A. Yu. Dnestrovskij

Reduced core transport in T-10 and TEXTOR discharges at rational surfaces with low magnetic shear

It has been observed in the T-10 tokamak that immediately after off-axis electron cyclotron resonance heating (ECRH) switch-off, the core electron temperature stays constant for some time, which can be as long as several tens of milliseconds, i.e. several energy confinement times (τE), before it starts to decrease. Whether or not the effect is observed depends critically on the local magnetic shear in the vicinity of the q = 1 rational surface, which should be close to zero. It is hypothesized that a small shear can induce the formation of an internal transport barrier. Measurements of density fluctuations in the transport barrier with a correlation reflectometer show immediately after the ECRH switch-off a clear reduction in the fluctuation level, corroborating the above results. The delayed temperature decrease has also been observed in similar discharges in the TEXTOR tokamak; however, the delay is restricted to ~ 1 × τE.

The main features of self-consistent pressure profile formation

The self-organization of a tokamak plasma is a fundamental turbulent plasma phenomenon, which leads to the formation of a self-consistent pressure profile. This phenomenon has been investigated in the T-10 tokamak in different experiments, excluding profiles with pronounced transport barriers. It will be shown that the normalized pressure profile can be expressed by the equation pN(r) = p(r, t)/p(0, t), over a wide range of plasma densities. It will also be shown that pN(r) is independent of the heating power and the deposition profile of electron cyclotron resonance heating. Experiments show that pN(r) depends only on the value of q at the plasma edge. During rapid current ramp-ups it has been demonstrated that the conservation of pN(r) is established during a time tc < 0.1τE, with τE the energy confinement time. It can be concluded that the self-consistent pressure profile pN(r) in tokamaks is linked to the equilibrium of a turbulent plasma.

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.

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.

Zero-dimensional relationships of tokamak scrape-off-layer parameters and the influence of these parameters on transport in the main plasma

The authors present a model for the plasma in the region outside the limiter which is suitable for describing the limiter and divertor configurations and could be used for a self-consistent study of plasma confinement in the main zone and at the edge. Integral zero-dimensional relationships are employed to describe the processes occurring in the scrape-off layer (SOL, wall plasma) region of a tokamak. This approach makes it possible to construct a model which takes into account, at least qualitatively, the principal effects that are important for the edge zone, such as ionization of neutrals, radiation, longitudinal heat transport by conduction and convection, and transverse Bohm diffusion. This model has been analysed for the main regimes of the SOL plasma. Because of the self-consistent modelling, it has been possible to describe the characteristic features of discharges in T-10 with regard to the density limit and the improved divertor confinement regimes in JT-60.

Charge-exchange recombination spectroscopy of the plasma ion temperature at the T-10 tokamak

Charge-exchange recombination spectroscopy (CXRS) based on a diagnostic neutral beam has been developed at the T-10 tokamak. The diagnostics allows one to measure the ion temperature profile in the cross section of the plasma column. In T-10 experiments, the measurement technique was adjusted and the elements of the CXRS diagnostics for ITER were tested. The used spectroscopic equipment makes it possible to reliably determine the ion temperature from the Doppler broadening of impurity lines (helium, carbon), as well as of the spectral lines of the working gas. The profiles of the plasma ion temperature in deuterium and helium discharges were measured at different plasma currents and densities, including with the use of active Doppler measurements of lines of different elements. The validity and reliability of ion temperature measurements performed by means of the developed CXRS diagnostics are analyzed.

Canonical profiles and transport model for the toroidal rotation in tokamaks

The equilibrium equation for a rotating plasma is constructed supposing the thermal Mach number is much less than unity. The canonical profile of angular rotation velocity is defined as the profile which minimizes the total plasma energy while conserving toroidal current and obeying the equilibrium condition. The transport model based on this canonical profile, with stiffness calibrated by JET ELMy H-mode and hybrid mode data, reasonably describes the velocity of the forced toroidal rotation. The RMS deviations of the calculated rotation profiles from the experimental ones do not exceed 10?15%. The developed model is also applied to the modeling of MAST rotation.

Simulation of START shots with the canonical profile transport model

The canonical profile transport model, which has been benchmarked previously for tokamaks with a conventional aspect ratio, is applied to simulations of the spherical tokamak START. A set of Ohmic shots is used to modify the model so that it is appropriate for the specific conditions of the spherical tokamak plasma. The application of the model as a tool to analyze neutral beam-heated START shots allows the estimation of the neutral beam-injection power absorbed by the plasma, PNBabs, which is experimentally uncertain. The modeling shows that both PNBabs and the energy confinement time increase with increasing the average density. Finally, the modified model is used to simulate the performance of the new megaampere spherical tokamak MAST at Culham.

Multi-machine studies of the role of turbulence and electric fields in the establishment of improved confinement in tokamak plasmas

An extensive (INTAS) research programme started in 2002 to investigate the correlations between, on the one hand, the occurrence of transport barriers and improved confinement in the medium-size tokamaks TEXTOR and T-10 and on the smaller tokamaks FT-2, TUMAN-3M and CASTOR, and on the other hand, electric fields, modified magnetic shear and electrostatic and magnetic turbulence using advanced diagnostics with high spatial and temporal resolution, and various active means to externally control plasma transport. It also requires one to characterize fluctuations of various important plasma parameters inside and outside transport barriers (TBs) and pedestal regions with high spatial and temporal resolution using advanced diagnostics, and to elucidate the role of turbulence driving and damping mechanisms, including the role of the plasma edge properties. Furthermore, one needs to determine the cross-field transport from the measurements and compare this with available theoretical models. This has been done in a strongly coordinated way, exploiting the complementarity of TEXTOR and T-10 and the backup potential of the three other tokamaks, which together have all the relevant experimental tools and theoretical expertise. Physical mechanisms of several TBs have been studied: electron internal transport barriers in T-10 and TEXTOR, ergodization-induced TB in TEXTOR, TB in ohmic discharges in TUMAN-3M, periodic bias-induced TBs in CASTOR. Geodesic acoustic modes (GAM) have been investigated in T-10, TEXTOR and TUMAN-3M. Core turbulence has been characterized in T-10, and small-scale turbulence has been revealed in FT-2.

Integrated modelling of DEMO-FNS current ramp-up scenario and steady-state regime

An approach to the integrated modelling of plasma regimes in the projected neutron source DEMO-FNS based on different codes is developed. The consistency check of the steady-state regime is carried out, namely, the possibility of the plasma current ramp-up, acceptance of growth rates of MHD modes in the steady-state regime, heat loads to the wall and divertor plates and neutron yield value. The following codes are employed for the integrated modelling. ASTRA transport code for calculation of plasma parameters in the steady-state regime, NUBEAM Monte Carlo code for NBI incorporated into the ASTRA code, DINA free boundary equilibrium and evolution code, SPIDER free boundary equilibrium and equilibrium reconstruction code, KINX ideal MHD stability code, TOKSTAB rigid shift vertical stability code, edge and divertor plasma B2SOLPS5.2 code and Semi-analytic Hybrid Model (SHM) code for self-consistent description of the core, edge and divertor plasmas based on the experimental scaling laws. The consistent steady-state regime for the DEMO-FNS plasma and the plasma current ramp-up scenario are developed using the integrated modelling approach. Passive copper coils are suggested to reduce the plasma vertical instability growth rate to below ∼30 s −1 .The outer divertor operation in the ‘high-recycling’ regime is numerically demonstrated with a maximal heat flux density of 7–9 MW m −2 that is technically acceptable.