Yu. N. Dnestrovskij

First results from MAST

MAST is one of the new generation of large, purpose-built spherical tokamaks (STs) now becoming operational, designed to investigate the properties of the ST in large, collisionless plasmas. The first six months of MAST operations have been remarkably successful. Operationally, both merging-compression and the more usual solenoid induction schemes have been demonstrated, the former providing over 400 kA of plasma current with no demand on solenoid flux. Good vacuum conditions and operational conditions, particularly after boronization in trimethylated boron, have provided plasma current of over 1 MA with central plasma temperatures (ohmic) of order 1 keV. The Hugill and Greenwald limits can be exceeded and H mode achieved at modest additional NBI power. Moreover, particle and energy confinement show an immediate increase at the L-H transition, unlike the case of START, where this became apparent only at the highest plasma currents. Halo currents are small, with low toroidal peaking factors, in accordance with theoretical predictions, and there is evidence of a resilience to the major disruption.

Recombination-induced neutral particle flux in tokamaks

On the Alcator device the main mechanism producing neutrals in the central region of the plasma at a density n > 4 × 1014 cm−3 is recombination of protons and electrons. The calculated neutral fluxes and spectra agree with the measured values. A suitable method of determining the ion temperature from the tail of the fast-neutral spectra for a dense plasma is described.

Transport model of canonical profiles for electron and ion temperatures in tokamaks

A set of transport equations using canonical ion and electron temperature profiles is proposed. Simulations of electron cyclotron resonance heating on T-10 and of the L-mode in TFTR, JET and ASDEX have been performed. From an analysis of the results of the calculations it is possible to construct universal expressions for heat fluxes without free parameters. On the basis of the developed model, several predictions are made for the International Thermonuclear Experimental Reactor (ITER).

The ballistic jump of the total heat flux after ECRH switching on in the T-10 tokamak

Analysis of experiments with electron cyclotron resonance heating (ECRH) requires a good knowledge of the ECRH power profile. This profile is reconstructed by analysis of the transient process after on-axis ECRH switching on in special experiments with suppressed sawtooth oscillations in the T-10 tokamak. The calculations show that the absorbed ECRH power, , determined by the change in time derivative of the electron temperature at the region of ECRH power input, and the absorbed ECRH power, , determined by the magnetic measurements, are several times different. Depending on the plasma density and plasma current, their relation, , changes from 0.2 to 0.4. Analysis of different explanations for this effect shows that adequate description of the transient process demands introduction of a ballistic jump in the total heat flux just after on-axis ECRH switching on. The effective heat diffusivity increases up to values of 10?15?m2?s?1 in the first 100?200??s and decreases down to values of 1.5?2.0?m2?s?1 during the following 1?2?ms. Note that such a non-monotone dependence of the effective heat diffusivity cannot be described by the modern critical gradient models. It seems that plasma reacts directly to the deposited power but not to the corresponding consequences (the increase in temperature or gradients). Different physical mechanisms could be proposed for this process (partial destruction of magnetic surfaces, fast transition of information through the turbulent cell connections), but each of them needs further confirmation.

Toroidal and electric field effects on current drive in tokamaks by lower hybrid and electron cyclotron waves

The current drive by HF waves in a tokamak with longitudinal electric field is studied on the basis of the two-dimensional kinetic equation for electrons. Analytical formulas for current and current drive efficiency are obtained for a low level of absorbed power. Numerical methods are used to solve the kinetic equation at high HF power level. It is shown that the dependence of the efficiency on the effective charge of the plasma changes with increasing power absorption. The existence of trapped particles reduces current drive efficiency. An analysis of the calculation results leads to simple approximate expressions for current and efficiency, convenient for comparisons with the experiments.

Improved confinement regimes within the transport model of canonical profiles

The canonical profiles transport model is extended to describe various modes with improved confinement in tokamaks. A generalized profile consistency principle is proposed and a corresponding mathematical formalism is formulated. This formalism is used for the modelling of various regimes, such as H modes in DIII-D, JET and ASDEX, the hot ion mode and enhanced performance after pellet injection (PEP mode) in JET. This modelling, together with a known global scaling law, allowed the dependence of the internal model parameters on the plasma geometry and other physical variables to be established. This makes the model predictive. The approximate analytical criteria for the L to H and L to hot ion mode transitions are also obtained

Self-consistency of pressure profiles in tokamaks

Plasma pressure profiles from various tokamaks are analysed. It is shown that in the gradient zone the pressure profiles are conserved under variation of the plasma density and deposited power. Usually these profiles are close to the canonical ones. Conservation of pressure profiles means that the density and temperature profiles are consistently correlated under different external actions on the plasma. A simple transport model for the plasma density based on the self-consistency of the pressure profiles is proposed.

Formation of electron transport barriers under ECR control of the q(r) profile in the T-10 tokamak

Abstract-the formation of transport barriers under electron cyclotron resonance heating and current drive in the t-10 tokamak is studied. in regimes with off-axis co-eccd and qL<4 at the limiter, a spontaneous transition to improved confinement accompanied by the formation of two electron transport barriers is observed. the improvement resembles an L-H transition. It manifests itself as density growth, a decrease in the Dα emission intensity, and an increase in the central electron and ion temperatures. Two deep wells on the potential profile (the first one at r/aL≈0.6, where aL is the limiter radius, and the second one near the edge) arise during the transition. the internal barrier is formed when dq/dr∼0 with q≈1 in the barrier region.

Self-organization of plasma in tokamaks

A review is given of the main ideas regarding self-organization of a tokamak plasma. The analysis begins with a simple model of canonical profiles that was proposed by Kadomtsev for a plasma column with a circular cross section. Kadomtsev’s model is then generalized to a tokamak plasma with an arbitrary cross section in toroidal geometry. In the generalized model, the canonical profiles are determined by the minimum of the plasma energy functional under the additional condition that the total current is conserved. The Euler equation for the energy functional leads to a second-order differential equation for the canonical profile of the function μ = 1/q. Transport models are constructed on the basis of a concept of critical gradients defined in terms of the canonical profiles. The structures of the heat and particle fluxes in the Ohmic heating regime and in the conventional L-mode are discussed. Examples of plasma self-organization in experiments are presented and are illustrated by the results of calculations based on the transport models developed. The expressions for the heat and particle fluxes are then generalized to regimes with improved confinement and with transport barriers. L-H transitions and approximate formulas for the transport barrier parameters are discussed in detail. Some unresolved problems are also discussed, namely, those concerning a description of the formation of internal transport barriers in terms of the canonical profile model. In the Appendix, the ranges of variations in the plasma parameters within which the temperature profiles remain stiff are considered.

Calculation of the diffusion of light impurities in tokamaks

Using numerical methods, the authors investigate plasma diffusion in tokamaks when impurity ions of light elements are present. The model considered makes use of neoclassical expressions for diffusion fluxes and takes ionization and recombination processes into account. The question of the boundary conditions for the initial system of equations is discussed. The new boundary conditions for the proton and impurity ion densities are zero partial ion-ion fluxes at the boundary of the plasma column. The computational results show that the presence of impurity ions in the plasma column of a tokamak – even in relatively small amounts – strongly influences the spatial distribution of the protons. The entire diffusion process can be broken down into a number of stages which differ one from the other with regard to the amount of impurities in the system. If the proportion of impurities ξim does not exceed 0.01 of the electron density, the highly ionized ions collect at the centre of the plasma. If ξim > 0.01, the proton profile becomes flat within a short time and the impurities become more evenly distributed over the plasma cross-section.