M. Cox

Effects of radial transport on current drive in tokamaks

The influence of radial transport of electrons on radiofrequency and Ohmic current drive in tokamaks is discussed. It is found that such processes can reduce the efficiency of current drive in tokamaks in which the energy confinement time is comparable with or less than the collision time of the heated electrons and that, even if this is not the case, they significantly broaden the driven current profile.

Overview of recent experimental results on MAST

Note: Proc. 19th IAEA Fusion Energy Conference, Lyon, France, October 2002, IAEA-CN-94/EX/OV2-3 Reference CRPP-CONF-2002-068 Record created on 2008-05-13, modified on 2017-05-12

Fokker–Planck studies of high power electron cyclotron heating in tokamaks

A Fokker–Planck formalism has been developed to interpret experimental data from high power electron cyclotron heating of tokamak plasmas in which the electron distribution function can be substantially distorted. The Fokker–Planck equation is solved using a 2-D code which incorporates electron trapping, a steady Ohmic electric field and a bounce averaged electron cyclotron heating term. The quasilinear RF diffusion coefficient is calculated using a single particle model which includes the mildly relativistic resonance condition and takes into account localized RF power injection and tokamak rotational transform effects. Comparisons are presented of the calculated and observed soft X-ray spectra from 60 GHz second harmonic electron cyclotron heating experiments on the CLEO tokamak. Good agreement between theory and experiment is found. In addition, predicted RF current drive efficiencies for the COMPASS tokamak are presented.

Neutral beam heating in the START spherical tokamak

The tight aspect ratios (typically A?1.4) and low magnetic field of spherical tokamak (ST) plasmas, when combined with densities approaching the Greenwald limit, provide a significant challenge for all currently available auxiliary heating and current drive schemes. NBI heating and current drive are difficult to interpret in sub-megampere machines, as in order to achieve suitable penetration into the plasma core, fast ions have to be highly suprathermal and, as a result of the low magnetic field, can be non-adiabatic (i.e. non-conserving of magnetic moment ?0). The physics of NBI heating in START is discussed. The neutral beam injector deployed on START was clearly successful, having been instrumental in producing a world record tokamak toroidal beta of ?40%. A fast ion Monte Carlo code (LOCUST) is described that was developed to model non-adiabatic fast ion topologies together with a high level of charge exchange loss and cross-field transport (present in START due to an envelope of high density gas surrounding the plasma). Model predictions compare well with experimental data, collected using a scanning neutral particle analyser, bolometric instruments and equilibrium reconstruction using EFIT. In particular, beta calculations based upon reconstruction of the pressure profile (by combining measurements from Thomson scattering, charge exchange recombination spectroscopy and model predictions for the fast ion distribution function) agree well with beta values calculated using EFIT alone (the routine method for calculation of START beta). These results thus provide increased confidence in the ability of STs to sustain high beta high confinement H?mode plasmas and in addition indicate that the injected fast ions in collisional START plasmas evolve mainly due to collisional and charge exchange processes, without driving any significant performance degrading fast particle MHD activity.

High- performance of the START spherical tokamak

Using additional heating provided by neutral-beam injection, the START spherical tokamak at UKAEA Fusion Culham has achieved high- (ratio of volume average plasma pressure to vacuum magnetic-field pressure) values of T > 30%, more than twice the value previously obtained in a tokamak. These plasmas reach normalized beta values of ND %=.I=aB/ 4 at values of auxiliary heating power comparable to the ohmic power. Operation at high normalized current IND Ip=aBT 8 is observed, so that the plasma current exceeds the central rod toroidal-field current for the first time in a hot tokamak.

ECRH current drive studies in the CLEO tokamak

Non-inductive current drive using second harmonic ECRH at both 28 GHz and 60 GHz has been studied in the CLEO tokamak. At 60 GHz, RF driven currents of up to 5 kA have been observed at e = 4 × 1018m−3 for 185 kW of injected power, indicating an efficiency of η ≡ eIRFR0/PRF = 0.001 (1020 m−3, A, m, W−1). The RF driven current scaled linearly with total plasma current in the range of 5-15 kA and was maximized when the cyclotron resonance was located near to the centre of the plasma. Sawtooth activity was normally strongly affected and transient sawtooth stabilization was often observed. With detailed theoretical studies it is possible to reproduce both the high absorption efficiencies and the scaling of RF driven current with resonance position seen in the 60 GHz experiments. However, the magnitude of the observed current is a factor of about three below that theoretically predicted. At 28 GHz, no evidence of RF driven current could be detected. Possible reasons for this are discussed.

MAST and the impact of low aspect ratio on tokamak physics

Low aspect ratio plasmas in devices such as the mega ampere spherical tokamak (MAST) are characterized by strong toroidicity, strong shaping and self fields, low magnetic field, high beta, large plasma flow and high intrinsic E × B flow shear. These characteristics have important effects on plasma behaviour, provide a stringent test of theories and scaling laws and offer new insight into underlying physical processes, often through the amplification of effects present in conventional tokamaks (e.g. impact of fuelling source and magnetic geometry on H-mode access). The enhancement of neoclassical effects makes MAST ideal for the study of particle pinch processes and neoclassical resistivity corrections, which can be assessed with unique accuracy. MAST data have an important influence on scaling laws for confinement and H-mode threshold power, exerting strong leverage on the form of these scaling laws (e.g. scaling with aspect ratio, beta, magnetic field, etc). The high intrinsic flow shear is conducive to transport barrier formation by turbulence suppression. Internal transport barriers are readily formed in MAST with both co- and counter-NBI, and electron and ion thermal diffusivities have been reduced to the ion neoclassical level. The strong variation in toroidal field (~ × 5 in MAST) between the inboard and outboard plasma edges, provides a useful test of edge models prompting, for example, a comparison of inboard and outboard scrape-off-layer transport to highlight magnetic field effects. Low aspect ratio plasmas are also an ideal testing ground for plasma instabilities, such as neoclassical tearing modes, edge localized modes (ELMs) and Alfven eigenmodes, which are readily generated due to the supra-Alfvenic ion population. Examples of how MAST is providing new insights into such instabilities (e.g. ELM structure) are described.

The distortion of the thermal-ion distribution during neutral-injection heating

It is shown that a high-energy tail may form on the background-ion distribution during neutral-injection heating. The temperature of this tail is found to depend critically upon the velocity dependence of the particle and energy loss mechanisms. – The Fokker-Planck equation for the equilibrium thermal-ion distribution is solved both numerically for all v and analytically for large v. Results from the numerical solution are presented for various cases of particle or energy loss including particle loss by charge exchange or diffusion and energy loss by thermal conduction. An analytic expression for the ratio of tail to actual temperature is derived for the case of good high-energy containment and for energy-independent particle loss (e.g. charge exchange). The expression derived for the latter case is shown to be in good agreement with the numerical results.

Solution of three-dimensional Fokker-Planck equations for tokamak plasmas using an operator splitting technique

Abstract A two-stage operator splitting algorithm has been used to time advance the three-dimensional Fokker-Planck equation for the electron distribution function in a tokamak. In the first stage, derivatives in the two velocity-space dimensions are advanced together implicitly. Derivatives in the remaining (spatial) dimension are advanced in the second stage. The treatment is restricted to problems which are diagonal in the spatial dimension. The algorithm gives accurate solutions in modest CPU times unlike alternative schemes considered. We described the technique which includes features that accomodate the internal boundary conditions arising from trapped electron effects.

Fokker-Planck calculations of rf heating in tokamaks

Abstract A bounce-averaged Fokker-Planck code has been developed for studying electron cyclotron heating in tokamak experiments. The equation solved and the numerical scheme used are discussed, and the advantages of the implicit time advancement emphasised. The numerical problems encountered while developing the code are described. The distribution functions predicted by the code are shown to be in good agreement with those produced in experiments.