D. Kh. Morozov

Impurity Radiation from a Tokamak Plasma

In tokamak operating modes, energy balance is often governed by impurity radiation. This is the case near the divertor plates, during impurity pellet injection, during controlled discharge disruptions, etc. The calculation of impurity radiation is a fairly involved task (it is sometimes the most difficult part of the general problem) because the radiation power is determined by the distribution of ions over the excited states and by the rate constants of elementary processes of radiation and absorption. The objective of this paper is to summarize in one place all the approximate formulas that would help investigators to describe radiation from the most often encountered impurities in a fairly simple way in their calculations accounting for plasma radiation, without reference to special literature. Simple approximating formulas describing ionization, recombination, and charge-exchange processes, as well as radiative losses from ions with a given charge, are presented for five impurity species: beryllium, carbon, oxygen, neon, and argon. Estimating formulas that allow one to take into account plasma opacity for resonant photons in line impurity radiation are also presented.

Influence of plasma opacity on current decay after disruptions in tokamaks

Current decays after disruptions as well as after noble gas injections in tokamaks are examined. As is shown, the cooled plasmas at the stage of current decay are partially opaque for radiation in lines giving the main impact into total thermal losses. The thermal balance is supposed to be determined by Ohmic heating and radiative losses. A zero-dimensional model for radiation losses and temperature distribution over minor radius is used. Plasma current evolution is simulated with DIMRUN and DINA codes. Impurity distribution over ionization states is calculated from the time-dependent set of differential equations. The opacity effects are found to be most important for simulation of JET disruption experiments with beryllium- and carbon-seeded plasmas. The decay times calculated are in good agreement with the experimental values. Current decays in beryllium-, carbon-, argon- and neon-seeded plasmas for ITER parameters are simulated. The temperatures after thermal quench are shown to be significantly higher in comparison with the model of transparent plasmas. Opacity effects are found to be most important for Be- and C-seeded plasmas. Runaway electron currents are damped significantly if opacity effects are taken into account in any case examined.

Ionization–recombination processes and ablation cloud structure for a carbon pellet

Modelling of carbon pellet injection into hot hydrogen plasma is performed. Models of ionization and radiation processes previously used for descriptions of the ablation clouds are discussed. It is demonstrated that the assumption made by other authors that the plasma is transparent significantly overestimated ionization lengths for carbon. The optical thickness of the cloud is estimated. With typical ablation rates, the cloud in the vicinity of the pellet is opaque for resonant radiation in lines, in contrast to the visual transparency for non-resonant photons. The ionization by incident electrons is not sufficient to provide the short experimental cloud sizes. A reduced model for the ion stripping dynamics and energy losses in optically thick plasmas is proposed. Two very important phenomena are taken into account: partial trapping of resonant photons in the cloud and ionization from the excited state. The model is included into the MHD pellet code LLP. Calculations with the new model show at least a qualitative agreement with the experimental sizes of the carbon clouds, in contrast to the models used earlier.

Nonstatistical temperature fluctuations and displacement of equilibrium

It is shown that an anomalously large displacement of equilibrium occurs in systems with rapidly oscillating temperature. The thermodynamic parameters of such a system differ substantially from the values corresponding to constant temperature. The dynamics of the distributions of hydrogen ions and impurity helium and carbon ions over ionization states in a hydrogen plasma and the dynamics of the intensity distribution of the line radiation of impurity carbon in a hydrogen plasma with oscillating temperature are calculated as an example. In systems with fluctuating temperature, the effect in question could be important in virtually all problems based on levelwise kinetics, for example, the energy balance and spectral diagnostics of turbulent plasma, the criterion of thermal stability, the dynamics of turbulent plasma and gas jets, the conditions for amplifier and oscillator operation in the active media of electric-discharge gas lasers, and so on.

Operation of a tokamak reactor in the radiative improved mode

The operation of a nuclear fusion reactor has been simulated within a model based on experimental results obtained at the TEXTOR-94 tokamak and other facilities in which quasistationary regimes were achieved with long confinement times, high densities, and absence of the edge-localized mode. The radiative improved mode of confinement studied in detail at the TEXTOR-94 tokamak is the most interesting such regime. One of the most important problems of modern tokamaks is the problem of a very high thermal load on a divertor (or a limiter). This problem is quite easily solved in the radiative improved mode. Since a significant fraction of the thermal energy is reemitted by an impurity, the thermal loading is significantly reduced. As the energy confinement time τE at high densities in the indicated mode is significantly larger than the time predicted by the scaling of ITERH-98P(y, 2), ignition can be achieved in a facility much smaller than the ITER facility at plasma temperatures below 20 keV. The revealed decrease in the degradation of the confinement time τE with an increase in the introduced power has been analyzed.

ECR heating power modulation as a means to ease the overcoming of the radiation barrier in fusion devices

A method is proposed to ease the overcoming of the impurity radiation barrier during current drive in tokamaks, as well as in alternative fusion and plasmochemical systems with ECR plasma heating. The method is based on the fact that the dependence of the ionization rate on the electron temperature is strongly nonlinear and the dependence of the recombination rate on the latter is weaker. The result is that, during temperature oscillations, the effective temperature for ionization-recombination processes is higher than that in a steady state, so the ionization equilibrium is shifted and strongly emitting ions are stripped more rapidly. Thereby, ECR plasma heating in the initial discharge stage can be made more efficient by modulating the heating power at a low frequency. The evolution of the electron temperature in a homogeneous hydrogen plasma with a carbon impurity and in small ISX-scale tokamaks is simulated numerically, as well as the evolution of the electron and ion temperatures and of the current during discharge startup in the ITER device. Numerical simulations of the effect of modulation of the ECR heating power on the rate of heating of nitrogen, oxygen, and argon plasmas were also carried out. The assumption of coronal equilibrium is not used. It is shown that the low-frequency modulation of the heating power can substantially ease the overcoming of the radiation barrier.

Edge plasma cooling during noble gas injection into tokamaks

Plasma edge cooling during noble gas injection into a tokamak is discussed. It is shown that a noble gas jet is not able to cool the edge sufficiently for MHD activity initiation. The possibility of additional cooling by natural carbon together with hydrogen neutrals penetration from the wall is analysed.

Reduced models of the dynamics of light impurity stripping

Abstract“Closed” and “open” reduced models of two or three most abundant light impurity ions in an optically thin hydrogen plasma are considered. The models are shown to satisfactorily describe the average ion charge and radiative losses within a wide range of parameters typical of laboratory and astrophysical plasmas, including the case when the relaxation time of the impurity distribution over ionization states is comparable to or longer than the characteristic times of the most important dynamic processes. The potentialities of the models are demonstrated using the carbon impurity as an example. The models proposed make it possible to analytically study the dynamics of a radiating plasma, obtain qualitatively new results, and significantly reduce the computation time when solving complicated self-consistent dynamical problems.

On the possibility of determining the sawtooth location from impurity ion density profiles

A new method is proposed for determination of the magnetic island location from the density profiles of multiply charged impurity ions. The method is based on (1) measuring the impurity ion’s emissivity profiles in T‐10 tokamak experiments and (2) a theoretical model for the behavior of the impurities under conditions of sawtooth oscillations. The main physical basis of the method is the fact that the impurity is forced out from the sawtooth region in such a way that the profile of impurity ions appears to be a composition of two different profiles. These two profiles are determined by the Braginskii mechanism of impurity diffusion sustained in the regions r≳rs and r<(rs−Δ), whereas in the transient region (rs−Δ)≤r≤rs the impurity density has a sharp drop with decreasing minor radius. Interpretation of T‐10 tokamak experimental data within the frame of a theoretical model allows one to determine the location of the surface q=1 and the width of magnetic islands. The method appears to be very sensitive to t...

Greenwald density limit and power balance in tokamaks

The critical density limit in tokamaks is investigated. It is shown that the equality of the input power and power radiated by impurities corresponds to the Greenwald limit. In Ohmic tokamak plasmas the auxiliary heating may increase the density limit, as it has been shown in experiments. The radiated power threshold for plasmas with heavy impurities, observed in experiments, is derived. Radiation produced by heavy impurities is spread practically uniformly along the plasma radius in contrast to the radiation of light impurities. The effective heating power is decreased by radiation losses and, as a consequence, becomes lower than the threshold for the H-L transition. If the input power is close to the radiated one, the disruption occurs.