2D interpolation and extrapolation of discrete magnetic measurements with toroidal harmonics for equilibrium reconstruction in a Tokamak

International audienceWe present a method based on the use of toroidal harmonics and on a modelization of the poloidal field coils and divertor coils for the 2D interpolation and extrapolation of discrete magnetic measurements in a Tokamak. The method is generic and can be used to provide Cauchy boundary conditions needed as input by a fixed domain equilibrium reconstruction code like Equinox. It can also be used to extrapolate the magnetic measurements in order to compute the plasma boundary itself. The proposed method and algorithm are detailed in the paper and results from numerous numerical experiments are presented. The method is foreseen to be used in the real time plasma control loop on the WEST Tokamak

Non regression testing for the JOREK code

Non Regression Testing (NRT) aims to check if software modifications result in undesired behaviour. Suppose the behaviour of the application previously known, this kind of test makes it possible to identify an eventual regression, a bug. Improving and tuning a parallel code can be a time-consuming and difficult task, especially whenever people from different scientific fields interact closely. The JOREK code aims at investing Magnetohydrodynamic (MHD) instabilities in a Tokamak plasma. This paper describes the NRT procedure that has been tuned for this simulation code. Automation of the NRT is one keypoint to keeping the code healthy in a source code repository.Comment: No. RR-8134 (2012

Automatic identification of the plasma equilibrium operating space in tokamaks

International audienceIn order to identify the plasma equilibrium operating space for future tokamaks, a new objective function is introduced in the inverse static free-boundary equilibrium code FEEQS.M. This function comprises terms which penalize the violation of the central solenoid and poloidal field coils limitations (currents and forces). The penalization terms do not require any weight tuning. Hence, this new approach automatizes to a large extent the identification of the operating space. As an illustration, the new method is applied on the ITER 15 and 17 MA inductive scenarios, and similar operating spaces compared to previous works are found. These operating spaces are obtained within a few (∼ 3) hours of computing time on a single standard CPU

Quasi-static Free-Boundary Equilibrium of Toroidal Plasma with CEDRES++: Computational Methods and Applications

International audienceWe present a comprehensive survey of the various computational methods in CEDRES++ for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilib-ria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a new Newton method for the discretized non-linear problem to tackle the various non-linearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we can handle in CEDRES++ as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate the performance of CEDRES++ and its application areas

Untersuchung zur Lernkultur in Online-Kursen

Ausgehend von einer veränderten, durch Lern- und Kompetenzorientierung geprägten Lernkultur analysieren die Autorinnen zwölf mehrwöchige Online-Kurse mit insgesamt 130 Teilnehmer/innen. Die Autorinnen nehmen ein Klima der hohen Wertschätzung unter den Lernenden wahr sowie gegenseitiges Feedback in den Reflexions- und Diskussionsprozessen, welches das Lernen verstärkt. Die Hypothese, dass in rein virtuellen, mehrwöchigen Weiterbildungskursen eine veränderte Lernkultur gefördert und gelebt wird, wird mittels halbstrukturierter Interviews sowie qualitativer Inhaltsanalyse der Beiträge in den Diskussionsforen untersucht. (DIPF/ Orig.

EUROfusion Integrated Modelling (EU-IM) capabilities and selected physics applications

International audienceRecent developments and achievements of the EUROfusion Code Development for Integrated Modelling project (WPCD), which aim is to provide a validated integrated modelling suite for the simulation and prediction of complete plasma discharges in any tokamak, are presented. WPCD develops generic complex integrated simulations, workflows, for physics applications, using the standardized European Integrated Modelling (EU-IM) framework. Selected physics applications of EU-IM workflows are illustrated in this paper

Modélisation non-linéaire du transport en présence d'instabilité MHD du plasma périphérique de tokamak.

The control of Edge Localized Modes (ELMs) is a capital question for the future ITER tokamak. The present work is dedicated to one of the most promising methods of control of the ELMs, based on a system of coils producing Resonant Magnetic Perturbations (RMPs! ), the efficiency of which was first demonstrated in the DIII-D tokamak in 2003. Our main objectives are, on the one hand, to improve the physical understanding of the mechanisms at play, and on the other hand to propose a concrete design of ELMs control coils for ITER. In order to calculate and analyze the magnetic perturbations produced by a given set of coils, we have developed the ERGOS code. The first ERGOS calculation was for the DIII-D ELMs control coils, the I-coils. It showed that they produce magnetic islands chains which overlap at the edge of the plasma, resulting in the ergodization of the magnetic field. We have then used ERGOS for the modelling of the experiments on ELMs control using the error field correction coils at JET and MAST, to which we participate since 2006. In the case of JET, we have shown the existence of a correlation between the mitigation of the ELMs and the ergodization of the magnetic field at the edge, in agreement with the DIII-D result. The design of ELMs control coils for ITER was done principally in the frame of an EFDA (European Fusion Development Agreement)-CEA contract, in collaboration with engineers from EFDA and ITER. We used ERGOS intensitvely, taking the case of the DIII-D I-coils as a reference. Three candidate designs came out, which we presented at the ITER Design Review, in 2007. Recently, the ITER management decided to provide a budget for building ELMs control coils, the design of which remains to be chosen between two of the three options that we proposed (or close to the ones we proposed). Finally, in order to understand better the non-linear magnetohydrodynamics phenomena taking place in ELMs control by RMPs, we performed numerical simulations, in particular with the JOREK code for a DIII-D case. The simulations reveal the existence of convection cells induced at the edge by the magnetic perturbations, and the possible screening of the RMPs in presence of rotation. The adequate modelling of the screening, which requires to add more physics into JOREK, has been started.Le contrôle des instabilités de bord connues sous le nom d' "Edge Localized Modes" (ELMs) est une question capitale pour le futur tokamak ITER. Ce travail est consacré à l'une des plus prometteuses méthodes de contrôle des ELMs, basée sur un système de bobines produisant des Perturbations Magnétiques Résonantes (PMRs), dont le fonctionnement a été démontré en premier lieu dans le tokamak DIII-D en 2003. Nos objectifs principaux sont, d'une part, d'éclaircir la compréhension physique des mécanismes en jeu, et d'autre part, de proposer un design concret de bobines de contrôle des ELMs pour ITER. Afin de calculer et d'analyser les perturbations magnétiques créées par un ensemble de bobines donné, nous avons développé le code ERGOS. Le premier calcul ERGOS a été consacré aux bobines de contrôle des ELMs de DIII-D, les I-coils. Il montre que celles-ci créent des chaines d'îlots magnétiques se recouvrant au bord du plasma, engendrant ainsi une ergodisation du champ magnétique. Nous avons par la suite utilisé ERGOS pour la modélisation des expériences de contrôle des ELMs à l'aide des bobines de correction de champ d'erreur sur JET et MAST, auxquelles nous participons depuis 2006. Dans le cas de JET, nous avons montré l'existence d'une corrélation entre la mitigation des ELMs et l'ergodisation du champ magnétique au bord, en accord avec le résultat pour DIII-D. Le design des bobines de contrôle des ELMs pour ITER s'est fait principalement dans le cadre d'un contrat EFDA (European Fusion Development Agreement)-CEA, en collaboration avec des ingénieurs et physiciens de l'EFDA et d'ITER. Nous avons utilisé ERGOS intensivement, le cas des I-coils de DIII-D nous servant de référence. Trois designs candidats sont ressortis, que nous avons présentés au cours de la revue de design d'ITER, en 2007. La direction d'ITER a décidé récemment d'attribuer un budget pour les bobines de contrôle des ELMs, dont le design reste à choisir entre deux des trois options que nous avons proposées (ou proches de celles que nous avons proposées). Enfin, dans le but de mieux comprendre les phénomènes de magnétohydrodynamique non-linéaires liés au contrôle des ELMs par PMRs, nous avons recouru à la simulation numérique, notamment avec le code JOREK pour un cas DIII-D. Les simulations révèlent l'existence de cellules de convection induites au bord du plasma par les perturbations magnétiques et le possible "écrantage" des PMRs par le plasma en présence de rotation. La modélisation adéquate de l'écrantage, qui demande la prise en compte de plusieurs phénomènes physiques supplémentaires dans JOREK, a été entamée

Contrôle des instabilités de bord par perturbations magnétiques résonnantes

PALAISEAU-Polytechnique (914772301) / SudocSudocFranceF

Automating the design of tokamak experiment scenarios

International audienceThe real-time control of plasma position, shape and current in a tokamak has to beensured by a number of electrical circuits consisting of voltage suppliers and axisymmetric coils.Finding good target voltages/currents for the control systems is a very laborious, non-trivial taskdue to non-linear effects of plasma evolution. We introduce here an optimal control formulationto tackle this task and present in detail the main ingredients for finding numerical solutions:the finite element discretization, accurate linearizations and Sequential Quadratic Programming.Case studies for the tokamaks WEST and HL-2M highlight the flexibility and broad scope of theproposed optimal control formulation.Le contrôle en temps réel de la position, de la forme et du courant du plasmadans un tokamak doit être assuré par un certain nombre de circuits électriques composés defournisseurs de tension et de bobines axisymétriques. Trouver de bonnes tensions / courantscibles pour les systèmes de commande est une tâche très laborieuse et non triviale en raison deseffets non linéaires de l’évolution du plasma. Nous présentons ici une formulation de contrôleoptimal pour aborder cette tâche et présentons en détail les principaux ingrédients permettant detrouver des solutions numériques: la discrétisation par éléments finis, des linéarisations préciseset la programmation séquentielle quadratique. Des études de cas sur les tokamaks WEST et HL-2M soulignent la flexibilité et le large champ d’application de la formulation de contrôle optimal proposée

Fast plasma dilution in ITER with pure Deuterium Shattered Pellet Injection

International audienceJOREK 3D non-linear MagnetoHydroDynamic (MHD) simulations of pure Deuterium Shattered Pellet Injection in ITER are presented. Considering a 15 MA L-mode plasma with a thermal energy content of 36 MJ from the non-activation phase of ITER operation, it is shown that such a scheme could allow diluting the plasma by more than a factor 10 without immediately triggering large MHD activity, provided the background impurity density is low enough. This appears as a promising strategy to reduce the risk of hot tail Runaway Electron (RE) generation and to avoid RE beams altogether in ITER, motivating further studies in this direction