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SOLPS-ITER code simulations with fluid drifts activated are used to examine the consequences for divertor performance, under burning plasma conditions, of a reduction in scrape-off layer (SOL) cross-field transport such that the outboard midplane SOL parallel heat flux width, λq is reduced to the very low values predicted by the experimental scaling in [T. Eich et al., Nucl. Fusion 53 (2013) 093031] for high plasma current operation on ITER. The decrease of λq from the standard value (~3.5 mm) used in the ITER SOLPS modeling database, to λq ~ 1–2 mm expected from the scaling, leads to a strong narrowing of the operational window in terms of divertor heat loading limits. To maintain similar levels of sub-divertor neutral pressure, pn (one of the key divertor operational parameters) as those obtained with standard transport, higher levels of neon impurity seeding are required when transport is reduced, yielding higher Zeff at the upstream separatrix and requiring further integrated modelling to assess the impact on confinement. The simulations also demonstrate that the strong increase in in-out target peak power loading asymmetry at low pn seen for standard transport when drifts are switched on in the code is preserved, and in fact worsens, for low transport. This significantly reduces margins for power handling control at lower pn if heat flux channels will be narrow on ITER.

The tokamak scrape-off layer (SOL) model is discussed on the assumption of drift mechanisms of electron heat transport and dominant role of recycling outside the separatrix comparing to the ion outflow from the core. The SOL width estimate is given. It is shown that drift mechanisms give minimal SOL width corresponding to present day scalings which is close by the order of magnitude to the experimental values.

The effects of drifts and associated flows and currents on the width of the parallel heat flux channel (λq) in the tokamak scrape-off layer (SOL) are analyzed using the SOLPS-ITER 2D fluid transport code. Motivation is supplied by Goldston’s heuristic drift (HD) model for λq, which yields the same approximately inverse poloidal magnetic field dependence seen in multi-machine regression. The analysis, focusing on a DIII-D H-mode discharge, reveals HD-like features, including comparable density and temperature fall-off lengths in the SOL, and up-down ion pressure asymmetry that allows net cross-separatrix ion magnetic drift flux to exceed net anomalous ion flux. In experimentally relevant high-recycling cases, scans of both toroidal and poloidal magnetic field (Btor and Bpol) are conducted, showing minimal λq dependence on either component of the field. Insensitivity to Btor is expected, and suggests that SOLPS-ITER is effectively capturing some aspects of HD physics. Absence of λq dependence on Bpol, however, is inconsistent with both the HD model and experimental results. The inconsistency is attributed to strong variation in the parallel Mach number, which violates one of the premises of the HD model. Keywords: Power scrape-off width, SOLPS-ITER, Drift effects, SOL flows

Using the new version of the SOLPS plasma boundary code package, SOLPS-ITER, this paper presents the first ever simulations of the ITER burning baseline H-mode edge plasma with drifts and currents activated. Neon (Ne) seeded discharges for divertor power dissipation are considered. The results for divertor and scrape-off layer (SOL) parameters with and without drifts are compared, both for the SOLPS-ITER simulations and against the earlier SOLPS-4.3 modelling (which did not include a drift description) constituting the bulk of the existing ITER divertor simulation database. Whereas the drift effect on the equatorial midplane (main chamber) density and temperature profiles is moderate, drifts increase the peak heat flow to the outer divertor target. This effect is more pronounced for regimes with low sub-divertor neutral pressure, when even drift-free SOLPS4.3 simulations find strong out-in target power asymmetries. An important conclusion is thus that if ITER operates as expected with partially detached divertor targets, drifts should not influence the power handling, but that in the case of divertor reattachment, they will act to worsen the target loading, increasing the need for development of reliable schemes for detachment control. Comparing SOLPS-4.3 and SOLPS-ITER results for the key peak target heat flux versus sub-divertor neutral pressure operating domain, SOLPS-ITER with drifts predicts a narrower operational window for the divertor pressure.

SOLPS-ITER is a code package for tokamak plasma boundary modeling comprising the B2.5 plasma fluid code and the EIRENE neutral kinetic code. The form of the momentum balance equation, used in the SOLPS-ITER code before version 3.0.6 (and in all previous versions of SOLPS codes), was simplified due to numerical reasons—the electric field term was replaced by the electron gradient pressure term; friction and thermal force terms were derived using the trace impurity assumption. It has now been decided to switch back to the general Braginskii version of this equation. Derivation of the new form of the parallel friction and thermal force terms has been required to allow the use of the general form of the equation and allow more accurate modeling of multicomponent plasmas. The new form is based on the theoretical description of multicomponent plasma derived by V. M. Zhdanov [Plasma Phys. Controlled Fusion 44(10), 2283 (2002)]. In the present paper, a detailed derivation of these terms is presented, and their implementation into the SOLPS-ITER code package is discussed.

Currents structure in the scrape-off layer (SOL) of a tokamak is analyzed. It is demonstrated that poloidal currents measured in the experiments are a combination of several current types of different physical nature. Besides known Pfirsch-Schluter (PS) currents and thermoelectric currents, so-called PCC (plate closing currents) flowing to/from the divertor plates are also analyzed. The latter close radial currents in the SOL and below/above the X-point. In particular, current flowing to the outer plate in the private flux region (PFR), opposite to thermolelectric current is predicted for the standard single-null configuration and favorable direction of ∇B drift (∇B drift of ions is directed towards active X-point). In addition, a pair of currents to and away from the outer plate should flow. In the single-null configuration they are often masked by a larger thermoelectric current, however for the connected double null (CDN) case, where thermoelectric current is strongly reduced due to less temperature asymmetry, these currents dominate. The suggested physical model is supported by results of simulations performed with SOLPS-ITER transport code. Simulations were done for ASDEX-Upgrade (AUG), L-mode , single-null configurations, and for Globus-M H-mode, both disconnected and connected double null configurations. Results of the simulations are compared with probe measurements for AUG and Globus-M tokamaks, and reasonable agreement has been found.

A numerical study is presented, using the SOLPS-ITER plasma boundary code with full drifts and currents activated, of impurity seeded JET discharges in support of high power H-mode experimental campaigns designed to compare two ITER candidate seeding species, nitrogen (N) and neon (Ne). Fluid-kinetic edge plasma simulations are first performed at lower levels of power into the scrape-off layer (SOL) and benchmarked against existing JET experimental data. Calculations are then performed for higher levels of SOL power to examine the impact of this key parameter on the efficiency of both radiators. From the code point of view, for the chosen JET parameters, Ne can be as efficient a divertor radiator as N at the same level of upstream separatrix Zeff

By modeling done with the SOLPS-ITER transport code, it is demonstrated that moderate radiating impurity seeding leads to the increase in the radial electric field by absolute value, while radial electric field remains close to the neoclassical one. In the seeded detached regime with a highly radiating X-point, the radial electric field deviates considerably from the neoclassical electric field. The radial dimension of the zone with increased poloidal E × B rotation shear is larger by absolute value than that corresponding to the moderate seeding. This effect might lead to the shift of the transport barrier further to the core and can partially compensate energy losses rise inside the separatrix, so the pedestal improvement might take place.

In the present paper the ASDEX Upgrade (AUG) experimental trend of reaching the radiating X-point with nitrogen seeding is reproduced by SOLPS-ITER code modeling. In these experiments the whole divertor region below the X-point is cooled down by the impurity radiation if the seeding rate is large enough, and the maximal radiation is registered from the X-point region, or even from the confinement zone above the X-point. It is demonstrated that for constant seeding rate SOLPS-ITER simulations of the intensively seeded AUG discharges result in that the confined plasma goes into the radiation collapse as a certain threshold in seeding rate is exceeded. This threshold value increases with increasing discharge power. No stable regimes with the electron temperature below 5 eV in the confinement zone even above the X-point are achieved in the modeling if the seeding rate is large enough, in contrast to the experiment. However, such a regime may be achieved if the fueling, seeding and pumping rates are changing in time. Since the SOLPS-ITER code can simulate only steady state, another modeling strategy is chosen. The fueling and seeding rates are artificially reduced by 3 orders of magnitude and the impurity content is set to satisfy the condition that the ratio of electrons contribution originating from fuel atoms to ones coming from impurity atoms is about unity. It is suggested that the radial width of the cooled region in the confinement zone is of the order of the scrape-off layer width λ q , since it is driven by the same physics leading the energy flux to go from mostly radial to mostly parallel. Under these conditions, the radiative spot above the X-point behaves as the energy sink similarly to the energy sink near the divertor in the conventional regime. In extreme regimes (with large seeding rate), the width of the cold region inside the separatrix may exceed λ q , and up to 90% of discharge power can be radiated from the confined region. An estimate of the poloidal length of the radiative spot is suggested as well. Flow patterns of neutrals, deuterium ions, impurities, electric current and heat flows are analyzed for the regimes with intensive X-point radiation. The formation of an electric potential peak above the X-point is observed in the simulations, and the corresponding E × B drift flux appears to give the largest contribution to the main ion and impurity fluxes. This E × B drift flux together with the large ionization source change the parallel velocity with respect to its neoclassical profile. Consequently, the radial E field deviates from the neoclassical one, which might improve the turbulence suppression.

Current structure in the scrape-off layer (SOL) of a tokamak is analyzed. It is demonstrated that poloidal currents measured in the experiments are a combination of several current types with different physical nature. Besides the known Pfirsch–Schlüter currents and thermoelectric currents, so-called plate closing currents flowing to/from the divertor plates are also analyzed. The latter close radial currents in the SOL and below/above the X-point in the SOL and private flux region (PFR). In particular, the current flowing to the outer plate in the PFR, opposite to the thermoelectric current, is predicted for the standard single-null configuration and favorable direction of ∇ B drift. In addition, a pair of currents should flow to and away from the outer plate. In the single-null configuration, they are often masked by a larger thermoelectric current. However, for the connected double null (CDN) case, where the thermoelectric current is strongly reduced due to smaller temperature asymmetry, these currents dominate. The suggested physical model is supported by the results of simulations performed with the SOLPS-ITER transport code. Simulations were done for ASDEX Upgrade (AUG), L- and H-modes, single-null configurations, and for Globus-M H-mode, both disconnected and CDN configurations. Results of the simulations are compared with probe measurements for AUG and Globus-M tokamaks, and reasonable agreement has been found. The role of parallel currents in the formation of the potential maximum/minimum in the vicinity of the X-point for strongly detached regimes is also analyzed.

The study aims to estimate the influence of machine scale size on the behavior of plasma with extrinsic seeded impurities in the scrape-off layer (SOL) and divertor. This is performed through the comparison of plasma boundary simulations using the SOLPS-ITER code including drifts and currents of nitrogen (N) and neon (Ne) injection in ITER and ASDEX Upgrade (AUG) geometries. Trends are examined between the two seeding species in each individual device and by a comparison of the differences between the two machines. In the modeling results, the radiated power peak is located near the X-point in the inner divertor for the AUG cases and in the vicinity of the strike points in both divertors in ITER. The simulations also find less Ne impurity ions in the divertor volume than N and more significant Ne radiation inside the separatrix for AUG, consistent with published experimental findings. In ITER, both species radiate mostly from the divertor, in agreement with the existing SOLPS-4.3 simulation database obtained without drifts and with a less sophisticated treatment of parallel impurity transport. Drifts are important players in determining the plasma background for AUG and are comparatively less important in ITER. In both devices, the spatial distribution of the impurity ion density is complex, with their parallel flow patterns correlating with the thermal and friction force balance. Within this isolated modeling study, the principal reasons for different behavior between N and Ne on AUG and ITER appear to be the combination of a stronger drift effect and reduced screening of recycled fuel and impurity from divertor to private flux region on AUG leading to a more extended, colder plasma than in ITER. The increased temperature in the confined region just inside the separatrix on ITER also means that impurity ions reaching this zone are fully ionized and do not contribute significantly to the radiation loss there. On the basis of this study, both N and Ne are found to be acceptable low Z radiators on ITER.

The SOLPS-ITER transport code was released in 2015 on the basis of older versions of SOLPS and the EIRENE Monte Carlo code for neutrals. In the parallel momentum balance equations of this first release, each of the ion species was combined with the parallel momentum balance for electrons so as to eliminate the electric field term. In doing so, the expressions for the thermal and friction forces were approximated for simplification. Such approximations break down for multi-component plasma modelling. It was subsequently proposed to return to solving the original (Braginskii) ion momentum balance equations, with the electric field term included, and with more accurate treatment of friction and thermal force terms, although the treatment of these terms still assumed trace impurities. In the present work, more general expressions for the friction and thermal forces, valid for high impurity densities (z(eff) - 1 > 1 at the separatrix), are suggested. This new form for the force terms within the Braginskii equation has now been implemented in SOLPS-ITER and has been tested through the use of simulation test cases of nitrogen-seeded scenarios in ASDEX Upgrade geometry, with drifts and currents switched on. This paper discusses the effect of the new form of the terms in the Braginskii equation, emphasizing the differences with the trace impurity approach. It demonstrates that the latter already begins to fail in simulations for which z(eff) = 1.5. The influence of the transition from the old form of the momentum balance equation to the new general Braginskii formulation with corrected friction and thermal force terms is demonstrated by comparing SOLPS-ITER ASDEX Upgrade simulations employing both descriptions.

Modeling of the transition to the detachment of ASDEX Upgrade tokamak plasma with increasing density is performed using the SOLPS-ITER numerical code with a self-consistent account of drifts and currents. Their role in plasma redistribution both in the confinement region and in the scrape-off layer (SOL) is investigated. The mechanism of high field side high-density formation in the SOL in the course of detachment is suggested. In the full detachment regime, when the cold plasma region expands above the X-point and reaches closed magnetic-flux surfaces, plasma perturbation in a confined region may lead to a change in the confinement regime.

On the eve of component procurement, this paper discusses the present physics basis for the first ITER tungsten (W) divertor, beginning with a reminder of the key elements defining the overall design, and outlining relevant aspects of the Research Plan accompanying the new “staged approach” to ITER nuclear operations which fixes the overall divertor lifetime constraint. The principal focus is on the main design driver, steady state power fluxes in the DT phases, obtained from simulations using the 2-D SOLPS-4.3 and SOLPS-ITER plasma boundary codes, assuming the use of the low Z seeding impurities nitrogen (N) and neon (Ne). A new perspective on the simulation database is adopted, concentrating purely on the divertor physics aspects rather than on the core-edge integration, which has been studied extensively in the course of the divertor design evolution and is published elsewhere. Emphasis is placed on factors which may increase the peak steady state loads: divertor target shaping for component misalignment protection, the influence of fluid drifts, and the consequences of narrow scrape-off layer heat flux channels. All tend to push the divertor into an operating space at higher sub-divertor neutral pressure in order to remain at power flux densities acceptable for the target material. However, a revised criterion for the maximum tolerable loads based on avoidance of W recrystallization, sets an upper limit potentially ∼50% higher than the previously accepted value of ∼10 MW m−2, a consequence both of the choice of material and the finalized component design. Although the simulation database is currently restricted to the 2-D toroidally symmetric situation, considerable progress is now also being made using the EMC3-Eirene 3-D code suite for the assessment of power loading in the presence of magnetic perturbations for ELM control. Some new results for low input power corresponding to the early H-mode operation phases are reported, showing that even if realistic plasma screening is taken into account, significant asymmetric divertor heat fluxes may arise far from the unperturbed strike point. The issue of tolerable limits for transient heat pulses is an open and key question. A new scaling for ELM power deposition has shown that whilst there may be more latitude for operation at higher current without ELM control, the ultimate limit is likely to be set more by material fatigue under large numbers of sub-threshold melting events. Keywords: ITER, Tungsten, Divertor, Heat fluxes, SOLPS

We present the results of calculation and experimental testing of an achromatic polarization converter and a composite terahertz waveplate (WP), which are represented by sets of plane-parallel birefringent plates with in-plane birefringence axis. The calculations took into account the effect of interference, which was especially prominent when plates were separated by an air gap. The possibility of development of a spectrum analyzer design based on a set of WPs is also discussed. (C) 2013 Optical Society of America

The article discusses key physical processes within the active area of an optoacoustic detector. Said area is a xenon-filled chamber subdivided into two cavities connected by a narrow channel. Original mathematical model of such area is proposed on the basis of thermodynamic processes that occur within. A method has been developed to measure a shape of a periodic pulse exceeding 0.5 ms duration at repetition rates ranging from zero to several hundred Hz. The measurement requires knowledge of a set of parameters describing a specific instrument. Principal points of detector calibration are discussed in brief.

Radial electric fields have been simulated using the B2SOLPS5.2 transport code. Simulations were performed for three different times of one H-mode shot of ASDEX-Upgrade with three different levels of heating power. Simulation results were compared with the values of electric field measured by means of He II spectroscopy. It is demonstrated that the radial electric fields obtained in the simulations are close to the neoclassical electric fields as in the previous simulations performed both for ASDEX-Upgrade and MAST for H and L-regimes. The calculated radial electric fields are in reasonable agreement with the field profiles obtained in the experiment. Both simulations and experiment are consistent with the neoclassical character of the radial electric field in the edge barrier. The calculated toroidal rotation at the low field side equatorial midplane is of the same order as measured in the experiment and is co-current directed.

Impurity seeding into a tokamak divertor for radiative cooling is considered as a tool for achieving detached/semi-detached regimes required to meet the condition of acceptable heat loads on divertor plates. Experiments aimed at searching for an operational window with a significant reduction of poloidal heat fluxes due to the impurity radiation and without decrease of confinement are performed on many tokamaks. A critical issue in these experiments is how large a fraction of impurities is retained in the divertor region and how much is extracted upstream to the scrape-off layer. In the present paper a physical mechanism of impurity transport from a divertor towards upstream and back to the divertor is analyzed. It is demonstrated that the widespread concept that the impurity leaks if the parallel thermal force exceeds the friction due to main ions and is retained otherwise—is not correct. In this paper, we contend that the impurity leaks if it crosses the stagnation point of the impurity ion poloidal velocity profile before being ionized, and is retained if it ionizes closer to the target than the location of that stagnation point. Thus the leakage efficiency depends on the relative spatial positions of the impurity atom ionization source and the stagnation point of the impurity ion poloidal velocity profile. The impurity ion poloidal velocity is to large extent the sum of the poloidal projection of its parallel velocity and the E × B drift velocity, where the former is derived from the parallel impurity force balance equation. It is demonstrated that the solution of this equation may be approximated by the balance of friction and thermal forces in all regimes, while other terms are smaller. This allows for expressing the impurity parallel velocity through the main ion one and makes the distribution of the parallel (poloidal) fluxes of the main ions, including Pfirsch–Schluter fluxes and E × B drift fluxes, to be an important element of the impurity transport. It is shown that the impurity distribution in the edge plasma is rather sensitive to the value of the impurity ion ionization rate. This analysis is supported by simulation results obtained for the ASDEX Upgrade tokamak with various seeding rates of N and Ne with the SOLPS-ITER code. The importance of the inclusion of self-consistent drift flows is demonstrated by comparison to results of corresponding simulations with the drifts turned off.

Reported is the first modeling of ITER H-mode. Simulations were made with the code B2SOLPS5.2 with drifts and currents, which was specially developed for simulation of tokamak H-regimes. The emphasis is made on the pedestal and edge transport barrier regions. It is demonstrated that the specific feature of the ITER discharges is the density profile in the edge barrier region typical for the low particle sources in the main part of the barrier. The density, temperature and radial electric field profiles are calculated for two values of the edge barrier width (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A new version of the B2SOLPS5.0 transport code, which is free from numerical problems in the barrier region, has been used to simulate H-mode shots from ASDEX-Upgrade and MAST. The radial electric field inside the edge transport barrier and in the pedestal region is close to the neoclassical prediction. The shear of poloidal E → × B → drift at the inner side of the barrier is close to the value before the transition, while inside the barrier it is significantly larger. It is demonstrated that to match the experimental density and temperature radial profiles the drop in the diffusion coefficient within the barrier should be significantly larger than the drop in the electron heat conductivity.

25th Fusion Energy Conference (FEC), Govt Russian Federat, St Petersburg, RUSSIA, OCT 13-18, 2014; International audience; In this paper we present the fusion related activities of the Plasma Physics Division at the Ioffe Institute. The first experiments on lower hybrid current drive (LHCD) in a spherical tokamak performed at the Globus-M tokamak (R = 0.36 m, a = 0.24 m, B-t = 0.4 T, I-p = 200 kA) with a novel poloidally oriented grill resulted in an RF driven current of up to 30 kA at (100kW, 2.5 GHz), exceeding the modelling predictions. At the FT-2 tokamak (R = 0.56 m, a = 0.08 m, B-t = 3T, I-p = 30 kA) experiments with a traditional toroidally oriented grill revealed no strong dependence of the LHCD density limit on the H/D ratio in spite of LH resonance densities differing by a factor of 3. Microwave Doppler reflectometry (DR) at the Globus-M, and DR and heavy ion beam probe measurements at the tokamak TUMAN-3M (R = 0.53 m, a = 0.24 m, B-t = 1.0T, I-p = 190 kA) demonstrated geodesic acoustic mode (GAM) suppression at the L to H transition. Observations at FT-2 using Doppler Enhanced Scattering showed that the GAM amplitude is anti-correlated both spatially and temporally to the drift turbulence level and electron thermal diffusivity. For the first time turbulence amplitude modulation at the GAM frequency was found both experimentally and in global gyrokinetic modelling. A model of the L-H transition is proposed based on this effect. The loss mechanisms of energetic ions' (EI) were investigated in the neutral beam injection (NBI) experiments on Globus-M and TUMAN-3M. Empirical scaling of the 2.45 MeV DD neutron rate for the two devices shows a strong dependence on toroidal field B-t(1.29) and plasma current I-p(1.34) justifying the B-t and I-p increase by a factor of 2.5 for the proposed upgrade of Globus-M. Bursts of similar to 1 MHz Alfvenic type oscillations correlating with sawtooth crashes were observed in ohmic TUMAN-3M discharges. The possibility of low threshold parametric excitation of Bernstein and upper hybrid waves trapped in drift-wave eddies resulting in anomalous absorption in electron cyclotron resonance heating (ECRH) experiments in toroidal plasmas was identified theoretically. A novel method of radial correlation Doppler reflectometry is shown to be capable of measuring the turbulence wave-number spectrum in realistic 2D geometry. On the progress in design and fabrication of three diagnostics for ITER developed in the Ioffe institute is reported: neutral particle analysis, divertor Thomson scattering and gamma spectroscopy.

Simulations have been performed to investigate the impact of gas puffing position on plasma toroidal rotation. It was demonstrated that inboard puffing generates counter-current rotation in agreement with experimental observations. On the basis of the simulations a physical model was put forward, which is based on momentum transport by vertical ∇B drifts and anomalous radial transport. Toroidal rotation is generated mainly due to radial transport of the inboard/outboard particle fluxes by ∇B drifts. Its value depends on the location, radial and poloidal dimensions of the ionization source on the closed field lines, increases linearly with the ion temperature and plasma density and is inversely proportional to the plasma current.

A method of reduction of the two-dimensional equation for the potential to a one-dimensional ordinary equation is suggested and implemented in the B2SOLPS5.0 transport code to simulate a divertor tokamak. The one-dimensional version, which gives similar results as the full two-dimensional version, provides better understanding of the role of various mechanisms of perpendicular conductivity and reduces computational time. The scheme of poloidal (parallel) current calculation is presented and compared to the two-dimensional code results both for the core region and for the scrape-off layer.

The impurity transport in the edge plasma of a divertor tokamak is simulated by means of B2-SOLPS5.0 2D multi-fluid code where diamagnetic and E → × B → drifts for all species are taken into account. It is demonstrated that these drifts to large extent determine the poloidal distribution of impurities near the separatrix and hence penetration of impurities to the core region. The influence of the drifts on the low ionized impurity distribution in the divertor region is more modest.

Mechanisms of the impurity transfer inside a tokamak separatrix have been studied. It is shown that poloidal rotation significantly influences the poloidal distribution of impurities. An analysis of the neoclassical component of the radial impurity flux showed that this fraction is described by an expression that is more complicated than the standard neoclassical variant.

The structure of the scrape-off layer (SOL) of a tokamak with little or no turbulent transport is analyzed. The analytical estimates of the density and electron temperature fall-off lengths of the SOL are put forward. It is demonstrated that the SOL width could be of the order of the ion poloidal gyroradius, as suggested in Goldston (2012 Nuclear Fusion 52 013009). The analytical results are supported by the results of the 2D simulations of the edge plasma with reduced transport coefficients performed by SOLPS-ITER transport code.

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.

Simulation of an H-mode ASDEX Upgrade shot with boron impurity was done with the B2SOLPS5.2 transport code. Simulation results were compared with the unique experimental data available for the chosen shot: radial density, electron and ion temperature profiles in the equatorial midplanes, radial electric field profile, radial profiles of the parallel velocity of impurities at the low-field side (LFS) and high-field side (HFS), radial density profiles of impurity ions at LHS and HFS. Simulation results reproduce all available experimental data simultaneously. In particular strong poloidal HFS?LFS asymmetry of B5+ ions was predicted in accordance with the experiment. The simulated HFS B5+ density inside the edge transport barrier is twice larger than that at LFS. This is consistent with the experimental observations where even larger impurity density asymmetry was observed. A similar effect was predicted in the simulation done for the MAST H-mode. Here the HFS density of He2+ is predicted to be 4 times larger than that at LHS. Such a large predicted asymmetry is connected with a larger ratio of HFS and LFS magnetic fields which is typical for spherical tokamaks. The HFS/LFS asymmetry was not measured in the experiment, however modelling qualitatively reproduces the observed change of sign of He+parallel velocity to the counter-current direction at LFS. The understanding of the asymmetry is based on neoclassical effects in plasma with strong gradients. It is demonstrated that simulation results obtained with account of sources of ionization, realistic geometry and turbulent transport are consistent with the simplified analytical approach. Difference from the standard neoclassical theory is emphasized.

The fluid simulation of a divertor tokamak edge plasma by the B2-SOLPS5.0 transport code gives the dependence of the radial electric field on the local and global plasma parameters. The shear of the radial electric field, which is responsible for the transition to an improved confinement regime, is a linear function of a local ion temperature and the local average toroidal velocity and is inversely proportional to the toroidal magnetic field. The scaling for the L-H transition threshold agrees with the experimental H-mode scaling of ASDEX Upgrade. The radial electric field shows no bifurcation and is close to the neoclassical electric field with the toroidal rotation contribution determined by the radial anomalous transport of the toroidal momentum. The fine structure of the electric field at the separatrix and its dependence on the toroidal magnetic field inversion is analysed.

The biasing experiments and the problem of the effective perpendicular conductivity in a tokamak are studied both analytically and numerically. The simulations were performed by means of the B2SOLPS5.0 transport code [V. A. Rozhansky et al., Nucl. Fusion 41, 387 (2001)] where the fluid set of equations is solved for the real divertor geometry. It is demonstrated that there exist three regimes, which correspond to the different values of the effective perpendicular conductivity and to different profiles of the radial electric field and toroidal and poloidal rotations. Simulation results are compared with existing and developed analytical models.

The radial electric field in the vicinity of the separatrix and its shear is studied in detail by means of the B2-SOLPS5.0 transport code. Calculations are performed for various regimes of ASDEX Upgrade. The dependencies of the radial electric field on the local temperature, density, toroidal and poloidal magnetic fields and mean toroidal rotation are investigated.

We present the results of calculation and experimental testing of the tunable wavelength terahertz polarization converter represented by a set of plane-parallel birefringent plates with an in-plane birefringence axis. An experimental device has been produced and tested. The calculations show that the effect of interference between the interfaces, including air gaps, may be neglected. The considered device may be used as a simple narrow achromatic waveplate, or a Solc band pass filter for the specified wavelength.

A complete system of transport equations with all the important perpendicular currents is derived for the simulation of tokamak edge plasma. These transport equations are implemented in the B2.5 code and solved for the parameters of the ASDEX Upgrade tokamak. The relative roles of different mechanisms of transverse conductivity in the formation of the potential profile are studied. It is demonstrated that a reasonable potential distribution in the tokamak edge plasma can be obtained without an ad hoc assumption of the existence of the anomalous perpendicular conductivity. The role of E ? B drifts in the redistribution of edge plasma and closing of the currents in the plasma is analysed.

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.

The radial electric field and toroidal rotation of tokamak plasma near a magnetic island have been calculated. Outside the magnetic island, the radial electric field varies from a value determined by the rotation of this island to the neoclassical value over a scale dependent on the anomalous viscosity and collisionality of the plasma. Inside the magnetic island, the radial electric field is constant.

Several simulations of the L-regimes of ASDEX Upgrade edge plasma have been performed with the B2 SOLP S5.0 2D fluid transport code for a wide range of parameters. A conclusion has been made that the radial electric field in the separatrix vicinity is close to the neoclassical value. The poloidal E × B drifts and compensating parallel fluxes in the scrape-off layer are larger in the H-mode due to steeper gradients while the qualitative pattern of the flows is similar to that of the L-mode.

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 Goldston's 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.

The edge plasma of five Globus-M discharges was modeled by the B2SOLPS5.2 code. Plasma current varied in 114–198 kA range, and all discharges were in the H-mode. The modeled scrape-off layer (SOL) width appeared to be inversely proportional to the plasma current. Such a relation is observed in many other tokamaks. Heat flux to the outer divertor target and radiation power was examined for these discharges. Radiation was found to be responsible for 40% of the energy loss. Energy flux to the low outer divertor target was about 1/3 of the energy loss in the single-null low X-point discharges.

Mechanisms of current generation in edge localized mode (ELM) filaments are discussed. It is shown that dipole type currents should flow in the filaments and that these currents are short-circuited through the ambient plasma of the scrape-off layer. The steady-state monopole currents in the filaments cannot be closed through the ambient plasma and oscillatory currents with Alfven frequency should emerge instead. The dipole type currents in the filaments are sufficient to produce magnetic field perturbations which create a stochastic layer inside the edge transport barrier (ETB) region. The dynamic of penetration of the magnetic field perturbations is analyzed and it is shown that the corresponding time is comparable with the life time of the filaments. At the stage when the ETB region is stochastized by the currents of the filaments the radial electric field becomes less negative or even positive inside the ETB and the onset of outward convective flux takes place. It is shown that this outward flux could lead to the significant pump-out effect—the density decrease in the pedestal region.

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.

The radial electric field Er at the tokamak plasma edge is simulated both with a two-dimensional (2D) fluid code solving the most complete system of transport equations and with five-dimensional (three-dimensional in configuration space and 2D in velocity space) Monte Carlo particle following code. At low to high confinement transition conditions, the E→r×B→ shearing rate is found to be high enough for turbulence suppression even though the field is essentially neoclassical. Here, B→ is the magnetic field. No bifurcation of Er is found.

Plasma rotation and radial electric field in the presence of resonant magnetic perturbations (RMPs) is considered. The situation is discussed in detail where no change of poloidal rotation is observed while the radial electric field and toroidal rotation are changing self-consistently when RMPs are switched on. Recent experimental results from DIII-D are discussed in connection with this model.

New diagnostic, modelling and plant capability on the Mega Ampère Spherical Tokamak (MAST) have delivered important results in key areas for ITER/DEMO and the upcoming MAST Upgrade, a step towards future ST devices on the path to fusion currently under procurement. Micro-stability analysis of the pedestal highlights the potential roles of micro-tearing modes and kinetic ballooning modes for the pedestal formation. Mitigation of edge localized modes (ELM) using resonant magnetic perturbation has been demonstrated for toroidal mode numbers n = 3, 4, 6 with an ELM frequency increase by up to a factor of 9, compatible with pellet fuelling. The peak heat flux of mitigated and natural ELMs follows the same linear trend with ELM energy loss and the first ELM-resolved Ti measurements in the divertor region are shown. Measurements of flow shear and turbulence dynamics during L-H transitions show filaments erupting from the plasma edge whilst the full flow shear is still present. Off-axis neutral beam injection helps to strongly reduce the redistribution of fast-ions due to fishbone modes when compared to on-axis injection. Low-k ion-scale turbulence has been measured in L-mode and compared to global gyro-kinetic simulations. A statistical analysis of principal turbulence time scales shows them to be of comparable magnitude and reasonably correlated with turbulence decorrelation time. Te inside the island of a neoclassical tearing mode allow the analysis of the island evolution without assuming specific models for the heat flux. Other results include the discrepancy of the current profile evolution during the current ramp-up with solutions of the poloidal field diffusion equation, studies of the anomalous Doppler resonance compressional Alfvén eigenmodes, disruption mitigation studies and modelling of the new divertor design for MAST Upgrade. The novel 3D electron Bernstein synthetic imaging shows promising first data sensitive to the edge current profile and flows. © 2013 IAEA, Vienna.

The non-linear reduced four-field RMHD model in cylindrical geometry was extended to include plasma rotation, neoclassical poloidal viscosity and two fluid diamagnetic effects. Interaction of the static resonant magnetic perturbations (RMPs) with the rotating plasmas in tokamaks was studied. The self-consistent evolution of equilibrium electric field due to RMP penetration is taken into account in the model. It is demonstrated that in the pedestal region with steep pressure gradients, mean flows perpendicular to the magnetic field, which includes and electron diamagnetic components plays an essential role in RMP screening by plasma. Generally, the screening effect increases for lower resistivity, stronger rotation and smaller RMP amplitude. Strong screening of central islands was observed limiting RMP penetration to the narrow region near the separatrix. However, at certain plasma parameters and due to the non-linear evolution of the radial electric field produced by RMPs, the rotation can be compensated by electron diamagnetic rotation locally. In this case, RMPs can penetrate and form magnetic islands. Typical plasma parameters and RMPs spectra on DIII-D, JET and ITER were used in modelling examples presented in the paper.

Steady-state screening of resonant magnetic perturbations (RMPs) in a tokamak is analysed taking into account a self-consistent electric field. On the one hand, the self-consistent radial electric field is determined by the balance of the electron radial conductivity in a stochastic magnetic field screened by the plasma and by the neoclassical ion conductivity. On the other hand, the parallel current of electrons, the radial projection of which is balanced by the ion current, determines the screening of RMPs. In this work, the self-consistent electric field and RMP screening are calculated. Two different regimes of screening are found: the ‘ion’ branch which corresponds to the negative radial electric field and the ‘electron’ branch for which the electric field is positive. Predictions of the model are compared with the experimental data and results of the simulation with various codes. The corresponding toroidal rotation and pump-out effect are discussed.