Table of contents

Different plasma responses to neutral beam injection in the directions co and counter to the plasma current have long been accepted as well understood in neutral beam heating of tokamak plasmas. Differences can also occur in fast wave heating and current drive in the ion cyclotron range of frequencies (ICRF) when antenna arrays are phased to drive current co and counter to the plasma current. The source of this asymmetry can be easily seen in the cold plasma wave equation with an applied magnetic field in the z direction and the parallel ICRF electric field set to zero (small electron mass limit). In the absence of absorption, the wave equation displays perfect up-down symmetry. However, when absorption is introduced, the up-down symmetry is destroyed by Hall terms, which depend on density and magnetic field gradients. This is confirmed by simple numerical solutions of the cold plasma wave equation with and without collisions. The same up-down asymmetry appears in three dimensional (3-D) antenna coupling calculations with outgoing boundary conditions. These show a natural poloidal shift in the antenna's radiated power spectrum even when no poloidal magnetic field is present. When a poloidal magnetic field is introduced, the up-down asymmetry acquires a toroidal component. This leads to differences in electron heating and current drive depending on the direction that fast waves are launched relative to the plasma current. Such differences are clearly seen in full wave modelling calculations of heating and current drive in NSTX, where poloidal and toroidal magnetic fields are comparable in magnitude near the antenna. When density gradients are forced to zero, both up-down and co-counter asymmetries disappear.

Progress in theory and in tokamak experiments leads to questions of the optimal development path for commercial tokamak power plants. The economic prospects of future designs are compared for several tokamak operating modes: (high poloidal beta) first stability, second stability and reverse shear. Using a simplified economic model and selecting uniform engineering performance parameters, this comparison emphasizes the different physics characteristics - stability and non-inductive current drive - of the various equilibria. The reverse shear mode of operation is shown to offer the lowest cost of electricity for future power plants.

A computational model has been developed that allows calculation of the radiofrequency (RF) power reflected by grill waveguide antennas, employed for additional heating of tokamak plasmas. The plasma surface impedance is evaluated using a full wave analysis with the SEMAL code (Sauter, O., Vaclavik, J., Comput. Phys. Commun. 84 (1994) 226), which solves the integrodifferential equations for the electric field of the wave in configuration space, in an inhomogeneous plasma, for any cyclotron harmonic and without any approximation with respect to the Larmor radius. These features are necessary for solving the problem of the antenna coupling of the ion Bernstein wave (IBW) plasma heating experiment, operating at an ion cyclotron harmonic higher than the second. In this experiment, the antenna coupling has to be carefully considered, in order to find suitable antenna-plasma conditions for avoiding parametric instabilities, a phenomenon that inhibits wave propagation in the plasma interior. As a result, for an IBW experiment on the FTU tokamak, a good antenna coupling is expected by assuming a low plasma density near the antenna-plasma interface. Nevertheless, by considering higher plasma densities, so that a low activity of the parametric instabilities is expected, a marginal antenna coupling has been found, with about 40% of RF power reflected at the antenna.

Electron cyclotron (EC) current drive experiments were carried out in lower hybrid current drive (LHCD) plasmas on the WT-3 tokamak. Using oblique injection of EC waves, plasma current is ramped up in a frequency range ω/Ω_e ≃ 1.2-1.4, where Ω_e is the EC frequency at the plasma centre. This ramp-up is ascribed to selective EC heating of fast electrons in LHCD plasmas via the fundamental EC resonance at the upshifted frequency due to the Doppler effect. Fast electron momentum distributions are estimated from bremsstrahlung hard X ray spectra. These distributions indicate that the parallel momentum input to the fast electrons in the relativistic energy range from oblique EC waves is effective for efficient EC current drive. Current ramp-up is also observed in the second harmonic frequency range ω/ Ω_e ≃ 1.9-2.2. In this case, bulk electrons are heated as well as fast electrons and no definite cause of current ramp-up is clarified.

Toroidal current penetration is studied in current ramp experiments on the JIPP T-IIU tokamak. The poloidal magnetic field profile in the peripheral region of a plasma (0.5 ⩽ r/a ⩽ 1.0) has been measured directly with a newly developed fast response Zeeman polarimeter. The experimental results indicate that a skin effect of the toroidal current density is clearly observed during both the current ramp-up (CRU) and the current ramp-down (CRD) experiments. The experimentally obtained toroidal current density profiles are well described by the profiles calculated on the assumption of neoclassical electrical resistivity, although the difference between the neoclassical electrical resistivity and the Spitzer electrical resistivity is not clearly distinguished because of the relatively collisional peripheral plasma region. Quasi-linear Δ' analysis of tearing modes for the measured current density profile is consistent with the time behaviour of the coherent magnetohydrodynamic (MHD) modes such as m = 4/n = 1 or m = 3/n = 1 (m is the poloidal mode number and n is the toroidal mode number) often observed during the CRU phase. An obvious enhancement of the current penetration by the MHD modes is not detected in this ramp-up experiment, where the relative amplitude of the poloidal field fluctuations is less than 0.8%.

Impurity toroidal rotation has been observed in the centre of Alcator C-Mod ion cyclotron range of frequencies (ICRF) heated plasmas, from the Doppler shifts of argon X ray lines. Rotation velocities greater than 1.2 × 10⁷ cm/s (ω = 200 krad/s) in the co-current direction have been observed in H mode discharges that had no direct momentum input. There is a correlation between the increase in the central impurity rotation velocity and the increase in the plasma stored energy (confinement enhancement), induced by ICRF heating, although other factors may be at play. The toroidal rotation velocity is highest near the magnetic axis, and decreases with increasing minor radius. A radial electric field of 300 V/cm at r/a = 0.3 has been inferred from the force balance equation. The direction of the rotation changes when the plasma current direction is reversed, remaining co-current. Impurity toroidal rotation in ICRF heated plasmas is in the direction opposite to the rotation in ohmic L mode plasmas; co-current rotation has also been observed during purely ohmic H modes. When the ICRF heating is turned off, the toroidal rotation decays with a characteristic time of order 50 ms, similar to the energy confinement time, and much shorter than the calculated neoclassical momentum damping time.

The possibility of using lower hybrid (LH) waves as a source of localized current for the control of MHD instabilities is investigated. A toroidal ray tracing code is used to define the requirements on the launched wave spectrum, in order to drive currents mostly localized inside the magnetic islands. Issues such as the radial diffusion of the non-inductive current, the impact of the radial profile of the power deposition on the stabilization process, the finite time response of the current to RF power modulations and its interplay with the island rotation are addressed by means of a three dimensional (3-D) Fokker-Planck code. It is shown that lower hybrid current drive (LHCD) is a viable option for the control of m = 2 tearing modes in present medium to large tokamaks: the method would be particularly effective in a reactor size machine.

High spatially resolved measurements of the radial electric field, E_r, have been made across the transition from L mode to H mode plasmas for many different plasma parameters and conditions. The evolution of the well-like structure of the E_r profile formed at the L-H transition has been investigated. No distinct variation in the shape or width of the E_r well at the L-H transition is observed as a function of the plasma parameters investigated, such as the plasma current, the toroidal magnetic field and the plasma density. The value of E_r is negative just inside the last closed flux surface (LCFS) for all the plasmas studied. There is a variation in the depth of the E_r well for different conditions. The experimental results have been compared with theoretical predictions for suppression of plasma turbulence by sheared E × B plasma flow.

The possibility of operations with advanced fuels in high temperature, high-β plasmas is investigated. At high β values, diamagnetic effects reduce the toroidal field strength in the plasma core and tend to localize the synchrotron radiation source in the outer part of the plasma column. Thus, the core energy balance is not affected by synchrotron radiation losses, but a large amount of the fusion power is radiated by the edge and the divertor power load is decreased. A small fraction of the radiated power can be recirculated for non-inductive current drive, to compensate for the large amount of bootstrap current, naturally present in such configurations. In this scheme, synchrotron radiation is also used to recover the fusion power, by direct conversion to electric power.

The temporal evolution of the edge electron pressure gradient during the development of a type I ELM shows that proximity of ∇p_edge to the ideal ballooning limit is not sufficient to trigger a type I ELM. Thus, the MHD structure of ELMs is investigated further. The present discussion focuses on the phenomenology of type I and type III ELM precursors. The ELM precursor types are well distinguished by their frequency behaviour and mode structure. The type I ELM precursor oscillation originates from a thin layer close to the plasma edge. For type III ELMs, on the contrary, ∇p_edge has a much stronger influence as indicated by their occurrence during L mode.

Various steady state non-inductive plasmas, with strong electron heating and significant modification of the current density profile, have been routinely obtained in Tore Supra discharges with lower hybrid current drive (LHCD) and/or fast wave electron heating (FWEH) experiments. The dependence of the electron heat diffusivity χ_e on the electron temperature gradient ∇T_e, the magnetic shear s and the safety factor q is demonstrated. The increase of χ_e with ∇T_e indicates the existence of a critical temperature gradient. Moreover, the current density profile affects the global confinement and the local transport. The electron heat flux q_e is found to be roughly proportional to q². The effect of magnetic shear on χ_e is studied in the improved confinement discharges obtained by modifying the current profile. When the magnetic shear increases in the confinement zone and/or vanishes in the plasma centre, χ_e decreases. The effect of the current profile is also observed in the saturated ohmic regime. The results for χ_e do not agree with the local transport models of Taroni et al. or Rebut-Lallia-Watkins (RLW) for all ranges of electron heating.

A two dimensional (2-D) combined edge plasma/Navier-Stokes neutral transport model is used in a computational study of dissipative divertor plasmas in the collisional limit for neutrals, with ITER-like plasma conditions and scale lengths. The neutral model contains three momentum equations that are coupled to the plasma through ionization, recombination and ion-neutral elastic collisions. The neutral transport coefficients are evaluated including both ion-neutral and neutral-neutral collisions. The structure of fully detached plasma solutions is studied for ITER plasma conditions. These detached solutions are obtained through a combination of impurity radiation, from a simplified impurity model, and neutral flow baffling. Solution sensitivities are elucidated to: (a) baffle location, (b) upstream plasma density and Lyman-α opacity, (c) volume recombination and (d) neutral-neutral collisions.