Development of Three-Dimensional Neoclassical Transport Simulation Code with High Performace Fortran on a Vector-Parallel Computer

A neoclassical transport simulation code (FORTEC-3D) applicable to threedimensional configurations has been developed using High Performance Fortran (HPF). Adoption of computing techniques for parallelization and a hybrid simulation model to the delta f Monte-Carlo method transport simulation, including non-local transport effects in three-dimensional configurations, makes it possible to simulate the dynamism of global, non-local transport phenomena with a self-consistent radial electric field within a reasonable computation time. In this paper, development of the transport code using HPF is reported. Optimization techniques in order to achieve both high vectorization and parallelization efficiency, adoption of a parallel random number generator, and also benchmark results, are shown

ASCOT: solving the kinetic equation of minority particle species in tokamak plasmas

A comprehensive description of methods, suitable for solving the kinetic equation for fast ions and impurity species in tokamak plasmas using Monte Carlo approach, is presented. The described methods include Hamiltonian orbit-following in particle and guiding center phase space, test particle or guiding center solution of the kinetic equation applying stochastic differential equations in the presence of Coulomb collisions, neoclassical tearing modes and Alfv\'en eigenmodes as electromagnetic perturbations relevant to fast ions, together with plasma flow and atomic reactions relevant to impurity studies. Applying the methods, a complete reimplementation of the well-established minority species code ASCOT is carried out as a response both to the increase in computing power during the last twenty years and to the weakly structured growth of the code, which has made implementation of additional models impractical. Also, a benchmark between the previous code and the reimplementation is accomplished, showing good agreement between the codes.Comment: 13 pages, 9 figures, submitted to Computer Physics Communication

토카막 통합 시뮬레이션 코드의 개발과 여러 장치에 대한 적용 연구

학위논문(박사) -- 서울대학교대학원 : 공과대학 에너지시스템공학부, 2022. 8. 나용수.The in-depth design and implementation of a newly developed integrated suite of codes, TRIASSIC (tokamak reactor integrated automated suite for simulation and computation), are reported. The suite comprises existing plasma simulation codes, including equilibrium solvers, 1.5D and 2D plasma transport solvers, neoclassical and anomalous transport models, current drive and heating (cooling) models, and 2D grid generators. The components in TRIASSIC could be fully modularized, by adopting a generic data structure as its internal data. Due to a unique interfacing method that does not depend on the generic data itself, legacy codes that are no longer maintained by the original author were easily interfaced. The graphical user interface and the parallel computing of the framework and its components are also addressed. The verification of TRIASSIC in terms of equilibrium, transport, and heating is also shown. Following the data model and definition of the data structure, a declarative programming method was adopted in the core part of the framework. The method was used to keep the internal data consistency of the data by enforcing the reciprocal relations between the data nodes, contributing to extra flexibility and explicitness of the simulations. TRIASSIC was applied on various devices including KSTAR, VEST, and KDEMO, owing to its flexibility in composing a workflow. TRIASSIC was validated against KSTAR plasmas in terms of interpretive and predictive modelings. The prediction and validation on the VEST device using TRIASSIC are also shown. For the applications to the upcoming KDEMO device, the machine design parameters were optimized, targeting an economical fusion demonstration reactor.본 연구에서는 TRIASSIC (tokamak reactor integrated automated suite for simulation and computation) 코드의 자세한 디자인과 실행 결과에 대해 소개합니다. 이 시뮬레이션 코드는 기존에 존재하던 플라즈마 평형, 1.5차원 및 2차원 플라즈마 수송, 신고전 및 난류 수송 모델, 전류 구동 및 가열 (냉각) 모델, 그리고 2차원 격자 생성기 등의 코드를 구성하여 만들어졌습니다. 프레임워크 내 데이터 구조로써 일반 데이터 구조를 채택함으로써 TRIASSIC의 코드 구성요소들은 완전한 모듈화 방식으로 결합될 수 있었습니다. 일반 데이터 구조에 의존하지 않는 독특한 코드 결합 방식으로 인해, 더 이상 유지보수되지 않는 레거시 코드들 또한 쉽게 결합될 수 있었습니다. 본 코드의 그래피컬 유저 인터페이스, 프레임워크와 코드 구성 요소들의 병렬 컴퓨팅에 관한 내용도 다뤄집니다. 평형, 수송, 그리고 가열 측면에서의 TRIASSIC 시뮬레이션의 검증 내용도 소개됩니다. 시뮬레이션 프레임워크 내 일반 데이터 구조의 데이터 모델과 데이터 정의를 만족시키기 위해, 데이터를 관리하는 프레임워크의 중심부에는 선언적 프로그래밍이 도입되었습니다. 선언적 프로그래밍을 통해 일반 데이터의 데이터 노드 간 관계식을 만족시킴으로써 데이터 간 내부 일관성을 확보하고, 코드의 유연성과 명시성을 추가적으로 확보할 수 있었습니다. TRIASSIC은 해석적, 예측적 모델링 측면에서 KSTAR 플라즈마를 대상으로 검증되었습니다. VEST 장치를 대상으로 한 예측 및 이에 대한 검증 내용 또한 서술됩니다. 경제적인 핵융합 실증로 건설을 목표로 KDEMO 장치에 대한 적용 및 장치 설계 최적화 연구도 소개됩니다.Abstract １ Table of Contents ２ List of Figures ４ List of Tables １０ Chapter 1. Introduction １１ 1.1. Background １１ 1.1.1. Fusion Reactor and Modeling １１ 1.1.2. Interpretive Analysis and Predictive Modeling １７ 1.1.3. Modular Approach ２１ 1.1.4. The Standard Data Structure ２４ 1.1.5. The Internal Data Consistency in a Generic Data ２８ 1.1.6. Integration of Physics Codes into IDS ２９ 1.2. Overview of the Research ３１ Chapter 2. Development of Integrated Suite of Codes ３３ 2.1. Development of TRIASSIC ３３ 2.1.1. Design Requirements ３３ 2.1.2. Overview of TRIASSIC ３５ 2.1.3. Comparison of Integrated Simulation Codes ４０ 2.2. Components in the Framework ４３ 2.2.1. Physics Codes Interfaced with the Framework ４３ 2.2.2. Physics Code Interfacings ４６ 2.2.3. Graphical User Interface ５２ 2.2.4. Jobs Scheduler and MPI ５５ 2.3. Verifications ５７ 2.3.1. The Coordinate Conventions ５７ 2.3.2. Coupling of Equilibrium-Transport ５９ 2.3.3. Neoclassical Transport and Bootstrap Current ６３ 2.3.4. Heating and Current Drive ６５ Chapter 3. Improvements in Keeping the Internal Data Consistency ６８ 3.1. Background ６８ 3.2. Possible Implementations of a Component ７１ 3.3. A Method Adopted in the Framework ７３ 3.3.1. Prerequisites and Relation Definitions ７３ 3.3.2. Adding Relations in the Framework ７８ 3.3.3. Applying Relations ８０ 3.4. Performance and Flexibility of the Framework ８３ 3.4.1. Performance Enhancement ８３ 3.4.2. Flexibility and Maintenance of the Framework ８５ Chapter 4. Applications to Various Devices ９１ 4.1. Applications to KSTAR ９１ 4.1.1. Kinetic equilibrium workflow and its validation ９１ 4.1.2. Stationary-state predictive modeling workflow ９５ 4.2. Application to VEST １０２ 4.2.1. Time-dependent predictive modeling workflow １０３ 4.3. Application to KDEMO １０６ 4.3.1. Predictive simulation workflow for optimization １０６ Chapter 5. Summary and Conclusion １１２ 5.1. Summary and Conclusion １１２ Appendix １１６ A. Code Snippet of the Relation Definition １１６ Bibliography １１８ Abstract in Korean １２６박

1997 international Sherwood fusion theory conference

Papers presented during the conference are indexed separately

CENTORI: a global toroidal electromagnetic two-fluid plasma turbulence code

A new global two-fluid electromagnetic turbulence code, CENTORI, has been developed for the purpose of studying magnetically-confined fusion plasmas on energy confinement timescales. This code is used to evolve the combined system of electron and ion fluid equations and Maxwell equations in toroidal configurations with axisymmetric equilibria. Uniquely, the equilibrium is co-evolved with the turbulence, and is thus modified by it. CENTORI is applicable to tokamaks of arbitrary aspect ratio and high plasma beta. A predictor-corrector, semi-implicit finite difference scheme is used to compute the time evolution of fluid quantities and fields. Vector operations and the evaluation of flux surface averages are speeded up by choosing the Jacobian of the transformation from laboratory to plasma coordinates to be a function of the equilibrium poloidal magnetic flux. A subroutine, GRASS, is used to co-evolve the plasma equilibrium by computing the steady-state solutions of a diffusion equation with a pseudo-time derivative. The code is written in Fortran 95 and is efficiently parallelized using Message Passing Interface (MPI). Illustrative examples of output from simulations of a tearing mode in a large aspect ratio tokamak plasma and of turbulence in an elongated conventional aspect ratio tokamak plasma are provided.Comment: 9 figure

Purdue Contribution of Fusion Simulation Program

The overall science goal of the FSP is to develop predictive simulation capability for magnetically confined fusion plasmas at an unprecedented level of integration and fidelity. This will directly support and enable effective U.S. participation in research related to the International Thermonuclear Experimental Reactor (ITER) and the overall mission of delivering practical fusion energy. The FSP will address a rich set of scientific issues together with experimental programs, producing validated integrated physics results. This is very well aligned with the mission of the ITER Organization to coordinate with its members the integrated modeling and control of fusion plasmas, including benchmarking and validation activities. [1]. Initial FSP research will focus on two critical areas: 1) the plasma edge and 2) whole device modeling including disruption avoidance. The first of these problems involves the narrow plasma boundary layer and its complex interactions with the plasma core and the surrounding material wall. The second requires development of a computationally tractable, but comprehensive model that describes all equilibrium and dynamic processes at a sufficient level of detail to provide useful prediction of the temporal evolution of fusion plasma experiments. The initial driver for the whole device model (WDM) will be prediction and avoidance of discharge-terminating disruptions, especially at high performance, which are a critical impediment to successful operation of machines like ITER. If disruptions prove unable to be avoided, their associated dynamics and effects will be addressed in the next phase of the FSP. The FSP plan targets the needed modeling capabilities by developing Integrated Science Applications (ISAs) specific to their needs. The Pedestal-Boundary model will include boundary magnetic topology, cross-field transport of multi-species plasmas, parallel plasma transport, neutral transport, atomic physics and interactions with the plasma wall. It will address the origins and structure of the plasma electric field, rotation, the L-H transition, and the wide variety of pedestal relaxation mechanisms. The Whole Device Model will predict the entire discharge evolution given external actuators (i.e., magnets, power supplies, heating, current drive and fueling systems) and control strategies. Based on components operating over a range of physics fidelity, the WDM will model the plasma equilibrium, plasma sources, profile evolution, linear stability and nonlinear evolution toward a disruption (but not the full disruption dynamics). The plan assumes that, as the FSP matures and demonstrates success, the program will evolve and grow, enabling additional science problems to be addressed. The next set of integration opportunities could include: 1) Simulation of disruption dynamics and their effects; 2) Prediction of core profile including 3D effects, mesoscale dynamics and integration with the edge plasma; 3) Computation of non-thermal particle distributions, self-consistent with fusion, radio frequency (RF) and neutral beam injection (NBI) sources, magnetohydrodynamics (MHD) and short-wavelength turbulence

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.Peer ReviewedPostprint (published version

Optimising a fluid plasma turbulence simulation on modern high performance computers

Nuclear fusion offers the potential of almost limitless energy from sea water and lithium without the dangers of carbon emissions or long term radioactive waste. At the forefront of fusion technology are the tokamaks, toroidal magnetic confinement devices that contain miniature stars on Earth. Nuclei can only fuse by overcoming the strong electrostatic forces between them which requires high temperatures and pressures. The temperatures in a tokamak are so great that the Deuterium-Tritium fusion fuel forms a plasma which must be kept hot and under pressure to maintain the fusion reaction. Turbulence in the plasma causes disruption by transporting mass and energy away from this core, reducing the efficiency of the reaction. Understanding and controlling the mechanisms of plasma turbulence is key to building a fusion reactor capable of producing sustained output. The extreme temperatures make detailed empirical observations difficult to acquire, so numerical simulations are used as an additional method of investigation. One numerical model used to study turbulence and diffusion is CENTORI, a direct two-fluid magneto-hydrodynamic simulation of a tokamak plasma developed by the Culham Centre for Fusion Energy (CCFE formerly UKAEA:Fusion). It simulates the entire tokamak plasma with realistic geometry, evolving bulk plasma quantities like pressure, density and temperature through millions of timesteps. This requires CENTORI to run in parallel on a Massively Parallel Processing (MPP) supercomputer to produce results in an acceptable time. Any improvements in CENTORI’s performance increases the rate and/or total number of results that can be obtained from access to supercomputer resources. This thesis presents the substantial effort to optimise CENTORI on the current generation of academic supercomputers. It investigates and reviews the properties of contemporary computer architectures then proposes, implements and executes a benchmark suite of CENTORI’s fundamental kernels. The suite is used to compare the performance of three competing memory layouts of the primary vector data structure using a selection of compilers on a variety of computer architectures. The results show there is no optimal memory layout on all platforms so a flexible optimisation strategy was adopted to pursue “portable” optimisation i.e optimisations that can easily be added, adapted or removed from future platforms depending on their performance. This required designing an interface to functions and datatypes that separate CENTORI’s fundamental algorithms from repetitive, low-level implementation details. This approach offered multiple benefits including: the clearer representation of CENTORI’s core equations as mathematical expressions in Fortran source code allows rapid prototyping and development of new features; the reduction in the total data volume by a factor of three reduces the amount of data transferred over the memory bus to almost a third; and the reduction in the number of intense floating point kernels reduces the effort of optimising the application on new platforms. The project proceeds to rewrite CENTORI using the new Application Programming Interface (API) and evaluates two optimised implementations. The first is a traditional library implementation that uses hand optimised subroutines to implement the library functions. The second uses a dynamic optimisation engine to perform automatic stripmining to improve the performance of the memory hierarchy. The automatic stripmining implementation uses lazy evaluation to delay calculations until absolutely necessary, allowing it to identify temporary data structures and minimise them for optimal cache use. This novel technique is combined with highly optimised implementations of the kernel operations and optimised parallel communication routines to produce a significant improvement in CENTORI’s performance. The maximum measured speed up of the optimised versions over the original code was 3.4 times on 128 processors on HPCx, 2.8 times on 1024 processors on HECToR and 2.3 times on 256 processors on HPC-FF

Inference of Experimental Radial Impurity Transport on Alcator C-Mod: Bayesian Parameter Estimation and Model Selection

We present a fully Bayesian approach for the inference of radial profiles of impurity transport coefficients and compare its results to neoclassical, gyrofluid and gyrokinetic modeling. Using nested sampling, the Bayesian Impurity Transport InferencE (BITE) framework can handle complex parameter spaces with multiple possible solutions, offering great advantages in interpretative power and reliability with respect to previously demonstrated methods. BITE employs a forward model based on the pySTRAHL package, built on the success of the well-known STRAHL code [Dux, IPP Report, 2004], to simulate impurity transport in magnetically-confined plasmas. In this paper, we focus on calcium (Ca, Z=20) Laser Blow-Off injections into Alcator C-Mod plasmas. Multiple Ca atomic lines are diagnosed via high-resolution X-ray Imaging Crystal Spectroscopy and Vacuum Ultra-Violet measurements. We analyze a sawtoothing I-mode discharge for which neoclassical and turbulent (quasilinear and nonlinear) predictions are also obtained. We find good agreement in diffusion across the entire radial extent, while turbulent convection and density profile peaking are estimated to be larger in experiment than suggested by theory. Efforts and challenges associated with the inference of experimental pedestal impurity transport are discussed.Comment: 38 pages, 19 figures, submitted for publication in Nuclear Fusio