with plasma current up to 3.2 MA, whereas for divertor discharges this improvement saturates when the safety factor drops below 3, independent of the location of the X-point. The JT-60 L-mode results indicate that the deterioration in energy confinement for q < 3, which is also found in H-mode regimes of other devices, may be a universal characteristic of divertor discharges. Regarding the scaling with plasma size, it is shown that the global/incremental confinement time increases with plasma minor radius. For sufficiently large plasmas, however, the global/incremental confinement time is no longer a function of minor radius.

Substantial losses of plasma stored energy and toroidal ion momentum are observed in JET during large amplitude oscillating or quasi-stationary MHD activity when mode coupling effects become important. The degradation in the diamagnetic stored energy due to low m,n MHD modes increases with amplitude, reaching ΔW/W > 30% at a mode amplitude of _r/B_θ > 0.4%. Favourable comparisons are made with the degradation in the incremental energy confinement time during such MHD activity as predicted by Chang and Callen. The reduction in the plasma ion toroidal momentum, from charge exchange measurements on C 6⁺ ions, depends on the extent of mode coupling within the plasma and on the oscillation frequency of the n = 1 mode. When _r/B_θ > 0.1% for more than about 300 ms, toroidal coupling between low m,n modes together with coupling of the plasma ions to the modes by a force equilibrates the toroidal ion rotation frequency with the MHD oscillation frequency over substantial regions of the plasma, depending on the radius of the rational q surface of the coupled MHD mode. This ion mode coupling force becomes particularly apparent when the mode frequency drops to nearly zero and the ion toroidal rotation frequency also drops to zero within 100–300 ms, despite continued neutral beam injection. In such cases, the toroidal ion momentum appears to be lost electromagnetically via the MHD modes to the external structure or to fixed stray fields of the tokamak, while the plasma stored energy losses must be accounted for by other processes.

Models are developed for estimating the effects of macroscopic phenomena in tokamaks (sawteeth, Mirnov oscillations, edge localized modes (ELMs), etc.) on plasma global energy confinement. The analysis is based on a recently developed formalism for determining the incremental energy confinement time τ_inc from a local transport model. The macroscopic phenomena are assumed to influence the plasma only in the regions where they occur, without changing the heat diffusivity elsewhere in the plasma. General expressions are presented in terms of a magnetic flux surface label (ρ). Simplified formulas for the effects are also given for a cylindrical geometry. For the Mirnov oscillation case (m/n = 2/1 or 3/1 tearing modes), two models (for 'belt' and island influenced regions) are investigated and compared. When a number of macroscopic phenomena are present simultaneously (but not overlapping) their net effect is shown to be a sum of the individual effects. Finally, for time dependent phenomena such as sawteeth and ELMs, appropriate time averages of their net effects are developed.

In JT-60, H-mode experiments with outer and lower divertors have been performed. In the outer divertor discharge, an H-mode similar to the modes observed in the lower/upper divertor discharges is obtained. Its threshold absorbed power and electron density are 16 MW and 1.8 × 10¹⁹ m⁻³. In the two schemes of combined heating with NB + ICRF and NB + LHRF, H-mode discharges are also obtained. Moreover, in the new configuration with the JT-60 lower divertor, H-mode phases with and without edge localized modes are obtained. The improvement in the energy confinement time in both divertor configurations is limited to values within 10%. The paper mainly presents the H-mode results of the outer divertor discharges. Also, typical results of the lower divertor discharges are shown for a comparison of the H-mode characteristics of the two configurations.

Two comparative heating experiments were carried out to test the role of the antenna screen angle during high power ICRF heating in JET. In the first experiment the magnetic field was practically aligned with the screen elements, whereas in the second experiment the toroidal field was reversed and the angle between the elements and the field was 25°. There were clear differences in the impurity influx, the heating efficiency and the coupling resistance between discharges with normal field and discharges with reversed field. The results indicate the impact of the Faraday screen design on the levels of RF enhanced metal influxes originating at the screen. This should be of particular relevance for the ICRF antennas in a reactor where, in contrast to small devices, most of the interaction between the RF fields and the plasma edge is expected to take place around the antenna structures because of the highly localized RF field patterns. A numerical code based on three-dimensional single-pass and full wave calculations of antenna-plasma coupling, including an arbitrary angle between the screen elements and the magnetic field, can qualitatively reproduce the observed difference in the coupling resistance. The experimental results are discussed with regard to possible mechanisms that can account for the observed differences in the two cases studied.

A concept of a steady state tokamak fusion reactor based on the bootstrap current is presented. Operation at high poloidal beta (β_p ≥ 2.0) and high q (4–5) with a relatively small limit on ∈β_p (< 0.5) makes it possible to drive a bootstrap current constituting up to 70% of the total plasma current without exceeding the Troyon beta limit. The rest of the plasma current can be driven by the high energy neutral beam with an energy multiplication factor Q of 30. Energy confinement scaling laws predict that the reactor condition is attainable by increasing the major radius up to 9 m in such a high β_p and high q plasma at a relatively low plasma current (12 MA) with a confinement enhancement factor of 2 compared with the L-mode scaling. This reactor has a reasonable size (V_p = 1500 m³) and fusion output power (2.5 GW) and is consistent with present knowledge regarding tokamak plasma physics, namely the Troyon limit, the energy confinement scalings, the bootstrap current and the current drive efficiency (neutral beam current drive with a total power of 70 MW and a beam energy of 1 MeV) with good prospects for the formation of a cold and dense divertor plasma.

Non-linear numerical simulations of a reversed field pinch (RFP) with RFX geometry are presented. Emphasis is on the probable effect of a thin (resistive) shell design on experimental operation. Calculations are performed over a range of Lundquist number S and pinch parameter Θ, with realistic geometric parameters. It is found that operation with a thin shell is likely to be characterized by an enhanced fluctuation level, increased loop voltage and generally degraded plasma performance. This conclusion is independent of the specific value of the design thin shell time constant as long as this value is significantly less than the design discharge time. Specific scalings of loop voltage with Lundquist and pinch parameter are given. Results relevant to toroidal phase locking are also reported.

The coupling characteristics of the fast wave excited by a phased four-loop antenna array are described. Fast waves in the lower hybrid frequency range have the potential of generating plasma current in hot and dense plasmas. Fast waves are excited at the plasma edge by an oscillating magnetic field parallel to the toroidal direction. The parallel wavenumber of the excited fast waves is determined by the relative phase of the RF current on each antenna. The loading resistance of the antenna increases with density, but at densities above 2 × 10¹⁹ m⁻³ it starts to decrease with density, because of the steepening of the density gradient. The loading resistance is strongly dependent on the antenna phasing. The maximum loading due to surface wave excitation is obtained at Δϕ = 0 and the minimum at Δϕ = π. Substantial absorption of the excited fast waves is observed at the plasma centre when the antenna phasing is Δϕ = π. The absorption efficiency rises with decreasing phase velocity of the excited waves. The experimental results obtained in the coupling experiment are consistent with theoretical predictions.

The concentration of deuterium in JET plasmas, expressed as a fraction of the electron concentration, has been determined using eight different methods, four of which involve neutron detection. The results from these various methods are found to be consistent within their experimental errors. The ratio n_D/n_e, measured at the moment of peak neutron emission strength, is found to lie in the range from nearly unity, for discharges into which deuterium pellets are injected, down to values of 0.4 or less, for some of the highest performance discharges. This finding is based on the analysis of discharges run in 1988, when the plasma facing components within the vacuum vessel were of carbon or were carbon coated.

The runaway tokamak equilibrium is analysed numerically. The runaway electrons with distributed energy are modelled by multi-energy electron beams. The model equations include a self-consistent orbit analysis of the beams. This aspect improves the accuracy of the theory compared with the usual calculations of beam-plasma equilibrium which model the beam effect by an enhanced pressure parallel to the magnetic field. Deformations of a tokamak equilibrium due to the beam inertial effect are studied. The beam component achieves a betatron equilibrium in a total poloidal magnetic field due to the plasma current and the external equilibrium coils.

Current drive in tokamak plasmas by a beat wave is considered in two-dimensional (2-D) geometry. The beat wave is excited by the non-linear interaction of two intense microwave pulses (free electron lasers) in the plasma. The three-wave non-linear interaction equations in steady state are solved numerically. The 2-D toroidal effect and the effect of finite spatial width of the pump microwave pulses are taken into account for the excitation of the beat mode. To illustrate the principle, two types of tokamak are considered: one is small, such as, typically, the Microwave Tokamak Experiment (MTX), and the other one is larger, such as the Joint European Torus (JET). In both cases, it is found that good beat wave coupling exists for a Langmuir beat wave with a phase velocity of around 2.0 to 4.0 times the thermal velocity of the electrons. The fraction of total input power of the right circularly polarized pump waves deposited in the beat mode can be as high as 29% in JET and 32% in MTX. In these cases, there is almost complete pump depletion of the higher frequency pump microwave. It is also found that, for the same input parameters, left circularly polarized pump waves are less efficient than right circularly polarized pump waves for depositing power in the beat mode.

The neoclassical bootstrap current effect is investigated in the JT-60 tokamak. The experimental resistive loop voltages are compared with the calculations, using the neoclassical resistivity, with and without the bootstrap current, and the Spitzer resistivity for a wide range of plasma current (I_p = 0.5-2 MA) and poloidal beta (β_p = 0.1-3.2). The neoclassical bootstrap current is calculated directly with the force balance equations for viscous and friction forces according to the Hirshman–Sigmar theory. The bootstrap current driven by the fast ion component is also included. The calculated resistive loop voltage is consistent with the neoclassical prediction including the bootstrap current. It is shown that up to 80% of total plasma current is driven by the bootstrap current in the regime with an extremely high poloidal beta value (β_p = 3.2) while the beam driven current is negligibly small.

The transport equations arising from the 'generalized Balescu-Lenard' collision operator are obtained and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases having the same structure. The resultant theory offers a possible explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/ΓT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy with neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest.

A new method of analysis for presenting the possible operating space for steady state, non-ignited tokamak reactors is proposed. The method uses contours of reactor performance and plasma characteristics, fusion power gain, wall neutron flux, current drive power, etc., plotted on a two-dimensional grid, the axes of which are the plasma current I_p and the normalized beta, β_n = β/(I_p/aB₀), to show possible operating points. These steady state operating contour plots are called SOPCONS. This technique is illustrated in an application to a design for the International Thermonuclear Experimental Reactor (ITER) with neutral beam, lower hybrid and bootstrap current drive. The utility of the SOPCON plots for pointing out some of the non-intuitive considerations in steady state eactor design is shown.

An analytical asymptotic expression of the response function χ for fast non-relativistic electrons of a magnetized plasma, accounting for the lowest order corrections introduced by a finite temperature of the bulk electrons, is deduced as a solution of a Spitzer problem. Toroidal effects are included by means of the square well approximation model for the magnetic field. It is shown that the absolute value of χ increases compared to the case where no finite bulk temperature is considered. The effects on current drive efficiency are also discussed.

Cross-sections for electron transfer into individual (n,ℓ) projectile states in Si^q+ + H collisions (q = 4, 6, 7-14) are calculated at impact energies of 0.5-14 keV/u. The calculations are performed within the semiclassical close-coupling formalism with one-electron atomic orbital basis sets. Calculated electron transfer crosssections for the dominantly populated projectile shell n_max ≃ q^¾ plus one to three additional shells are presented in tabular form and are discussed with regard to their dependence on the energy and charge states. The prominent role of the electronic core for the ℓ-distributions of cross-sections is pointed out.