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DOE OSTI2024

Design and Analysis of Liquid Lithium Plasma Facing Components

In this study, liquid metal (LM) on plasma-facing components (PFCs) creates a renewable protective cover enhancing power exhaust and protecting the solid substrate. Additionally, energy confinement improvement through particle pumping can be achieved in the case of liquid lithium (LL). A new variant of PFCs was recently introduced at Princeton Plasma Physics Laboratory (PPPL) where a porous wall is used to stabilize the LM surface, while using magnetohydrodynamic (MHD) drive to push the LM flow inside the component. This arrangement allows efficient heat exhaust, and enhanced control of the LM surface temperature, leading to spatial control of evaporation and condensation of LL on the plasma interface. This feature is particularly attractive when vapor shielding is introduced to allow heat flux redistribution. This system has the advantage that as the heat flux increases, the evaporation rate will increase, while decreasing heat flux will decrease the evaporation rate of lithium, ideally creating a feedback effect which could self-regulate the amount of lithium evaporated. Analytical and numerical models for LL PFCs were developed in PPPL. To calculate the target temperature distribution for the case of evaporation from the divertor, we apply an iterative process allowing two-way coupling between the fluid-kinetic analysis of plasma using SOLPS-ITER code and the flow and heat transfer analysis of the PFC using an analytical model. In the last stage, the results are validated using computational fluid dynamics (CFD) analysis with customized version of the CFX code from ANSYS. CFX was modified at PPPL to allow MHD analysis at the high magnetic field typical for fusion applications. Results of the analysis for NSTX-U tokamak conditions will be presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Techniques for Automated Performance Analysis

The performance of a particular HPC code depends on a multitude of variables, including compiler selection, optimization flags, OpenMP pool size, file system load, memory usage, MPI configuration, etc. As a result of this complexity, current predictive models have limited applicability, especially at scale. We present a formulation of scientific codes, nodes, and clusters that reduces complex performance analysis to well-known mathematical techniques. Building accurate predictive models and enhancing our understanding of scientific codes at scale is an important step towards exascale computing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

The multi-assumption architecture and testbed (MAAT v1.0): R code for generating ensembles with dynamic model structure and analysis of epistemic uncertainty from multiple sources

Abstract. Here, computer models are ubiquitous tools used to represent systems across many scientific and engineering domains. For any given system, many computer models exist, each built on different assumptions and demonstrating variability in the ways in which these systems can be represented. This variability is known as epistemic uncertainty, i.e. uncertainty in our knowledge of how these systems operate. Two primary sources of epistemic uncertainty are (1) uncertain parameter values and (2) uncertain mathematical representations of the processes that comprise the system. Many formal methods exist to analyse parameter-based epistemic uncertainty, while process-representation-based epistemic uncertainty is often analysed post hoc, incompletely, informally, or is ignored. In this model description paper we present the multi-assumption architecture and testbed (MAAT v1.0) designed to formally and completely analyse process-representation-based epistemic uncertainty. MAAT is a modular modelling code that can simply and efficiently vary model structure (process representation), allowing for the generation and running of large model ensembles that vary in process representation, parameters, parameter values, and environmental conditions during a single execution of the code. MAAT v1.0 approaches epistemic uncertainty through sensitivity analysis, assigning variability in model output to processes (process representation and parameters) or to individual parameters. In this model description paper we describe MAAT and, by using a simple groundwater model example, verify that the sensitivity analysis algorithms have been correctly implemented. The main system model currently coded in MAAT is a unified, leaf-scale enzyme kinetic model of C 3 photosynthesis. In the Appendix we describe the photosynthesis model and the unification of multiple representations of photosynthetic processes. The numerical solution to leaf-scale photosynthesis is verified and examples of process variability in temperature response functions are provided. For rapid application to new systems, the MAAT algorithms for efficient variation of model structure and sensitivity analysis are agnostic of the specific system model employed. Therefore MAAT provides a tool for the development of novel or toy models in many domains, i.e. not only photosynthesis, facilitating rapid informal and formal comparison of alternative modelling approaches.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Path Forward: Materials Data Modernization for ASME Codes and Standards in the Artificial Intelligence Era

Development of the ASME Materials Properties Database was initiated in the early 2010s to support the ASME Codes and Standards. As information technologies advance at an accelerated pace with the artificial intelligence era on the horizon, the ASME Materials Properties Database must be further modernized from a database to a knowledgebase to ride the wave of digital information revolution and effectively support the ASME Codes and Standards in the new era. This paper is intended to provide an overview of the ASME Materials Properties Database and discuss a roadmap for its future development to facilitate understanding of and participation from different sectors of the Codes and Standards community. Further, it first reviews the basic concepts of data, information, knowledge, database, and database system as well as the pros and cons in different types of data management and then discusses the path forward for a desired evolution of the database into a self-explanatory and machine-readable knowledgebase that is consistent with human cognitive processes for the Codes and Standards development and, furthermore, provides resources for data processing and analysis to reach an eventual goal of streamlining the Codes and Standards development from the initial inquiry, throughout data submission, analysis, …, to Codes and Standards rule establishment for final publication.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Path Forward: Materials Data Modernization for ASME Codes and Standards in the Artificial Intelligence Era

Development of the ASME Materials Properties Database was initiated in the early 2010s to support the ASME Codes and Standards. As information technologies advance at an accelerated pace with the artificial intelligence era on the horizon, the ASME Materials Properties Database must be further modernized from a database to a knowledgebase to ride the wave of digital information revolution and effectively support the ASME Codes and Standards in the new era.This paper is intended to provide an overview of the ASME Materials Properties Database and discuss a roadmap for its future development to facilitate understanding of and participation from different sectors of the Codes and Standards community. It first reviews the basic concepts of data, information, knowledge, database, and database system; as well as the pros and cons in different types of data management, and then discusses the path forward for a desired evolution of the database into a self-explanatory and machine-readable knowledgebase that is consistent with human cognitive processes for the Codes and Standards development and furthermore provides resources for data processing and analysis to reach an eventual goal of streamlining the Codes and Standards development from the initial inquiry, throughout data submission, analysis, …, to Codes and Standards rule establishment for final publication.

Ren, Weiju↗

DOE OSTI2024

Development of Whole System Digital Twins for Advanced Reactors: Leveraging Graph Neural Networks and SAM Simulations

Here, in this work, we introduce a novel method to develop whole system digital twins (DTs) for advanced nuclear reactors. This method treats a complex reactor system as a heterogeneous graph: with the system components as different types of graph nodes and their physical interconnections as edges. Based on the heterogeneous graph, a graph neural network combining graph convolution and temporal node attention is developed as the DT, facilitating a comprehensive understanding of the system's dynamic behavior. By utilizing the System Analysis Module (SAM) code for simulating various operational transients, we develop a graph-based database that trains the DT. This DT is characterized by two primary functions: It can infer the entire system's status using sparse node information, and it can predict the progress of transients based on current and historical system information. Our approach is validated through case studies on the Experimental Breeder Reactor II (EBR-II) system and a generic Fluoride-salt-cooled High-temperature Reactor (gFHR), demonstrating the DT's accuracy in forecasting operational transients. The DT's rapid computation capabilities enhance its potential for supporting advanced reactor operations, offering benefits in intelligent simulation, autonomous control, and anomaly detection, paving the way for improved safety analysis and intelligent component health management for advanced reactor systems and reducing their operations and maintenance cost.

EBR-II↗

DOE OSTI2017

Economic Assessment of Nuclear Hybrid Energy Systems: Optimization using RAVEN

The energy market supply is under pressure to achieve competing goals, such as minimizing the cost of electricity and greenhouse gas emissions while achieving grid resilience and reliability and meeting regulatory requirements. To study different scenarios for possible evolutions of the energy market that assume a certain renewable penetration and the possible introduction of hybrid nuclear reactors, the HYBRID modeling and simulation project has been initiated by INL. The term hybrid nuclear reactor here refers to nuclear power plants that not only produce electricity, but can also sell heat to an industrial process, like a hydrogen generation or water desalination plant. The RAVEN (Risk Analysis Virtual Environment) code developed at INL together with the modeling language Modelica (the Dymola compiler is used) have been selected as the main modeling tools for the HYBRID modeling and simulation project. This summary outlines the challenge, presents an overview of the developments in the RAVEN code needed to solve it and shows an illustrative example calculation. The HYBRID modeling and simulation project is a multi laboratory effort, involving research teams from three different U.S. national laboratories, led by the Idaho National Laboratory (INL) and supported by the Argonne National Laboratory (ANL) and the Oak Ridge National Laboratory (ORNL)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2019

Preliminary Energy Costs and Savings Estimates: 2018 IECC Residential Requirements

This report provides preliminary estimates of the incremental costs and savings associated with the residential provisions of the 2018 International Energy Conservation Code (IECC). The analysis is provided to the U.S. Department of Energy (DOE) to help quantify the costs and savings impacts of the latest published edition of the IECC, the 2018 IECC. The incremental cost of building to the 2018 IECC, relative to the 2015 IECC, ranges from $\$398$ to $\$1,071$ depending on the climate zone, and payback periods range from 0 (immediate) to 1.8 years, depending on the climate zone.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2015

Impact of Dutch nuclear fuel cycle scenarios on radionuclide inventory intended for disposal - 15201

One of the main subjects of Dutch five-year research program into geological disposal of radioactive waste, OPERA, is the post-closure radiological safety assessment. Reliable estimates of the radionuclide inventory and matrix composition are an important input for the safety assessment. The amounts and categories of waste foreseen to be disposed in 2130 the Netherlands have been compiled by the Dutch waste management organisation COVRA. Additionally, NRG has made a characterisation of the waste (radionuclides and matrix). This reference inventory is based on the Dutch base nuclear energy scenario of operating the Dutch single reactor, the Borssele NPP, until its presently scheduled shut-down in 2033. However, changes in the presently adopted nuclear fuel cycle strategy in the Netherlands may impact both the quantities of generated radioactive waste and its composition, and therefore the source term of the radiological safety assessment. To get a grip on this uncertainty a set of alternative future fuel cycle scenarios in the Netherlands, which are in compliance with scenarios formulated in the Dutch vision documents, has been considered and evaluated. The scenarios have been analysed with the computer code DANESS, 'Dynamic Analysis of Nuclear Energy System Strategies'. The result of the DANESS analyses concerns the amount and type of the radioactive waste to be finally disposed in a deep geological repository. This also includes the inventories of the individual radionuclides that are relevant for the post-closure safety assessment to be performed in a subsequent stage of the OPERA program. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2025

Market Driven Residential Energy Codes: Comparing Performance in a Changing Technological Environment

The research project is undertaken to better understand the changing relationship between the two basic methods of building energy code compliance – prescriptive and performance – and how those methods relate to each other with respect to advancements in building energy computer simulation standards and capabilities. The International Energy Efficiency Code (IECC) is a model code adopted by many jurisdictions across the United States. Historically, the prescriptive compliance methodology has been preferred in most jurisdictions. The prescriptive methodology requires meeting or exceeding specific efficiency minimums for each envelope component. This tends to be a simple method to teach and verify. A more involved prescriptive alternative called the Total UA alternative is sometimes used. This method requires some multiplication, summing, and comparison to compute, so it is done with a fairly simple computer program. However, advances in computer and building energy simulation technology have resulted in increased use of more detailed performance compliance methods. The performance compliance method establishes the annual energy cost threshold via hourly simulation models. The compliance threshold is determined with a comparison building model simulation with geometry similar to the proposed home and with energy feature parameters and efficiencies as specified in the IECC. This project examines relationships between the two methods of building energy code compliance, including: • Overall annual energy use based on utility bill analysis by compliance method • Code official work processes with respect to compliance methods • Gaps and issues associated with building code compliance methods • Simulated energy use difference between compliance methods • Code compliance cost as a function of compliance method • Code compliance labeling effectiveness for high performance residences • Getting to net zero energy use and net zero greenhouse gas emissions through high performance code alternatives • Electronic code permitting and compliance alternatives

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

KENO V.a Primer: Performing Calculations using SCALE’s Criticality Safety Analysis Sequence (CSAS5) with Fulcrum

The SCALE code system developed at Oak Ridge National Laboratory is widely used and accepted around the world for criticality safety analyses. The well-known KENO V.a three-dimensional Monte Carlo criticality computer code is one of the primary criticality safety analysis tools in SCALE. The KENO V.a primer is designed to help a new user understand and use the SCALE/KENO V.a Monte Carlo code for nuclear criticality safety analyses. It assumes that the user has a college education in a technical field. There is no assumption of familiarity with Monte Carlo codes in general or with SCALE/KENO V.a in particular. The primer is designed to teach by example, with each example illustrating two or three features of SCALE/KENO V.a that are useful in criticality analyses. The primer is based on SCALE 6.2 and 6.3, which includes the Fulcrum graphical user interface (GUI). Each example uses Fulcrum to provide the framework for preparing input data and viewing output results. Starting with a Quickstart section, the primer gives an overview of the basic requirements for SCALE/KENO V.a input and allows the user to quickly run a simple criticality problem with SCALE/KENO V.a. The sections that follow Quickstart include a list of basic objectives at the beginning that identifies the goal of the section and the individual SCALE/KENO V.a features that are covered in detail in the sample problems in that section. Upon completion of the primer, a new user should be comfortable using Fulcrum to set up criticality problems in SCALE/KENO V.a. The primer provides a starting point for the criticality safety analyst who uses SCALE/KENO V.a. Complete descriptions are provided in the SCALE/KENO V.a manual. Although the primer is self-contained, it is intended as a companion volume to the SCALE/KENO V.a training and documentation. The SCALE manual and training schedule are available at https://scale.ornl.gov. The primer provides specific examples of using SCALE/KENO V.a for criticality analyses; the SCALE/KENO V.a manual provides information on the use of SCALE/KENO V.a and all its modules. The primer also contains an appendix with sample input files. In addition, this primer, its errata and sample inputs are also available at https://code.ornl.gov/scale/primers/kenova.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2020

Application of GOTHIC to Groundwater Transport Analysis - 20152

Migration of pollutants and hazardous wastes, potentially containing radioactive isotopes, via groundwater transport is a concern at most waste cleanup sites. Predictive analysis can be used to evaluate mitigating actions intended to minimize impact on the environment and public exposure. GOTHIC is a multipurpose thermal hydraulics code that is used extensively in the nuclear industry for design, licensing and operation evaluations. It combines the capabilities of typical one-dimensional system codes and the essential features of Computational Fluid Dynamics (CFD) codes for three-dimensional analysis. There are other codes that are specifically developed for groundwater transport analysis and the results presented here are consistent with prior analyses. However, GOTHIC has some unique features that offer advantages for applications related to nuclear waste. Most importantly, it has been developed and maintained under a Quality Assurance program in compliance with the requirements of 10CFR50 Appendix B [2] and applicable portions of ASME NQA-1 [3] since 1995. Available GOTHIC capabilities that make the code especially useful for groundwater transport of nuclear materials include: - Tracking of any number of tracer elements for contaminants and other species of interest; - Radioactive decay and progeny of tracer elements; - Adsorption/desorption of tracer elements; - Tracking of any number of dissolved gases; - Release and absorption for dissolved gases; - Vapor phase tracking; - Non-Newtonian fluid modeling. The general porous body modeling approach makes GOTHIC well suited to groundwater transport analysis. The multi-region modeling approach used by GOTHIC simplifies model construction for regions of varying hydrologic characteristics and focuses the computational effort on regions of particular interest while simultaneously capturing the macroscopic response and any feedback effects across the larger domain. The applicability of GOTHIC to groundwater transport applications is demonstrated by comparing code results with available analytic or semi-analytic solutions for groundwater behavior. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2013

SCALE Code Validation for Prismatic High-Temperature Gas-Cooled Reactors

Using experimental data published in the International Handbook of Evaluated Reactor Physics Benchmark Experiments for the fresh cold core of the High Temperature Engineering Test Reactor, a comprehensive validation study has been carried out to assess the performance of the SCALE code system for analysis of high-temperature gas-cooled reactor configurations. This paper describes part of the results of that effort. The studies performed included criticality evaluations for the full core and for the annular cores realized during the fuel loading, as well as calculations and comparisons for excess reactivity, shutdown margin, control rod worths, temperature coefficient of reactivity, and reaction rate distributions. Comparisons of the SCALE results with both experimental values and MCNP-calculated values are presented. The comparisons show that the SCALE calculated results, obtained with both multigroup and continuous energy cross sections, are in reasonable agreement with the experimental data and the MCNP predictions.

code validation↗

DOE OSTI2016

Towards a Consolidated Approach for the Assessment of Evaluation Models of Nuclear Power Reactors

The STARS project at the Paul Scherrer Institut (PSI) has adopted the TRACE thermal-hydraulic (T-H) code for best-estimate system transient simulations of the Swiss Light Water Reactors (LWRs). For analyses involving interactions between system and core, a coupling of TRACE with the SIMULATE-3K (S3K) LWR core simulator has also been developed. In this configuration, the TRACE code and associated nuclear power reactor simulation models play a central role to achieve a comprehensive safety analysis capability. Thus, efforts have now been undertaken to consolidate the validation strategy by implementing a more rigorous and structured assessment approach for TRACE applications involving either only system T-H evaluations or requiring interfaces to e.g. detailed core or fuel behavior models. The first part of this paper presents the preliminary concepts of this validation strategy. The principle is to systematically track the evolution of a given set of predicted physical Quantities of Interest (QoIs) over a multidimensional parametric space where each of the dimensions represent the evolution of specific analysis aspects, including e.g. code version, transient specific simulation methodology and model "nodalisation". If properly set up, such environment should provide code developers and code users with persistent (less affected by user effect) and quantified information (sensitivity of QoIs) on the applicability of a simulation scheme (codes, input models, methodology) for steady state and transient analysis of full LWR systems. Through this, for each given transient/accident, critical paths of the validation process can be identified that could then translate into defining reference schemes to be applied for downstream predictive simulations. In order to illustrate this approach, the second part of this paper presents a first application of this validation strategy to an inadvertent blowdown event that occurred in a Swiss BWR/6. The transient was initiated by the spurious actuation of the Automatic Depressurization System (ADS). The validation approach progresses through a number of dimensions here: First, the same BWR system simulation model is assessed for different versions of the TRACE code, up to the most recent one. The second dimension is the "nodalisation" dimension, where changes to the input model are assessed. The third dimension is the "methodology" dimension. In this case imposed power and an updated TRACE core model are investigated. For each step in each validation dimension, a common set of QoIs are investigated. For the steady-state results, these include fuel temperatures distributions. For the transient part of the present study, the evaluated QoIs include the system pressure evolution and water carry-over into the steam line.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

Uncertainty quantification and sensitivity analysis applications to fuel performance modeling

Best-estimate fuel performance codes such as BISON currently under development at the Idaho National Laboratory, utilize empirical and mechanistic lower-length-scale informed correlations to predict fuel behavior under normal operating and accident reactor conditions. Traditionally, best-estimate results are presented using the correlations with no quantification of the uncertainty in the output metrics of interest. However, there are associated uncertainties in the input parameters and correlations used to determine the behavior of the fuel and cladding under irradiation. Therefore, it is important to perform uncertainty quantification and include confidence bounds on the output metrics that take into account the uncertainties in the inputs. In addition, sensitivity analyses can be performed to determine which input parameters have the greatest influence on the outputs. In this paper we couple the BISON fuel performance code to the DAKOTA uncertainty analysis software to analyze a representative fuel performance problem. The case studied in this paper is based upon rod 1 from the IFA-432 integral experiment performed at the Halden Reactor in Norway. The rodlet is representative of a BWR fuel rod. The input parameters uncertainties are broken into three separate categories including boundary condition uncertainties (e.g., power, coolant flow rate), manufacturing uncertainties (e.g., pellet diameter, cladding thickness), and model uncertainties (e.g., fuel thermal conductivity, fuel swelling). Utilizing DAKOTA, a variety of statistical analysis techniques are applied to quantify the uncertainty and sensitivity of the output metrics of interest. Specifically, we demonstrate the use of sampling methods, polynomial chaos expansions, surrogate models, and variance-based decomposition. The output metrics investigated in this study are the fuel centerline temperature, cladding surface temperature, fission gas released, and fuel rod diameter. The results highlighted the importance of the thermal conductivity of the fuel, the thermal conductivity of the cladding, the gap thickness, the fuel thermal expansion, and the system power factor as influential parameters.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Uncertainty analysis for VERA problem 2 using the cell-code Condor v2.8.05

Condor is a cell-level neutronic calculation code that applies multi-group collision probabilities with heterogeneous response coupling method within generic geometry configurations. Under the Condor's code continuous development, the incorporation of up-to-date methodologies and state-of-the-art practices in reactor analysis represents a driving force. In this work, the capabilities of Condor v2.8.05 to develop an uncertainty analysis for realistic PWR-kind fuel assemblies are studied. The Total Monte Carlo approach is applied to quantify the impact of fabrication tolerances in the code's results for reactivity and power distributions, by means of randomly sampled input values using the VERA problem 2 as basis. The VERA problem 2 proposes a series of Westinghouse 2D 17 x 17-type fuel lattices, to be calculated reflected at beginning-of-life without Xe. The configurations correspond to a modern PWR. Selected neutronic parameters from Condor runs are thus analyzed in terms of the observed spread as well as the obtained distributions for the randomly perturbed cases, showing the capability of the code to handle the required input data, as well as its ability to provide valuable insights regarding uncertainty quantification.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2020

KENO-VI Primer: Performing Calculations using SCALE’s Criticality Safety Analysis Sequence (CSAS6) with Fulcrum

The SCALE code system developed at Oak Ridge National Laboratory is widely used and accepted around the world for criticality safety analysis. The well-known KENO-VI three-dimensional Monte Carlo criticality computer code is one of the primary criticality safety analysis tools in SCALE. The KENO-VI primer is designed to help a new user understand and use the SCALE/KENO-VI Monte Carlo code for nuclear criticality safety analysis. It assumes that the user has a college education in a technical field. There is no assumption of familiarity with Monte Carlo codes in general or with SCALE/KENO-VI in particular. The primer is designed to teach by example, with each example illustrating two or three features of SCALE/KENO-VI that are useful in criticality analysis. The primer is based on SCALE 6.2 and 6.3, which includes the Fulcrum graphical user interface. Each example uses Fulcrum to provide the framework for preparing input data and viewing output results. Starting with a Quickstart section, the primer gives an overview of the basic requirements for SCALE/KENO-VI input and allows the user to quickly run a simple criticality problem with SCALE/KENO-VI. Each following section begins with a list of basic objectives identifying the goal of the section and the individual SCALE/KENO-VI features covered in detail in the section’s sample problems. Upon completion of the primer, a new user should be comfortable using Fulcrum to set up criticality problems in SCALE/KENO-VI. The primer provides a starting point for the criticality safety analyst who uses SCALE/KENO-VI. Complete descriptions are provided in the SCALE/KENO-VI manual. Although the primer is self-contained, it is intended as a companion volume to the SCALE/KENO-VI training and documentation. The SCALE manual and training schedule are available at https://scale.ornl.gov. The primer provides specific examples of using SCALE/KENO-VI for criticality analysis; the SCALE/KENO-VI manual provides information on the use of SCALE/KENO-VI and all its modules. The primer also contains an appendix with sample input files. In addition, this primer, its errata, and sample inputs are also available at https://code.ornl.gov/scale/primers/kenovi/.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2013

Nonlinear excitation of low-n harmonics in reduced magnetohydrodynamic simulations of edge-localized modes

Nonlinear simulations of the early edge-localized mode (ELM) phase based on a typical type-I ELMy ASDEX Upgrade discharge have been carried out using the reduced MHD code JOREK. The analysis is focused on the evolution of the toroidal Fourier spectrum. It is found that during the nonlinear evolution, linearly subdominant low-n Fourier components, in particular the n = 1, grow to energies comparable with linearly dominant harmonics. A simple model is developed, based on the idea that energy is transferred among the toroidal harmonics via second order nonlinear interaction. The simple model reproduces and explains very well the early nonlinear evolution of the toroidal spectrum in the JOREK simulations. Furthermore, it is shown for the n = 1 harmonic, that its spatial structure changes significantly during the transition from linear to nonlinearly driven growth. The rigidly growing structure of the linearly barely unstable n = 1 reaches far into the plasma core. In contrast, the nonlinearly driven n= 1 has a rigidly growing structure localized at the plasma edge, where the dominant toroidal harmonics driving the n = 1 are maximal and in phase. The presented quadratic coupling model might explain the recent experimental observation of strong low-n components in magnetic measurements [Wenninger et al., “Non-linear magnetic perturbations during edge localized modes in TCV dominated by low n mode components,” Nucl. Fusion (submitted)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗