I. Yu. Senichenkov

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.

Review of Globus-M spherical tokamak results

The first experiments on noninductive current drive (CD) using lower hybrid waves in a spherical tokamak are described. Waves at 2.45 GHz were launched by a 10 waveguide grill with 120° phase shift between neighbouring waveguides. The experimental results for a novel poloidal slowing-down scheme are described. The CD efficiency is found to be somewhat larger than that predicted theoretically whilst at the same time being somewhat less than that for standard tokamak lower hybrid CD. Geodesic acoustic modes (GAM) have been discovered in Globus-M. GAMs are localized 2–3 cm inside the separatrix. The GAM frequency agrees with theory. The mode structures of plasma density and magnetic field oscillation at the GAM frequency have been studied. Fast particle confinement during neutral beam injection has been investigated and numerically simulated. Alfven instabilities excited by fast particles were detected by a toroidal Mirnov probe array. Their excitation conditions are discussed and the dynamics of fast ion losses induced by Alfven eigenmodes is presented. Preliminary experiments on the isotopic effect influence on global confinement in the ohmic heating (OH) regime are described. Scrape-off layer (SOL) parameters were measured and compared with results from self-consistent integrated transport modelling. Results showed that SOL width scales inversely proportional to plasma current. The behaviour of an a priori damaged tungsten divertor plate mock-up exposed to plasma flows was investigated. Preliminary conclusions are that the initial damage gives rise to a loose layer formation with low thermal conductivity right beneath the surface. Finally, engineering design issues of the next step—Globus-M2 (1 T, 500 kA) and the status of component manufacture are described.

Investigation of beam– and wave–plasma interactions in spherical tokamak Globus-M

The experimental and theoretical results obtained in the last two years on the interaction of neutral particle beams and high-frequency waves with a plasma using the spherical tokamak Globus-M are discussed. The experiments on the injection of low-energy proton beam of ~300 eV directed particle energy are performed with a plasma gun that produces a hydrogen plasma jet of density up to 3 × 1022 m−3 and a high velocity up to 250 km s−1. A moderate density rise (up to 30%) is achieved in the central plasma region without plasma disruption. Experiments on high-energy (up to 30 keV) neutral beam injection into the D-plasma are analysed. Modelling results on confinement of fast particles inside the plasma column that follows the neutral beam injection are discussed. The influence of the magnetic field on the fast particle losses is argued. A neutral beam injection regime with primary ion heating is obtained and discussed. The new regime with fast current ramp-up and early neutral beam injection shows electron temperature rise and formation of broad Te profiles until the q = 1 flux surface enters the plasma column. An energetic particle mode in the range of frequencies 5–30 kHz and toroidal Alfven eigenmodes in the range 50–300 kHz are recorded in that regime simultaneously with the Te rise. The energetic particle mode and toroidal Alfven eigenmodes behaviour are discussed. The toroidal Alfven eigenmode spectrum appears in Globus-M as a narrow band corresponding to n = 1. The first experimental results on plasma start-up and noninductive current drive generation are presented. The experiments are carried out with antennae providing mostly poloidal slowing down of waves with a frequency of 920 MHz, which is higher than a lower hybrid one existing under the experimental conditions. The high current drive efficiency is shown to be high (of about 0.25 A W−1), and its mechanism is proposed. Some near future plans of the experiments are also discussed.

On the Ablation Models of Fuel Pellets

The neutral gas shielding model and neutral-gas-plasma shielding model are analyzed qualitatively. The main physical processes that govern the formation of the shielding gas cloud and, consequently, the ablation rate are considered. For the neutral gas shielding model, simple formulas relating the ablation rate and cloud parameters to the parameters of the pellet and the background plasma are presented. The estimates of the efficiency of neutral gas shielding and plasma shielding are compared. It is shown that the main portion of the energy flux of the background electrons is released in the plasma cloud. Formulas for the ablation rate and plasma parameters are derived in the neutral-gas-plasma shielding model. The question is discussed as to why the neutral gas shielding model describes well the ablation rate of the pellet material, although it does not take into account the ionization effects and the effects associated with the interaction of ionized particles with the magnetic field. The reason is that the ablation rate depends weakly on the energy flux of hot electrons; as a result, the attenuation of this flux by the electrostatic shielding and plasma shielding has little effect on the ablation rate. This justifies the use of the neutral gas shielding model to estimate the ablation rate (to within a factor of about 2) over a wide range of parameters of the pellet and the background plasma.

Analysis of drift effects on the tokamak power scrape-off width using SOLPS-ITER

SOLPS-ITER, a comprehensive 2D scrape-off layer modeling package, is used to examine the physical mechanisms that set the scrape-off width () for inter-ELM power exhaust. Guided by Goldstons heuristic drift (HD) model, which shows remarkable quantitative agreement with experimental data, this research examines drift effects on in a DIII-D H-mode magnetic equilibrium. As a numerical expedient, a low target recycling coefficient of 0.9 is used in the simulations, resulting in outer target plasma that is sheath limited instead of conduction limited as in the experiment. Scrape-off layer (SOL) particle diffusivity (D SOL) is scanned from 1 to 0.1 m2 s−1. Across this diffusivity range, outer divertor heat flux is dominated by a narrow (~3–4 mm when mapped to the outer midplane) electron convection channel associated with thermoelectric current through the SOL from outer to inner divertor. An order-unity up–down ion pressure asymmetry allows net ion drift flux across the separatrix, facilitated by an artificial mechanism that mimics the anomalous electron transport required for overall ambipolarity in the HD model. At m2 s−1, the density fall-off length is similar to the electron temperature fall-off length, as predicted by the HD model and as seen experimentally. This research represents a step toward a deeper understanding of the power scrape-off width, and serves as a basis for extending fluid modeling to more experimentally relevant, high-collisionality regimes.

Globus-M plasma physics research for fusion application and compact neutron source development

During the past decade, plasma physics research promoting the physics base of ITER and developing novel concepts such as a compact fusion neutron source has been conducted on the Globus-M spherical tokamak (ST) (R = 36 cm, a = 24 cm, I p ≤ 250 kA, B T ≤ 0.4 T). Tokamak reconstruction is imminent. The upgraded tokamak Globus-M2 will have the same vacuum chamber and an enhanced magnetic system to provide B T = 1 T and I p = 500 kA. In this paper we outline the most important research directions and the main results obtained on Globus-M and make some predictions about the possibilities and parameters of Globus-M2.

Modelling of the pellet cloud evolution and mass deposition with an account of ∇B induced drift

Modelling of the pellet ablation cloud evolution including the ∇B induced drift motion is performed. The model includes cloud heating, expansion and ionization, acceleration in the low-field side (LFS) direction, Alfven conductivity of the background plasma, compensation of ∇B currents in different parts of the cloud during its propagation along the magnetic field, cooling of the background plasma and simulation of the pellet ablation rate in a self-consistent manner. The time evolution of cloud density and temperature profiles and the mass deposition after the pellet injection are calculated. The LFS and high-field side injection scenarios with plasma and pellet parameters typical for the ASDEX-Upgrade tokamak are compared. An effect of pre-cooling on the pellet penetration depth is studied. The calculated size of the neutral part of the cloud, the characteristic values of cloud density and temperature far from the pellet and the fuelling efficiency (for LFS pellets) are in reasonable agreement with those observed in experiments on the ASDEX-Upgrade.

Integrated modeling of H-mode tokamak discharges with ASTRA and B2SOLPS numerical codes

The numerical codes ASTRA and B2SOLPS5.2 are coupled to perform an integrated modeling of particle and energy transport and to obtain continuous self-consistent profiles of the main plasma parameters from the magnetic axis up to target plates. The unique distinguishing feature of the new coupling scheme is the presence of a region of overlap of the 1D and 2D computational domains, where the 1D solution coincides with the 2D one at the equatorial midplane. In the 2D transport equation system, all relevant drift flows and currents are taken into account, which allows us to calculate the poloidal variation of the density, temperatures and electrostatic potential, and obtain neoclassical radial fluxes in a self-consistent manner. Such an approach allows us to model tokamaks for which neoclassical effects give a significant contribution to the ion heat transport, and in particular, spherical tokamaks.

1D equation for toroidal momentum transport in a tokamak

A 1D equation for toroidal momentum transport is derived for a given set of turbulent transport coefficients. The averaging is performed taking account of the poloidal variation of the toroidal fluxes and is based on the ambipolar condition of the zero net radial current through the flux surface. It is demonstrated that taking account of the Pfirsch–Schluter fluxes leads to a torque in the toroidal direction which is proportional to the gradient of the ion temperature. This effect is new and has not been discussed before. The boundary condition at the separatrix, which is based on the results of the 2D simulations of the edge plasma, is formulated.

Integrated modelling of the Globus-M tokamak plasma and a comparison with SOL width scaling

Recently a scheme for the coupling of the one-dimensional core transport code ASTRA and the two-dimensional edge transport code B2SOLPS was developed, thus providing the integrated modelling of tokamak discharge. Here, this scheme is improved by taking impurities into account and by considering a real flux surface shape using the equilibrium code SPIDER. This integrated modelling is applied to discharges of the spherical tokamak Globus-M to study the dependence of the scrape-off layer (SOL) width and divertor heat loads on the discharge power and the plasma current. Since these values, together with the magnetic field, are relatively small in Globus-M, this study can test the existing scaling against data in a wider range of tokamak operational parameters. The modelling results agree reasonably with Thomson scattering and Langmuir probe measurements and allow, in principle, the determination of the physical mechanisms responsible for the SOL structure formation. It is found that the SOL width is approximately inversely proportional to the plasma current, in agreement with existing experimental scaling, while its dependence on discharge power is found to be quite weak.