Introduction
Fusion energy is considered as an important future source for reliable, sustainable base load power. To address its demanding and costly science and technology challenges, fusion energy is being developed today with a concerted world-wide co-operation. Fusion energy uses plasma as a fuel. Plasma is the fourth state of matter and exists at very high temperatures. Its physics is very complex and its modelling for fusion reactors needs high performance computing resources. Today, with current supercomputing resources, it is impossible to perform first principles physics calculations of fusion plasma discharges in reactors. The major reason for this is the small-scale plasma turbulence structures affecting the plasma confinement. Exascale supercomputers could make these calculations feasible.
The Aalto University, ÅA, and VTT transport team have taken an initiative to develop a kinetic simulation code ELMFIRE for studying turbulence and transport in toroidal magnetized plasmas [1]. ELMFIRE is a global full particle distribution function (f) particle gyrokinetic [i] code. The particle orbits are solved in time in a 5D phase space, and a 3D electrostatic potential solver is included to capture turbulence that arises, e.g., from ExB convective cells due to pressure gradient and toroidicity, resulting in enhanced transport. ELMFIRE is compatible with strong variations of the bulk plasma distributions with a variety of heat sources and sinks.
ELMFIRE followed the development of the ASCOT 5D guiding-center particle code at the Helsinki University of Technology and VTT for plasma simulation [2]. Since then, the ASCOT code has become widely used for fusion experiment analysis. The need to model full 3D electrostatic (or electromagnetic) potential together with particle motion to capture the turbulence was identified. This pushed the full f ELMFIRE project to start up.
The present ELMFIRE work concentrates on turbulence in magnetized tokamak fusion plasmas. In Low (L) to High (H) energy confinement transition of the transport in tokamaks [3], a transport barrier that gives a better particle and heat confinement is created spontaneously by external heating. This is presently considered as an important part, e.g., of a fusion reactor or ITER plasma operation. The enhanced confinement resulting from flow shear stabilization of turbulence is of considerable scientific interest; systems seldom self-organize to a higher energy state, with reduced turbulence and transport, when an additional source of free energy is applied. Such a self-organization together with zonal flow generation may well be responsible for the confinement transition in many tokamaks [4], but the very mechanism behind it is still uncovered. Self-organization and zonal flow generation with turbulence is important not only in fusion plasmas but also in other fluids like planetary atmospheres and solar plasma (the well-known examples are Jovian belts and zones, jet streams, and solar dynamo).
Other global gyrokinetic full f efforts have been started, e.g., at Princeton University (XGC1), CEA, LPMIA-Univ, IRMA-Univ, LSIIT-Illkirch (GYSELA), MPI in Germany (FEFI), JAERI in Japan (GT5D), and at LLNL in USA (COGENT). In connection to all these efforts, the multi-scale approach built on reduced models is studied. Noting also the multi-scale efforts exploiting delta f codes, one finds that there exists a serious, widespread and worldwide effort to resolve, from the first principles of physics, the details of plasma transport in fusion reactors.
This research like all HPC work for fusion has been well coordinated in Europe by the EFDA Integrated Tokamak Modeling (ITM) and High Level Support Team (HLST) Task Forces, which is expected to continue in the forthcoming EU framework programme. The code benchmarking, standardized input and output forms and a workflow platform (Kepler), and continuous exchange of ideas and experiences between the groups at Code Camps and workshops are examples of the EFDA ITM Task force. Through these channels, co-operation in various forms, e.g., between the GYSELA, FEFI, and ELMFIRE groups has been active. The ELMFIRE group has also organized a two-week EU Goal Oriented Training course at Aalto University for introducing young European scientists to gyrokinetic methods and ELMFIRE/ASCOT codes. The ELMFIRE group has been very active in disseminating its results and experiences with the US and Japan full f code groups. According to Google Scholar, all the main full f codes have received similar attraction from the fusion community showing a widespread interest to various approaches, e.g., particle vs. continuum, electrostatic vs. electromagnetic, magnetostatic vs. inductive, Lagrangian vs. Eulerian vs. semi-Lagrangian, etc.
Status of the ELMFIRE Work
ELMFIRE has several novel full f properties, e.g., nonlinearity in ion polarization [5], drift-kinetic electrons with semi-implicit and implicit parallel nonlinearity [5,6], and momentum-conserving interpolation routine [7], so that it has been possible to validate it directly to experimental diagnostics. Within the Academy of Finland grants, configuring ELMFIRE with the limiter defined scrape-off-layer (SOL) and with electromagnetic perturbations has been advanced to an extent that the latter features can be introduced and to be used within the present CRESTA project. With the help of the Academy project and the EU EUFORIA project, the integration of the ELMFIRE code onto the EU fusion code common platform has been active. Within the EU CRESTA project, the ELMFIRE code is provided with a 3D Domain Decomposition (DD) feature, among others, which is of paramount importance for enhanced memory usage of ELMFIRE. As the polarization drift is explicitly solved and the polarization density and parallel nonlinearities are implicitly solved in the gyrokinetic Poisson equation, the 3D DD has a strong impact on the memory usage of the coefficient matrix of the gyrokinetic Poisson equation.
ELMFIRE has been used for analysing FT-2 experiments (Ioffe Institute) and TEXTOR experiment (IPP, Juelich). The tokamaks have well developed diagnostics with Doppler reflectometry, spectroscopy, enhanced scattering, and probes. Quantitative reproduction of selected micro, meso, and macro-scale transport phenomena as measured in are reached by ELMFIRE predictions [8,9]. A detailed agreement with mean equilibrium flows, oscillating fine-scale zonal flows and turbulence spectra observed by a set of microwave back-scattering techniques as well as a good fit of the thermal diffusivity data are demonstrated. Both the shift and the broadening of the power spectrum of synthetic and experimental Doppler reflectometry diagnostics is found to overlap perfectly at various radial positions, indicating similar rotation and spreading of the selected density fluctuations. At the same time similar radial electric field dynamics and outward geodesic acoustic mode (GAM) propagation are observed by analysis of the probability distribution function, coherence, standard deviation and dominant frequency of the simulated and experimentally measured radial electric field fluctuations with impurity ions, identifying the turbulence driven GAM as a key contributor to the observed burstiness of the radial electric field [8]. These results are a breakthrough in the development of gyrokinetic full f tool for the use in prediction and interpretation of tokamak transport.
The work has been based on the use of the largest supercomputers available for EU scientists by DECI, PRACE, and IFERC. The basic development is based on the national CSC supercomputer resources. PRACE approved 30 millions CPUhours (SuperMUC in Germany) for the ELMFIRE code runs in 2012-2013.
As the computing time and required memory with ELMFIRE grows with the size of the grid (grid cell size bound to ion Larmor radius) and with the number of simulation particles, the simulation requires the larger computing resources the larger the simulated plasma device is. For a reasonable simulation time scale for a JET (the largest tokamak in the world presently) plasma, ELMFIRE requires an exascale supercomputing power. ELMFIRE has been selected as the only test code relevant for fusion studies in the EU CRESTA project (8.57 M€). The CRESTA project assists in the development of exascale supercomputing to be available in 2017-2019.
After code optimizations performed at Aalto and at Åbo Academi (supported by the Academy of Finland, by CSC, TEKES, and EU), ELMFIRE can be run with 32 000 cores in PRACE’s Curie supercomputer for a 100´600´32 grid using 3000 particles per cell, acceptable for turbulence saturation studies in reasonably sized volumes inside the ASDEX Upgrade (Garching, Germany) plasma. This will further improve with the introduction of the new features under development within the CRESTA project.
CPU effective calculations for the transient need a long testing phase. However, due to fast time scale of transient in experiments (0.01 – 1 ms), apart from the much slower transport time scale, the ELMFIRE analysis (with time step of 50 ns) is feasible. Heat source (radiofrequency or neutral beam injection) often necessary for the transient already exist in ASCOT and can be transferred to ELMFIRE.
If successful, the work gives valuable information on the dynamic turbulent processes in magnetized plasmas within the gyrokinetic approximation. Issues like full discharge time scale, formation of very steep pedestal gradients (at gyroradius scale), sheath dynamics with gyroradius effects, dense divertor region, or large dynamic magnetic field reordering may need a more sophisticated approach with possible extension of gyrokinetic theory or use of more advanced computers than presently available. In spite of these caveats, the work represents the best feasible method presently available to see transport transients. With co-operation and with the progress of computing power, networking and data storage, an appropriate simulation tool for fusion reactors is expected.
Synopsis
The project will have an added value to the physics research on the mystery of structure formation in turbulent media. By focusing on details of self-organization of emergent structures it can contribute to diverse areas of nature and everyday life. If successful, the project may result in the first physics first principles simulation of transport barrier formation in toroidal plasmas. First detailed comparisons of full f gyrokinetic simulations with edge turbulence in medium-sized tokamaks are expected. The project aims to clarify the scaling of unexplained transport barrier transients in experiments. Such scaling laws – fundamental and critical, e.g., to ITER fusion reactor operation and control – are to a large extent not understood by physics principles today. The greatest challenge in physics involving also the most prominent risk of the project is to adapt the SOL region to the core plasma simulation with sufficient validation to experimental results, not tried before with gyrokinetic codes alone.
Bibliography
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[i] In gyrokinetic equations, an appropriate particle gyrophase averaging is done analytically thus reducing the phase space dimensions needed to be numerically resolved by one.
