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

Plasma Edge Kinetic-MHD Modeling in Tokamaks Using Kepler Workflow for Code Coupling, Data Management and Visualization

A new predictive computer simulation tool targeting the development of the H-mode pedestal at the plasma edge in tokamaks and the triggering and dynamics of edge localized modes (ELMs) is presented in this report. This tool brings together, in a coordinated and effective manner, several first-principles physics simulation codes, stability analysis packages, and data processing and visualization tools. A Kepler workflow is used in order to carry out an edge plasma simulation that loosely couples the kinetic code, XGC0, with an ideal MHD linear stability analysis code, ELITE, and an extended MHD initial value code such as M3D or NIMROD. XGC0 includes the neoclassical ion-electron-neutral dynamics needed to simulate pedestal growth near the separatrix. The Kepler workflow processes the XGC0 simulation results into simple images that can be selected and displayed via the Dashboard, a monitoring tool implemented in AJAX allowing the scientist to track computational resources, examine running and archived jobs, and view key physics data, all within a standard Web browser. The XGC0 simulation is monitored for the conditions needed to trigger an ELM crash by periodically assessing the edge plasma pressure and current density profiles using the ELITE code. If an ELM crash is triggered, the Kepler workflow launches the M3D code on a moderate-size Opteron cluster to simulate the nonlinear ELM crash and to compute the relaxation of plasma profiles after the crash. This process is monitored through periodic outputs of plasma fluid quantities that are automatically visualized with AVS/Express and may be displayed on the Dashboard. Finally, the Kepler workflow archives all data outputs and processed images using HPSS, as well as provenance information about the software and hardware used to create the simulation. The complete process of preparing, executing and monitoring a coupled-code simulation of the edge pressure pedestal buildup and the ELM cycle using the Kepler scientific workflow system is described in this paper

Self-consistent simulation of plasma scenarios for ITER using a combination of 1.5D transport codes and free-boundary equilibrium codes

Self-consistent transport simulation of ITER scenarios is a very important tool for the exploration of the operational space and for scenario optimisation. It also provides an assessment of the compatibility of developed scenarios (which include fast transient events) with machine constraints, in particular with the poloidal field (PF) coil system, heating and current drive (H&CD), fuelling and particle and energy exhaust systems. This paper discusses results of predictive modelling of all reference ITER scenarios and variants using two suite of linked transport and equilibrium codes. The first suite consisting of the 1.5D core/2D SOL code JINTRAC [1] and the free boundary equilibrium evolution code CREATE-NL [2,3], was mainly used to simulate the inductive D-T reference Scenario-2 with fusion gain Q=10 and its variants in H, D and He (including ITER scenarios with reduced current and toroidal field). The second suite of codes was used mainly for the modelling of hybrid and steady state ITER scenarios. It combines the 1.5D core transport code CRONOS [4] and the free boundary equilibrium evolution code DINA-CH [5].Comment: 23 pages, 18 figure

Stellar Explosions by Magnetic Towers

We propose a magnetic mechanism for the collimated explosion of a massive star relevant for GRBs, XRFs and asymmetric supernovae. We apply Lynden-Bell's magnetic tower scenario to the interior of a massive rotating star after the core has collapsed to form a black hole with an accretion disk or a millisecond magnetar acting as a central engine. We solve the force-free Grad-Shafranov equation to calculate the magnetic structure and growth of a tower embedded in a stellar environment. The pressure of the toroidal magnetic field, continuously generated by differential rotation of the central engine, drives a rapid expansion which becomes vertically collimated after lateral force balance with the surrounding gas pressure is reached. The collimation naturally occurs because hoop stress concentrates magnetic field toward the rotation axis and inhibits lateral expansion. This leads to the growth of a self-collimated magnetic tower. When embedded in a massive star, the supersonic expansion of the tower drives a strong bow shock behind which an over-pressured cocoon forms. The cocoon confines the tower by supplying collimating pressure and provides stabilization against disruption due to MHD instabilities. Because the tower consists of closed field lines starting and ending on the central engine, mixing of baryons from the cocoon into the tower is suppressed. The channel cleared by the growing tower is thus plausibly free of baryons and allows the escape of magnetic energy from the central engine through the star. While propagating down the stellar density gradient, the tower accelerates and becomes relativistic. During the expansion, fast collisionless reconnection becomes possible resulting in dissipation of magnetic energy which may be responsible for GRB prompt emission.Comment: 19 pages, 8 figures, accepted to ApJ, updated references and additional discussion adde

Quasi-separatrix layers and three-dimensional reconnection diagnostics for line-tied tearing modes

In three-dimensional magnetic configurations for a plasma in which no closed field line or magnetic null exists, no magnetic reconnection can occur, by the strictest definition of reconnection. A finitely long pinch with line-tied boundary conditions, in which all the magnetic field lines start at one end of the system and proceed to the opposite end, is an example of such a system. Nevertheless, for a long system of this type, the physical behavior in resistive magnetohydrodynamics (MHD) essentially involves reconnection. This has been explained in terms comparing the geometric and tearing widths [1, 2]. The concept of a quasi-separatrix layer[3, 4] was developed for such systems. In this paper we study a model for a line-tied system in which the corresponding periodic system has an unstable tearing mode. We analyze this system in terms of two magnetic field line diagnostics, the squashing factor[3-5] and the electrostatic potential difference used in kinematic reconnection studies[6, 7]. We discuss the physical and geometric significance of these two diagnostics and compare them in the context of discerning tearing-like behavior in line-tied modes. [1] G. L. Delzanno and J. M. Finn. Physics of Plasmas, 15(3):032904, 2008. [2] Y.-M. Huang and E. G. Zweibel. Physics of Plasmas, 16(4):042102, 2009. [3] E. R. Priest and P. D\'emoulin. J. Geophys. Res., 100(A12):23443-23463, 1995. [4] P. D\'emoulin, J. C. Henoux, E. R. Priest, and C. H. Mandrini. Astron. Astrophys., 308:643-655, Apr. 1996. [5] V. S. Titov and G. Hornig. Advances in Space Research, 29(7):1087-1092, 2002. [6] Y. Lau and J. M. Finn. The Astrophysical Journal, 350:672-691, Feb. 1990. [7] Y. Lau and J. M. Finn. The Astrophysical Journal, 366:577-591, 1991.Comment: 13 pages, 9 figures, Submitted to Commun Nonlinear Sci Numer Simula

Three dimensional magnetohydrodynamics of fusion plasmas

The primary aim of the research on nuclear fusion is to obtain a new energy source to help satisfying a growing and sustainable consumption. This objective has to be reached through scientific research, both from the physics point of view and through the demonstration of the technological feasibility of a nuclear fusion reactor. The option on which the major efforts of the international community are focused is to obtain controlled nuclear fusion using a magnetic field to confine a plasma formed by deuterium and tritium, in a vacuum chamber of toroidal shape. The most promising magnetic configuration is the so called tokamak configuration. The scientific community aims at addressing the remaining problems connected with physics performing the experiment ITER (International Thermonuclear Experimental Reactor) and to verify the technological feasibility of a nuclear fusion reactor with the DEMO experiment. An important part of the scientific efforts is addressed to the study of configurations alternative to the tokamak, like the stellarator and the reversed-field pinch (RFP). These configurations achieve three dimensional helical states: in the RFP a global helical state is obtained spontaneously, due to the presence of a strong current flowing in the plasma, while currents flowing in external helically shaped coils generate a global helical state in the stellarator. Helical states can be obtained also in the tokamak configuration, for instance due to the presence of external magnetic field perturbations. The research activity of my PhD focuses on the study of the 3D nonlinear magnetohydrodynamics model applied to the numerical study of the RFP and tokamak helical configurations. The main aim of my research is the characterization, under three different aspects later described, of the three dimensional helical states. These states are presently believed to provide possible scenarios for reducing dangerous MHD activity for both RFP (magnetic chaos transport reduction) and tokamak (sawtooth mitigation, disruption avoidance). The research activity included the development and the exploitation of advanced numerical tools to deal with the numerical solution of the 3D nonlinear MHD model, while the interaction with the experimental environment provided the opportunity to develop tools for model-experiment comparison (validation) and benchmarking of numerical tools (verification). The results obtained during my PhD provide a further step towards a predictive capability of the employed modelling tools. In fact, the boundary conditions are proved to be a key ingredient in bringing the comparison of MHD simulations with the experiment at a quantitative level. Moreover it recently inspired a successful and promising experimental activity in RFX-mod, the biggest RFP experiment in the world, located in Padova. My PhD research activity and results can be divided into three main areas. The first is the dynamical simulation of a magnetically confined plasma through numerical solution of the 3D nonlinear visco-resistive MHD model. The second area of research consists in the topological study of the magnetic field configurations obtained from MHD simulations. The third area is the study of transport due to magnetic stochasticity in both tokamak and RFP states, with data coming from MHD simulations, gyrokinetics simulations and experimental results. The first area of research deals with the simulation of the dynamical properties of a magnetically confined plasma, performed using the 3D nonlinear MHD codes SPECYL and PIXIE3D. The most important achievement is represented by the level of agreement between MHD simulation and experimental dynamics of the RFP, a degree of agreement obtained in simulations where, for the first time, a helical boundary condition is applied. It is also demonstrated that by imposing a finite helical radial magnetic field at the edge it is possible to induce a global helical regime with the chosen helicity. As for the tokamak configuration the study of helical boundary conditions shows that they can favour a steady helical equilibrium, thus mitigating the sawtooth dynamics typically detrimental for the confinement. This area of research leads to a unifying vision for the RFP and the tokamak, as the use of helical boundary condition for the magnetic field seems to allow the easier establishment of a helical equilibrium in both configurations, with interesting properties for the configurations. The second area of research is centred on the topological study of the magnetic configurations obtained from the MHD simulations of the RFP. The separatrix expulsion of the dominant helical mode has been studied analyzing the magnetic field topology with the field line tracing code N EMATO. Two so called paradigmatic cases, characterized by a simplified MHD dynamics, have been analyzed. In the first one it was shown that the dominant mode separatrix expulsion can reduce the level of magnetic field lines stochasticity remarkably, in the second case an “exotic” (before these studies) dynamics was considered, i.e. the development of a helical equilibrium from a non-resonant mode. These results confirmed older studies that placed separatrix expulsion in direct connection with helical RFP states obtained in RFX-mod, which develop internal transport barriers observed as electronic temperature steep gradients. Furthermore it showed that the helical equilibrium based on a non-resonant mode can result in particularly strong magnetic order. The favourable properties found led to the proposal to experimentally drive QSH states built upon non-resonant MHD modes in the RFX-mod experiment: these states were successfully produced in the experiment, and the study of thermal properties is presently ongoing. Topological studies on more realistic cases coming from MHD simulations that show a quantitative agreements with the standard operation of the RFX-mod experiment are also tackled in this thesis. The results obtained underline the importance of the spectrum of secondary perturbations to the helical equilibrium. The third area of research focuses on the consequences of transport produced by the presence of magnetic stochasticity. Two specific cases relevant for the RFP and the tokamak are considered: the magnetic chaos produced by microtearing activity at the electron internal transport barrier in the RFP, and the case of edge magnetic stochasticity due to the action of edge helical magnetic perturbations in the tokamak. The tools to study transport were developed and used to calculate the energy diffusion coefficient and other meaningful quantities. Such tools are now available for further and more general applications. On a numerical ground two important activities were performed during the PhD. The parallelization of the field line tracing code NEMATO, during one month mobility at Oak Ridge National Laboratory, was fundamental for the speeding up of the research activity. The numerical verification of NEMATO and ORBIT was also performed. The verification gave a positive result, showing a satisfactory agreement, both qualitative and quantitative, on the features of the magnetic field topology in the RFP configuration

Axisymmetric simulations of vertical displacement events in tokamaks: A benchmark of M3D-C1, NIMROD and JOREK

A benchmark exercise for the modeling of vertical displacement events(VDEs) is presented and applied to the 3D nonlinear magneto-hydrodynamic codesM3D-C1, JOREK and NIMROD. The simulations are based on a vertically unstableNSTX equilibrium enclosed by an axisymmetric resistive wall with rectangular crosssection. A linear dependence of the linear VDE growth rates on the resistivity ofthe wall is recovered for sufficiently large wall conductivity and small temperatures inthe open field line region. The benchmark results show good agreement between theVDE growth rates obtained from linear NIMROD and M3D-C1simulations as wellas from the linear phase of axisymmetric nonlinear JOREK, NIMROD and M3D-C1simulations. Axisymmetric nonlinear simulations of a full VDE performed with thethree codes are compared and excellent agreement is found regarding plasma locationand plasma currents as well as eddy and halo currents in the wall.</p