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An appropriate choice of growth conditions has made feasible fabrication of thin epitaxial NiFe2O4 / SrTiO3 films with parameters close to those of bulk nickel ferrite. Spin waves with a damping parameter as low as 10-2 and a very narrow ferromagnetic resonance line were observed in the samples subjected to post-growth high temperature annealing in oxygen. The analysis of electron and X-ray diffraction has shown substantial improvement of the crystalline quality of the annealed films. X-ray absorption spectroscopy and X-ray magnetic circular dichroism data simulation have revealed that the films exhibit a completely inverted spinel structure characterized by the maximal possible net magnetic moment.

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.

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

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.

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.

A systematical study of E → × B → drift and parallel current effects is reported based on the analysis of the simulations by B2SOLPS5.2 transport code. It is demonstrated that divertor asymmetry for connected double null (CDN) configuration is established due to poloidal E → × B → drift and parallel thermal current. For single-null configuration the existing asymmetry is amplified by account of these effects.

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.

Modeling of the edge toroidal rotation and its dependence on the edge plasma parameters is performed by means of the B2SOPS5.0 transport code for Ohmic shots both for MAST and ASDEX Upgrade configurations. The impact of plasma current, toroidal magnetic field, plasma density and temperature is investigated. A connection between the toroidal rotation and edge radial electric field is also studied. The results of the simulation are consistent with the parametric dependence predicted analytically.

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.

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.

In this paper, recent progress in plasma edge modelling is presented, using the SOLPS B2–Eirene Scrape-Off Layer Plasma Simulation code. The code capabilities have been extended so that is it now possible to investigate reliably regimes dominated by strong neutral sources in the plasma edge. Two main improvements are reported. First, a fluid plasma treatment including drift and currents effects has been coupled to a Monte-Carlo treatment for the neutrals. Concurrently, a grid adaptation algorithm compatible with the coupling is demonstrated. We present simulations taking advantage of these new tools, and discuss their impact on the results. 2003 Elsevier Science B.V. All rights reserved.

New form of momentum balance equations for ion species is suggested and implemented into B2SOLPS5.2 code. The original form of Braginskii parallel momentum balance equations is used with parallel electric field on the left hand side which does not require any assumptions in contrast to the existing momentum balance equations solved in SOLPS codes. General expressions for friction and thermal force which are valid for arbitrary densities of different ions are suggested. Convergence of the simulations is the same as in existing B2SOLPS versions. It is demonstrated that results for arbitrary impurity density differs from that obtained for trace impurities due to correct account of friction and thermal forces.

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.