An Input Output Approach to the Analysis of Intercountry Differences in Per Capita Energy Consumption

Comparisons of energy consumption patterns in different countries can serve as a tool for identifying inefficiencies in the use of energy in individual countries. However, differences in terms of relations such as the use of energy per capita or per unit of GDP are not usually very good indicators of intercountry differences in the efficiency of energy use. Factors such as climatic conditions, the sectoral structure of the production system etc. often hide more basic differences in production methods and consumption patterns. Moreover, differences in production methods with similar output may not only be due to differences in the efficiency of energy utilization, but can be the result of intercountry differences in relative prices. In this study, input-output data for the Federal Republic of Germany, France and the Netherlands is used to identify intercountry differences in per capita consumption patterns which can be assigned to differences in production methods and domestic consumption patterns. It appears that such differences do exist. In particular the technologies used in the three countries differed significantly in terms of energy intensity. However, when these results were combined with data on relative prices, the observed differences in energy intensities in most cases were quite consistent with intercountry differences in relative prices. Thus, the observed differences between the sample countries do not seem to reflect intercountry differences in the efficiency of energy utilization

Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations

A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at $q\approx 1$, thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C$^1$ code. In these simulations, the most important mechanism responsible for the flux pumping is that a saturated $(m=1,n=1)$ quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect. It is shown that sawtoothing is prevented in the simulations if $\beta$ is sufficiently high to provide the necessary drive for the $(m=1,n=1)$ instability that generates the dynamo loop voltage. The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile.Comment: submitted to Physics of Plasmas (23 pages, 15 Figures

3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C1^1, NIMROD and JOREK

In recent years, the nonlinear 3D magnetohydrodynamic codes JOREK, M3D-C$^1$ and NIMROD developed the capability of modelling realistic 3D vertical displacement events (VDEs) including resistive walls. In this paper, a comprehensive 3D VDE benchmark is presented between these state of the art codes. The simulated case is based on an experimental NSTX plasma but with a simplified rectangular wall. In spite of pronounced differences between physics models and numerical methods, the comparison shows very good agreement in the relevant quantities used to characterize disruptions such as the 3D wall forces and energy decay. This benchmark does not only bring confidence regarding the use of the mentioned codes for disruption studies, but also shows differences with respect to the used models (e.g. reduced versus full MHD models). The simulations show important 3D features for a NSTX plasma such as the self-consistent evolution of the halo current and the origin of the wall forces. In contrast to other reduced MHD models based on an ordering in the aspect ratio, the ansatz based JOREK reduced MHD model allows capturing the 3D dynamics even in the spherical tokamak limit considered here

Electron acceleration in a JET disruption simulation

Runaways are suprathermal electrons having sufficiently high energy to be continuously accelerated up to tens of MeV by a driving electric field [1]. Highly energetic runaway electron (RE) beams capable of damaging the tokamak first wall can be observed after a plasma disruption [2]. Therefore, it is of primary importance to fully understand their generation mechanisms in order to design mitigation systems able to guarantee safe tokamak operations. In a previous work, [3], a test particle tracker was introduced in the JOREK 3D non-linear MHD code and used for studying the electron confinement during a simulated JET-like disruption. It was found in [3] that relativistic electrons are not completely deconfined by the stochastic magnetic field taking place during the disruption thermal quench (TQ). This is due to the reformation of closed magnetic surfaces at the beginning of the current quench (CQ). This result was obtained neglecting the inductive electric field in order to avoid the unrealistic particle acceleration which otherwise would have happened due to the absence of collision effects. The present paper extends [3] analysing test electron dynamics in the same simulated JET-like disruption using the complete electric field. For doing so, a simplified collision model is introduced in the particle tracker guiding center equations. We show that electrons at thermal energies can become RE during or promptly after the TQ due to a combination of three phenomena: a first REs acceleration during the TQ due to the presence of a complex MHD-induced electric field, particle reconfinement caused by the fast reformation of closed magnetic surfaces after the TQ and a secondary acceleration induced by the CQ electric field

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

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