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DIII-D Research to Provide Solutions for ITER and Fusion Energy
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UEDGE modeling of plasma detachment of CFETR with ITER-like divertor geometry by external impurity seeding
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PREDICTION OF PELLET MASS THRESHOLDS FOR ELM TRIGGERING IN LOW-COLLISIONALITY, ITER-LIKE DISCHARGES
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A Full Multigrid Method for the Self-Adjoint Angular Flux Equation Based on Cellwise Block Jacobi Iteration
Previous work by Densmore et al. has demonstrated that multigrid methods for the self-adjoint angular flux (SAAF) equation with cellwise block Jacobi smoothing can be extremely effective at solving for the angular flux in one dimension. The extension of that work to two dimensions demonstrated that while the smoother works well, the use of a direct coarse-grid approximation can severely limit the rate of convergence for optically thin cells. In that paper, this convergence limit was evaded through the use of a partially Galerkin coarse-grid approximation. However, relying on a Galerkin coarse-grid approximation is not ideal as constructing the coarse-grid discretization in this approach is complicated. The motivation for this summary is to find a method that can work without the need for a Galerkin coarse-grid approximation. The Full Multigrid (FMG) method is well known as a method that can theoretically solve a problem to its discretization accuracy with optimal linear computational complexity, that is in just O(N) operations for N unknowns. Indeed, we develop an FMG method for the 2-D SAAF equation that yields discretization accuracy and does not require the use of a Galerkin coarse-grid approximation. Until recently, aside from proofs about the order of the error for FMG, little work had been done in quantifying when and how FMG can obtain discretization accuracy. However, recent work by Rodrigo et al. has introduced a Fourier analysis technique called worst-case right-hand side analysis used to calculate the FMG accuracy measure. The FMG accuracy measure is the upper bound on the constant of proportionality between the error of the FMG solution and the discretization error. In this summary, we develop and implement an FMG method for the 2-D Cartesian SAAF equations. We then perform worst-case right-hand side analysis and give numerical examples that demonstrate under what circumstances the method can solve the 2-D SAAF equations to discretization accuracy, for optically thin cells, without the need for a Galerkin coarse-grid approximation. (authors)
Handling Iterative Solvers in an Algorithmic Differentiation Framework Using Implicit Methods
Differentiable programming is a powerful concept as it enables the seemly propagation of gradients through functions, algorithms, and/or whole physics simulations. These gradients are useful for a wide variety of applications, including sensitivity studies and machine learning, but one of particular interest is optimization. Gradient-based optimization, enabled through automatic/algorithmic differentiation (AD), can be used on predictive physical models to efficiently optimize a set of design variables. AD methods are a particularly promising approach to complex physics simulations because they can be shown to scale well with an increasing number of design variables; however, care must be taken when coupling between different models or different states of a single model.
Iterative Error-Driven Ensemble Labeling (IEDEL) Algorithm for Enhanced Data Quality Control for the Atmospheric Radiation Measurement (ARM) Program User Facility
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Impact of Higher Fidelity Design Iterations on Critical System Criteria
Nuclear criticality experiments are effective at informing the performance of nuclear data libraries across many applications. This work explores the implications of refining critical experiment MCNP models from their low fidelity optimization phase to penultimate neutronic models. Specifically, this work is focused on two series of plutonium fueled experiments funded through internal programs at Los Alamos National Laboratory building off previous efforts under the EUCLID (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) collaboration. Thales, the first of the two collaborations, is a fast spectrum Ta-reflected plutonium experiment to support operations at PF-4. The second experiment are twin configurations designed to target the intermediate energy cross sections in 239 Pu. Motivation for this experiment stems from the PARallel Approach of Differential and InteGral Measurements (PARADIGM) collaboration which hopes to achieve a significant reduction in 239 Pu cross section uncertainties in the intermediate region.
Iterative Solvers & Algebraic Multigrid (with Trilinos, Belos & MueLu)
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TIME-DEPENDENT SOLPS-ITER SIMULATIONS OF THE TOKAMAK PLASMA BOUNDARY FOR MODEL PREDICTIVE CONTROL
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Diagnostics: Chapter 8 of the special issue: on the path to tokamak burning plasma operation
This chapter presents the activity conducted by the ITPA topical group (TG) on Diagnostics over about the last 15 years. Following a general introduction of the ITER Diagnostics led by their measurement roles, the document is organized in several subchapters detailing the design support, research and development activity conducted by each of the specialist working groups (WGs) of the TG. Please note that the magnetic diagnostics were supported at the TG without a specific WG. Their status is included in the general introduction. In the following some highlights of the subchapter’s contents are provided. Recent advances in ITER first wall (FW) diagnostics for the measurements of plasma-metallic wall interaction in support of the ITER research plan are reported. An InfraRed imaging Video Bolometer for ITER has been developed and tested on several tokamaks to measure the radiated power loss. A laser-induced breakdown spectroscopy (LIBS) technique which utilizes a pulsed laser beam to ablate locally by forming a crater, will measure local tritium inventory in the FW material. Real-time Residual Gas Analyzers will measure the neutral gas composition in a divertor port and an equatorial port during plasma operation. Due to the full metallic FW environment, the plasma-wall interaction in ITER will face several challenges such as the compromised radiated power and divertor heat flux measurements by reflection. Ray tracing and analysis codes have been developed to eliminate and correct the effects of reflection in the measurements. The characteristics of the reflecting surfaces depending on the roughness and angle of the incidence have been measured by dedicated experiments, and the results were applied to the reflection elimination. For the measurement of the metallic impurity radiation induced by eroded metallic atoms, a vacuum ultraviolet spectrometer has been developed and tested. An extensive thermonuclear diagnostic suite will be required to support the operation of ITER and the planned experimental program for future burning plasma experiments. Due to the harsh environmental conditions, the implementation of diagnostic systems in ITER is a major challenge. These conditions include high levels of neutron and gamma fluxes, neutron heating, particle bombardment. Therefore, the selection and design of diagnostic systems must take into account a number of phenomena previously unseen in diagnostic design. For this reason, the measurement of neutrons and confined or lost fast ions, with particular emphasis on alpha particles, is critical to ITER. The diagnostics associated with these measurements will be important for future plasma-burning experiments at ITER. The high neutron emission and very large plasma size in ITER make neutron diagnostics the main diagnostic method used to measure plasma parameters such as fusion power, fusion power density, ion temperature, energy of fast ions and their spatial distributions in the plasma core. Active spectroscopy techniques are methods where a neutral particle beam is injected into the plasma and information on plasma parameters is extracted from the measurement of line emission resulting from the beam-plasma interaction, either by plasma ions or by beam atoms. Spatial localization is achieved by crossing the beamline and multiple observation lines. The ITER plasma will be a high temperature, moderately dense, fully ionized collisional plasma. The plasma facing surfaces are principally metallic being fashioned from beryllium or tungsten but many other elements, arising from either structural or from operational needs, may enter this plasma. The energy range of the emitted photons range from meV (infra-red) to multi keV (x-rays) and originate from all areas of the plasma volume. The primary role of passive emission diagnostics is to identify what is in the plasma from spectral signatures. Extracting quantitative information from these measurements such as impurity content, ion temperature, rotation, degree of detachment and radiated power depends on calibrated instruments, a physics model of the atomic and molecular processes and plasma transport and an analysis workflow that takes into account environmental effects such as reflections. The particular needs for ITER have prompted a multi-machine, many-year effort to address all these aspects and this chapter reviews the work on diagnostic design, experiments and new analysis techniques. An overview of the laser diagnostics to be implemented on ITER is also provided in this paper. This includes descriptions of the Thomson scattering in the core, edge and divertor regions, polarimetry and interferometry diagnostics used for measuring plasma density and also measurements of helium density in the divertor using Laser Induced Flourescence. Techniques which can allow improvements on current measurements are also addressed in particular expanding poloidal polarimetry measurements to measure field fluctuations and proposed use of dispersion interferometery which has a number of advantages over existing methods. This paper identifies particular areas where further research and testing on existing tokamaks is useful even at this advanced stage to inform the design of diagnostics for ITER. Outstanding areas of concern for the implementation of laser diagnostics, in particular with a view to reliable operation are identified. An overview of the latest developments of microwave diagnostic systems and techniques is given. The primary focus is the contributions for ITER—the next step burning plasma experiment—which is supplemented by describing recent progress of techniques applicable for fusion experiments beyond ITER. The contributions are intentionally kept concise, and are being supplemented by a rich list of references for further studies. Radiation induced effects are receiving continuous and well-deserved attention of the ITER diagnostic community and they are in many cases one of the primary design drivers of the ITER diagnostic systems. The paper summarizes recent progress in this area focusing primarily on the ITER diagnostics but in some cases provides also outlook for the possible solutions for even more demanding radiation environment of fusion reactors beyond ITER. Despite advancements in the area of modeling and simulation of various radiation induced effects, experimental testing in a nuclear environment as close as possible to the target one is still seen as unavoidable for proper qualification of particular diagnostic functional elements. Recent advancement within three diagnostic areas: optical diagnostics, magnetics and bolometers is covered. Encouraging results on qualification of silica glass vacuum window assemblies are presented. In the area of magnetic sensors, progress of irradiation tests performed on ITER in-vessel LTCC inductive sensors is presented with outlook for novel technological approaches to inductive sensors utilizing thick printing and photolithography technologies being highlighted. Summary of advancements in the area of steady state magnetic field sensors based on Hall effect is given. New results of neutron irradiation test of the ITER borosilicate glass inserts for vacuum electrical feedthroughs are summarized finding negligible swelling at target level of neutron fluence. Off-line irradiation tests of fiber optic current sensors for plasma current measurement demonstrated that both for gamma doses up to 5 MGy and a total neutron fluence up to 10 15 cm −2 , radiation induced changes are still compatible with required measurement accuracy on ITER. The ITER bolometers are given as an example how considering radiation effects may influence the diagnostic design. Finally, outlook for future main R&D directions is outlined. All optical and laser-based diagnostics in ITER will be using mirrors to guide plasma radiation toward detectors, cameras and sensors. In the hostile plasma, radiation and particle environment the optical characteristics of diagnostic mirrors will degrade directly affecting the entire performance of involved diagnostic systems. An assessment of factors affecting mirror performance is provided. Among the prime adverse factors are deposition of plasma impurities, sputtering of mirror surface and steam ingress in the vicinity of mirrors. Within the International Tokamak Physics Activity with active support by ITER central team and domestic agencies, the structured research and development (R&D) program on mitigation of risks for diagnostic mirrors is underway. Within this program the mirror material development, the passive mitigation of mirror degradation by using diagnostic ducts and shutters along with an active mirror recovery program comprising the in-situ mirror cleaning and calibration is underway. Recent developments in diagnostic mirror R&D are described in this Chapter along with an example of their implementation of R&D solutions in ITER Infrared Thermography diagnostic. An assessment of still open engineering and physics questions, considerations on mirror risks during an early phase of ITER operation are given along with an overview of diagnostic mirror evolution in the late ITER operation stage toward the demonstration fusion power plant. Several crucial areas of diagnostic R&D outlined in ITER Research Plan are addressed. The basic control groups in a fusion reactor can be broken-down in five categories: (1) plasma position, magnetic configuration, and plasma current control, (2) profile control and confinement optimization, (3) MHD control and suppression, (4) edge dissipation control, radiation and plasma exhaust control and (5) break-down optimization. These categories are coupled via the physics (a control action in one domain will affect the other domains) and via shared actuators (e.g. ECRH for impurity accumulation avoidance, current density distribution control and MHD suppression). Consequently, a supervisory control system should determine the priority of the various control tasks, their couplings, and the interfaces with the safety and interlock system. For the systematic development of the various controllers taking the complexity of the plasma and the control system into account, a model-based approach is required. A short historical overview is given of the developments in systems and control theory and control engineering with special emphasis on those developments that are most relevant for Nuclear Fusion research and operation. An overview is given of the state of the field of fusion plasma control for the control categories. It will be shown how synthetic diagnostics are being developed in ITER and how they are used in diagnostic design and design validation and how they can be in model-based controller synthesis using relatively simple models. In modern control methods, multiple diagnostics are used to constrain relatively simple models. The constrained models provide an estimate for the state. This opens the route to state controllers, such as model predictive control. A major challenge in nuclear fusion research is the coherent combination of data from heterogeneous diagnostics and modeling codes for machine control and safety as well as physics studies. Measured data from different diagnostics often provide information about the same subset of physical parameters. Additionally, information provided by some diagnostics might be needed for the analysis of other diagnostics. A joint analysis of complementary and redundant data allows, e.g. to improve the reliability of parameter estimation, to increase the spatial and temporal resolution of profiles, to obtain synergistic effects, to consider diagnostics interdependencies and to find and resolve data inconsistencies. Physics-based modeling and parameter relationships provide additional information improving the treatment of ill-posed inversion problems. A coherent combination of all kind of available information within a probabilistic framework allows for improved data analysis results. The concept of integrated data analysis (IDA) in the framework of Bayesian probability theory is outlined and contrasted with conventional data analysis. Components of the probabilistic approach are summarized and specific ingredients beneficial for data analysis at fusion devices are discussed.
Space-Dependent Wielandt Shift Methods for Multigroup Diffusion Eigenvalue Problems
In the calculation of neutronic eigenfunctions and eigenvalues, it is often desirable to approximate the neutron transport equation by a diffusion equation that requires significantly less computational resources to solve. Even when a full transport solution is needed, the solution of the diffusion system can be used to accelerate iterative methods for calculating the transport eigenfunction and eigenvalue. The convergence rate of the basic power iteration method for eigenvalue problems is governed by the dominance ratio; realistic reactor core problems often have high dominance ratios and the power iteration method can converge slowly as a result. A common technique for accelerating the convergence of power iteration is the Wielandt shift (WS) method, which reduces the dominance ratio by 'shifting' the eigenvalue spectrum using an estimate of the desired eigenvalue. WS provides a significant speedup over power iteration if the eigenvalue estimate is close to the true eigenvalue, but it can be difficult to obtain such an estimate. In practice, the shift in the WS method can be dynamically updated in the iteration scheme, in a way that depends on the eigenvalue estimates from the most recent iterations. We present a physically-motivated Space-Dependent Wielandt Shift (SDWS) for solving multigroup diffusion eigenvalue problems. The space-dependence of the eigenvalue shift in SDWS enables a more effective acceleration of the power iteration scheme than WS at the beginning of the iteration scheme, when the current estimate of the eigenvalue is not close to the actual eigenvalue. Several variants of SDWS are discussed here, including an SDWS method that combines the strengths of SDWS (in the early iterations) with those of standard WS (in the later iterations). Numerical results from a 1-D multigroup diffusion problem demonstrate an order of magnitude speedup over power iteration and a 41% speedup over a standard WS technique. This speedup is problem-dependent and appears to be greater for 'more difficult' problems. In this summary, the term 'speedup' refers to a reduction in the number of iterations required to converge to the correct eigenvalue and eigenfunction. Because the scattering is treated fully implicitly (i.e., it is part of the left-hand side of the diffusion system and directly inverted), the computational cost of a single iteration does not vary significantly among the methods discussed in this summary. The number of iterations is therefore representative of the total computational cost for a method. We acknowledge that certain iterative solvers for linear systems (e.g., GMRES) require more computational time to converge when the system is nearly singular (i.e., when a very aggressive Wielandt shift is applied). Nonetheless, when using SDWS in the manner described in this summary, we have seen that the reduction in computational time from reducing the number of power iterations generally outweighs the extra computational time required by iterative solvers such as GMRES. (authors)
Effects of ray profile modeling on resolution recovery in clinical CT
Purpose: Iterative image reconstruction gains more and more interest in clinical routine, as it promises to reduce image noise (and thereby patient dose), to reduce artifacts, or to improve spatial resolution. However, among vendors and researchers, there is no consensus of how to best achieve these goals. The authors are focusing on the aspect of geometric ray profile modeling, which is realized by some algorithms, while others model the ray as a straight line. The authors incorporate ray-modeling (RM) in nonregularized iterative reconstruction. That means, instead of using one simple single needle beam to represent the x-ray, the authors evaluate the double integral of attenuation path length over the finite source distribution and the finite detector element size in the numerical forward projection. Our investigations aim at analyzing the resolution recovery (RR) effects of RM. Resolution recovery means that frequencies can be recovered beyond the resolution limit of the imaging system. In order to evaluate, whether clinical CT images can benefit from modeling the geometrical properties of each x-ray, the authors performed a 2D simulation study of a clinical CT fan-beam geometry that includes the precise modeling of these geometrical properties. Methods: All simulations and reconstructions are performed in native fan-beam geometry. A water phantom with resolution bar patterns and a Forbild thorax phantom with circular resolution patterns representing calcifications in the heart region are simulated. An FBP reconstruction with a Ram–Lak kernel is used as a reference reconstruction. The FBP is compared to iterative reconstruction techniques with and without RM: An ordered subsets convex (OSC) algorithm without any RM (OSC), an OSC where the forward projection is modeled concerning the finite focal spot and detector size (OSC-RM) and an OSC with RM and with a matched forward and backprojection pair (OSC-T-RM, T for transpose). In all cases, noise was matched to be able to focus on comparing spatial resolution. The authors use two different simulation settings. Both are based on the geometry of a typical clinical CT system (0.7 mm detector element size at isocenter, 1024 projections per rotation). Setting one has an exaggerated source width of 5.0 mm. Setting two has a realistically small source width of 0.5 mm. The authors also investigate the transition from setting one to two. To quantify image quality, the authors analyze line profiles through the resolution patterns to define a contrast factor (CF) for contrast-resolution plots, and the authors compare the normalized cross-correlation (NCC) with respect to the ground truth of the circular resolution patterns. To independently analyze whether RM is of advantage, the authors implemented several iterative reconstruction algorithms: The statistical iterative reconstruction algorithm OSC, the ordered subsets simultaneous algebraic reconstruction technique (OSSART) and another statistical iterative reconstruction algorithm, denoted with ordered subsets maximum likelihood (OSML) algorithm. All algorithms were implemented both without RM (denoted as OSC, OSSART, and OSML) and with RM (denoted as OSC-RM, OSSART-RM, and OSML-RM). Results: For the unrealistic case of a 5.0 mm focal spot the CF can be improved by a factor of two due to RM: the 4.2 LP/cm bar pattern, which is the first bar pattern that cannot be resolved without RM, can be easily resolved with RM. For the realistic case of a 0.5 mm focus, all results show approximately the same CF. The NCC shows no significant dependency on RM when the source width is smaller than 2.0 mm (as in clinical CT). From 2.0 mm to 5.0 mm focal spot size increasing improvements can be observed with RM. Conclusions: Geometric RM in iterative reconstruction helps improving spatial resolution, if the ray cross-section is significantly larger than the ray sampling distance. In clinical CT, however, the ray is not much thicker than the distance between neighboring ray centers, as the focal spot size is small and detector crosstalk is negligible, due to reflective coatings between detector elements. Therefore,RM appears not to be necessary in clinical CT to achieve resolution recovery.
Plasma Wall Interaction with 3-D Plasma Boundaries
The interaction of the edge plasma and the material surfaces is one of the most critical challenges on the path to harness fusion power as new, fundamental energy source. This challenge typically combines the thrust to reach high density, low temperature (detached) plasmas in front of the divertor target plates as well as understanding the plasma material interaction (PMI) in particular in this regime. The combination of both research thrusts represents an extraordinarily challenging subject encompassing spatial scales spanning nanometers to meters in all states of matter and across a broad energy range. Modeling capabilities, which help to interpret data from nowadays experiments and enable extrapolation to future devices are urgently required. This is in particular true for toroidal magnetic confinement devices with three-dimensional (3D) plasma boundaries. Such plasma boundary geometries occur in tokamaks, when small amplitude magnetic perturbations are used to stabilize the unruly edge plasma or in stellarators, that are inherently 3D plasma confinement devices. In this project, the impact of 3D plasma boundaries on the plasma material interaction (PMI) was assessed. This work focused on plasma boundary conditions, in which high-density conditions at the material surfaces yield mitigation of the otherwise immense heat and particle loads that these materials would see. These so-called high recycling and eventually detached plasma regimes are of great interest for future reactor operation. In the project, key features that are unique to 3D boundaries were explored in comparison to canonically assumed axisymmetric plasma edge situations in tokamaks. In particular, the relevance of the 3D boundary situation in the extrapolation to the plasma boundary solution at ITER, the next step fusion energy experiment under construction as a multi-national, world-wide large-science experiment in southern France, has been explored. The EMC3-EIRENE plasma edge fluid and kinetic neutral transport code has been advanced to cope with the challenging and unprecedented conditions in the ITER boundary plasma including 3D fields that are planned to be used to suppress harmful edge instabilities, the so-called edge localized modes. This is a vital integration challenge for ITER and the results from this grant have provide a leading capability for this assessment. It was shown that the detachment process in a 3D edge solution for ITER follows the recycling regimes that are known from axisymmetric solutions, but that multiple plasma exhaust channels connected to the material surfaces are established which feature individual recycling characteristics. Because these channels touch the material surfaces in the divertor in a 3D geometry, the compatibility with the plasma material interaction (PMI), including erosion and impurity generation has been found to be an important part of the integration challenge. To address this, the fully 3D plasma material interaction code ERO2 has been adapted to these ITER specific geometries and a homogeneous mixing model was implemented, that allows to consider the mixing of Be and Was used at ITER in the PMI modeling. This model enhancement has been used to study non-local migration of Be in the JET ITER like wall configuration and it has been shown that with this model such complex migration processes in ITER relevant plasma shapes and with ITER relevant plasma boundary conditions can be addressed. The combined modeling approach using EMC3-EIRENE as a plasma boundary transport code and the ERO2 specialized PMI model will be an asset for the continued preparations of ITER operation as well as for Fusion Pilot Plant efforts that have emerged in the U.S. during the evolution of this grant. The predictive capability of this numerical tool has been validated at the DIII-D US national fusion facility. Here, dedicated plasma edge diagnostics were implemented to measure the impurity household around a 3D edge plasma during ELM suppression by 3D fields. Dedicated experiments with local material probes using these diagnostics and the state-of-the-art suite of boundary measurements at DIII-D have shown that the 3D perturbation of the plasma edge that is excreted by such 3D control fields yield a perturbation of the plasma boundary flux structure and hence also of the resulting PMI. The 3D boundary plasma is composed out of helical magnetic flux channels that intersect the divertor targets at an angle relative to the main guiding field, i.e., the toroidal magnetic field component of the tokamak. A similar effect has been measured as well on limiter surfaces during the startup campaign at the new stellarator experiment Wendelstein 7-X. These experiments ad initial analysis with the ERO plasma material interaction model, suggested that the place of erosion for a given particle from the surface and its re-deposition can be different in such 3D field geometries yielding potentially a significant level of net-erosion. This is not the case for axisymmetric solutions, where it was shown in the past that the eroded particles are effectively re-deposited into gaps produced by erosion at the same position and hence the net-erosion levels are small. For ITER, the quest to suppress the ELMs and at the same time maintain the integrity of the divertor is an issue, which these fundamental findings will help to resolve. The coupling of this work to the extrapolation in the ITER program has been addressed by both the PI and the lead numerical scientist being ITER Science Fellows in the duration of the contract and forward. A second focus in the exploration of 3D boundary effects on tokamaks and stellarators has been set on the measurement of helium exhaust features with such 3D fields. This is important because He represents the ash of the fusion process and needs to be exhausted. It was shown that 3D field application compatible with suppression of ELMs yields an increase of the helium exhaust performance. The ratio of the effective helium confinement time over the energy confinement time was reduced by almost 50% which demonstrated that the impact of helium accumulation in the plasma core with respect to the confinement of energy to sustain the fusion reaction is significantly improved with such 3D control fields. It was shown that this is the case for tokamaks as well as stellarators. At the Large helical Device in Japan, a similar enhancement of the helium exhaust features when small amplitude additional 3D fields were applied was measured. This is an important additional function of 3D field application and its impact on ITER is presently being studied in combination with investigations of helium exhaust in 3D field geometries of stellarator devices.
Progress in preparing scenarios for operation of the International Thermonuclear Experimental Reactor
The development of operating scenarios is one of the key issues in the research for ITER which aims to achieve a fusion gain (Q) of ∼10, while producing 500 MW of fusion power for ≥300 s. The ITER Research plan proposes a success oriented schedule starting in hydrogen and helium, to be followed by a nuclear operation phase with a rapid development towards Q ∼ 10 in deuterium/tritium. The Integrated Operation Scenarios Topical Group of the International Tokamak Physics Activity initiates joint activities among worldwide institutions and experiments to prepare ITER operation. Plasma formation studies report robust plasma breakdown in devices with metal walls over a wide range of conditions, while other experiments use an inclined EC launch angle at plasma formation to mimic the conditions in ITER. Simulations of the plasma burn-through predict that at least 4 MW of Electron Cyclotron heating (EC) assist would be required in ITER. For H-modes at q{sub 95} ∼ 3, many experiments have demonstrated operation with scaled parameters for the ITER baseline scenario at n{sub e}/n{sub GW} ∼ 0.85. Most experiments, however, obtain stable discharges at H{sub 98(y,2)} ∼ 1.0 only for β{sub N} = 2.0–2.2. For the rampup in ITER, early X-point formation is recommended, allowing auxiliary heating to reduce the flux consumption. A range of plasma inductance (l{sub i}(3)) can be obtained from 0.65 to 1.0, with the lowest values obtained in H-mode operation. For the rampdown, the plasma should stay diverted maintaining H-mode together with a reduction of the elongation from 1.85 to 1.4. Simulations show that the proposed rampup and rampdown schemes developed since 2007 are compatible with the present ITER design for the poloidal field coils. At 13–15 MA and densities down to n{sub e}/n{sub GW} ∼ 0.5, long pulse operation (>1000 s) in ITER is possible at Q ∼ 5, useful to provide neutron fluence for Test Blanket Module assessments. ITER scenario preparation in hydrogen and helium requires high input power (>50 MW). H-mode operation in helium may be possible at input powers above 35 MW at a toroidal field of 2.65 T, for studying H-modes and ELM mitigation. In hydrogen, H-mode operation is expected to be marginal, even at 2.65 T with 60 MW of input power. Simulation code benchmark studies using hybrid and steady state scenario parameters have proved to be a very challenging and lengthy task of testing suites of codes, consisting of tens of sophisticated modules. Nevertheless, the general basis of the modelling appears sound, with substantial consistency among codes developed by different groups. For a hybrid scenario at 12 MA, the code simulations give a range for Q = 6.5–8.3, using 30 MW neutral beam injection and 20 MW ICRH. For non-inductive operation at 7–9 MA, the simulation results show more variation. At high edge pedestal pressure (T{sub ped} ∼ 7 keV), the codes predict Q = 3.3–3.8 using 33 MW NB, 20 MW EC, and 20 MW ion cyclotron to demonstrate the feasibility of steady-state operation with the day-1 heating systems in ITER. Simulations using a lower edge pedestal temperature (∼3 keV) but improved core confinement obtain Q = 5–6.5, when ECCD is concentrated at mid-radius and ∼20 MW off-axis current drive (ECCD or LHCD) is added. Several issues remain to be studied, including plasmas with dominant electron heating, mitigation of transient heat loads integrated in scenario demonstrations and (burn) control simulations in ITER scenarios.
On the Degradation of the Effectiveness of Nonlinear Diffusion Acceleration with Parallel Block Jacobi Splitting
MOOSE's radiation transport module Rattlesnake comprises a first order S N solver that can be accelerated with a flexible Nonlinear Diffusion Acceleration. At each NDA iteration, the streaming and collision operator of the S{sub N} equations are (approximately) inverted using a transport sweep. When executed on multiple processors parallel block Jacobi (PBJ) splitting is utilized lagging the processor sub-domain's incoming angular fluxes making the implemented method asynchronous, i.e. the convergence properties of NDA become dependent on the number of concurrent tasks and details of the partitioning. Within this work, we study the NDA convergence properties for the two-dimensional C5G7 benchmark problem PBJ with p = 1, 2, 4, 8, 12, 16, 24, 32, 48, 60, 72, 96 and 144 concurrent tasks. Rosa studied the convergence properties of PBJ splitting methods with and without transport synthetic acceleration (TSA) in slab geometry and two-dimensional Cartesian geometry, respectively. Rosa's iteration scheme lags both the incoming angular fluxes and the scattering source making it very similar to the method described here. Rosa found by means of Fourier analysis that convergence of unaccelerated PBJ can degrade for optically thin subdomains, i.e. for a large number of processors given a fixed domain size. Depending on the choice of parameters application of TSA can lead to an effective algorithm. In contrast to Rosa's work, this work focuses on PBJ splitting for NDA accelerated solution of the multigroup eigenvalue problem. Later, Zerr and Anistratov used their integral transport matrix method in conjunction with PBJ. This iteration scheme is different as it does not lag the scattering source. Nevertheless, Fourier analysis with Diamond Difference spatial discretization showed that the method degrades with increasing the overall size of the spatial domain while keeping the sub-domain size constant. In the case of an infinite medium, the observed spectral radius becomes unity. These references establish the iterative performance of PBJ for one-group fixed source problems discretized on rectangular cells, but for the Rattlesnake first order NDA method, an emphasis lies on multigroup eigenvalue problems. In this setting, the additional complication arises that the low order equations are not exactly inverted, but only to some iterative criterion. Further, as the low order problem is solved using Jacobian-Free Newton Krylov methods, a suitable preconditioner for the GMRES iterations is required. As the effectiveness of the preconditioners may decrease when more concurrent processes are used, we expect the low order solve to impact the overall effectiveness of the NDA method in parallel execution as well. Therefore, this work focuses on the question of how detrimental the asynchronicity of the high and low order iterative solutions is for the effectiveness of NDA solutions of realistic, unstructured grid, multigroup eigenvalue problems. The iterative convergence properties of Rattlesnake's NDA method for multigroup eigenvalue problems are studied for varying number of concurrent processes. Rattlesnake's NDA method is asynchronous because the high order transport sweep uses PBJ splitting and because the low order solve's preconditioners, algebraic multigrid and additive Schwarz, are asynchronous. We found that up to 144 processes the number of Picard iterations increases by a factor of 2-3 affecting but not destroying NDA's parallel performance for the C5G7 benchmark problem, a representative LWR (light water reactor) configuration. The solution of the NDA low order eigenvalue problem posed greater problems than expected for the solvers currently available in Rattlesnake mainly because of problems to effectively precondition the modified low-order problem. As a matter of fact, the low order problem becomes an advection-diffusion problem. Non-robustness was observed for the AMG preconditioned coarse mesh acceleration for more than 60 concurrent processes, which was fixed by increasing the number of permissible V-cycles per AMG call. For fine mesh acceleration AMG proved to be ineffective and we resorted to ASM. For both AMG and ASM, increasing number of linear iterations per nonlinear are observed when increasing the number of processes, but for ASM this problem appears to be worse. The results from this work also indicate that initial development efforts should be diverted from implementation of a high-order parallel sweeping algorithm to the effective and robust iterative solution of the low order NDA multigroup eigenvalue problem. (authors)
A Universal Tare Load Prediction Algorithm for Strain-Gage Balance Calibration Data Analysis
An algorithm is discussed that may be used to estimate tare loads of wind tunnel strain-gage balance calibration data. The algorithm was originally developed by R. Galway of IAR/NRC Canada and has been described in the literature for the iterative analysis technique. Basic ideas of Galway's algorithm, however, are universally applicable and work for both the iterative and the non-iterative analysis technique. A recent modification of Galway's algorithm is presented that improves the convergence behavior of the tare load prediction process if it is used in combination with the non-iterative analysis technique. The modified algorithm allows an analyst to use an alternate method for the calculation of intermediate non-linear tare load estimates whenever Galway's original approach does not lead to a convergence of the tare load iterations. It is also shown in detail how Galway's algorithm may be applied to the non-iterative analysis technique. Hand load data from the calibration of a six-component force balance is used to illustrate the application of the original and modified tare load prediction method. During the analysis of the data both the iterative and the non-iterative analysis technique were applied. Overall, predicted tare loads for combinations of the two tare load prediction methods and the two balance data analysis techniques showed excellent agreement as long as the tare load iterations converged. The modified algorithm, however, appears to have an advantage over the original algorithm when absolute voltage measurements of gage outputs are processed using the non-iterative analysis technique. In these situations only the modified algorithm converged because it uses an exact solution of the intermediate non-linear tare load estimate for the tare load iteration.
Integrated operation scenarios: Chapter 6 of the special issue: on the path to tokamak burning plasma operation
Here we report the progress of the development and optimization of operational scenarios for ITER and beyond, focusing upon baseline, hybrid, and steady-state scenarios since 2007. This includes advancements made by the integrated operation scenarios (IOS) topical group of the international tokamak physical activity as well as contributions from the broader tokamak community. The key area of research involves developing IOSs that encompass tokamak physics, operation, and technology by utilizing integrated modeling and control strategies. This requires leveraging available actuators to simultaneously control plasma position and shape, MHD activities that could lead to disruptions, transport, plasma-wall interaction and power exhaust, fuel cycle, fusion burn, and tritium breeding. The control extends from the plasma initiation phase, through the current ramp-up, flattop, start and end of the fusion burn, and current ramp-down, to the plasma termination phase. A review of the currently developed scenarios and modeling is provided in terms of (i) optimizing plasma initiation in ITER, (ii) preparing for the low activation phase to fully commission all tokamak systems and establish and validate physics and scenario conditions in preparation for deuterim-tritium (DT) operation, (iii) developing and preparing baseline and hybrid scenarios to demonstrate the feasibility of achieving these regimes within device constraints, (iv) exploring steady-state scenarios to meet ITER’s steady-state goals, (v) evaluating and preparing actuators for ITER, (vi) developing integrated control solutions using shared actuators. The most notable achievements include; (i) the development of ITER demonstration discharges by matching various dimensionless parameters, (ii) the development of scenarios in an ITER-like tungsten environment and DT operation, and (iii) the development of scenarios in superconducting tokamaks, enabling long-pulse operations with similar coil constraints to ITER. Along with these significant achievements, outstanding issues and recommendations for further research and development are provided. Importantly, this study goes beyond simply updating the ITER Physics Basis; it carries profound implications for the broader field of burning plasma research, offering valuable insights and guidance for the next generation of fusion experiments and devices.