Table of contents

Fokker-Planck simulations of the Tokamak Fusion Test Reactor (TFTR) energetic ion mode discharges were performed to evaluate the utility of deriving the central ion temperature T_i from deuterium neutral beam charge exchange spectra above the neutral beam injection energy. The T_i values obtained from fitting the calculated spectra obtained from sightlines nearly tangent to the neutral beam injection radius reproduce the central ion temperature within ±10% over the full range of TFTR energetic ion mode parameters. The code simulations demonstrate that the ion temperature obtained from the high energy tangential deuterium charge exchange spectrum is insensitive to variations in plasma density, Z_eff, plasma current, loop voltage, and injected neutral beam power and energy. The use of this method to reduce charge exchange data from TFTR energetic ion mode plasmas is demonstrated.

A thermal barrier plasma potential structure in a three-cell axisymmetric tandem mirror has been produced using only the ion cyclotron range of frequencies (ICRF), with a central cell density of up to 10¹³ cm⁻³ and a central cell ion temperature of approximately 40 eV. Thermal barrier like potential dips occurred in the region of a magnetic field gradient, at a magnetic beach of a slow wave launched in the end cell. The barrier formation is a result of a combination of radiofrequency trapping, radiofrequency enhanced potentials and μ∇B forces. The barrier pumping is consistent with μ∇B forces and _θ × drifts.

Results are presented of the first Lower Hybrid Current Drive (LHCD) experiments in JT-60. 2 MA of RF driven current is successfully produced for the first time in a reactor grade tokamak. The magnetic divertor works quite well in eliminating the impurities released by the current carrying fast electrons which have allowed the generation of the reactor relevant RF current in a very low density plasma. The efficiency which is defined as η_CD = _eRI_RF/P_LH(10¹⁹ m⁻³ A·W⁻¹), reaches values of 0.8 to 1.7. NBI heating enhances the current drive efficiency by a factor of 1.5, and LHCD improves the confinement time of high power NBI heated plasma. The key to confinement improvement is found to be the active control of the current profile by LHCD.

A steepest descent algorithm is used to obtain a least-squares approximation for threedimensional, toroidal stellarator flux surfaces represented by a discrete set of Poincare puncture points. A stream function λ(ρ,θ,ϕ) is introduced as a renormalization parameter to improve the mode convergence properties of the double Fourier series for the inverse co-ordinates (R, Z) representing toroidally nested magnetic surfaces: R(ρ, θ,ϕ) = Σ R_mn(ρ) cos(mθ – nϕ) and Z(ρ, θ,ϕ) = Σ Z_mn(ρ) sin(mθ − nϕ), where ρ is a scaled radial flux co-ordinate and (R, ϕ, Z) are standard cylindrical co-ordinates. The variable ϕ is the geometric toroidal angle, and θ is a parametric co-ordinate representing a poloidal angle. The stream function λ(ρ, θ,ρ) = Σ λ_mn(ϕ) sin(mθ–nϕ) and the rotational transform profile ι(ρ) are determined by solving a system of simultaneous linear equations obtained from the MHD equilibrium condition ∇ × ⋅∇ρ = 0, together with the stellarator condition for zero net toroidal current on each flux surface, ⟨∇ × ⋅∇ϕ⟩ = 0. Numerically computed Fourier representations are presented for vacuum configurations of the Advanced Toroidal Facility (ATF), Uragan-3 and TJ-II stellarator devices.

The application of a novel but practical technique for central fuelling of reactor-grade tokamak plasmas by compact torus (CT) plasma rings driven by a coaxial accelerator is examined. It is emphasized that this is the only advanced method of controlled and localized deep penetration fuelling which can be developed in the near term and which is already applied in a currently operating experimental system. Assessment of the dynamics of the CT as it traverses the plasma requires quantification of several interrelated constraints, including ring decay, tilting, field line reconnection, deceleration in the external field gradient and ring expansion/contraction. A self-consistent, radial zoning scheme is employed to model the transport of the CT to the desired plasma deposition point. It is demonstrated that the injection velocity requirements are usually dominated by CT tilting and reconnection with the external toroidal field of the tokamak. The implications for CT fuel transport around the reconnection point are then examined. The application of this formalism to the TIBER Engineering Test Reactor permits the parameterization of fuelling requirements in terms of injection velocity, fuel mass, penetration distance, CT dimensions and repetition rate. The hardware implications for near-term applications are also assessed.

Initial ideal MHD stability results for the Tokamak Configuration Variable (TCV) tokamak with variable elongation are presented. Two configurations have been studied: a racetrack shape and a D-shape at a fixed elongation of 2.5. Low beta studies indicate the existence of stable racetrack equilibria at currents up to an edge safety factor value of q_s = 2, but the window of operation is limited in qo to narrow bands above each integer value. For the D-shape, q_s = 3 gives the current limit at low beta, but the operating range in q₀ is much wider than that for the racetrack. Beta optimization studies show that the maximum beta set by the n= 1 freeboundary stability limit decreases as the current increases, except for the lowest currents in the range studied. Although further optimization cannot be ruled out, considerable enhancement of the beta over that for an equivalent circular cross-section of the same major radius and aspect ratio can be obtained by elongation of the plasma cross-section.

By using a transport code combined with an ion Bernstein wave tokamak ray tracing code, a modelling code for the ion Bernstein wave heting has been developed. With this code, the ion Bernstein wave heating experiment on the JIPPT-II-U tokamak has been analysed. It is assumed that a resonance layer is formed by the third harmonic of deuterium-like ions, such as fully ionized carbon, and oxygen ions near the plasma centre. As wave absorption mechanisms, electron Landau damping, ion cyclotron harmonic damping, and collisional damping are considered. The characteristics of the ion Bernstein wave heating experiment, such as an increase in ion temperature, a strong dependence of the quality factor on the magnetic field strength and a dependence of the ion temperature increment on the input power are well reproduced.

The combined theory of ion cyclotron wave coupling, mode conversion and absorption is developed for bounded inhomogeneous plasmas in slab geometry. The plasma response to the RF waves is described by the linearized Vlasov equation, with an equilibrium distribution function and a poloidal magnetic field profile which are selfconsistent solutions of the equilibrium Vlasov and Maxwell's equations. A general form of the wave equation, valid to arbitrary order in Larmor radius and including first order gradient terms, is derived. Expressions are also derived for the plasma intrinsic impedance. The wave equation, keeping second order terms in Larmor radius, is solved numerically for a plasma bounded by two conducting walls using the INTOR tokamak design parameters. It was found that the effect of the one-dimensional poloidal field is small. Also, a rough estimate of the error due to truncation to second order in Larmor radius was made and was found to be very small except in the high temperature regions. The effects of plasma boundedness and reflections from the mode conversion region on the coupling of waves from the RF source as a function of the plasma parameters and antenna spectra are studied. It is found that, at certain values of the plasma and antenna parameters, eigenmodes are formed, resulting in an increase in the loading impedance. It is verified that the impedance is not symmetric with respect to the spectrum in the poloidal direction, with highly peaked resonances. As the plasma temperature is increased, the resonances broaden and eventually disappear at very high temperatures. This is attributed to increased single pass absorption and decreasing reflection from the mode conversion region.

Plasma heating and current drive in tokamaks by means of high power electron cyclotron waves result in generating non-Maxwellian electron distribution functions. The properties of the radiation emitted at the electron gyro frequency and its harmonics by such non-thermal distributions are investigated. The electron distribution function is evaluated by means of a 3-D bounce averaged Fokker-Planck code for some typical heating scenarios, and the related emission spectra are computed. It is shown that the peculiar features of the spectra are sensitively related to subtle kinetic processes such as quasi-linear flattening of the electron distribution or formation of perpendicular tails and toroidal effects on the electron orbits, which are known to play an important role in electron cyclotron heating and current drive.

A hybrid particle simulation shows that the m = 2 rotational instability in a field reversed configuration may be suppressed by ion beams which follow a betatron motion across the field null surface. The energy of the beam ions which contribute to the stabilization is comparable to or a little higher than the field plasma ions, and the averaged beam density needed for the suppression is as low as 1 × 10¹⁹ m⁻³. The mechanism of stabilization due to the ion beams is elucidated by using a simple physical model including the effects of a change of beam orbits caused by the onset of the instability.

Neutral molecular densities were measured just outside the plasma edge at 14 axial locations in the Tandem Mirror Experiment Upgrade (TMX-U). Bayard-Alpert gauges can be operated routinely as calibrated pressure gauges in magnetic fields between 0.3 and 0.7 T. The pressures at the outer turning point and at the midplane of the plug are moderately low, 1 × 10⁻⁶ torr, but during plasma operation the inner turning point pressure is as high as 2 × 10⁻⁵ torr. This high pressure is consistent with a wall reflux coefficient of approximately 14, assuming that local anomalous radial loss is the cause. Fokker-Planck modelling of the plasma densities with molecular and energetic atomic fuelling shows that this high inner turning point pressure does not account for the measured plasma densities. However, an as yet undetermined additional radial transport of sloshing ions with a 1 ms rate does produce agreement. Both measurements and modelling show that the charge exchange rate at the exposed sloshing ion turning points is high (0.5 ms), but the plasma is self-shielding for most of the remaining axial distance, and the bounce averaged, charge exchange radial loss time constant is 5 ms.

Scattering functions are calculated for conditions anticipated for D-T plasmas in JET. It is concluded that scattering at millimetre wavelengths may be capable of providing useful information about the alpha particle velocity distribution function, but scattering of CO₂ laser radiation at a wavelength of 10.6 μm will not. The alpha distribution function is most easily determined when the geometry is such as to minimize the effect of the plasma magnetic field.

Empirical scaling relations for the electron heat diffusivity χ_e, the diffusion coefficient D and the inward drift velocity v_in in L and H plasmas of ASDEX are presented. They hold for injection powers which are high compared with the Ohmic input. Expressing χ_e in dimensionless form reveals that particle orbit, collisionality and finite beta effects are involved in the anomalous transport. The empirical χ_e scaling is incompatible with theoretical expressions derived from present drift wave models and from a non-linear gyrokinetic Vlasov equation. To reconcile empirical and theoretical scalings, it seems to be necessary to include effects due to finite beta and profile parameters.

Density fluctuations in the outer edge of the plasma, behind the limiter, have been investigated in the TEXTOR tokamak by a new technique using a probing beam of thermal neutral lithium. With this method, radial profiles of the electron density and its fluctuations are obtained and thus also the relationship between turbulence and plasma parameters, especially the density gradient scale lengths. The turbulences are found to consist of coherent fluctuations in the frequency range of sawtooth oscillations (<100 Hz) and fluctuations having a broadband spectrum of frequencies up to ∼1 MHz. The frequency spectra vary, depending on radial position and the density gradient scale length. It is also shown that the fluctuation level is well correlated with the density gradient scale length.

A more complete radiation treatment is introduced into the zero-dimensional magnetized fuel inertial confinement fusion (ICF) model of Lindemuth and Kirkpatrick. In particular, the effects of synchrotron radiation and the inverse Compton effect are considered. Only slight changes in the high gain regions of initial shell velocity/initial fuel density parameter space were observed. This more complete radiation treatment removes some objections to the Lindemuth-Kirkpatrick model and lends further support to the idea that magnetic thermal insulation can significantly reduce driver requirements for ICF targets.

The IAEA Technical Committee Meeting on Disruptions and Density Limits was hosted by the JET Joint Undertaking at the instigation of the International Atomic Energy Agency and was attended by 49 participants from 9 countries. This report is intended as a brief review of the meeting for readers who are not necessarily specialists in disruptions. The meeting commenced with a review by J.A. Wesson (JET) of our present understanding of disruptions. He identified five different types of disruption: density limit, low q, current rise, beta limit and vertical instability. The density limit disruption has been the most extensively studied. Wesson identified four distinct phases in its development.