Table of contents

The interaction between ion Bernstein waves (IBWs) and well passing ions is considered in the limit α ≡ Ω/(ω_ci ω_t)^1/2 >> 1 (here Ω is the phase oscillation frequency in the wave field, = r/R is the inverse aspect ratio, and ω_ci and ω_t are the ion cyclotron and transit frequencies, respectively). In this case stochasticity arises due to repeated separatrix crossings, caused by successive trapping by waves, when the ions pass through a cyclotron resonance on the transit trajectory. According to general theory, changes in the adiabatic invariant do not correlate for successive resonance passages. As a result, diffusion in velocity space should arise. The calculated diffusion coefficient scales as D_μ ∝ α^-4, while in the opposite limit, α<<1 and D_μ ∝ α². A possible application of this result to the problem of alpha channelling is discussed.

The β_p value for the onset of the neoclassical (3, 2) tearing mode at ASDEX Upgrade is found to be proportional to the ion gyro-radius as proposed in the ion polarization model. This scaling law has been proven by varying the ion temperature, the magnetic field and the mass of the plasma ions.

The time evolution of radiating vapour shields over eroding solid surfaces and the resulting erosion rates are modelled by one dimensional (1-D) and 1½-D resistive MHD codes. Graphite or carbonized divertor plates subjected to high energy deuterium plasma particles during disruptions or giant ELMs are considered. The energy flux range assumed corresponds to ITER conditions. Various physical phenomena having a primary effect on the erosion rate, such as collisional interaction of the energy carriers with the target (solid surface or vapour particles), electrostatic shielding, magnetohydrodynamic interaction and radiant energy transport, are investigated in detail. In the 1-D and 1½-D approximations used and for the energy input parameter range considered (Q₀ = 10¹¹ W/m²) ablation rates of the order of 10²⁸ m^-2·s^-1 were obtained. It is shown that processes, such as lateral expansion, lateral drift, radiation losses through the lateral surfaces of the scrape-off layer (SOL) and the Hall effect, may notably change the predicted erosion rates and warrant a more elaborate, at least 2-D, treatment of the problem.

Giant edge localized modes (ELMs) play an important role in the transport of plasma at the edge of tokamaks with a divertor. The loss of plasma, by mechanisms that are not well understood, causes very high power loading on parts of the wall structure. The flows of particles and energy have been determined on a rapid time-scale for the first time in JET. The soft X ray measurements have a complex structure and show a rapid onset of the instability. They prove that some plasma is lost outside the divertor and that recycling occurs to well within the separatrix. The implications of the results for the ELM instability mechanism and the design of tokamaks are discussed.

Systematic stability studies of the negative central shear (NCS) configuration reveal a synergistic relationship between the gains in the ideal n = 1 magnetohydrodynamic (MHD) β limit from optimizing the profiles and from optimizing the shape. For a circular cross-section with highly peaked pressure profiles, β_N = β/(I/aB) is limited to β_N∼2% (mT/MA). Small to moderate improvements in β_N result either from broadening the pressure or from strong cross-section shaping. At fixed safety factor the latter translates to a much larger increase in β and the root mean square β denoted as β*. With both optimal profiles and strong shaping, however, the gain in all the relevant fusion performance parameters is dramatic, and β and β* can be increased by a factor of 5. The calculations show that stabilization from a nearby conducting wall greatly contributes to this large improvement, since coupling of the plasma to the wall is increased for the optimum profiles and cross-section. Moreover, the alignment of the bootstrap current density profile with the total current density profile is also optimized with broad pressure, strong cross-section shaping and high β_N, thus minimizing steady state current drive requirements. Sensitivity studies using other profiles show some variation in the actual β limits, but the general trends remain robustly invariant.

It is recognized that tokamak plasma disruptions and vertical displacement events, with the attendant appearance of `halo currents', are a threat to future experiments such as ITER. Halo currents, flowing between the plasma and the wall, can develop large spatially localized components. Here, this is ascribed to a new instability that can occur in a composite circuit of a magnetized plasma and a solid conductor. The presence of the conductor divides the current perturbation into topologically distinct stable and unstable composite plasma-wall circuits. The plasma paths of such circuits are subject to hydromagnetic motions, which alter circuit geometry and conductivity while self-consistently preserving toroidal and poloidal periodicity. A simple prototype model is developed that is solved numerically and analytically to illustrate the geometrical aspect of the mechanism. The heterogeneity of the true plasma-wall system is shown to introduce considerable complexity. The basic concept may underlie a wider class of instabilities and waves.

The plasma density of a field reversed configuration (FRC) needs to be decreased below the present experimental regime in order to heat the plasma and sustain the configuration by a high energy neutral beam in an FRC reactor. However, as the plasma is produced in a linear vacuum vessel, there exists a severe breakdown limit at a low fill pressure as compared with a toroidal system. A method to form FRCs beyond the breakdown limit is proposed here. The preionized plasma is compressed by a strong bias field to enhance the plasma flow from the confinement region to the outside region and is then diluted before the start of the confinement field on the NUCTE device. The use of a diluted plasma enables the critical density of the FRC to be lowered from 1.1 × 10²¹ to 5.6 × 10²⁰m^-3 and the sum of the electron and ion temperatures to be increased from 0.35 to 0.81 keV.

Kinetic corrections to a previous ideal MHD ballooning stability study of the TJ-II heliac standard configuration are numerically calculated using a criterion derived from the gyrokinetic Maxwell equations for modes with perpendicular wavelengths on the scale of the ion gyroradius in a general magnetic geometry. In this criterion, finite ion gyroradius and trapped particle effects are retained at first order. The existence of temperature gradients and different ion and electron temperatures are accounted for. The relevant kinetic regime for TJ-II is found to be the intermediate frequency regime, with ω_bi, ω_ti < γ < ω_be, ω_te across all the relevant region whenever electron cyclotron resonance heating (ECRH) plasmas are considered. Therefore, only trapped electrons are included in the calculations. The threshold poloidal wavenumber m_u for diamagnetic stabilization of unstable ballooning modes is obtained, and a reduction of about 30% of the instability region radial width has been found. The trapped electron contribution to the growth rate is shown to be destabilizing for all modes with poloidal wavenumber below this threshold and is evaluated perturbatively, showing that an important part of it is due to those electrons trapped in the ripple of the magnetic field.

This article extends the work of Skupsky and Lee (Skupsky, S., Lee, K., Appl. Phys. 54 (1983) 3662) and Murakami et al. (Murakami, M., et al., J. Appl. Phys. 74 (1993) 802) in presenting analytic formulas that predict the laser flux asymmetry, in various inertial confinement fusion (ICF) targets from low order modes, due to beam geometry, variations in beam power and beam pointing errors. The variance per l mode σ²_l is given for both direct drive and tetrahedral hohlraums, as a function of mode number, the beam geometry, and the pointing and power balance errors. For the National Ignition Facility (NIF), a proposed 1.8 MJ laser, the flux asymmetry on a direct drive capsule is dominated by power balance errors in modes 1 and 2. For the Omega, a 30 kJ laser at the Laboratory for Laser Energetics at the University of Rochester, the flux asymmetry on a direct drive capsule is dominated by pointing errors in modes 1 to 5. The flux asymmetry on a tetrahedral indirect drive target is dominated by the Y_3,2 mode resulting from the laser entrance holes.

The rotation of cylindrical plasmas has been investigated using visible spectroscopy. The rotations of variously charged impurity ions have been measured. Since the detected signal is the line integrated emission, the measurement technique of plasma rotation and the parametric Abel inversion technique have been developed to obtain the local impurity emission profile and the potential profile. Three different types of fitting functions for the parametric Abel inversion technique have been examined using numerical simulations. The following significant observations are made: (a) the radial profiles of the electrostatic potential obtained from rotations of various ions are identical, (b) the Doppler shift profile due to diamagnetic rotation is different for the different ion species. This is the first clear experimental observation of diamagnetic drift in high temperature plasmas.

New theoretical and experimental tools are applied to the analysis of ICRF antenna-edge plasma interactions in the TFTR tokamak. A new numerical method for computing the three dimensional (3-D) rf sheath voltage distribution is used, and the quantitative predictions of rf sheath theory are compared with measurements of the edge density profile obtained by microwave reflectometry and with titanium impurity concentration data. It is shown that the local density depletion at the antenna is consistent with density pump-out by strong E × B convection into the Faraday screen (FS). Modelling of the FS impurity influx shows that the calculated titanium impurity concentration based on this direct influx agrees with the measured concentration for π phasing. It is also shown that screening of impurity neutrals by ionization in the SOL is a large effect and increases with rf power. At high power over many shots, a fraction of the metal impurities migrates around the machine and is deposited on the limiters, providing a secondary source of titanium. The data show that the central titanium concentration is strongly dependent on antenna phasing. Possible explanations for this phasing dependence are discussed.

The results of a Fokker-Planck simulation of the ripple induced loss of charged fusion products in TFTR are presented. It is shown that the main features of the measured `delayed loss' of partially thermalized fusion products (FPs), such as the differences between deuterium-deuterium (DD) and deuterium-tritium (DT) discharges and the plasma current and major radius dependences, are in satisfactory agreement with the classical collisional ripple transport mechanism. The inclusion of an inward shift of the vacuum flux surfaces turns out to be necessary for an adequate and consistent explanation of the origin of the partially thermalized fusion product loss to the bottom of TFTR.

Correction to Nuclear Fusion 38 (1998) 1001, figure 9