Table of contents

The effectiveness of a warm ion and hot electron population in the Tara outboard minimum-B anchors in stabilizing MHD flute-like modes in the central cell and axicells is assessed. With a combination of ECH and ICRF heating in the anchors, β_he > 15% and β_i ∼ 0.5% have been obtained. The ICRH component has a generally stabilizing effect on global MHD activity, but the stabilization is not linear in ion beta. Pinhole camera pictures indicate that the hot electron density profile is radially peaked. The resulting creation of a deeper magnetic well for the warm ions was expected to enhance the MHD stabilizing properties of the anchor. However, the addition of hot electron beta to an ICRF heated anchor plasma was observed to have no beneficial effect on MHD stability.

Electromagnetic waves with ordinary polarization, propagating almost perpendicularly to the magnetic field in a tokamak with random density fluctuations, are investigated numerically. The fluctuations are assumed to be located mainly at the plasma edge, as is appropriate for drift wave type fluctuations. The wave propagation in this fluctuating plasma is described in the limit of geometrical optics by a ray tracing code. Even low levels of relative density fluctuations (around 1%) result in significant scattering of the incoming wave beam. The variations in the wave intensity are investigated by analysing the relative dispersion of rays. Caustic formation is demonstrated in localized regions, where the amplitude predictions based on geometrical optics break down. A statistical analysis of the results is performed by tracing many rays for a wide range of fluctuation parameters and subsequently averaging the ray trajectories. The results may be relevant to tokamak plasma heating experiments and current generation schemes. Analytical results for the statistics of the ray propagation are presented for simplified geometries.

The effect of spatial loss on ICRF (ion cyclotron range of frequency) wave heating is studied. A simple model for the energy-dependent loss term is adopted in the Fokker-Planck equation. The case of the minority ion heating by fundamental cyclotron resonance is analysed. It is found that the high energy particle loss imposes a limit on the heating power density, above which an increase in the heating power does not raise the energy transfer to the bulk particles, i.e. the heating efficiency deteriorates. This power limit is serious for losses with strong energy dependence such as ripple diffusion. Small spatial loss can annihilate the increment of the fusion reaction by tail generation.

The kinetic theory of the m = 1 kink instability of a Z-pinch with Bennett profile is presented. The dominant particle trajectories in the equilibrium field are the large excursion betatron orbits. To deal with these orbits, an integral formulation of the stability analysis is adopted. In this case, the dispersion relation is expressed as the determinant of a matrix. In the limit where the electrostatic perturbation is neglected, the eigenmodes are computed numerically from this dispersion relation. Two methods are used to obtain the growth rates, and the computed values agree very well. The Landau damping of the mode is found to be strong enough to stabilize the mode at shorter wavelengths. This may explain the stability of the kink mode in some experiments.

The paper presents a study of anchor cell plasma buildup in the tandem mirror GAMMA 10 with the use of central cell ICRF antennas. For plasma buildup, it is demonstrated that an ion cyclotron resonance layer exists within the closed mod-B surface in the minimum-B anchor cell. The experimental plasma buildup rate in the anchor cell is compared with a one-dimensional Fokker-Planck simulation. A rapid increase in the anchor plasma density is observed and an associated reduction of the end-loss current when radiofrequency is applied.

A halo plasma, which is a low density plasma surrounding field reversed configurations (FRC), was observed in the Staged Theta Pinch-Linear experiment. As long as the plasma is kept free from the end walls with the help of a guide field structure, azimuthal ion flow builds up in the halo. The direction of the ion flow at the edge of the halo is opposite to that in the vicinity of the separatrix. This double structure of the ion flow can be explained by a model which assumes that the halo plasma is formed by energetic ions shuttling between the FRC and the open field region. The numerical results are in good agreement with the experiment. The model also suggests that the FRC has a good confinement ability for energetic particles if the plasma is not in contact with the discharge tube.

The total heat flux q arising in steady state from Ohmic and neutral beam heating is calculated for a series of power scan experiments on JET. A radial resolution of q at selected radii is made to examine the dependence of q upon local plasma parameters such as density n_e, temperature T_e, current I and their gradients. Non-linear regression analysis techniques are applied to fit the data on q to empirical expressions q_fit, involving the local plasma parameters. The most plausible fit emerging from the analysis is q_fit = − (C/I)n_e ∇T_e− q_pinch, in which C is a constant, I the current enclosed by a plasma surface and q_pinch a constant so-called heat pinch. The net heat diffusivity inferred from this relationship agrees with estimates from heat pulse propagation measurements and it leads to a scaling law for the incremental energy confinement time which agrees with the one determined experimentally. There is a substantial amount of scatter in the data due to approximations made in the analysis and due to uncertainties in the experimental measurements.

Tokamak discharges with repetitive pellet fuelling were investigated in the ASDEX divertor device. The importance of sufficiently high divertor recycling for a high density at the separatrix and for successful density buildup in the bulk plasma was demonstrated. In contrast to low recycling discharges where no permanent improvement of the energy confinement time was achieved, in OH-heated discharges with high recycling an energy confinement time of 160 ms was reached, the normal value being 80 ms in the rollover region. The peaked density profiles in this case were accompanied by reduced or suppressed sawtooth activity and finally ended in a phase of strong central impurity accumulation. The particle transport was characterized by strong, non-classical inward drift, while the improved energy transport can be explained by the following alternatives: (la) a local model which assumes neo-Alcator χ_e for the electrons and χ_i= 3χ_neocl for the ions in the gas puff cases, reducing to χ_i= χ_neocl for the optimum pellet cases; (1b) the assumption χ_i= χ_neocl under all conditions and an electron energy confinement worse than neo-Alcator in the rollover region in gas-puff-discharges; (2) a profile consistency picture where T_e(a) determines the energy confinement. Low power, NI heated discharges with pellet fuelling behave like Ohmic discharges, while for high power in the L-mode no successful density buildup was possible, and τ_E was not improved. The H-regime was extended from a density maximum _e = 0.8 × 10²⁰ m^-3 without pellets to _e = 1.2 × 10²⁰ m^-3 by the injection of pellets. In this case a density buildup takes place, but further density profile peaking could not be observed.

A superthermal tail is simulated by adding a drifted Maxwellian distribution to a bulk Maxwellian distribution, f_a = (l−μ)f_b + μf_t. The values of the tail temperature (T_t), drift velocity (v₀) and weight coefficient (μ) are chosen so as to reproduce the experimental residual current observed in the Wendelstein VII-A stellarator. An analytical expression for the resulting dielectric tensor coefficients is obtained. It is shown that, even for small tails, the global absorption coefficient increases for both the first harmonic (ω = 28 GHz) and the second harmonic (ω = 56 GHz) propagation. The effect is more dramatic for wave propagation in the first harmonic. The spatial bandwidth of the absorption region increases sensibly with respect to the pure Maxwellian distribution in both harmonics.

The effect of varying the magnetic field configuration by adding an ℓ = 1 helical winding to the standard heliac has been studied experimentally. Equilibrium plasma configurations in the range 0.7 ≤ t(0) ≤ 1.86 have been obtained. Analyses of the plasma pressure profiles measured by Langmuir probes in this range show good agreement between the plasma isobars and the computed vacuum magnetic surfaces; for configurations with a rotational transform t(0) close to unity it is necessary to take known error fields into account. When low-order rational surfaces are present, a deterioration of the plasma confinement is clearly observed. Magnetic islands, resulting from the resonance between the low-order rational surface ι = 3/2 and the m = 2, n = 3 vacuum field harmonics inherent in the geometry, are identified with features observed in both the plasma pressure and the floating potential profiles.

A three-dimensional equilibrium code (NEAR) is used to study plasma equilibrium in torsatron configurations having various winding laws. The harmonic spectra describing the variation of || along magnetic field lines are calculated at finite plasma pressure and then used to calculate the geometric factors that determine the magnitudes of the neoclassical transport coefficients in the helical ripple trapping regime, where the particle and heat fluxes are inversely proportional to the collision frequency. The results show that an appropriate choice of winding law can reduce helical ripple transport by a factor of about 2 in the vacuum field and at high plasma pressure.

Princeton Beta Experiment (PBX) discharges run at the lowest q and highest ⟨β_t⟩ always terminated in a hard disruption. The discharges, with ⟨β_t⟩ values of up to 5.5% and q-values down to 2.2, were obtained by employing large current ramps and large gas feed rates during neutral beam injection. Previous work has indicated that the achieved ⟨β_t⟩ values were consistent with the limit imposed by the n = l ideal external kink with a conducting wall at b/a = 2. The authors of the paper investigate further the validity of ideal MHD theory in explaining the low q_ψ disruptions. In particular, the characteristics of the pre-disruption MHD activity in these low-q discharges, specifically the time-scale of growth and internal and external mode structures, are compared with those determined from theoretical calculations. The results of these comparisons indicate that non-ideal effects must be considered in order to obtain detailed agreement between theory and experiment.

Experiments on the maximum attainable beta values of ASDEX discharges show that the limits for this parameter lie in the range of theoretical predictions. In a previous publication a theoretical identification of the corresponding instabilities has been attempted. No significant correlation with global plasma instabilities could be found, but the two-dimensional MHD equilibria calculated on the basis of ASDEX experimental parameters turned out to be close to the marginal ideal ballooning limit. In the work presented here, the previous investigation on resistive ballooning modes is extended. Separatrix bounded as well as limiter controlled plasma equilibria are considered. Because of the small aspect ratio of ASDEX (A ≅ 4) all equilibrium as well as stability calculations are performed in full toroidal geometry. After the formulation of a system of four equations describing the resistive evolution of velocity and magnetic fields in the high-m stability limit in co-ordinate invariant form and its Fourier approximation in the neighbourhood of a localization field line, the resulting quasimode equations are solved, applying methods of finite-element discretization. Complex growth rates γ are found, with a positive real part for values of the toroidal mode number n below 100. Calculated values of Re {γ} ≤ 10⁻³/τ_A S₋₁ (with τ_A being the Alfvén time) are small and therefore in agreement with the experimentally observed non-disruptive behaviour at the β_p limit. Thus we believe that the characteristic signatures which govern ASDEX high β_p discharges can be explained by resistive ballooning modes.

The signatures of resistive ballooning modes in ASDEX high beta discharges are investigated. It is shown that the growth rates of these modes increase significantly when β_p reaches its maximum value during the discharge and therefore they can be used to explain the 'hard β_p saturation' behaviour. A simple estimate of the corresponding electron heat conductivity gives values of χ_e > 1 m²·s⁻¹ in agreement with expectations from the observed confinement deterioration at maximum beta.

Time resolved power deposition profiles on the D III-D divertor target plates have been measured for Ohmic and neutral beam injection heated plasmas using fast response infrared thermography (τ ≤ 150 μs). Giant Edge Localized Modes have been observed which punctuate quiescent periods of good H-mode confinement and deposit more than 5% of the stored energy of the core plasma on the divertor armour tiles on millisecond timescales. The heat pulse associated with these events arrives approximately 0.5 ms earlier on the outer leg of the divertor relative to the inner leg. The measured power deposition profiles are displaced relative to the separatrix intercepts on the target plates, and the peak heat fluxes are a function of core plasma density.

A mechanism taking into account electron trapping by a discrete RF spectrum is proposed which allows electrons outside the resonance region to interact with the fast wave. This effectively spreads out the wave energy over a wider range of velocity space and causes a higher driven current.

A simple procedure has been devised to extend the analysis of external magnetic measurements, using a freeboundary equilibrium solver with the additional constraint of diamagnetic measurement. The paper discusses the application of the method to ohmically and auxiliarily heated JET plasmas where pressure anisotropy could occur. It is shown that approximate relations commonly in use for a fast calculation of poloidal beta and internal inductance are not accurate in the case of JET. A better approximation for isotropic pressure is given.

A small set of magnetic pickup coils inside the thin resistive shell and an extensive set outside are used to monitor high frequency (3-50 kHz) MHD activity in a reversed field pinch discharge of duration long compared to the shell time constant. The MHD activity is dominated by nearly equal amplitude m = 0 and m = −1 poloidal modes both of whose frequency spectra peak near the drift frequency, i.e. about 8 to 10 kHz. The m = 0 and m = −1 activities are uncorrelated and exhibit strong turbulence; the autocorrelation times for both are about 40 μs, and the toroidal correlation lengths are about equal to the 20 cm shell minor radius b. The toroidal variation of the m = 0 activity at a given time when Fourier analysed in toroidal mode n has a power spectrum peaking at n = 4-5 or nb/R_o ≈ 1. The n spectrum for m = −1 is nearly zero up to n = 10 and substantial at 11 ≤ n ≤ 16, i.e. those modes which are pitch resonant in the plasma interior. The aperiodic development of a localized helical kink, the slinky mode, stabilizes, i.e. turns off, in turn the m = −1 high frequency activities of the n = 11 and 12 modes. This is postulated to be due to the slinky mode flattening the gradient in μ near the axis (μ is the ratio between current density parallel to the magnetic field and the magnetic field strength).

The variation of frequency shift for stimulated Raman sidescattered radiation has been calculated theoretically as a function of the laser intensity, the density scale-length and the plasma electron temperature for a 1.06 μm laser produced plasma. Although this variation depends on all three parameters, the dependence is very strong on the density scale-length in the domain of 1 to 100 μm. On the basis of this strong dependence, a new technique for estimating the density scale-length is proposed.

The Fokker-Planck coefficients for interaction of coherent, narrowband microwaves with a spatially limited region of tokamak plasma are obtained. As a function of energy, the coefficients exhibit regions of negligible diffusion interspersed with regions of strong diffusion.