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Plasma Edge Physics with B2-Eirene
Abstract
The B2-Eirene code package was developed to give better insight into the physics in the scrape-off layer (SOL), which is defined as the region of open field-lines intersecting walls. The SOL is characterised by the competition of parallel and perpendicular transport defining by this a 2D system. The description of the plasma-wall interaction due to the existence of walls and atomic processes are necessary ingredients for an understanding of the scrape-off layer. This paper concentrates on understanding the basic physics by combining the results of the code with experiments and analytical models or estimates. This work will mainly focus on divertor tokamaks, but most of the arguments and principles can be easily adapted also to other concepts like island divertors in stellarators or limiter devices.
... Historically there has been a division in terms of simulation tools and to an extent also research communities, between multi-fluid transport codes such as SOLPS [1], UEDGE [2], EDGE2D [3] and BOUT++/trans-neut [4], which employ simplified models for the cross-field transport (typically diffusive) but evolve many different species, and the turbulence codes including GBS [5,6,7], TOKAM3X [8,9], (H)ESEL [10], and various models built on BOUT++ [11,12,13] such as Hermes [14] and STORM [15,16]. These latter models can solve for the 3D time-varying turbulent transport, but typically only evolve a single ion species. ...
... The same code that is used in a 1D domain in the previous sections can be applied to 2D tokamak domains with one or two X-points. By introducing cross-field diffusion of both charged and neutral species, an axisymmetric tokamak transport simulation in the spirit of SOLPS [1], EDGE2D [3] or UEDGE [2] can be performed, though not yet at a comparable level of maturity or completeness. To demonstrate the ability of Hermes-3 to solve axisymmetric transport problems, simulations are performed with deuterium ions and neutral atoms. ...
... The plasma equilibrium is based on a COMPASS-like equilibrium generated using analytic Grad-Shafranov solutions [65,66] The deuterium ion species is configured with a set of components representing the equations solved, given in listing 7 1 [d+] 2 type = (evolve_density, evolve_momentum, evolve_pressure, which is similar to the configuration in 1D simulations given in listing 3, but adds anomalous cross-field diffusion terms. Reactions between species are calculated using Amjuel rates [58], comprising ionisation, recombination, and charge exchange processes as described in section 4.1. ...
A new open source tool for fluid simulation of multi-component plasmas is presented, based on a flexible software design that is applicable to scientific simulations in a wide range of fields. This design enables the same code to be configured at run-time to solve systems of partial differential equations in 1D, 2D or 3D, either for transport (steady-state) or turbulent (time-evolving) problems, with an arbitrary number of ion and neutral species. To demonstrate the capabilities of this tool, applications relevant to the boundary of tokamak plasmas are presented: 1D simulations of diveror plasmas evolving equations for all charge states of neon and deuterium; 2D transport simulations of tokamak equilibria in single-null X-point geometry with plasma ion and neutral atom species; and simulations of the time-dependent propagation of plasma filaments (blobs). Hermes-3 is publicly available on Github under the GPL-3 open source license. The repository includes documentation and a suite of unit, integrated and convergence tests.
... Moreover, the open and non-uniform magnetic field used in MPEX will affect the parallel transport of particles and power to the target region due to kinetic and mirror effects during RF heating as demonstrated in reference [11][12]. The final state of the plasma, subject to all these interactions (RF heating, collisions, kinetic transport, mirror effects, open and non-uniform magnetic field), cannot be fully described with fluid models [15][16][17] or bounced-averaged kinetic codes [18][19]. Addressing this transport problem requires solving the Vlasov equation with appropriate particle and energy sources and coupled to electromagnetic field equations. ...
... defined at the grid point 9 shown in Eq. 13 where = 9 − ' ? is the so-called assignment function presented in Appendix 2 (Eq. 48) [15], [17]. ...
... In this section, we present the numerical results produced using PICOS++. To explore the various physics involved: (1) fluid plasma and (2) magnetic mirror effects, PICOS++ simulation results are benchmarked with the fluid code B2.5 EIRENE [15,53] and Proto-MPEX experimental data. Next, we introduce the numerical setup used for modeling the parallel transport in MPEX with and without the use of ICH. ...
The Material Plasma Exposure eXperiment (MPEX) is a steady state linear device with the goal to perform plasma material interaction (PMI) studies at future fusion reactor relevant conditions. A prototype of MPEX referred as ‘Proto-MPEX’ is designed to carry out research and development related to source, heating and transport concepts on the planned full MPEX device. The auxiliary heating schemes in MPEX are based on cyclotron resonance heating with radio frequency (RF) waves. Ion cyclotron heating (ICH) and electron cyclotron heating (ECH) in MPEX are used to independently heat the ions and electrons and provide fusion divertor conditions ranging from sheath-limited to fully detached divertor regimes at a material target. A Hybrid Particle-In-Cell code- PICOS++ is developed and applied to understand the plasma parallel transport during ICH in MPEX/Proto-MPEX to the target. With this tool, evolution of the distribution function of MPEX/Proto-MPEX ions is modeled in the presence of (1) Coulomb collisions, (2) volumetric particle sources and (3) quasi-linear RF-based ICH. The code is benchmarked against experimental data from Proto-MPEX and simulation data from B2.5 EIRENE. The experimental observation of “density-drop” near the target in Proto-MPEX and MPEX during ICH is demonstrated and explained via physics-based arguments using PICOS++ modeling. In fact, the density drops at the target during ICH in Proto-MPEX/MPEX to conserve the flux and to compensate for the increased flow during ICH. Furthermore, sensitivity scans of various plasma parameters with respect to ICH power are performed for MPEX to investigate its role on plasma transport and particle and energy fluxes at the target.
... It also can be used for divertor performance and geometry optimization and estimates of key related parameters by simulation, which provides strong support for achieving experimental targets. SOLPS-ITER was obtained by coupling the two-dimensional multi-fluid plasma code B2.5, [14][15][16][17][18][19] which serves as a plasma fluid solver, with the neutral particle transport code EIRENE 20,21 from FZJ. 22 The two-dimensional multi-fluid transport equations 23 include the balance equations of the particle, momentum, electric charge, and energy. The balance equations of the particle, electric charge, energy, and momentum were solved using the B2.5 code in SOLPS-ITER. ...
... From Fig. 8, the density of the total tungsten impurities is ∼7.0 × 10 16 impurities in the low ionization state are mainly distributed in the region near the target plates of the divertor. As the number of charge states increased, the tungsten impurities tended to concentrate first toward the X-point and then toward the region near the separatrix and the separatrix in the lower-right SOL and eventually accumulate near the core boundary of the computational domain. ...
In recent years, the materials of plasma facing components, such as divertor target plates, domes, and outer walls of tokamaks, such as ASDEX Upgrade, WEST, JET, EAST, and ITER, have been changed from carbon to tungsten because of its lower erosion and tritium retention rates. Impurities are produced by interactions between the plasma and the first wall. This study provides an investigation to simulate the transport and distribution of tungsten impurities in the edge plasma on EAST. The 2D multi-fluid edge plasma transport code SOLPS-ITER and 2D kinetic Monte Carlo impurity transport code DIVIMP were used in the simulations. The multi-fluid model in SOLPS-ITER and the kinetic Monte Carlo model in DIVIMP were employed to treat tungsten impurity ions. The 2D density contour distributions in the computational region and the 1D density radial profiles at the inner and outer midplanes of tungsten impurity particles with ionization states (W⁰–W⁺⁷⁴) and the total tungsten particles with all charge states were obtained. With the heating power 1.5 MW and the line-averaged plasma density 2 × 10¹⁹ m⁻³, the results from SOLPS-ITER and DIVIMP show that the maximum density of tungsten ion with single ionization state is about 10¹⁴ m⁻³ and the total density of tungsten impurities with all charge states is about 10¹⁵ m⁻³ at the core boundary. To the best of our knowledge, the simulation results from SOLPS-ITER and DIVIMP are compared for the first time to benchmark SOLPS-ITER with the multi-fluid mode and DIVIMP with the kinetic model for tungsten impurity transport. The density distributions of tungsten impurities with different ionization states from SOLPS-ITER and DIVIMP are highly similar, and good agreement can be found under similar conditions involved in the calculation. From the comparison benchmark between SOLPS-ITER and DIVIMP for tungsten impurity transport, it can be concluded that the impurity transport approximation used by DIVIMP is good.
... In this work, we explore the effects of Li sourcing with a more realistic profile to identify an acceptable solution for FNSF. A fast-flowing open-surface configuration is modeled by coupling the boundary plasma transport code SOLPS-ITER [28][29][30] and an LM MHD/heat transfer code [31]. This coupling allows us to conduct scrape-off layer (SOL) and divertor simulations, integrating flowing liquid metal fluid behavior with near-surface physics. ...
... The geometry of the SOLPS-ITER (abbreviated to SOLPS) simulation is illustrated in figure 1. SOLPS is an integrated tokamak boundary transport code suite that couples a multifluid plasma code 'B2.5' and a kinetic Monte-Carlo code 'EIRENE' which handles neutral dynamics, plasma-neutral interactions, and plasma-wall interactions processes [29,30]. The current simulation involves 14 fluid plasma charge states (D, Ne, and Li) and 4 neutral species (D 2 molecule, D 0 , Ne 0 , and Li 0 ). ...
The SOLPS-ITER code is utilized to analyze the boundary plasma associated with a fast-flow lithium (Li) divertor configuration in the fusion nuclear science facility (FNSF) tokamak and identify operational regimes with acceptable divertor and core conditions. Plasma transport from the SOLPS-ITER code has been coupled with a liquid metal (LM) MHD/heat transfer code to model a Li open-surface divertor design and assess its impact on the scrape-off-layer (SOL) and core plasma performance. Simulations with only Neon (Ne) impurity seeding have been conducted to evaluate its impact on meeting FNSF design demands for the divertor and upstream plasma parameters. Simulation results indicate that Ne seeding significantly mitigates divertor heat flux but potentially reduces both upstream electron and main ion density due to fuel dilution. The combined application of Ne seeding and deuterium (D2) puffing is required to satisfy the FNSF design requirements on upstream density ( ne,sepOMP ∼1× 10²⁰ m⁻³) and divertor energy flux ( q⊥,maxOdiv < 10 MW m⁻²). D2 puffing plays a role in counteracting upstream density drops and augmenting energy and momentum losses through atomic and molecular processes.
The inlet Li flow velocity is systematically varied across a wide range to identify acceptable flows and corresponding LM surface temperatures. This comprehensive analysis identifies the acceptable Li flow parameters, LM surface temperature, and emitted Li fluxes necessary to meet the major design constraints. The emitted Li fluxes exhibit minimal impact on the main plasma at surface temperatures up to approximately ∼525 ∘C, corresponding emitted Li fluxes of up to φ Li ∼2 ×1023 atoms s⁻¹. Uncertainties in the Li emission processes from the surface are also investigated, primarily influencing Li loss in the lower surface temperature range ( <525∘ C), with simulation results indicating a minor impact on the divertor and upstream plasma. Conversely, evaporation predominantly drives the Li loss processes at higher surface temperature ranges ( >525∘ C), contaminating both the divertor and upstream plasma.
... In the SOLPS-ITER simulation, the two-dimensional Braginskii equations are solved on the poloidal and radial grid coordinates [30] of figure 1(a). In the two-dimensional simulation, the x-coordinate is along the poloidal direction, and the y-coordinate varies perpendicular to flux surfaces. ...
... In the two-dimensional simulation, the x-coordinate is along the poloidal direction, and the y-coordinate varies perpendicular to flux surfaces. By solving the two components of the Braginskii momentum conservation equation [30] for ions perpendicular to a magnetic surface, the velocities V x and V y of the ions can be evaluated by: Here the subscript '⊥' means the direction perpendicular both to magnetic field B and the y-axis. z is the toroidal direction. ...
A new drift module has been developed in the DIVIMP code, enabling two-dimensional simulations of tungsten (W) transport in the edge plasma with full drifts included. By using the SOLPS-DIVIMP code package, the impact of drifts on W transport and screening has been investigated for various levels of dissipative divertor conditions and different divertor geometric configurations in EAST. Simulation results reveal that E ⃗×B ⃗ drifts can enhance the W leakage by more than one order of magnitude. Under the favorable Bt direction, W erosion mainly occurs on the outer divertor target, making the W leakage from the outer divertor region the dominator. A leakage path from the near-SOL region is revealed by the modeling results. In the leakage path, both the ion temperature gradient force and the reversed poloidal E ⃗×B ⃗ drift are pointing upstream. With the radial E ⃗×B ⃗ drift pushing W ions from the well-screened far-SOL region to the near-SOL region, the leakage from the near-SOL region becomes significant. As the divertor condition varies from the low-recycling regime to the deep detachment regime, the decrease of the ion temperature gradient velocity and poloidal E ⃗×B ⃗ drift velocity narrows the width of the near-SOL leakage tunnel and thus enhances W screening. While under the unfavorable Bt, W erosion and leakage from the inner divertor target matters, the leakage mechanism especially the leakage path from the near-SOL region is similar as the favorable Bt cases. Furthermore, the effect of different divertor geometries on the W screening has been investigated. The configuration with the outer strike point (OSP) on the horizontal divertor plate is proved to narrow the near-SOL leakage tunnel, and thus the unreversed poloidal E ⃗×B ⃗ drift pointing to the divertor target dominates and helps to enhance the divertor W screening. For the same D2 puffing rate, the W leakage ability of cases with the OSP on the horizontal target can be more than 10 times weaker than the cases with the OSP on the vertical target, especially when the divertor is detached.
... FINDIF is a fi nite difference, three-dimensional, multifl uid plasma edge transport code [5]. In the model the parallel transport follows Braginskii formulas [6] in B2 form [7], while the cross-fi eld transport is assumed to be predominantly anomalous and modelled by diffusive approximation [8]. In the current code version, mesh creation is largely automatized [9]. ...
... The core BC are imposed at inner simulation boundary (ISB), which coincides with a fl ux surface and is located inside last closed fl ux surface (LCFS), a few centimetres into the core. This approach is similar to the method employed concerning tokamak edge codes [7,16]. We set X ISB where X = n i , v i , T i , T e , common for all points at ISB. Due to the perturbing effect of the near-by SOL, the profi les at LCFS are far from fl at, despite a strong smoothing effect of parallel transport. ...
Modelling of the plasma transport for inherently three-dimensional (3D) problems as in stellarators requires dedicated complex codes. FINDIF is a 3D multifluid plasma edge transport code that has been previously successfully used for the analysis of energy transport in the TEXTOR-DED tokamak [1], where 3D perturbations led to an ergodic structure of field lines in the plasma edge. The ongoing efforts to apply it meaningfully to Wendelstein 7-X (W7-X) plasma problems resulted in advancements in the main model and accompanying tools for mesh generation and post-processing. In order to verify the applicability of the code and to compare with the reported simulation (EMC3-EIRENE) and experimental (OP1.1) results, a series of simulations for varying plasma density, temperature and anomalous transport coefficients as well as for fixed input power were performed. The connection length pattern of FINDIF traced magnetic field lines on the limiter was reproduced and its impact on heat loads was confirmed. An increase in the peak heat load on the limiter with a rise in plasma density, temperature and anomalous plasma transport coefficients was observed. The decay lengths of density, electron temperature and heat flux did not change with density, and were decreasing with temperature and increasing with anomalous plasma transport coefficient, which was compared to the simple scrape-off layer (SOL) model.
... One of the processes on which the operating regime of the tokamak divertor depends is the anomalous transport of matter and energy across the magnetic field lines. Within the framework of calculations in the SOLPS transport code, its influence on the plasma dynamics is taken into account by introducing the effective transport coefficients-diffusion, D an , and thermal diffusivity, χ an -a priori specified for calculations [73]. Such an approach makes it possible to obtain a detailed picture of the turbulence effects on the parameters of SOL plasma, in particular, on the features of the transition and characteristics of the detachment regime. ...
... Philosophically, numerical simulation is a "bridge" connecting theory and experiment. Indeed, equations describing the behavior of scrape-off-layer plasma in a tokamak are too complicated (see, for example, [73,119]) to be solved analytically. As a rule, simplified models are used in the theory, which to some extent correspond to these equations and make it possible to find an analytical solution and obtain a qualitative understanding of the main physical mech-anisms that determine the divertor operation mode. ...
... Numerical meshes are created according to the magnetic field and vacuum vessel structure as shown in figure 1(c). SOLPS is an integrated multi-fluid plasma and kinetic neutral transport code that couples the B2.5 and EIRENE codes [21,22]. The blue rectangular cells in figure 1(c) represent the plasma mesh aligned with the magnetic field while the black triangular cells represent the neutral particle mesh. ...
... SOLPS solves a set of fluid transport equations which use adhoc radial transport coefficients [21]. Fluid simulations are widely used to describe plasma transport in linear and tokamak fusion devices, as kinetic simulations such as Particle-In-Cell [30] can be prohibitively computationally expensive and timeconsuming. ...
The Material Plasma Exposure Experiment (MPEX) is being constructed at Oak Ridge National Laboratory (ORNL) to investigate critical fusion reactor issues such as plasma-material interactions (PMI) under reactor-relevant conditions and time scales. The linear device Proto-MPEX was used as a test bed to address anticipated research and development issues associated with heating scenarios and establish the physics basis for MPEX. The SOLPS-ITER code suite, has been applied to understand plasma and neutral transport in Proto-MPEX to increase confidence in predictive simulations for MPEX. Coupling between COMSOL and SOLPS is performed to implement a 2D electron heating profile of the helicon source. The simulations show reasonable agreement with the experimental data for plasma with helicon and auxiliary Electron Cyclotron Heating (ECH). Both Bohm and constant diffusion (D: 0.5 m2/s and χ: 1 m2/s) simulations show similar levels of agreement with respect to the sparse experimental data available, assuming a few percent impurity concentration. ECH significantly increases target electron temperature, however the target electron density is reduced compared to helicon-only heated plasmas due to an increase in flow velocity and radial losses. In the simulations, further increasing the ECH power results in an increase in the target electron density due to increased recycling flux and ionization. The results indicate that ECH significantly enhances target heat flux, with ECH power of 50 kW increasing target heat flux from 0.4 to 17 MW/m2. It is found that a small amount of gas puffing near the target plate can further increase the target heat fluxes at the higher ECH power cases, but the target heat flux is reduced at higher gas puffing conditions due to a significant reduction in electron temperature via radiation. ECH and gas puffing scenarios can generate higher target flux, facilitating improved PMI studies with more reactor-relevant plasma conditions.
... This approach is used in several modelling studies of detachment. For example, the SOLPS-ITER code [15] is used to model a TCV density ramp in Ref. [10] and the ASDEX detachment regimes in Ref. [16], while deuterium molecular emissions in DIII-D ohmic discharges are studied by using the EDGE2D-EIRENE [12]. Despite the significant progress obtained by using fluid-diffusive models, simulating the plasmaneutral reactions self-consistently with turbulence is crucial to improve our predictive capabilities and, ultimately, the control of detachment [1,7]. ...
... In our model they are obtained by combining the density and temperature sources in Eqs. (1)(2)(3)(4)(5)(6)(7)(8)(9), and they appear in Eq. (15). The losses associated with the neutral-plasma reactions considered in our model, evaluated separately in order to estimate their relative importance, are shown in Fig. 3 along a flux tube close to the separatrix, 1 ≤ ρ ψ ≤ 1.08, as a function of the poloidal coordinate χ. ...
Simulations of high-density deuterium plasmas in a lower single-null magnetic configuration based on a TCV discharge are presented. We evolve the dynamics of three charged species (electrons, D$^{+}$ and D$_{2}^{+}$), interacting with two neutrals species (D and D$_2$) through ionization, charge-exchange, recombination and molecular dissociation processes. The plasma is modelled by using the drift-reduced fluid Braginskii equations, while the neutral dynamics is described by a kinetic model. To control the divertor conditions, a D$_2$ puffing is used and the effect of increasing the puffing strength is investigated. The increase in fuelling leads to an increase of density in the scrape-off layer and a decrease of the plasma temperature. At the same time, the particle and heat fluxes to the divertor target decrease and the detachment of the inner target is observed. The analysis of particle and transport balance in the divertor volume shows that the decrease of the particle flux is caused by a decrease of the local neutral ionization together with a decrease of the parallel velocity, both caused by the lower plasma temperature. The relative importance of the different collision terms is assessed, showing the crucial role of molecular interactions, as they are responsible for increasing the atomic neutral density and temperature, since most of the D neutrals are produced by molecular activated recombination and D$_2$ dissociation. The presence of strong electric fields in high-density plasmas is also shown, revealing the role of the $E \times B$ drift in setting the asymmetry between the divertor targets. Simulation results are in agreement with experimental observations of increased density decay length, attributed to a decrease of parallel transport, together with an increase of plasma blob size and radial velocity.
... The HL-2A device has a closed divertor with a major radius of 1.65 m and a minor radius of 0.4 m, a toroidal magnetic field B t of up to 2.8 T, an average electron density ne of up to 6 × 10 19 m −3 , a plasma current I p of up to 0.5 MA. SOLPS-ITER [24] is a widely used program for simulating boundary plasmas that combines the fluid transport program B2.5 [25]with the neutral particle transport program EIRENE [26]. Figure 1 shows the positions for impurity injection, D 2 injection, and pumping port. The simulated particle species include neutral particles D 0 , primary ions D + , and impurity ions N 1−7+ , Ne 1−10+ , and Ar 1−18+ . ...
Divertor detachment has significant potential for reducing the divertor target thermal load, and impurity seeding is the primary method for achieving divertor detachment. In this study, different impurity seeding scenarios (N, Ne, and Ar) at the boundary region of HL-2A were simulated using the SOLPS-ITER code. Density scans revealed that when the divertor target electron temperature dropped below 5 eV, a rollover in impurity radiation from the core edge regions of Ar, N, and Ne occurred, and the radiation from impurities in the divertor started to increase concurrently, indicating a correlation between impurity radiation rollover and divertor detachment. Impurity radiation rollover is discovered to be primarily related to impurity transport, which is governed by thermal and friction forces.Prior to divertor detachment, the dominance of thermal forces over friction forces causes impurity ions to transport upstream. However, after detachment, friction forces dominate the impurity ions transport to the divertor region. After analyzing the density and velocity of impurity ions in different charge states, it was found that the core radiation rollover after detachment is mainly caused by high charge state impurity ions. Furthermore, the ability of the divertor to achieve particle flow rollover primarily depends on whether the decrease in plasma pressure (P t) exceeds the decrease in plasma temperature (T t 1/2).
... In this equation, each of the source terms corresponds to the divergence of the momentum stress tensor, centrifugal force, friction force, thermal force, ionization, recombination, charge exchange, anomalous contribution, and EIRENE (plasma-neutral interaction) contribution, respectively. Detailed expressions for these terms can be found in [32]. The parameters h x , h y , and h z are the geometric factors corresponding to the lengths in the poloidal, radial, and toroidal directions, respectively. ...
The ITER divertor design and performance assessment, primarily based on the SOLPS-4.3 burning plasma database \cite{pitts2019physics}, assumes the use of beryllium (Be) as the divertor surface material and the injection of gas from the main chamber top. However, the current ITER baseline favours gas injection from the more toroidally symmetric sub-divertor region. This paper evaluates the implications of these assumptions for divertor performance in the ITER fusion power operation phase. The impact of the divertor surface material and the gas injection location on the main ions mirrors the hydrogen only low power phase scenario shown in \cite{park2020assessment}. However, during burning plasma operation, extrinsic impurity seeding will be required. In the case of neon (Ne), studied here, impurity retention is influenced by both the divertor surface material and the fueling location. Neon leakage increases due to more energetic reflection from tungsten than beryllium, but equivalent divertor performance can be achieved by adjusting the neon seeding rate. While the impurity seeding location does not affect the distributions of impurity or radiation, the fueling location does. Top fueling provides local ionization sources mainly in the mid-SOL under detached conditions, enhancing divergences of the flux there (source-driven flow), bringing stagnation points close to the fueling location, and equilibrating flows towards both targets. In contrast, the global flow pattern (in the absence of fluid drifts) in the case of sub-divertor fueling is biased towards the inner target. Impurity flows, driven by force balance, largely mirror those of the main ion flow, including the stagnation point. The case with top fueling enhances Ne retention and corresponding radiation in the outer divertor, effectively reducing the total and peak target heat fluxes by 20-40 \%, compared to the case with divertor fueling. Meanwhile, the case with outer target fueling also achieves similar reductions by enhancing plasma-neutral interactions. These results suggest the possibility that the selection of the fueling location and throughput can be used as an actuator to control impurity divertor retention and divertor radiation asymmetry.
... SOLPS-ITER [36,37] consists of the multi-fluid transport code B2.5 and the Monte Carlo neutral tracer EIRENE [38], which is utilized here to reproduce the experimental measurements and analyze the relevant detachment physical processes. The simulation cases are based on the similar basic background plasma parameters in shots #102528 and #102531. ...
It is necessary for future fusion reactor to reduce the heat fluxes on the entire divertor target, especially if view of long pulse high performance operation. In recent EAST experiments, partial energy detachment without confinement degradation, and deep energy detachment with protection of the entire divertor target have both been confirmed on EAST corner slot divertor by argon (Ar) seeding, which can provide reference for the divertor protection on future fusion reactors. In the deep energy detachment state, the electron temperature Tet along entire lower outer divertor target decreases to less than 10 eV and heat fluxes are also strongly mitigated with peak heat flux reduction of more than 90%. Compared to the attached state, there is a moderate confinement degradation with H98,y2 from ~1 to ~0.9 because of Ar radiation in the core region. This confinement degradation can be avoided in the partial energy detachment state, where the radiative power losses in the core are reduced. The experiment and SOLPS-ITER simulation results show that there is no decrease of particle flux js on the divertor target in the partial energy detachment state because the momentum loss in the SOL region is not strong enough. With increasing Ar seeding, there is a js decrease in the deep energy detachment state. The increases of momentum and power losses in the SOL region, and the decrease of upstream pressure all contribute to the js reduction.
... John et al., 1994), which uses the kinetic neutrals 1D transport model NEUCG (Burrell, 1978). SOLPS/EIRENE (Schneider et al., 2006) modeling was used to adjust the flux expansion parameter (for modeling a 2D neutral distribution) and neutral energy in the ONETWO 1D model to match SOLPS. This modeling includes the effects of both ionization and charge exchange on the penetration of the neutrals (Casali et al., 2020). ...
The path to fusion in the United States requires partnership between public and private sector. While the private sector provides the vigor to take some of the major steps necessary, there is a depth of expertise and capability in the public sector that is vital to resolving feasible approaches. As an open national user facility, DIII-D provides a crucial testbed to develop the required new technologies and approaches in relevant conditions. It has unparalleled potential to meet this challenge, thanks to its extreme flexibility and world leading diagnostics. This provides a basis to rapidly develop solutions that project to future reactors with confidence. The program has thus been redeveloped to enable public and private sector engagement and testing of new concepts. A new technology program has been launched to resolve plasma interacting technologies. With modest heating upgrades, the facility can confront the crucial “Integrated Tokamak Exhaust and Performance” gap, to resolve core, exhaust and technology solutions together. The device is also being redeveloped as a training facility, with dedicated student run time, a mentorship program, and open access to all opportunity roles, part of wider efforts to diversify and open pathways through inclusion, access, and equity. This exciting agenda is enabling scientists and technology researchers to pioneer the solutions needed for a Fusion Pilot Plant (FPP) and ITER this decade. As a national user facility, DIII D has singular potential to provide the tools, teams, and insight necessary, to do its part in moving the United States rapidly toward the commercialization of fusion energy.
... These expressions are the Spitzer-Harm heat fluxes used in the popular transport code SOLPS [23]. ...
This work investigates the parallel coherence of plasma filaments through numerical simulations using the hot-ion 2-fluid \texttt{hermes-2} model within the \texttt{BOUT++} framework. Realistic field lines in the scrape-off layer (SOL) of magnetic fusion devices, especially in stellarator configurations possess a highly varying curvature along the magnetic field line. A varying curvature creates a parallel $\mathbf E\times\mathbf B$ velocity gradient which might tear the filament apart. The main parameters controlling this process are the collisionality and the electron plasma beta. Simulations of realistic curvature variations along field lines in a circular ASDEX Upgrade-like tokamak (AUG) and Wendelstein 7-X stellarator (W7-X) show the parallel displacement between different filament sections to correlate with the curvature. The rapidly varying W7-X curvature and the low average curvature drive reduce the propagation of the filament to only a few hundred meters per second. The effect of a finite ion temperature on filament propagation in a W7-X field line geometry is found to be a higher diamagnetic current resulting in stronger charge separation. This work supports simulations and experimental findings that filaments in W7-X are comparably slow due to the large major radius of the device. They do not perform ballistic motion and hence do not drive significant turbulence spreading in the SOL.
... Due to insufficiency of diagnosing different impurity parameters over the edge and divertor regions for a tokamak, it is inevitable to apply numerical simulation to understand better the impurity behaviors. For simulations in this work, the geometry of HL-2A and computational mesh are shown in figure 1(b) and SOLPS-ITER is applied for numerical simulation [34][35][36]. HL-2A tokamak computational region is divided into an orthogonal grid region (blue) for fluid computation and a triangular grid region (black) for neutral particles. The two-dimensional boundary plasma fluid simulation program, SOLPS-ITER, is coupled by 2D fluid code (B2.5) and Monte Carlo neutral particle code named EIRENE. ...
Excessive heat load on the divertor target has been identified as a major challenge for present and future tokamaks. Divertor detachment achieved by injecting radiating impurity is an effective method to reduce heat load onto the divertor target surface. However, extremely serious effects on the core plasma could be given by the injected extrinsic impurity, such as fuel dilution and cooling due to energy radiation loss by the impurity in the core plasma region. Therefore, understanding the impurity behavior and then controlling the impurity content during divertor impurity injection are important issues of a tokamak. The closed divertor has the advantage of realization of divertor detachment and the Huan Liuqi-2A (HL-2A) tokamak has a very closed symmetrical divertor structure. In this work, experiments and SOLPS-ITER simulation gave the picture of the impurity behavior and showed that the friction force can play a more key role in screening and controlling radiated impurity, comparing with pressure/temperature gradient force during detachment in HL-2A with the closed divertor. Increasing the degree of divertor detachment (DoD), the screening ability of the divertor is strengthened, which is conducive to the control of impurity ions. It implies that the injected impurity can be confined in the closed divertor under detachment and, to some extent, the effect of DoD or impurity gas flux on main plasma can be attenuated for HL-2A with extrinsic impurity gas injection. During divertor detachment, the screening effect of N+ and Ar+ ions is stronger than that of Ne+ ions. As a result, the behavior and control of impurity with impurity injection in the closed divertor of HL-2A are presented with experimental and simulated results, which gives meaningful understanding and suggestion for heat load mitigation and controlling the effect of impurity in HL-2A and other tokamaks.
... In this work, the SOLPS-ITER code package [28] has been used to perform two parameter scans to transition from attached (high-recycling), through the detachment threshold, to strongly detached conditions in the MAST-U Super-X geometry [29]. The primary focus of this work is on the role of parallel B-field gradients in detachment control, the core characteristic of the Super-X. ...
The SOLPS-ITER code has been utilised to study the movement of the detachment front location from target towards the X-point for MAST-U Super-X plasmas. Two sets of detached steady state solutions are obtained by either varying the deuterium ($D_2$) fuelling rate or the nitrogen ($N$) seeding rate to scan the corresponding ‘control’ parameters of outboard midplane density, $n_u$, and the divertor impurity concentration, $f_I$. At seeding and fuelling rates $\sim$10x and $\sim$5x that required to start detachment at the divertor target, the detachment front only reaches $\sim$50\% of the poloidal distance to the X-point, $l_{pol}$, corresponding to a region of strong parallel gradients in the total magnetic field $B$. The region of strong total field gradients correlates with where the detachment front location becomes less sensitive to control parameter variation. This result is qualitatively consistent with the predictions of a simple, analytic Detachment Location Sensitivity (DLS) model (B. Lipschultz \textit{et al}, Nuclear Fusion \textbf{56} 2016 056007) which is based in a scaled parallel-to-$B$ space, $z$. While the DLS model predictions are in agreement with SOLPS-ITER results in terms of where the front location becomes less sensitive to controls (i.e. in the region of strong parallel gradients in $B$), the DLS model predicts a higher sensitivity in the region of weak parallel gradients in $B$ downstream as compared to the simulation results. Potential sources of differences between the SOLPS-ITER and DLS model predictions were explored: The DLS model does not include energy sinks beyond radiation from a single impurity nor cross-field energy transport. Momentum and particle balance are also not included in the DLS model. The tight opening into the divertor for flux surfaces could lead to variations in plasma-neutral pressure balance as the detachment front reaches that region, exactly how this affects the front movement needs further investigation.
... Other simulations with different initial energy E 0 and reflection coefficient R coeff ¼ 0 show similar qualitative results for the distribution of lithium impurities density. The results presented above, in particular the effect of E Â B drifts on confinement and transport, are in agreement with multi-fluid edge simulations of impurities in tokamak plasmas, see, for example, Sec. 6.4 of Ref. 21. ...
In this work, we study the transport of lithium impurities as they are transported from the wall where they are sputtered into the core plasma of the experimental device Pi3 that uses solid lithium walls at General Fusion. We perform time-dependent full-orbit simulations of initially neutral lithium impurities entering a Pi3 deuterium plasma that evolve their charge states and follow their full-orbit dynamics in axisymmetric Pi3 plasmas. This is done by extending the capabilities of the KORC-T code [L. Carbajal et al., Phys. Plasmas 24, 042512 (2017); J. Martinell et al., Bulletin of the American Physical Society (American Physical Society, 2020), Vol. 65] to include atomic collisions of ionization, recombination, and charge-exchange (CX) with neutral hydrogenic species by interpolating rates of these atomic processes from OPEN-ADAS tables to local plasma conditions. We assess the effect of hydrogenic neutrals, initial energy of sputtered lithium impurities, and the inclusion of E × B drifts caused by a radial electric field obtained from a radial force balance equation. It is found that both penetration of lithium impurities into the core and electron energy losses are enhanced by the radial electric field, with a weaker dependence on initial energy with which neutral lithium is sputtered off the lithium wall. Hydrogenic neutrals are not found to have a visible effect on transport of lithium impurities. Also, it is shown that ionized lithium impurities are not thermalized with the background deuterium ions at the edge plasma of Pi3 in studied timescale. From an analysis of electron cooling and radiation losses driven by lithium impurities, we find that energy losses are not significant in these plasmas.
... In this study, we have used the SOLPS-ITER code package [26] to investigate differences between detached states achieved using these two different approaches to detachment in the MAST-U SXD configuration. We have chosen nitrogen for the seeded impurity while carbon is the intrinsic impurity for both methods. ...
The role of ion-molecule ( D + − D 2 ) elastic collisions in strongly detached divertor conditions has been studied in the MAST-U Super-X configuration using SOLPS-ITER. Two strongly detached steady state solutions were compared, one obtained through a main-ion fuelling scan and the other through a nitrogen seeding scan at fixed fuelling rate. A significant difference in the electron–ion recombination (EIR) levels was observed; significant EIR in strongly detached conditions in the fuelling scan and negligible EIR throughout the seeding scan. This is partly because the fuelling scan achieves electron temperatures ( T e ) as low as 0.2 eV near the divertor target, compared to 0.8 eV in the seeding scan (EIR increases strongly below T e ≈ 1 eV), and partly due to higher divertor plasma densities achieved in fuelling scan. Features of the strongly detached seeded cases, i.e. higher temperatures and negligible EIR, are recovered in the fuelling scan by turning off D + − D 2 elastic collisions. Analysis suggests that dissipation mechanisms like line radiation and charge exchange (important for detachment initiation) become weak when T e falls below 1 eV, and that D + − D 2 elastic collisions are necessary for further heat dissipation and access to strongly recombining conditions in the fuelling scan. In the seeding scan, heat dissipation through D + − D 2 elastic collisions is weak. This could be because our nitrogen seeding simulations do not include interactions between nitrogen ions and neutrals, and the strongly detached cases contain high levels of N + in the divertor. As a result, the N + acts like a reservoir of energy and momentum which appears to weaken the impact of D + − D 2 elastic collisions on the divertor plasma energy and momentum balance, making it more difficult to access recombining conditions. This suggests that some of the differences between seeding and fuelling scans could be because energy and momentum exchange between impurities and neutrals is not sufficiently captured in our simulations.
... The results of several such studies are summarized in table 1, which shows transport coefficients for electron thermal transport χ e , ion thermal transport χ i , perpendicular particle transport D ⊥ , various ratios of these coefficients as well as ratios of χ e and χ i to their neoclassical values, χ neo e and χ neo i , respectively. These studies include data from four tokamaks and a number of different approaches, including an analytic model, 1.5D transport models GTEDGE [119,120], ASTRA [121], ONETWO [122], the plasma-neutral edge models SOLPS [123], UEDGE [124], OEDGE [125] and the integrated modeling package JINTRAC [93]. The 1.5D codes contain reduced models for the ionization source as compared to the edge models. ...
This paper reviews current understanding of key physics elements that control the H-mode pedestal structure, which exists at the boundary of magnetically confined plasmas. The structure of interest is the width, height and gradient of temperature, density and pressure profiles in the pedestal. Emphasis is placed on understanding obtained from combined experimental, theoretical and simulation work and on results observed on multiple machines. Pedestal profiles are determined by the self-consistent interaction of sources, transport and magnetohydrodynamic limits. The heat source is primarily from heat deposited in the core and flowing to the pedestal. This source is computed from modeling of experimental data and is generally well understood. Neutrals at the periphery of the plasma provide the dominant particle source in current machines. This source has a complex spatial structure, is very difficult to measure and is poorly understood. For typical H-mode operation, the achievable pedestal pressure is limited by repetitive, transient magnetohydrodynamic instabilities. First principles models of peeling- ballooning modes are generally able to explain the observed limits. In some regimes, instability occurs below the predicted limits and these remain unexplained. Several mechanisms have been identified as plausible sources of heat transport. These include neoclassical processes for ion heat transport and several turbulent processes, driven by the steep pedestal gradients, as sources of electron and ion heat transport. Reduced models have successfully predicted the pedestal or density at the pedestal top. Firming up understanding of heat and particle transport remains a primary challenge for developing more complete predictive pedestal models.
... It has powerful impurity transport simulation capabilities to handle complex atomic and molecular processes and the complex geometries involved. SOLPS-ITER couples the 2D plasma multi-fluid code B2.5 [10][11][12][13][14][15] and the Monte Carlo neutral particle transport code EIRENE 16,17 with triangular meshes to the wall. The two-dimensional multi-fluid transport equations 18 are solved by the B2.5 code in SOLPS-ITER. ...
Impurity transport is a highly significant research topic in international fusion plasma simulations, which are mainly simulated by numerical codes at present. Most of the numerical simulation codes for impurity transport adopt multi-fluid or kinetic model to treat impurity particles. Therefore, it is necessary to select a suitable transport model for the simulation process. For impurity particles, if the mean free path of particles λ is much smaller than the gradient scale length of particles λ g, it is sufficient to treat the particles by the multi-fluid model. However, under some conditions, λ will be much larger than λ g. The applicability of the fluid model is limited when λ is larger than or equal to λ g. A comparison with the simulations on impurity transport treated with multi-fluid and kinetic models is necessary, respectively. In this study, the simulation results of carbon (C) impurity transport in the EAST scrape-off layer with the 2D edge plasma fluid code SOLPS-ITER and the 2D Monte Carlo impurity transport code DIVIMP are compared. The comparison between the distributions of carbon impurities ( C 0 ∼ C + 6) in the different ionization states and the CIII emissivity predicted by SOLPS-ITER and DIVIMP shows that the density distributions of carbon atoms C 0 predicted by the SOLPS-ITER and DIVIMP codes are similar. However, for carbon ions in different ionization states, the variations between the density distributions simulated from the SOLPS-ITER and DIVIMP codes can become larger with the increase in ionization states. DIVIMP performs slightly better than SOLPS-ITER in reproducing the shape of the CIII profile when drifts are switched off in SOLPS-ITER, but the difference is extremely small in terms of the uncertainties involved in these calculations.
... To capture these effects correctly, more sophisticated SOL modeling would be required as it is included in the SOLPS code package. 95 Figure 21 shows the E r profiles, which were calculated with the main ion velocities as predicted by NEOART (solid lines) and the experimental E r profiles (squares and stars) for the three different phases. The predicted E r profiles reproduce qualitatively the changes in the experimental data with increasing plasma density, but a decent quantitative agreement between the experimental and the predicted E r profile is only found for the L-mode phase with highest density, for which v i;NEO Â B % 0. ...
The formation of the equilibrium radial electric field (Er) has been studied experimentally at ASDEX Upgrade (AUG) in L-modes of “favorable” (ion ∇B-drift toward primary X-point) and “unfavorable” (ion ∇B-drift away from primary X-point) drift configurations, in view of its impact on H-mode access, which changes with drift configurations. Edge electron and ion kinetic profiles and impurity velocity and mean-field Er profiles across the separatrix are investigated, employing new and improved measurement techniques. The experimental results are compared to local neoclassical theory as well as to a simple 1D scrape-off layer (SOL) model. It is found that in L-modes of matched heating power and plasma density, the upstream SOL Er and the main ion pressure gradient in the plasma edge are the same for either drift configurations, whereas the Er well in the confined plasma is shallower in unfavorable compared to the favorable drift configuration. The contributions of toroidal and poloidal main ion flows to Er, which are inferred from local neoclassical theory and the experiment, cannot account for these observed differences. Furthermore, it is found that in the L-mode, the intrinsic toroidal edge rotation decreases with increasing collisionality and it is co-current in the banana-plateau regime for all different drift configurations at AUG. This gives rise to a possible interaction of parallel Pfirsch–Schlüter flows in the SOL with the confined plasma. Thus, the different H-mode power threshold for the two drift configurations cannot be explained in the same way at AUG as suggested by LaBombard et al. [Phys. Plasmas 12, 056111 (2005)] for Alcator C-Mod. Finally, comparisons of Er profiles in favorable and unfavorable drift configurations at the respective confinement transitions show that also the Er gradients are all different, which indirectly indicates a different type or strength of the characteristic edge turbulence in the two drift configurations.
... The modeling has been performed with the SOLPS-ITER code package (for the SOLPS-ITER description, see Ref. 10). The stationary part of the discharges during the NBI heating was modeled for the discharge with nitrogen seeding-the quiescent state at the end of the seeding. ...
First experiment with nitrogen seeding has been performed at the compact spherical tokamak Globus-M2. Significant reduction of the electron temperature and the energy flux to the outer lower divertor target has been observed experimentally and reproduced in the modeling with the SOLPS-ITER code.
... Fluid plasma boundary transport simulations (e.g. SOLPS [17], UEDGE [18], etc), on the other hand, can contain detailed plasmaneutral and plasma-surface models while using ad-hoc models to represent cross-field turbulent transport. In this work the coupled 2D fluid plasma and kinetic neutral transport code SOLPS-ITER is applied [19]. ...
Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the Sparse Identification of Nonlinear Dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane $\nesepm$ and the electron temperature at the outer divertor $\tesepa$. Note that $\tesepa$ is not necessarily the peak value of $T_e$ along the divertor. The identified reduced models are interpretable by construction (i.e., not black box), and have the form of coupled ordinary differential equations (ODEs). Despite significant noise in $\tesepa$, the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5$\%$ in $\nesepm$ and 5 - 10$\%$ in $\tesepa$ for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A Model Predictive Control (MPC) strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in $\nesepm$ using the Integrated Plasma Simulator (IPS) framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.
... This is typically done using a combination of the DivGeo software for basic input specification, the standard grid builder CARRE [19], and other preprocessing routines. After generating the relevant input files, the physics simulations can be run, which for SOLPS-ITER is typically a coupled simulation of the fluid solver B2.5 and the kinetic Monte Carlo code EIRENE [20]. ...
The design and understanding of alternative divertor configurations may be crucial for achieving acceptable steady-state heat and particle material loads for magnetic confinement fusion reactors. Multiple x-point alternative divertor geometries such as Snowflakes and X-point targets have great potential in reducing power loads, but have not yet been simulated widely in codes with kinetic neutrals. This paper discusses recent changes made to the SOLPS-ITER code to allow for the simulation of X-point target and low-field side snowflake divertor geometries. Snowflake simulations using this method are presented, in addition to the first SOLPS-ITER simulation of the X-point target. Analysis of these results show reasonable consistency with the simple modelling and theoretical predictions, supporting the validity of the methodology implemented.
... The SOLPS5.1 52 has been used to investigate the mechanism of the DPD, which includes a multi-fluid transport code B2.5 53 with the E Â B drift effect and a neutral particle transport code EIRENE. 54 The modeling meshes consist of 96 poloidal and 36 radial cells, and the basic parameters are taken from the discharge 37 067. ...
Double-peaked distribution (DPD) of particle flux has only been observed on the outer divertor target in electron cyclotron resonance heating deuterium plasmas with [Formula: see text] toward the X-point in the HL-2A tokamak using high spatiotemporal Langmuir probe arrays. The experimental results demonstrate that the formation of the DPD is mainly due to the enhanced poloidal [Formula: see text] drift flow stimulated in the divertor region, which is dependent on the plasma density, heating power, and divertor structure. The experimental results are qualitatively consistent with the SOLPS simulation. The experiment also shows that the formation of the DPD might be related to the enhanced cross field transport in the far scrape-off layer. This experimental findings presented here reveal the crucial role played by the synergistic effect of poloidal E × B drift flow and the closed divertor structure in the redistribution of the particle flux, which provides a potential way for the control of high heat flux in future fusion devices.
In order to simulate hydrogen (H) plasma in the linear plasma device NAGDIS‐II, we have modified the fluid code LINDA‐NU to allow the simultaneous calculation of multiple ion species consisting of hydrogen atomic ions () and molecular ions (). In this simulation, H and neutrals are assumed to be uniformly distributed in space in order to obtain initial qualitative results. The fraction of ions increases as the molecular density increases, and the recombination process between and electrons is observed to reduce the particle flux to the target plate. With an increase in H density, the electron density increases due to the decrease in ion flow velocity due to the change exchange process, and the electron temperature decreases to less than 1 eV, leading to the detached plasma formation attributed to the electron‐ion recombination process.
In our previous paper (Hunana et al. 2022) we have employed the Landau (Coulomb, Fokker-Planck) collisional operator together with the moment method of Grad and considered various generalizations of the Braginskii model, such as a multi-fluid formulation of the 21-and 22-moment models valid for general masses and temperatures, where all of the considered moments are described by their evolution equations (with fully non-linear left-hand-sides). Here we consider the same models, however, we employ the Boltzmann operator and calculate the collisional contributions via expressing them through the Chapman-Cowling collisional integrals. These "integrals" just represent a useful mathematical technique/notation introduced roughly 100 years ago, which (in the usual semi-linear approximation) allows one to postpone specifying the particular collisional process and finish all of the calculations with the Boltzmann operator completely. Additionally, by considering the cases of self-collisions and m a ≪ m b , we express all of the Braginskii transport coefficients through the Chapman-Cowling integrals as well. We thus offer a multi-fluid 22-moment model as well as the Braginskii model, which are valid for a large class of (elastic) collisional processes describable by the Boltzmann operator. The particular collisional process-the hard spheres, the Coulomb collisions, the Maxwell molecules, the inverse interparticle force ∼ 1/r^ν (or other cases not discussed here), are specified only at the end, by simply selecting few (pure) numbers. In the Appendix, we introduce the Boltzmann operator in a way suitable for newcomers and we discuss a surprisingly simple recipe how to calculate the collisional contributions with analytic software.
Pабота дивертора в режиме детачмента (“отрыва”) плазмы необходима для снижения нагрузок на пластины дивертора в токамаках ITER и DEMO до приемлемых величин. Обсуждаются результаты анализа ряда эффектов, оказывающих непосредственное влияние на операционное окно детачмента и его устойчивость: поперечный перенос тепла в диверторе, запирание излучения, развитие плазменных неустойчивостей, особенности устойчивости двухнулевого дивертора – полученные с использованием численного моделирования, в том числе при помощи транспортного кода SOLPS4.3 и турбулентного кода BOUT++. Рассмотрено функционирование дивертора с жидкометаллическими пластинами на примере лития. Обсуждаются вопросы верификации расчетной модели, используемой для моделирования детачмента.
The processes in far scrape‐off layer (SOL) and the plasma interaction with the first‐wall (FW) elements may notably affect the tokamak discharge, since they define fuel and impurity recycling, material erosion and redeposition, wall surface heating, etc. For a long time, the far SOL description in most plasma edge transport codes was insufficient or absent at all, and so particle and heat fluxes onto the FW (except divertor plates) were out of consideration. Recently some codes, for example, SOLEDGE and SOLPS‐ITER are upgraded allowing for the extension of the computational grid up to real walls and for corresponding account of the vacuum vessel shape and all in‐vessel elements. The new release of SOLPS‐ITER (the version 3.2.0) required a development of a new code data structure and new approach to numerical approximation of fluid equations compatible with unstructured non‐orthogonal computational grid. Intensive testing of the new code in different conditions is still required. In the present contribution, such a testing is performed for the EAST disconnected double null (DDN) L‐mode discharge. For the first time, the SOLPS‐ITER 3.2.0 modeling results with drifts and currents turned on are presented, and a comparison to former SOLPS‐ITER version (3.0.8) is performed. The far SOL transport and its effects on the discharge performance are studied by comparing the computational results obtained on several meshes which differ by their width in equatorial midplane. A single null (SN) one (with mesh width limited by distance to the secondary separatrix) was examined versus two DDN meshes (one with actual and one with artificially extended targets to make mesh wider) and a true unstructured (the widest) mesh. The notable difference in results obtained on different meshes appears in those places where plasma density does not vanishes at the computational domain boundaries. For the cases on true unstructured (the widest) mesh, the particle and heat fluxes onto central column, limiters, far SOL part of targets, dome umbrella and other EAST far SOL in‐vessel structures are calculated for the first time by SOLPS‐ITER, allowing assessment of the plasma interaction with those surfaces.
Formation of a high-field-side high-density (HFSHD) regime and the role of the high-field-side (HFS) poloidal electric field in the scrape-off layer of the spherical tokamak Globus-M2 are analyzed using SOLPS-ITER edge plasma simulations. The dependence of the HFS poloidal electric field sign and, consequently, radial drift fluxes on the discharge density is discussed. It is demonstrated that the HFS poloidal electric field is the key element in the formation of a HFSHD regime in the Globus-M2 tokamak as in ASDEX Upgrade. It is demonstrated that the physics of HFSHD formation in a small spherical tokamak is similar to that suggested by Kaveeva et al (2009 36th EPS Conf. on Plasma Physics ) and is in line with experimental observations and modeling, performed later on ASDEX Upgrade.
The successful operation of a tokamak requires effective and appropriate methods of plasma fueling. In the development plan for Thailand Tokamak-1 (TT-1), the use of supersonic molecular beam injection (SMBI) has been proposed as a method that can more effectively and deeply deliver fueling gas compared to the gas puffing method. In this study, we used 2D fluid simulation to investigate the impact of SMBI on plasma transport in TT-1. Our model incorporated the continuity equations, energy balance equations, momentum equation, continuity of fuel equations, and momentum equation of fuel. BOUT++ is then used to solve these equations by a finite difference method with the field-aligned coordinates in the edge region of the tokamak. Our simulation results showed that when hydrogen fuel gas is injected into the plasma via SMBI from the low-field side at the speed in the range of 600 - 1200 m/s, the electron density in the edge region locally increases due to dissociation and ionization in the region where the fuel gas meets the plasma. This subsequently leads to a decrease in the ion and electron temperatures. The increased density then spreads throughout the plasma volume within approximately 10 ms. Increasing the injection speed leads to a deeper penetration length for the fuel deposition.
Divertor heat loads are one of the most significant issues affecting fusion reactors. Atomic processes play a crucial role in reduction of the divertor heat load. Notably, elastic scattering between ions and neutral particles can be characterized as large-angle scattering. A large fraction of ion energy is transferred to neutral particles, and the ion direction can be significantly changed by a single large-angle scattering event. In abundant neutral particle regions such as divertor plasmas, the large-angle elastic scattering results in additional ion transport perpendicular to magnetic field lines. Effect of the additional ion transport is expected to be significant at low magnetic field strength and long Larmor radii, such as in a case of advanced divertors (e.g., Super-X and Snowflake divertors). In this study, we investigated the effect of the large-angle elastic scattering at low magnetic field strength and long divertor legs with reference to advanced divertor configurations using an orbital calculation. The large-angle elastic scattering transport is seen to cause a spread in density profiles and a reduction of heat flux. The results of this study show that for the short (long) leg divertor configuration like JT-60U (advanced divertor), the peak heat flux is reduced by around 15% (21%) when the magnetic field strength is 0.5 T in comparison to the model that assumes no guiding center movement due to the elastic scattering. It is also shown that the assumption of isotropic elastic scattering with neutral particles leads to excessive suppression of ion flows.
In divertor plasmas, atomic processes play a significant role in reducing the divertor heat load. In particular, the elastic scattering between ions and neutral particles can be characterized as a large‐angle scattering; this is in contrast with Coulomb scattering, which is dominated by small‐angle scattering. In a large‐angle scattering, a large fraction of the ion energy is transferred to the neutral particle, and the particle flight direction can be changed significantly. This process can generate additional particle transport perpendicular to magnetic field lines and affect plasma density profile in neutral‐rich divertor regions. However, in most edge plasma simulation codes, the elastic scattering with neutral particles is not taken into account in the direction perpendicular to the magnetic field lines. In this study, we performed a 2D orbital calculation without other drifts such as diamagnetic and E × B drifts to assess the effect of the elastic scattering on the density profile. The peak density is found to be decreased by 11.1 (6.3)% compared with the model that ignores the transport due to the elastic scattering, even at 3.0 (5.0) T magnetic field similar to that of the JT‐60SA (JA DEMO reactor) class. In addition, the ion transport can be expressed as a diffusion model by integrating the differential cross section over the large‐angle scattering range . The proposed method may be easily introduced into any integrated codes to consider the elastic scattering.
The coupling of transport code SOLPS with the turbulence code BOUT++ was reported in Reference [D. R. Zhang et al., Phys. Plasmas 26 , 012508 (2019)], while the grids of SOLPS and BOUT++ are not completely consistent with each other, especially in the divertor region. In the present work, a method of replacing the grids of BOUT++ with the grids of SOLPS is proposed to make the simulation region fully consistent with each other for the SOLPS/BOUT++ coupling. A SOLPS grid file is generated with an MHD equilibrium and used in BOUT++ code to simulate the profiles of plasma density, ion temperature, and electron temperature with the six‐field two‐fluid model. The profiles of the main plasma parameters simulated with the SOLPS grids are similar with the profiles simulated with the BOUT++ grids at the midplane, while the profiles are deformed compared with the profiles simulated with the BOUT++ grids at the outer divertor target because of the differences of the distributions of SOLPS grids and BOUT++ grids in the divertor region. The radial particle transport coefficient and heat transport coefficients are also calculated by using the BOUT++ code with the two grids, and the comparisons of the radial particle transport coefficient and heat transport coefficients simulated with the two grids at the midplane and outer divertor target plate are discussed.
A linear plasma device (LPD) module has been developed under the BOUT++ framework to simulate plasma transport in the MPS‐LD. However, previously, the LPD module used a simplistic neutral particle model that only includes particle density and velocity, which prevents the full understanding of the plasma‐neutrals interactions. In this work, we further optimize the neutral model by using a more complete neutral fluid model containing the continuity equation, momentum equation, and energy equation. The reactions such as charge exchange, excitation, and radiation collisions are included. Since the neutral particle source is mainly provided by particle recycling from the target, a particle recycling model is employed, which includes both fast reflection and slow thermal release. The upgraded LPD module is applied to simulate the argon (Ar) discharge experiment of MPS‐LD, and the benchmark against experiment measurement and SOLPS‐ITER simulation results are presented. Good agreements are obtained, showing the validation of the upgraded module. After that, the impact of particle recycling on Ar plasma is investigated. It is found that a higher recycling coefficient ( R ) promotes the achievement of high‐density plasma at the target. The recycled Ar atoms change target plasma pressure as well as plasma‐neutral collisions, which both contribute to plasma momentum loss, thus promoting the rollover of ion flux to the target.
Accumulation of tungsten (W) in core is a serious challenge for the achievement of high-performance plasmas in future tokamak reactors and thus, currently, W impurity transport is a highly concerned topic in the worldwide community of the tokamak physics research. Multi-fluid and kinetic models are the widely used numerical tools for the interpretation and/or prediction of impurity behaviors in the edge of tokamak plasmas. Generally, the applicability of multi-fluid model for impurity transport modeling requires that the collision mean-free-path should be smaller than the gradient scale lengths of particles, which may not be always satisfied. To evaluate the applicability of multi-fluid model for W impurity transport modeling, multi-fluid (SOLPS-ITER) and kinetic (DIVIMP) modeling of W impurity transport in the edge of high-confinement plasmas in Experimental Advanced Superconducting Tokamak (EAST) during neon impurity seeding have been performed and comparatively investigated. It is found that low-charge-state W ions are mainly located in the divertor region near the target plates where plasma collisionality is relatively high due to the relatively low/high local plasma temperature/density. Hence, the fluid assumption for transport of lowly-charged W ions can be well satisfied. Consequently, density of lowly-charged W ions predicted by SOLPS-ITER and that calculated by DIVIMP are almost similar. Due to the fact that density of highly-charged W ions is relatively low and these particles mainly exist in the upstream (e.g the main SOL and core) where plasma collisionality is relatively low, the fluid approximation cannot be well satisfied. However, the total W impurity density calculated by the kinetic code DIVIMP and the multi-fluid model SOLPS-ITER are found to agree within a factor of 1.5 for the simulation cases presented in this contribution. Besides, the multi-fluid simulation with bundled charge state model has also been performed, results from which have been compared with those from the multi-fluid modeling with W ions treated as 74 fluids. It is revealed that, in simulation cases with neon impurity seeding and with divertor plasmas in high-recycling or partially detached regimes, the bundling scheme, which is commonly used for saving the computation cost in multi-fluid modeling, tends to overestimate the average charge state of W ions and thus tends to underestimate the radiation power loss, especially in the divertor region. Consequently, under the circumstance that W impurity radiation dominates the radiative power loss in divertor region, plasma temperature/density can be largely overestimated/underestimated, leading to the underestimation of W ion ionization source and W impurity density. Moreover, simulation results demonstrate that W accumulation in core can be effectively decreased during divertor detachment promoted by neon seeding.
Mitigating tungsten (W) wall erosion and core accumulation is vitally important to the steady-state operation of tokamaks. It is well known that drifts have a great impact on the transport of charged particles in the edge region, which could affect W source and W impurity transport. In this work, SOLPS-ITER modeling is applied to study the W impurity behavior on EAST during neon seeding with the consideration of E×B drift. The objective is to find out the relationship between the eroded W flux, W transport and corresponding accumulation in core in different discharge regimes. The effect of drift on W sputtering at targets and W impurity distribution in the cases of different toroidal magnetic field (Bt) directions is assessed. The simulation results indicate that drift could influence W transport via W impurity retention and redistribution in divertor, and the leakage from divertor. In forward Bt (B×∇B points to the X-point), eroded W flux at outer target is increased remarkably, and most of the W ions transport from outer to inner divertor and escape to upstream region in high field side. While W ions mainly transport from inner to outer divertor and escape from divertor in low field side in reversed Bt due to the opposite drift flux. Ne puffing rate is scanned in forward Bt and without drift cases to further investigate the W erosion and W impurity transport in different divertor regimes. It is found that W source from targets is generally enhanced by drift compared to the without drift cases. The core accumulation as well as poloidal asymmetry is also influenced significantly by the drift. In attached regime, intense W source and strong drift flux lead to enhanced W accumulation in the core, and obvious poloidal asymmetry of W density distribution appears. The drift flux is reduced, and W erosion is suppressed after detachment. W concentration in the core and poloidal asymmetry declines consequently. Therefore, adequate Ne impurity seeding can be applied to control the W accumulation in the core.
The Material Plasma Exposure eXperiment (MPEX) vacuum pumping system is responsible for creating prototypic conditions in the plasma material interaction chamber that mimic those in a fusion reactor divertor region. Additionally, the vacuum system needs to minimize the pressure in the plasma heating region to improve the coupling of the electron cyclotron heating and ion cyclotron heating to the plasma, minimizing waste heat exhausted to high heat flux components. The final design of the system has been sized to comply with the vacuum pump operating environment and to reduce the number of unique pumps required while meeting performance requirements. Bounding cases with and without the plasma present have been developed in the pumping analysis, and an initial calculation has been performed based on the plasma pumping identified in Proto-MPEX operation though this result will remain unverified until MPEX operation.
Comprehensive studies of energy and particle balances in the transition to plasma detachment in an alternative divertor configuration with long outer legs are shown. Numerical simulations are performed with the 2D code suite SOLPS 4.3, using a disconnected double null grid with narrow, tightly baffled long poloidal leg divertors at the outer lower target and outer upper target. A density scan is performed using the “closed gas box” model, where the tunable parameter in the simulations is the total number of deuterium particles in the simulation space and all other parameters are held fixed, including a constant input power and trace neon impurity radiation, to assess the physics of the transition to detachment in the system as the density increases. Three main aspects of the physics of divertor detachment are addressed: the criteria for the local onset of divertor detachment in each of the divertors, the distribution of heat flux and other plasma parameters between the four divertors as each divertor transitions to detachment, and the role of perpendicular transport in the transition to the detached regime. A synergistic mechanism by which the cross-field transport is reduced by factors associated with the onset of plasma recombination effects is identified. These results are compared to the existing understanding of the physics of the transition to plasma detachment in standard divertors.
This paper demonstrates the benefits of the HL-2M SF (snowflake) minus divertor on power exhaust and impurity screening in comparison with the LSN (lower single null) conventional divertor using SOLPS 5.0 code package. In order to estimate the effectiveness of the impurity screening capability in the HL-2M SF minus divertor, we analyze the impurity transport behavior with intrinsic carbon impurity (P sol =4MW) and external injected nitrogen impurity (P sol =6MW) in the LSN and SF minus divertor. The simulation results reveal that an input power of 4MW and electron density of nesep=2.5×10 ¹⁹ s ⁻¹ on the outer mid-plane can induce a nearly 80% pressure drop in the SOL (scrape-off layer) flux tube, representing the transition of the detachment regime in the SF minus divertor. For the higher power operation with P sol =6MW, a nitrogen gas puffing rate at 3.0×10 ²⁰ s ⁻¹ is sufficient to exhaust excessive energy and facilitate detachment in the SF minus divertor. However, a higher gas puffing rate is necessary for the LSN divertor, indicating an improved power exhaust capability in the SF minus divertor. Furthermore, the maximum effective charge (Z eff ) in the SF minus divertor SOL region is nearly 1.45 versus 3.5 in the LSN case with P sol =4MW. The maximum Z eff in the SF minus divertor SOL region is below 2.4, versus 5.5 in the LSN case with the same impurity gas puffing rate when P sol =6MW. Moreover, the impurity ions accumulate in the divertor region in the SF minus case, which demonstrates the effectiveness of the impurity screening capability in the HL-2M SF minus divertor. We find that the higher ionized state impurity ions contribute to the increase of Z eff and determine the impurity level upstream. On the one hand, the detached divertor regime has the benefit of suppressing the impurity particles ionizing to a higher ionized state. On the other hand, the ionization rate distribution and the poloidal velocity influenced by the friction and thermal forces determine the impurity transport behavior.
One of the major design limitations for tokamak fusion reactors is the heat load that can be sustained by the materials at the divertor target. Developing a full understanding of how machine or operation parameters affect the conditions at the divertor requires an enormous number of simulations. A promising approach to circumvent this is to use machine learning models trained on simulation data as surrogate models. Once trained such surrogate models can make fast predictions for any scenario in the design parameter space. In future such simulation based surrogate models could be used in system codes for rapid design studies of future fusion power plants. This work presents the first steps towards the development of such surrogate models for plasma exhaust and the datasets required for their training. Machine learning models like neural networks usually require several thousand data points for training, but the exact amount of data required varies from case to case. Due to the long runtimes of simulations we aim at finding the minimal amount of training data required. A preliminary dataset based on SOLPS-ITER simulations with varying tokamak design parameters, including the major radius, magnetic field strength and neutral density is constructed. To be able to generate more training data within reasonable computation time the simulations in the dataset use fluid neutral simulations and no fluid drift effects. The dataset is used to train a simple neural network and Gradient Boosted Regression Trees and test how the performance depends on the number of training simulations.
A high-level design study for a new experimental tokamak shows that advances in fusion science and engineering can be leveraged to narrow the gaps in energy confinement and exhaust power handling that remain between present devices and a future fusion pilot plant (FPP). This potential new U.S. facility, an Exhaust and Confinement Integration Tokamak Experiment (EXCITE), will access an operational space close to the projected FPP performance regime via a compact, high-field, high-power-density approach that utilizes advanced tokamak scenarios and high-temperature superconductor magnets. Full-device optimization via system code calculations, physics-based core-edge modeling, plasma control simulations, and finite element structural and thermal analysis has converged on a BT=6 T, IP=5 MA, R0=1.5 m, A=3, D-D tokamak with strong plasma shaping, long-legged divertors, and 50 MW of auxiliary power. Such a device will match several absolute FPP parameters: plasma pressure, exhaust heat flux, and toroidal magnetic field. It will also narrow or close the gap in key dimensionless parameters: toroidal beta, bootstrap fraction, collisionality, and edge neutral opacity. Integrated neutron shielding preserves personnel access by limiting nuclear activation and maximizes experimental run time by reducing site radiation. In addition to design study results and optimization details, parameter sensitivities and uncertainties are also discussed.
The striation pattern of heat loads on the divertor targets is determined by the plasma response to external resonant magnetic perturbations (RMPs) applied for suppression of edge localized modes (ELMs). Ideal and kinetic plasma response analysis with the general perturbed equilibrium code (GPEC) has shown that the extent of this striation pattern is very sensitive to the radial location of equilibrium truncation in GPEC, and that a significantly smaller extent is found if the equilibrium is truncated closer to the separatrix. Depending on the choice of truncation, it is shown in EMC3-EIRENE simulations that the peak heat load can be reduced by adjusting RMP coil parameters (phase, amplitude) within a window that is consistent with ELM suppression.
Due to substantial edge transport of particles, I-mode operations offer a high potential for divertor heat load mitigation. In this work, divertor parameters of I-mode operations on EAST have been investigated by SOLPS-ITER code, and the comparison with H-mode operations has also been made, with modeling the operated I- and H-mode processes on EAST. The simulation finds that, for the same separatrix electron density on outer mid-plane (OMP) n_(e,OMP)^sep, the upstream electron density of the I-mode is higher than that of H-modes with no density pedestal, while the upstream temperature of the I-mode is almost the same as that of H-mode with the temperature pedestal similar to that of H-modes. As a combined result, temperature and energy flux peaks of the I-mode are thus lower than those of H-modes at the divertor target. Further parameter scanning investigation reveals that, under low density condition (n_(e,OMP)^sep=1.16×〖10〗^19 m^(-3)), the peak energy flow at the target is reduced by ~ 34.1%, comparing the I-mode case to the H-mode, while the peak target temperature is dropped by ~ 54.6%. Under high density condition (n_(e,OMP)^sep=4.04×〖10〗^19 m^(-3)), on the other hand, energy flux and temperature peaks are weakened by ~ 28% and ~ 30.1%, respectively. The upstream density at detachment onset of an I-mode is also lower than that of an H-mode, by a fraction of 18.5%. These results suggest that the I-mode operation is more appropriate for divertor heat load mitigation than the H-mode.
In 1997 the new 'LYRA' divertor went into operation at ASDEX Upgrade and the neutral beam heating power was increased to 20 MW by installation of a second injector. This leads to the relatively high value of P/R of 12 MW/m. It has been shown that the ASDEX Upgrade LYRA divertor is capable of handling such high heating powers. Mea-surements presented in this paper reveal a reduction of the maximum heat flux in the LYRA divertor by more than a factor of two compared to the open Divertor I. This reduction is caused by radiative losses inside the divertor region. Carbon radiation cools the divertor plasma down to a few eV where hydrogen radiation losses become significant. They are increased due to an effective reflection of neutrals into the hot separatrix region. B2-Eirene modelling of the performed experiments supports the experimental findings and refines the understanding of loss processes in the divertor region.
Extensive studies of the H-mode density limit (DL) in JET gas-puffed discharges have been performed in the past four years targeting at an improved database for extrapolation to ITER. This paper reviews the arguments for the particular DL definition (pedestal density at the H–L boundary), the logic underlying the choice of parameters under focus (toroidal field, major radius, triangularity, safety factor) as well as some improvement in the interpretation of typical JET density ramp-up signatures that led to a critical review of the existing data. An empirical scaling is derived and compared with existing empirical and model based scalings. ASDEX Upgrade data are included in this analysis to provide information on the size dependence. The main results are: earlier findings on the Bt, R and q95-dependences are confirmed. The triangularity dependence, if any, is weak. The SOL-based BLS (Borrass, Lingertat, Schneider) scaling and the empirical scaling are virtually indistinguishable. The Greenwald scaling provides values in the right absolute range, but the overall fit is comparatively poor. The proposed scaling predicts ITER critical densities considerably below the reference value. Fuelling methods other than gas-puffing are outside the scope of this paper, but pellet fuelling, envisaged for ITER as an option to alleviate the situation, is discussed.
Significant recombination of the majority ion species has been observed in the divertor region of Alcator C-Mod [I. H. Hutchinson &etal;, Phys. Plasmas 1, 1511 (1994)] under detached conditions. This determination is made by analysis of the visible spectrum from the divertor, in particular the Balmer series line emission and the observed recombination continuum, including an apparent recombination edge at ∼375 nm. The analysis shows that the electron temperature in the recombining plasma is 0.8–1.5 eV. The measured volume recombination rate is comparable to the rate of ion collection at the divertor plates. The dominant recombination mechanism is three-body recombination into excited states (e+e+D+⇒D0+e), although radiative recombination (e+D+⇒D0+hν) contributes ∼5% to the total rate. Analysis of the Balmer series line intensities (from nupper=3 through 10) shows that the upper levels of these transitions are populated primarily by recombination. Thus the brightnesses of the Balmer series (and Lyman series) are directly related to the recombination rate.
The chemical erosion of carbon in interaction with a hydrogen plasma has been studied in detail in ion beam experiments, and erosion yield values are available as a function of ion energy and surface temperature. However, the conditions in the ITER divertor cannot be simulated by ion beam experiments, especially as far as ion flux is concerned. Therefore, a joint attempt was made through the EU Task Force on plasma-wall interaction and the international tokamak physics activity involving seven different fusion devices and plasma simulators to clarify the flux dependence. For each data point the local plasma conditions were normalized to an impact energy of 30 eV, care was taken to select data for a surface temperature close to the maximum yield or room temperature and the calibration of the diagnostic was performed in situ. Through this procedure the previous large scatter was significantly reduced, revealing a clear trend for a decreasing yield with increasing ion flux, Phi. After the attribution of an error to each data point a fit using Bayesian probability analysis was performed, yielding a decrease in the erosion yield with Phi-0.54 at high ion fluxes.
The theory of plasma-wall transition is reviewed including the effect of a magnetic field oblique to the wall leading to a double structure of the sheath. The implications of the conditions at the sheath edge on the flow in the presheath are discussed.
The objective of this paper is to provide an introduction to those aspects of atomic collision physics which underly the unavoidably generalised base of cross section data and scaling relationships which is currently employed in plasma modelling. Both experimental and theoretical methods are outlined and, where practicable, general trends in collisional behaviour are illustrated by examples of measured data. Atomic and molecular processes are considered on the basis of their particular relevance to the plasma edge region so that the discussion emphasises the properties of collisions in the regimes of low plasma temperature and low charge state of impurity ions. Nevertheless the basic concepts apply with equal validity throughout the plasma. Particular attention is devoted to recycling of hydrogen atoms and molecules because of its powerful influence upon plasma properties adjacent to boundary surfaces. References are selected with the objective of providing easy access to detailed reviews on topics which perforce cannot be included in this brief account. The method of presentation is firstly to discuss the general roles of atomic and molecular collisions in the plasma edge, then to identify the types of collision involved and subsequently to describe the methods adopted to calculate or measure the relevant cross sections. Cross section data are introduced in increasing order of the complexity of their atomic interactions. Finally the influence of the plasma environment upon atomic collision rates is discussed.
The ITER Physics Basis presents and evaluates the physics rules and methodologies for plasma performance projections, which provide the basis for the design of a tokamak burning plasma device whose goal is to demonstrate the scientific and technological feasibility of fusion energy for peaceful purposes. This Chapter summarizes the physics basis for burning plasma projections, which is developed in detail by the ITER Physics Expert Groups in subsequent chapters. To set context, the design guidelines and requirements established in the report of ITER Special Working Group 1 are presented, as are the specifics of the tokamak design developed in the Final Design Report of the ITER Engineering Design Activities, which exemplifies burning tokamak plasma experiments. The behaviour of a tokamak plasma is determined by the interaction of many diverse physics processes, all of which bear on projections for both a burning plasma experiment and an eventual tokamak reactor. Key processes summarized here are energy and particle confinement and the H-mode power threshold; MHD stability, including pressure and density limits, neoclassical islands, error fields, disruptions, sawteeth, and ELMs; power and particle exhaust, involving divertor power dispersal, helium exhaust, fuelling and density control, H-mode edge transition region, erosion of plasma facing components, tritium retention; energetic particle physics; auxiliary power physics; and the physics of plasma diagnostics. Summaries of projection methodologies, together with estimates of their attendant uncertainties, are presented in each of these areas. Since each physics element has its own scaling properties, an integrated experimental demonstration of the balance between the combined processes which obtains in a reactor plasma is inaccessible to contemporary experimental facilities: it requires a reactor scale device. It is argued, moreover, that a burning plasma experiment can be sufficiently flexible to permit operation in a steady state mode, with non-inductive plasma current drive, as well as in a pulsed mode where current is inductively driven. Overall, the ITER Physics Basis can support a range of candidate designs for a tokamak burning plasma facility. For each design, there will remain a significant uncertainty in the projected performance, but the projection methodologies outlined here do suffice to specify the major parameters of such a facility and form the basis for assuring that its phased operation will return sufficient information to design a prototype commercial fusion power reactor, thus fulfilling the goal of the ITER project.
Theory has shown that completely detached gas targets are completely controlled by the transverse ion–neutral collisionality. In order to transform this information to a format of practical relevance, knowledge of the plasma density width Δ*n at the gas target entrance (GTE) is required. In a previous work, Δ*n was determined with the relation Δ*n∝ΔT, where ΔT is the upstream temperature fall-off length, which can be reliably estimated. This paper provides evidence for this relation, which is not a priori obvious. In the absence of empirical data, one has to rely on a computational (B2-EIRENE) database. Proportionality between Δ*n and ΔT is confirmed. Complementary analytical considerations are presented to elucidate the underlying physics.
B2-Eirene is one of the standard SOL transport code packages used worldwide for various devices. We describe the newest B2 version introducing both new physics and numerics. Especially, the effect of drifts on field reversal scenarios are discussed for ASDEX Upgrade: the ExB drifts are quite important for multifluid cases, where they lead to a switch of the asymmetry of the divertor loads due to magnetic field reversal.
Recent progress in plasma performance in experiments on controlled thermonuclear fusion will lead to next-generation fusion experiments with the ultimate goal to make a power-generating fusion reactor reality. A major issue in the design of fusion experiments is the selection of the first wall material. Due to its outstanding thermal properties and its low Z carbon is and will be a first choice material, either elemental or in compounds and composites. Given the fact that in magnetically confined hydrogen plasmas of high density and temperature substantial wall fluxes of H species occur, the surface chemistry, in particular chemical erosion and H retention, becomes a concern. Although for more than a decade materials science studies on the Hcarbon interaction have been performed, the elementary reaction steps of this interaction have become clear only recently. This report reviews work performed on the surface chemistry under the aspects of chemical erosion. It presents in detail model studies directed towards identifying elementary reaction steps. Related fields, e.g. the surface chemistry as relevant for the production of hard a-C:H coatings and low pressure diamond synthesis are covered in the review.
Recent work, both theoretical and computational, in the modelling of time-dependent phenomena (Edge Localized Modes (ELMs)) in the plasma edge is reviewed.
We consider the effect of perpendicular energy transport in the low temperature divertor region on impurity radiation loss from the SOL plasma. We show that the perpendicular energy transport results in enlargement of the volume with relatively low temperature and a very high density of the plasma. High plasma density causes a strong energy loss due to impurity radiation peak in this low temperature region. For low Z impurity the energy transport due to plasma convection and neutrals also can strongly influence the volume of low temperature region.
This book covers the most important issues of plasma - wall interactions in nuclear fusion devices. Several authors, all actively working in that particular field, have written articles on surface phenomena (erosion mechanisms, particle recyling, wall coatings and ablation) and bulk material properties (thermal stability, radiation damage). The latest developments and findings are provided. Nevertheless, the basic principles are also given for each issue in a concise style, such that this book may serve as an excellent introduction for everyone entering the field of plasma - wall interactions. For other scientists in fusion, in particular the non-specialists, this book provides a useful survey of the present status of plasma - wall interaction issues and the most important processes involved, a broad knowledge of which is of growing importance in solving the problems of energy and particle exhaust in fusion devices.
Scaling laws found under the assumption that two-body collisions dominate can be effectively used to benchmark complex multi-dimensional codes dedicated to investigating tokamak edge plasmas. The applicability of such scaling laws to the interpretation of experimental data, however, is found to be restricted to the relatively low plasma densities (<10(19) m(-3)) at which multistep processes, which break the two-body collision approximation, are unimportant. (C) 1996 American Institute of Physics.
A brief review of nonlocal heat-flow models is presented. Numerical difficulties associated with their implementation, as recently demonstrated by Prasad and Kershaw [Phys. Fluids B 1, 2430 (1989)], are discussed and a simple solution is proposed. A new nonlocal heat-flow formula is developed, based on numerical simulations of the decay of linearized thermal waves, using the electron Fokker–Planck code spark. The formula is tested by modeling the full implosion of a CH shell driven by 351 nm laser irradiation. Results are shown to be in good agreement with spark simulations.
Electron heat transport equations with a nonlocal heat flux are in general ill-posed and intrinsically unstable, as proved by the present authors [Phys. Fluids B 1, 2430 (1989)]. A straightforward numerical solution of these equations will therefore lead to absurd results. It is shown here that by imposing a minimal set of constraints on the problem it is possible to arrive at a globally stable, consistent, and energy conserving numerical solution.
Several types of edge plasma perturbations in the TUMAN-3 tokamak [Proceedingsofthe 13thInternationalAtomicEnergyAgencyConferenceonPlasmaPhysicsandControlledNuclearFusionResearch, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 509] have been demonstrated to trigger the Ohmic H-mode transition. It is shown that three different methods, (1) radial electric field of either sign imposed by an electrode biased up to 500 V, (2) perturbation of the edge plasma density by strong gas puffing, and (3) LiD pellet injection, bring about the Ohmic H mode. In biasing experiments, the degree of improvement of particle and energy confinement depends on the polarity of the electric field and is higher for negative biasing. The evaporation of a LiD pellet (V∼150 m/sec, size ∼0.3 mm, density perturbation∼50%) in the peripheral region of the plasma column can also lead to the H-mode transition. Experimental results are shown to be in reasonable agreement with the theory of radial electric fields in tokamaks.
The plasma flow velocity in the Plasma Generator PSI-2 has been investigated by using of Mach probe. PSI-2 is a stationary high-current arc discharge in which the quasi-neutral plasma expands along the magnetic field lines. The low-temperature (Te < 20 eV), medium density (ne ∼ 1018 -1019m-3) plasma in the discharge is similar to the plasma in the divertor region of tokamaks. From the ratio of ion saturation currents collected from opposite sides of the probe the flow velocities (Mach numbers) in argon and hydrogen discharges are obtained.
The issue of transport on open field lines is addressed using a fluid approach invoking anomalous inertia and viscosity. The emphasis of the model is on the transport of the toroidal momentum, which is notoriously anomalous. The model suggests that tokamaks with divertors may benefit from a significant amplification of the electric field. It is shown that biasing of the scrape-off layer (SOL) with respect to the grounded first wall results in fundamental phenomena, affecting the performance of a divertor. The theoretical model appears to be consistent with experimental results obtained on Tokamak de Varennes [Phys. Plasmas 1, 1485 (1994)].
It is well known that usual assumptions of neoclassical theory become invalid if very large gradients occur at the plasma edge. Therefore neoclassical theory of plasma rotation in tokamaks is revisited in order to account for anomalous transport driven by a turbulence. It is shown that this model yields both steep and gradual profiles for the poloidal rotation velocity at the edge corresponding to the H and L regimes of confinement, respectively. Results and conclusions are focused on experiments employing the biased electrode technique. Regimes with fast poloidal rotation in excess of poloidal sound speed are considered with the emphasis on relaxation.
Global and local edge parameters at the H-mode transition are investigated at edge densities below and near the H-mode density limit. Conditions for onset of edge magnetohydrodynamic (MHD) instability (ELMs) and sustaining the H-mode define an operational window for H-mode with a maximum edge density, which can only be reached with optimum adjustment of both heating and fuelling fluxes. Careful experiments are carried out to vary the edge density in a wide range and allow comparison with H-mode theories in various collisionality regimes.
The current status of research concerned with classical (due to pair collisions) processes of particle and energy transfer in a partially ionized plasma is reviewed. Solutions are presented to various problems arising in the physics of the ionosphere, gas discharge, and semiconductors. The problems considered cover a variety of boundary conditions, nonlinearities, magnetic field effects, forms of initial inhomogeneity, and degrees of plasma ionization. Particular attention is given to self-consistent electric fields and eddy current produced by such fields, which are of primary importance in the phenomena discussed here.
The classical fluid transport equations are analyzed in a magnetized slab geometry containing two regions, the first being where the magnetic field lines are in contact with material surfaces and the second adjoining region where fields lines form closed flux surfaces. These fluid equations are used as a framework to describe the transport of particles, momentum, and energy. Anomalous transport across the magnetic field arising from turbulence is modeled by assuming enhancement of the classical terms in a systematic manner by increasing the collision frequencies, thereby retaining the basic symmetry and conservation properties of the ion and electron system. A reduced set of equations is derived for the plasma edge region by taking advantage of the strong magnetic field and long-thin geometry of the edge to eliminate variables and subdominant terms. As a specific example, parameters typical of the tokamak edge region are considered.
Marfes are toroidally symmetric bands of high density radiating plasma that form at the edge of tokamak plasmas. The marfe results from a process of radiative condensation: A local increase in the plasma density increases the radiation rate and lowers the temperature, allowing the density to rise further to maintain pressure balance. It is demonstrated that the marfe onsets when the plasma density exceeds a critical threshold that is just below the density limit, in agreement with observations. This threshold results from a balance between condensation and cross-field thermal flux from the central hot plasma. Finally, it is noted that radiative condensation is also the driving mechanism of solar prominences and other astrophysical objects.
The effect of secondary electron emission and sputtered impurity ions on the sheath potential drop has been studied. An analytical model has been developed which allows a self-consistent description of the above mentioned effects. In the analysis different materials (two kinds of graphite and tungsten) have been compared and a considerable dependence of the potential drop on the material choice has been observed. It is shown that the most of energy coming from the plasma to the target is carried by electrons because of both the decrease of potential drop caused by SEE and the enhancement of electron current to the plate caused by sputtering.
1. Introduction.- 2. The Binary Collision Model.- 2.1 Laboratory System.- 2.2 Centre-of-Mass System.- 2.3 Relations Between Laboratory and Centre-of-Mass Systems.- 2.4 Energy Transfer.- 2.5 Classical Scattering Theory.- 2.6 Asymptotic Trajectories.- 2.7 Determination of the Scattering Angle and the Time Integral.- 2.8 Limitations of the Binary Collision Approximation.- 2.9 Limitations of the Classical Mechanics Treatment.- 3. Classical Dynamics Model.- 3.1 Newton's Equations.- 3.2 Integration of Newton's Equations.- 3.2.1 Central Difference Scheme.- 3.2.2 Average Force Method.- 3.2.3 Euler-Cauchy Scheme.- 3.2.4 Predictor-Corrector Scheme.- 3.2.5 The Verlet Scheme.- 3.2.6 Nordsieck Method.- 3.3 The Time Step, Bookkeeping.- 4. Interaction Potentials.- 4.1 Screened Coulomb Potentials.- 4.2 The Born-Mayer Potential.- 4.3 Attractive Potentials.- 4.4 Combined Potentials.- 4.5 Empirical Potentials.- 4.6 Embedded Atom Method.- 4.7 Analytical Methods.- 4.8 Comparison of Potentials.- 5. Inelastic Energy Loss.- 5.1 Local Electronic Energy Loss.- 5.2 Continuous Electronic Energy Loss.- 5.3 Comparison.- 6. Thermal Vibrations and Specific Energies.- 6.1 Thermal Vibrations.- 6.2 Specific Energies.- 6.2.1 Cutoff Energy.- 6.2.2 Displacement Energy.- 6.2.3 Bulk Binding Energy.- 6.2.4 Surface Binding Energy.- 7. Programs Based on the BCA Model.- 7.1 Random Target Structures.- 7.2 Monte Carlo Programs.- 7.3 Crystalline Targets.- 7.4 Lattice Programs.- 7.5 TRIM.SP and TRIDYN.- 7.5.1 TRIM.SP.- 7.5.2 TRIDYN.- 7.6 MARLOWE.- 8. Programs Based on the Classical Dynamics Model.- 8.1 Stable, Metastable and Quasi-Stable Programs.- 8.2 Classical Dynamics Programs.- 9. Trajectories.- 10. Ranges.- 10.1 Definitions.- 10.2 Literature.- 10.3 Examples.- 11. Backscattering.- 11.1 Definitions.- 11.2 Literature.- 11.3 Examples.- 12. Sputtering.- 12.1 Definitions.- 12.2 Negative Binomial Distribution.- 12.3 Literature.- 12.4 Examples.- 13. Radiation Damage.- 13.1 Definitions.- 13.2 Component Analysis.- 13.3 Fuzzy Clustering.- 13.4 Literature.- 13.5 Examples.- Abbreviations Used in the Tables.- Constants.- References.- Author Index.
A fast scanning Langmuir probe system (LPS) for ASDEX-Upgrade's divertor plasma investigations was designed, manufactured and operated. Profiles of ion saturation current density, Jsat, electron temperature, Ted, electron density, Ned, floating potential, Vfl, and Mach number have been recorded for ohmic (OH) and low/medium power neutral beam heated (NI) discharges. In these cases the probe can access both divertor legs, allowing comparison of plasma parameters in the two divertors and investigations of the private flux region. Strong divertor asymmetries, complex plasma flow patterns and changes in the power flow to the divertor targets, depending on ion gradB drift direction, density and divertor geometry, have been observed.
Tungsten coated graphite tiles were mounted in the divertor of the ASDEX Upgrade tokamak and exposed to approximately 800 plasma discharges. After the experimental campaign, a poloidally complete set of samples was removed. The poloidal tungsten distribution pattern is presented and compared to those of other metallic impurities. The amount of tungsten detected on main chamber plasma facing components is found to be nearly unaffected by the operation of a fully tungsten covered divertor. Modifications of the tungsten surfaces are analyzed. Deposition is observed to dominate in the inner divertor while erosion prevails in the outer divertor. The influence of this result on the target plate deuterium inventories is demonstrated. Finally, a model description for the deuterium inventories observed in the main chamber is presented.
Detachment at the separatrix is a promising possibility to reduce the peak power load onto the divertor target plates. We investigated this topic spectroscopically at ASDEX Upgrade by measuring particle velocities using Doppler spectroscopy. The experimental data show a reduction of the chord averaged hydrogen velocity along the separatrix by about a factor of 3. Another important subject is flow reversal: after a brief discussion of 2D-code predictions and the conditions for detection we present spectroscopic evidence for flow reversal of C2+-ions in the ASDEX Upgrade divertor II. The comparison of these spectroscopic data with B2-EIRENE modeling shows good qualitative and quantitative agreement.
A new divertor was installed in ASDEX Upgrade and went into operation in spring of 1997. The divertor was designed to handle heat fluxes relevant to ITER-like scenarios. For this, the tiles expected to receive the maximum load (strike point modules) are hardened by the use of carbon fibre composites covering about 20% of the total divertor area. The maximum heat flux detected by thermography in a H-mode discharge is only 4 MW/m2 or below for a total input power of 20 MW without radiating mantle, except some ELMs showing a moderately higher heat flux. A broad distribution of the power load found in the measured poloidal distribution of the heat flux as well as the energy distribution, shows that less than half of the power flowing into the divertor is received by the strike point modules. The remaining power is loaded to other tiles of the divertor, particularly the transition module and parts of the roof baffle near to the strike point modules. The reconstructed radiation pattern reveals that the fraction of power radiated outside the divertor is comparable for both geometries. But the radiated fraction inside the divertor is increased by 10–15% in the Lyra shaped divertor.
A calorimeter probe used in combination with a Langmuir double probe for studies of the plasma boundary layer of ASDEX is described. The scope and the limitations of the device are discussed.The combined probe is designed for measuring the energy flux parallel to the magnetic field, on the ion and the electron drift side simultaneously. In addition the electron temperature and the density can be determined. First experimental results from discharges employing different heating methods, i.e. OH, LHRH and NBI are presented.Besides yielding decay lengths for and n, the asymmetry of the energy flux during neutral beam injection indicates a toroidal plasma rotation in the case of tangential neutral beam injection.
The coefficients of electrical and thermal conductivity have been computed for completely ionized gases with a wide variety of mean ionic charges. The effect of mutual electron encounters is considered as a problem of diffusion in velocity space, taking into account a term which previously had been neglected. The appropriate integro-differential equations are then solved numerically. The resultant conductivities are very close to the less extensive results obtained with the higher approximations on the Chapman-Cowling method, provided the Debye shielding distance is used as the cutoff in summing the effects of two-body encounters.
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.
One of the most critical parameters for the predictive capability of edge transport calculations is the description of the radial turbulent (anomalous) transport. Due to the complexity of the edge, highly sophisticated 2d numerical transport codes have been developed with run times per case of order of weeks, which limits their application to a small number of typical scenarios. Downgraded versions with a simpler neutral model, coarser grid (one half normal resolution) and eventually simplified radiation losses, can be fast enough (hours per run) to allow a routine mid-plane profile analysis, at least for cases where divertor details are less important. Implementation of appropriate iteration and control loops allow an automatic fit of the anomalous transport coefficients with the new B2-SOLPS5.0. The minimization algorithm is generalized such that additional experimental information such as neutral fluxes, divertor profiles or spectroscopic measurements, can easily be included for a better discrimination of different anomalous transport laws (constant transport coefficients, 1/n like scaled or Bohm-like scaled). A special feature of the fit routine is the determination of the position of the separatrix from the power balance equations. This is necessary because the experimental uncertainty of about +/-0.5 cm is comparable to the experimentally observed gradient lengths.
Multi-fluid two-dimensional transport models such as the UEDGE code model [T. D. Rognlien &etal;, J. Nucl. Mater. 196–198, 34 (1992)] are widely used in the simulation of tokamak edge plasmas. Usually these models are based on the assumption of anomalous plasma diffusion in the direction perpendicular to magnetic field lines. As will be shown, the pure diffusive cross-field transport model is inadequate and fails to match properly plasma parameters measured both in the scrape-off layer (SOL) and in the divertor of the DIII-D tokamak. Recently it has been suggested that specific nondiffusive transport occurs in the edge plasma [S. I. Krasheninnikov, Phys. Lett. A 283, 368 (2001)]. The nondiffusive transport is incorporated to the UEDGE model by adding the anomalous cross-field convective velocity for plasma species and by prescribing a specific two-dimensional profile to this velocity. A series of highly radiative discharges obtained on the DIII-D tokamak is analyzed using the UEDGE code with the hybrid, convective and diffusive, cross-field transport model. For these discharges, anomalous convective velocity profiles are adjusted until the simulated radial profiles agree with measurements in the SOL and in the divertor. It is found that in order to reproduce most of the extensive experimental data, anomalous plasma convection should play the dominant role in the outboard edge-plasma region.