Performance analysis and optimization of the JOREK code for many-core CPUs

This report investigates the performance of the JOREK code on the Intel Knights Landing and Skylake processor architectures. The OpenMP scaling of the matrix construction part of the code was analyzed and improved synchronization methods were implemented. A new switch was implemented to control the number of threads used for the linear equation solver independently from other parts of the code. The matrix construction subroutine was vectorized, and the data locality was also improved. These steps led to a factor of two speedup for the matrix construction

Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak

When electron cyclotron (EC) driven current is first applied to the inside of a magnetic island, the current spreads throughout the island and after a short period achieves a steady level. Using a two equation fluid model for the EC current that allows us to examine this early evolution in detail, we analyze high-resolution simulations of a 2/1 classical tearing mode in a low-beta large aspect-ratio circular tokamak. These simulations use a nonlinear 3D reduced-MHD fluid model and the JOREK code. During the initial period where the EC driven current grows and spreads throughout the magnetic island, it is not a function of the magnetic flux. However, once it has reached a steady-state, it should be a flux function. We demonstrate numerically that if sufficiently resolved toroidally, the steady-state EC driven current becomes approximately a flux function. We discuss the physics of this early period of EC evolution and its impact on the size of the magnetic island.Comment: 12 pages, 7 figure

Development and application of a hybrid MHD-kinetic model in JOREK

Energetic particle (EP) driven instabilities will be of strongly increased relevance in future burning plasmas as the EP pressure will be very large compared to the thermal plasma. Understanding the interaction of EPs and bulk plasma is crucial for developing next-generation fusion devices. In this work, the JOREK MHD code is extended to allow for the simulation of EP instabilities at high EP pressures using realistic plasma and EP parameter in a full-f formulation with anisotropic pressure coupling to the bluid background. The code is first benchmarked linearly for the ITPA-TAE as well as the experiment based AUG-NLED cases, obtaining good agreement to other codes. Then, it is applied to a high energetic particle pressure discharge in the ASDEX Upgrade tokamak using a realistic non-Maxwellian distribution of EPs, reproducing aspects of the experimentally observed instabilities. Non-linear applications are possible based on the implentation, but will require dedicated verification and validation left for future work

PB3D: A new code for edge 3-D ideal linear peeling-ballooning stability

A new numerical code PB3D (Peeling-Ballooning in 3-D) is presented. It implements and solves the intermediate-to-high-n ideal linear magnetohydrodynamic stability theory extended to full edge 3-D magnetic toroidal configurations in previous work [1]. The features that make PB3D unique are the assumptions on the perturbation structure through intermediate-to-high mode numbers n in general 3-D configurations, while allowing for displacement of the plasma edge. This makes PB3D capable of very e cient calculations of the full 3-D stability for the output of multiple equilibrium codes. As first verification, it is checked that results from the stability code MISHKA [2], which considers axisymmetric equilibrium configurations, are accurately reproduced, and these are then successfully extended to 3-D configurations, through comparison with COBRA [3], as well as using checks on physical consistency. The non-intuitive 3-D results presented serve as a tentative first proof of the capabilities of the code.This research was sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2015-6826

Transition from no-ELM response to pellet ELM triggering during pedestal build-up—insights from extended MHD simulations

Pellet edge localized mode (ELM) triggering is a well-established scheme for decreasing the time between two successive ELM crashes below its natural value. Reliable ELM pacing has been demonstrated experimentally in several devices, increasing the ELM frequency considerably. However, it was also shown that the frequency cannot be increased arbitrarily due to a so-called lag-time. During this time, after a preceding natural or triggered ELM crash, neither a natural ELM crash occurs nor is it possible to trigger an ELM crash by pellet injection. For this article, pellet ELM triggering simulations are advanced beyond previous studies in two ways. Firstly, realistic E B and diamagnetic background flows are included. And secondly, the pellet is injected at different stages of the pedestal build-up. This allows us to recover the lag time for the first time in simulations and investigate it in detail. A series of nonlinear extended MHD simulations is performed to investigate the plasma dynamics resulting from an injection at different time points during the pedestal build-up. The experimentally observed lag-time is qualitatively reproduced. In particular, a sharp transition is observed between the regime where no ELMs can be triggered and the regime where pellet injection causes an ELM crash. Via variations of pellet parameters and injection time, the two regimes are studied and compared in detail, revealing pronounced differences in the nonlinear dynamics. The toroidal mode spectrum is significantly broader when an ELM crash is triggered, enhancing the stochasticity and therefore also the losses of thermal energy along magnetic field lines. In the heat fluxes to the divertor targets, pronounced toroidal asymmetries are observed. In the case of high injection velocities leading to deep penetration, the excitation of core modes like the 2/1 neoclassical tearing mode is also observed

Understanding the effect resonant magnetic perturbations have on ELMs

All current estimations of the energy released by type I ELMs indicate that, in order to ensure an adequate lifetime of the divertor targets on ITER, a mechanism is required to decrease the amount of energy released by an ELM, or to eliminate ELMs altogether. One such amelioration mechanism relies on perturbing the magnetic field in the edge plasma region, either leading to more frequent, smaller ELMs (ELM mitigation) or ELM suppression. This technique of Resonant Magnetic Perturbations (RMPs) has been employed to suppress type I ELMs at high collisionality/density on DIII-D, ASDEX Upgrade, KSTAR and JET and at low collisionality on DIII-D. At ITER-like collisionality the RMPs enhance the transport of particles or energy and keep the edge pressure gradient below the 2D linear ideal MHD critical value that would trigger an ELM, whereas at high collisionality/density the type I ELMs are replaced by small type II ELMs. Although ELM suppression only occurs within limitied operational ranges, ELM mitigation is much more easily achieved. The exact parameters that determine the onset of ELM suppression are unknown but in all cases the magnetic perturbations produce 3D distortions to the plasma and enhanced particle transport. The incorporation of these 3D effects in codes will be essential in order to make quantitative predictions for future devices.Comment: 32 pages, 9 figure

Non-linear Simulations of MHD Instabilities in Tokamaks Including Eddy Current Effects and Perspectives for the Extension to Halo Currents

The dynamics of large scale plasma instabilities can strongly be influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK has been coupled with the resistive wall code STARWALL, which allows to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described.Comment: Proceeding paper for Theory of Fusion Plasmas (Joint Varenna-Lausanne International Workshop), Varenna, Italy (September 1-5, 2014); accepted for publication in: to Journal of Physics: Conference Serie

Three-dimensional linear peeling-ballooning theory in magnetic fusion devices

Ideal magnetohydrodynamics theory is extended to fully 3D magnetic configurations to investigate the linear stability of intermediate to high n peeling-ballooning modes, with n the toroidal mode number. These are thought to be important for the behavior of edge localized modes and for the limit of the size of the pedestal that governs the high confinement H-mode. The end point of the derivation is a set of coupled second order ordinary differential equations with appropriate boundary conditions that minimize the perturbed energy and that can be solved to find the growth rate of the perturbations. This theory allows of the evaluation of 3D effects on edge plasma stability in tokamaks such as those associated with the toroidal ripple due to the finite number of toroidal field coils, the application of external 3D fields for elm control, local modification of the magnetic field in the vicinity of ferromagnetic components such as the test blanket modules in ITER, etc.This research was sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2012-38620-C02-02 and also in part by Comunidad de Madrid Project No. S2009/ENE-1679.Publicad