THE WAY TOWARDS THERMONUCLEAR FUSION SIMULATORS

1. THE WAY TOWARDS THERMONUCLEAR FUSION SIMULATORS Presented by Alain Bécoulet Acknowledgements to G. Giruzzi, D. Campbell and L.G. Eriksson TF Leader & Deputies: A. Bécoulet, P. Strand and M. Romanelli EFDA CSU Contact Person: K. Thomsen

2. OUTLINE • ITER: a brief introduction • The major physics issues of magnetic fusion modelling • Towards Magnetic Fusion Simulators • Conclusion

3. ITER is a major international collaboration infusion energy researchinvolving the EU (plus Switzerland, Romania, Bulgaria), China, India, Japan, the Russian Federation, South Korea and the United States • The overall programmatic objective: • to demonstrate the scientific and technological feasibility of fusion energy for peaceful purposes • The principal goal: • to design, construct and operate a tokamak experiment at a scale which satisfies this objective • ITER is designed to confinea DT plasma in which -particle heating dominatesall other forms of plasma heating: •  a burning plasma experiment Courtesy D. Campbell, EFDA

4. The ITER Site Cadarache(France) • On 28 June 2005, a Ministerial Agreement was reached between the project’s partners to build ITER at Cadarache in France: • “As a project of unprecedented complexity spanning more than a generation, ITER marks a major step forward in international science cooperation. This decision today demonstrates the recognition of the parties concerned that working together is the best way to find responses to the challenges faced by all of us” - J Potocnik, EU Commissioner for Research

5. ITER Design Parameters A detailed engineering design for ITER was delivered in July 2001

6. ITER Main Features

7. Plasma Fusion Performance • Temperature (Ti):1-2 108 °C (10-20 keV) • (~10  temperature of sun’s core) • Density (ni):1 1020 m-3 • (~10-6 of atmospheric particle density) • Energy confinement time (E):few seconds • (plasma pulse duration ~1000s)

8. A plasma discharge scenario 400 MW fusion 400 seconds Fusion Power Time(s) Plasma Current Inductive Flux D-T Fuelling Plasma Density a-particle Fraction Additional Power

9. An ITER Plasma ne Te 1019m-3 keV Ti 10nHe Zeff % fHe qY m2s-1 ce MA/m2 A Q=10 scenario with: Ip=15MA, Paux=40MW, H98(y,2)=1 Current Ramp-up Phase

10. Basic ingredients of a tokamak simulator • Geometry: magnetic equilibrium • at least 2-D (plasma shaping, separatrix) • self-consistent with current and pressure • Fluid equations (1-D) • time evolution of ne, ni,Te,Ti, j, V, impurities • Sources • heat, injected matter, current, momentum, wall • Losses • diffusion/convection of heat and particles • pumping / neutralisation • radiation (bremsstrahlung, synchrotron, line radiation) • viscosity • Limit conditions & Plasma-Structure interaction • Link to tokamak data bases

11. Input parameters Impurities, radiations Equilibrium solver Fusion power,a particle dynamics Sawteeth, ELMs, recon- nections Pellet /gas injection Transport coefficients LH wave propag. & absorp., el. distrib. func. Transport solver tt+Dt (1.5D) MHD stability ICRF wave propagation, resonating ion distrib. function Linear stability, gyrokinetics, NBI deposition & distrib. function Model of plasma for edge+SOL Simulation output ECRF wave propagation

12. Neutral transport Transport coefficients Input wave forms Plasma transport in edge/SOL (2D) Core confinement solver (1.5D) Plasma wall interaction Bulk Plasma transport controller Fusion power; alpha particle source Equilibrium solver Pilot; t  t+t; communication and repository of data Bulk plasma transport coeff MHD stability NBI deposition Fast ion transport coeff Solver of non-thermal ion distributions ICRF wave propagation Solver of non-thermal electron distribution Simulation output LH wave propagation Parallel computing ECRF wave propagation Dielectric tensor contributions Dielectric tensor contributions Possible structure of a tokamak simulator

13. Equilibrium: the internal plasma geometry ITER Equil. rev. shear • Solution of Grad-Shafranov equation- 2D PDE • Method of solution: Finite Elements (FEM)- Typically bi-cubic (third order) Hermite elements • Typical CPU requirement: 20 Gflop /t(/ t, indicates per time step, i.e. per equilibrium in this case). Fluxsurface

14. Core confinement: the diffusion equations • A set of coupled parabolic PDEs (typically >4) for flux surface averaged bulk plasma quantities (ni, ne, Ti, Te, V etc.), i.e. one independent coordinate, the flux surface label. • Method of solution: FEM, FD. Numerically difficult sincethe transport coefficients often depend strongly on the calculated quantities(the profiles of the plasma quantities tend to be such that the instabilities causing the transport are near marginal stability. • Typical CPU requirement: 15 Tflop / simulated second of discharge (based on GLF23)

15. The turbulent nature of transport MHD in Core Plasma, Plasma Disruption Turbulence in Peripheral Plasma MHD at plasma boundary Ion turbulence

16. Linear MHD: the overall plasma stability N=1 resistive kink mode near separatrix • Solution of linear Magnetohydrodynamic equations.- Two coupled PDEs for ideal incompressible model (8 for resistive MHD) • Method of solution: Finite Elements (FEM)- Typically bi-cubic (third order) Hermite elements • Typical CPU requirement: 30 Gflop / t and toroidal mode number (16 for resistive MHD). • Required toroidal mode numbers 1-3 for the core; 10-30 in steps of ~5 for the edge; i.e. ~8 in total Courtesy G. Huysmans

17. Non linear MHD: plasma performance & heat losses Edge Localized Modes : • non-linear evolution of ballooning modes • Full toroidal geometry • Full time evolution Courtesy G. Huysmans

18. Plasma transport in the plasma edge region • A set of coupled 2D PDEs for bulk plasma quantities. Coupled to Neutral particle transport code. • Method of solution: FEM/FD, Finite Volume. • Typical CPU requirement: 10-500 Tflop /t (includes coupling to Neutral particle transport code) . • The CPU requirement depends strongly on the model assumptions; the field is developing rapidly. ne after MARF event B2-Eirene code See S. Kuhn, I-29

19. Non-thermal ions • Fokker-Planck equation 5D+time (gyro-averaged), can be reduced to 3D+time by orbit averaging. Should take into account collisions, wave-particle interaction and finite orbit width effects. • Method of solution: Orbit following Monte Carlo, or FEM/FD and Monte Carlo for 3D equation. • Typical CPU requirement: 15 Tflop / simulated second (Monte Carlo, ~ 5000 MC particles and acceleration scheme). -part. orbits in ITER -part. driven curr. dens. M. Schneider,SPOT code.

20. Non-thermal electrons fe(r, p||, p), r/a  0.3 • Relativistic Fokker-Planck equation 3D (gyro and guiding centre orbit averaged). Should take into account collisions, wave-particle interaction, bootstrap current etc. • Method of solution: FD/FEM • Typical CPU requirement: 1 Tflop/t(succession of semi steady-states). p/pth p||/pth. Courtesy, Y. Peysson, DKE code

21. ICRF wave propagation • Maxwell’s equations, toroidal Fourier decomposition  three coupled 2D PDEs. Wave length comparable to machine size necessitates full wave solution. • Method of solution: FEM • Typical CPU requirement: 60 Gflop / t and toroidal mode number (to resolve fast wave, for mode converted Bernstein wave multiply by ~100). • Toroidal mode numbers needed ~ 40 Full wave solution, E+ z R LION code

22. Real Time Control of a Tokamak Discharge • Sustaining performant regimes (improved energy confinement) • Controlling (Avoiding) MHD instabilities Profile Control Actuators Plasma Heat Diffusion Current Diffusion Non linear coupling with various timescales:MHD stability, energy confinement, plasma current resistive diffusion, equilibrium with wall, …

23. Example of an ITER basic simulation • The most CPU intensive part of an ITER simulation will be the start-up phase (significant evolution of many parameter). The example below should be representative of this phase. • Assume that boundary conditions for the core transport can be found from a simplified model, i.e. no need for plasma wall interaction module. • Only core MHD is considered, i.e. only three mode numbers needed. • The reacting species (D and T) are assumed to have Maxwell distributions, and the only non-thermal species is alpha particles. • We assume that a general time step of t= 0.1 sec. will be sufficient.

24. A basic simulation of a minute of an ITER ohmic discharge will then require: • Equilibrium 60 10  20 ~ 1.2 Tflop • Linear MHD (non-resistive): 60 10  90 ~ 50 Tflop • Core confinement: 60  15 ~ 850 Gflop. • Non-thermal ions: 60  1500 ~ 85 Tflop. • In total: ~ 150 Tflop. • On a typical workstation of 1Gflops/s, this translates into about 1.7 day of CPU.

25. A basic simulation of a minute of an ITER heated discharge will then require: • Equilibrium 60 10  20 ~ 1.2 Tflop • Linear MHD (non-resistive): 60 10  90 ~ 50 Tflop • Core confinement: 60  15 ~ 850 Gflop. • Non-thermal ions: 60  1500 ~ 85 Tflop. • H&CD source terms: 60  10  20  60+1500 ~ 700 Tflop • In total: ~ 800 Tflop. • On a typical workstation of 1.0 Gflops/s, this translates into about 10 days of CPU. • Consequently, there is a great interest to utilize parallel computing for many of the sub-problems. NOT TO MENTION DATA STORAGE ISSUE

26. a long term scope: the fusion simulator SIMULATION Codes & physics quantities (Te, ne, …) EXPERIMENT PILOT Geometry & waveforms Experiment Instrumental Measurements (diagnostics) Interpretative simulation

27. A European Task Force EFDA(03)-21/4.9.2 (June 24th, 2003) Executive summary: The aim of the task force is to co-ordinate the development of a coherent set of validated simulation tools for the purpose of benchmarking on existing tokamak experiments, with the ultimate aim of providing a comprehensive simulation package for ITER plasmas. The remit of the Task Force would extend to the development of the necessary standardized software tools for interfacing code modules and for accessing experimental data. In the medium term, this task force’s work would support the development of ITER-relevant scenarios in current experiments, while in the long term it would aim to provide a validated set of European modelling tools forITER exploitation EFDA recently approved a three year extension to the TF

28. General structure of TF’s activities (2005-6 work programme) The initial ITM Project structure covers: - The Integrated Modelling Projects (IMPs), addressing modelling issues of fusion plasma physics which require a sufficiently high degree of integration. - The Code Platform Project (CPP), responsible for developing, maintaining and operating the code platform structure. Support to IMPs is included. - The Data Coordination Project (DCP), supporting IMPs and CPP for Verification and Validation aspects and standardisation of data interfaces and access.

29. 2005 2006 200X the 2005-2006 work programme schedule prototype platform platform release CPP V&V proc. data management univ. access layer DCP V&V support code identif. standardisation V&V, documentation extend linear MHD codes IMP#1 edge MHD, core MHD, disruptions IMP#2 edge transport, core transport, integrated discharge evolutions IMP#3 code catalogue IMP#4 Linear mstab, turbulence, neocl. transport IMP#5 H&CD, fast particle instab. and losses

30. Data Coordination Project (DCP) Objectives: • Provide tools for data access and exploration, • Develop and manage databases needed for physics exploration and validation activities. • Assessment and collection of experimental data for V&V • Definition of V&V and performance metrics Project Structure – 5 topical areas: • Data and database management • Universal data access layer (transparent access to data) • Validation and verification activities (with IMP’s) • Taskforce Software Strategies • Monitoring and evaluating emerging technologies: Grids

31. Data models and database management Short term storage system solution in place: • ~ 1Tb of storage available through MDS+ server hosted by ENEA a further 1Tb may be made available through other collaborations beginning 2006. • http://fusfis.frascati.ena.it/FusionCell • Physics project storage needs are estimated for 4Tb end of 2006; more than 15 Tb longer term Data structures: • Abstract description (XML schemas) of the data model for the Equilibrium reconstruction project (IMP#1) – prototyping the TF wide data model. • Automatic generation of data descriptions in client languages (fortran, matlab,...) • Provides unambiguous, standard description of data structures but hides complexity from end user • http://crppwww.epfl.ch/~lister/euitmschemas Database exploration tools - user access: Start up work defining needs for • Logbook browser – finding and characterizing TF database entries • Relational search capabilities and graphical/plotting engines

32. Data Access methods UAL API Switch/Mapper ??? HDF5 MDS+ Interim data access system: • Simple C library with fortran bindings. http://www.ipp.mpg.de/~Wolfgang.Suttrop/mdsplus/libitdb • Further prototyping (IMP#1 efforts): • Improved memory handling (G. Huysmans) • Tighter connectivity w datastructures (L. Appel) Universal Access layer: • “Device independent” access to data • Extensible through plug-in technology • MDS+, HDF5, … • Single interface to many data sources • Detailed specification being written • Needs further resources for implementation USER FILES ITM DBs ITPA DBs

33. Procedures, protocols and strategies Confidence in modelling results at the end user level can only be achieved through openness, accessibility, reproducibility and traceability throughout the V&V process. DCP coordinates • Experimental data access and validation • Definition of performance metrics • Development of the V&V procedures with the Integrated modelling projects DCP is starting to evaluate software usage and needs within the fusion community to Formulate “Taskforce Software Strategies” defining the • Use of commercial packages (Matlab, IDL,…) • Replacement strategies for commercial numerical libraries (NAG, IMSL,..) • Recommendations on code restructuring for increased portability, performance and compatibility. Several associations are entering into GRID technology related activities: A study to evaluate the opportunities for TF has been initiated and a strategy for TF participation is being formulated

34. Integrated Modelling Project 1 • Objective: • To provide an integrated suite of self-consistent codes (modules) for equilibrium reconstruction and linear MHD stability analysis • Topic 1A : Experimental Equilibrium reconstruction • CEDRES, CLISTE, EFIT, EQUINOX • Topic 1B : Equilibrium codes and linear MHD stability • Equilibrium : CAXE, CHEASE, DIVA, HELENA, VMEC, DINA • Mapping : COTRANS, JMC • MHD Stability : CAS3D, CASTOR, KINX, MISHKA, TERPSICHORE • Also: • Equilibrium toolbox : FLUSH

35. IMP#1: equilibrium and MHD Stability magnetics MSE code spec.parameters diagnostic(1)description machine description diagnostic(2)description MHD output description equilibrium description equilibrium description code spec.parameters code spec.parameters MHD stability • Standardise contributed codes to become independent of machine /diagnostic data. • Use only external geometry data (from database) • Definition of interfaces between codes and machine and diagnostics • Validation and Verification • compare equilibrium and MHD stability codes on benchmark case • Apply codes to a relevant experimental problem/data • MHD Stability limits in plasmas with an internal transport barrier. equilibrium reconstruction high resolution equilibrium

36. EFIT has been adapted to use the ITM structures and to use external geometry information A unique version of EFIT can now be used for ITER, Tore Supra, JET, etc Using only TF tools for Data storage, access and data structures Machine independent EFIT_ITM Validation effort underway

37. Code Platform Project • Requirements: version (December 2005) • End User • Tools to define the simulation • Tools to run & monitor the simulation • Tools for post-processing • Developer • Integrate the codes • Component based • Debug & test • Administrator • Deploy the simulator • Monitor it • Manage the archive • Additional constraints

38. CPP: Frameworks under consideration TF applications range from loosely coupled to very tightly coupled - No single tool likely to be sufficient. Need to explore different approaches for different applications

39. Integrated Modelling Projects 2 to 5 • IMP2: Non linear MHD phenomena • Initial work on RWMs, sawteeth and ELMs has started • IMP3: To provide the computational basis for a modular transport code, taking account of the core, the pedestal and the scrape-off layer. Ultimately, to enable the simulation of complete tokamak scenarios, e.g. for ITER. • A common interface to existing transport codes is underway • Edge code benchmarking • Fast particle effects in edge codes underway IMP4: To develop a suite of unified, validated codes to provide quantitative predictions for the linear properties of a range of instabilities, including: ion-temperature-gradient (ITG) modes, trapped electron modes (TEM), trapped ion modes (TIM), electron-temperature-gradient (ETG) modes, micro-tearing modes, etc.  Large Benchmark exercises underway (Cyclone + Edge) • IMP5: develop the computational basis for a modular package of codes simulating heating, current drive and fast particle effects • Goal: self-consistent calculations validated against experiments • Priority: realistic modelling applicable to ITER standard and advanced scenarios

40. Progress on hardware issues European 7th FP(2007 onward): the Petaflop’s world - massive parallel computing in Europe for Research purposes - UK; Germany; Spain; France willing to participate - scientific cases made in Barcelona in Dec 05 - organisational issues in Cadarache in Feb 06 Fusion: EU vs Broader Approach - need for dedicated HPC in the very near future (~100Tflops permanently) - Infrastructure support for theory and modelling being discussed - IFERC proposal under study (broader approach) - GRID computing solutions? ITM-TF: the gateway - need for unique entry point (platform tools, database repository, computer access, data storage capability ..) - mutualisation of support

41. International collaborative activity • ITER is the main customer for tokamak simulators, but not the only one (existing & new devices, DEMO). • Other Integrated Fusion Initiatives exist around the world (USA, Japan, China, ….) • There is a strong need for a joint effort in terms of standards, formats, V&V, for the various descriptions to be compatible • A coordinated structure, initiated by EU-ITM-TF, has been put in place between the ITER partners in order to address these issues

42. Conclusion • The route towards magnetic thermonuclear fusion simulators is now open, mobilizing a large part of the world-wide research community. • Two major lines are followed, one massively using first principle models at the forefront of new physics discoveries and one progressively integrating the existing knowledge into the most complete description of a fusion plasma within its environment. • One can reasonably expect rapid progress on both lines, together with the necessary cross-fertilization, as well as the existence of validated simulators delivered to ITER prior to its first plasma

43. www.efda-taskforce-itm.org Public Homepages Welcome Agenda Contacts Links General Documentation Private Homepages (Password protected) Detailed Documentation Code Server (FTP,CVS,…) Discussion Forum (Password protected for write access) Webmanager: M. Romanelli (ENEA) Webmaster: B. Knaepen (ULB)