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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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

The transport code B2SOLPS5.2 is used to simulate L- and H-mode discharges on MAST with and without resonant magnetic perturbations (RMP). The simulated variation of the radial electric field (less negative for RMP) and toroidal rotation (spin-up in the co-current direction for RMP) is in agreement with the experiment. The pump-out effect in the L-modes with high and medium plasma density and in the H-mode is caused by the additional neoclassical radial plasma flow in the electric field modified due to the electron loss along the stochastic field lines. The pump-out in the low-density L-mode can be reproduced only by a significant rise in the turbulent transport coefficients. The modelling suggests strong RMP screening. An analytical model for RMP screening is proposed.

The impact of resonant magnetic perturbations (RMPs) on the structure of the edge transport barrier has been studied. A model for the density pump-out mechanism during the stochastization of the plasma edge is proposed. The observed phenomena are explained as a result of the impact of the ambipolar electric field, which is modified during RMP, on the particle fluxes in the pedestal region. It is demonstrated that the rise of the particle fluxes inside the transport barrier leads to the pump-out effect on density, while the pedestal temperature increases in spite of the big electron heat conductivity in the stochastic magnetic field. The latter is not sufficient to change significantly turbulent heat conductivity in the barrier region and only compensates the rise of the pedestal temperature caused by the density drop for constant heating power. The analytical approach is supported by results of simulations with the B2SOLPS5.2 2D transport code which uses a full description of particle sources and transport phenomena in the pedestal region. Simulations are performed for ASDEX-Upgrade and MAST configurations for various values of electron stochastic conductivity. The radial electric field with RMPs is predicted to be less negative than without RMP. The density drop and temperature rise in the pedestal region are observed in accordance with the experimental results. Generation of toroidal rotation in the co-current direction is predicted. Extrapolations to ITER are discussed.

A new B2SOLPS5.2 transport code has been developed and implemented for the simulation of H-mode shots. A new equation system is proposed, which is equivalent to the system which was used in B2SOLPS5.0 previously. The main idea is to replace the major part of the large radial ∇B driven convective fluxes by poloidal fluxes with the same divergence both in the particle balance and in the energy balance equations. This is of special importance for the H-mode where the diffusion coefficient is strongly reduced inside the barrier and large radial convective flows are strongly undesirable from the numerical point of view. The H-mode shots of ASDEX-Upgrade and MAST have been simulated with the new version with reasonable time steps and convergence. It is demonstrated that the radial electric field inside the edge transport barrier and in the pedestal region is close to the neoclassical electric field as in previous simulations of Ohmic shots. The toroidal rotation is co-current directed as in L-mode but is significantly larger in absolute value. It is shown that the shear of the poloidal drift at the inner side of the barrier is close to the value of the shear before the transition, while inside the barrier the value of the shear is significantly bigger. This fact determines self-consistently the width of the edge transport barrier. It is demonstrated that to match the experimental density and temperature radial profiles the drop in the diffusion coefficient within the barrier needs to be significantly larger than the drop in the electron heat conductivity coefficient. For the H-mode the pedestal region usually corresponds to the collisionless regime, so several corrections were introduced into the transport coefficients to extend the applicability of the code to the plateau and banana regimes in the inner regions of the simulation domain.

A theoretical model for the toroidal rotation spin-up and generation of a positive radial electric field during the stochastization of plasma edge is put forward. Equations for the toroidal velocity and for modification of the core radial electric field have been derived. A detailed comparison of the model results with the radial electric field and plasma potential measurements during MHD activity in the TUMAN-3M tokamak is presented.