Table of contents

On Saturday, 9 November 1991, the first significant controlled release of fusion energy was obtained using the deuterium-tritium reaction in the JET Tokamak. JET is an experimental device, constructed and operated as a joint venture by 14 European nations (the EC countries together with Switzerland and Sweden). In order to be compatible with the future planned JET programme, only two high fusion yield discharges were attempted and these two were limited to a plasma tritium content of approximately 10%. Both discharges produced more than 1.5 MW of fusion thermal power, the peak was 1.7 MW (6*10¹⁷ D-T neutrons per second) with a total release of 2 MJ (7.2*10¹⁷ neutrons) of energy. The author examines the significance of this event in the context of fusion research as a whole.

The review begins with an introduction to some of the various solar phenomena that may be investigated using stability theory. The geometry of the coronal magnetic field for many models is either a loop or an arcade and it is the stability properties of these structures that are investigated. The author presents a simple physical description of the basic MHD instabilities and describes the main difference between laboratory and coronal plasmas due to the presence of an extremely dense plasma at the footpoints of the coronal magnetic fieldlines. The implications of this density interface are discussed. Linear stability theory is applied to some solar situations and some non-linear simulations are discussed.

Impurity puffing experiments have been performed in ultra-clean ASDEX discharges (via wall boronization) in order to explore the role of impurities for the confinement in high-density Ohmic discharges. Successful changes in confinement are achieved by neon puffing where edge radiation is increased such that the power load onto the divertor plates takes its minimum value. This low value correlates with a reduced separatrix pressure and hence may trigger a peaking of the density profile leading to favourable transport behaviour in the bulk plasma. Therefore, the access to improved Ohmic confinement can now be understood in terms of impurity radiation and recycling fluxes.

In deriving the expression for the Debye length, the assumption e phi << kappa T is often invoked casually. Using a scaling technique this assumption is put in perspective. Furthermore, it is shown that the commonly accepted linearization condition is in fact much more stringent (by two orders of magnitude) than necessary.

The effect of plasma rotation on stability to rigid displacement of the plasma column in a Tokamak is studied. It is shown that for typical parameters of present-day experiments, plasma rotation may cause significant changes in the stability boundary and oscillation frequency for horizontal displacements. The effect is mainly due to conservation of angular momentum. It may be possible to detect these changes and invert them to obtain information about rotation velocities.

The problem of axisymmetric toroidal equilibrium with mass flows is studied using incompressibility of flows as the equation of state. It is shown that the assumption of incompressibility results in considerable simplification of the general problem. The equation is always elliptic and simple in form, hence analytically tractable expressions for shift of magnetic surfaces etc. in a large aspect ratio torus can be obtained. Further, it is argued that the condition for incompressibility of flows is well satisfied in most of the present and future Tokamaks employing high power neutral beam injection.

Particle transport towards the scrape-off layer (SOL) region and the low-frequency instabilities occurring in the edge plasma have been studied in a small research Tokamak. The results obtained show that there exists enhanced particle transport in the plasma. The drift-wave-like instabilities observed in that region are related to this enhanced particle transport to the edge region.

The theoretical stability of high- beta JET discharges is discussed. For discharges near the beta limit, a significant fraction of the core is found to be marginally stable to high-n ballooning modes. For low-n internal modes (n=1 and 2) the theoretical predictions are found to correlate well with the experimentally observed soft X-ray behaviour, and provide a basis for predicting the central q-profile.

A model of drift waves for the cylindrical plasmas in the UMIST Linear System (ULS) is derived on the basis of the two-fluid equations. Both the radial electron temperature variation and the sheared E*B rotation in the plasmas have been taken into account. The author's calculation shows that the temperature variation and the rotation are important in the predictions of drift-wave frequency and radial amplitude distribution.

An expression is derived for the magnetic scalar potential due to helical currents in toroidal surfaces. Nonlinearity of helical windings and noncircularity of the cross-section are taken into account as the work was carried out during an attempt to quickly evaluate the spectra of sinusoidal modes produced by instability currents in Tokamaks. Taking the inverse aspect ratio as the order of magnitude reference parameter, a successive approximations method is developed that provides a solution with any desired accuracy.

In the authors' previous study (1989) on TEXTOR it has been shown that an excited Faraday-shielded fast-wave antenna draws a large DC electron current from the plasma due to the sheath rectification effect. They show for the first time that this DC current (up to 400 A) extends toroidally all around the circumference of the machine and returns to the wall via conducting objects which are electrically connected to the wall. Preliminary measurements of r.f. currents in the scrape-off layer were performed using a specially designed Rogowski coil.

The time evolution of the electron distribution function under the action of lower hybrid waves is studied by means of the quasilinear theory. A model spectrum is assumed for the lower hybrid waves, and the dependence of the resulting lower hybrid diffusion coefficient on the electron temperature, electron density, and ambient magnetic field is investigated. A set of parameters typical of small tokamaks is utilized in a numerical analysis, and the dynamics of the formation of an electron tail is investigated. The outcome is a nearly linear dependence between current density and wave power. The transient state after the sudden disappearance of the driving wave is also illustrated.

The authors discuss the Townsend plasma at low current densities where the dominating conduction process is the Townsend discharge. The existence of solitary waves of small amplitude described by the Korteweg-de Vries equation has been proved.

The nonlinear interaction of ultra-short pulse high brightness lasers with a uniform plasma is studied numerically in 1-D. Apart from the usual nonlinear steepening and periodic lengthening of the plasma wave, modification of the laser pulse also occurs if the pulse has a relatively long trailing edge compared to the leading edge. This induced modulation results in the formation of spikes on the laser pulse which are coincident with the Langmuir wave density maximum.

The variation in peak intensity of parametrically excited second-harmonic emissions, as a function of laser intensity, was measured from plasmas produced from planar, slab targets of carbon, aluminium and copper, using a 20 J-5 ns, p-polarized Nd:glass laser. At and beyond a laser intensity of 10¹⁴ W cm^-2, the second-harmonic emission showed saturation behaviour in the cases of all three materials. The observed behaviour is attributed to the saturation of the convective parametric decay instability due to ion-nonlinear Landau damping of plasmons. The consequences of plasmon convection have also been considered. It is inferred that the harmonic generation occurs within the parametric decay instability region.

The authors study the modelling of light impurity transport in TdeV (Tokamak de Varennes) Ohmic discharges with graphite poloidal limiters. The impurity fraction, the diffusivity and the convective velocity were determined by comparison of measured C IV, O VII and Ne IX line intensities (VUV spectroscopy) with MIST simulated profiles. It is found that the diffusion of the intrinsic impurities C and O, and of the artificial impurity Ne, is strongly anomalous (an order of magnitude above neoclassical values). To obtain good fits to the experimental data the diffusivity must be a varying function of minor radius. No convective velocity is needed to produce good fits. The oxygen content in the plasma is found to be strongly dependent on the electron density: I=I₀.n_e^1.5.I_p^-0.8. Carbon and oxygen densities are roughly equal, as found typically on 'all carbon' machines.

A set of nonlinear equations describing the relative diffusion process of charged particles, or the decay process of clumps, in turbulent electric fields is systematically derived from the stochastic equations of motion using the weak-plasma-turbulence approximation. The solutions show that (r²(t)) varies as (u²(t)) varies as exp (t/t_rd) in the initial stage and (r²(t)) varies as (u²(t))³ varies as (t/t_sd)³ in the final stage, where r and u are separations in position and velocity between two particles treated as a pair, respectively. Note that t_rd>t_sd for broad k spectra and t_rd=t_sd for a semibroad k spectrum. A divergent effect due to long-wavelength waves is excluded in the initial stage of the relative diffusion process owing to the fact that each pair of particles behaves in a strongly correlated way in this stage.

A decrease in the edge magnetic and density fluctuations is always seen at the L-H transition in DIII-D. Also, a sudden change of the perpendicular rotation v_{perpendicular to} in the edge has been observed at the transition, which indicates the formation of shear in the radial electric field. This region coincides with the region where the density fluctuations are suppressed. These experimental observations are consistent with earlier theoretical models. Comparisons between the theories and the experimental observations will be discussed.

Results are presented from experiments on the effects of glow discharge and carbonization on RFP plasma performance in REPUTE-1. With the proper choice of wall conditioning, control of plasma density behavior was demonstrated. Radiated power and carbon V intensity decreased by a factor of two after He glow. Using the carbonization technique, decreases in the plasma resistance and ion temperature as derived by the CV line and charge exchange neutral particles were observed, whereas the electron temperature did not change as much.

Evidence is given for wave acceleration of primary electrons in a 1 cm radius helicon plasma source. The second root of the dispersion relation is also seen at low B fields. Electrostatic confinement of primaries appears to be important at these small diameters.

A method to deduce the 2*2 transport matrix for coupled heat and particle transport in Tokamaks is proposed. The method applies to perturbative experiments, and is based on a Fourier transform of the measured signals of temperature and density. By analyzing different linear combinations of temperature and density, the eigenvectors and eigenvalues of the transport matrix are determined. The method is tested for a number of illustrative cases using simulated data, and the sensitivity to noise on the signals is evaluated.