Handling Uncertainties in Linear Programming Models

A frequently used approach to linear programming problems with only vaguely known coefficients of the objective function is to treat these coefficients as random variables; this means that the lack of knowledge is described by a distribution function. For the case in which such a procedure cannot be justified, S.Ya. Chernavsky and A.D. Virtzer of the working Consultative Group for the President of the Academy of Sciences of the USSR developed a decision theoretical approach, some aspects of which are described here for pedagogical purposes. In this paper first the problem of handling uncertainties in linear programming models is outlined, and the decision criteria to be used are explained. Thereafter, a method of finding optimal strategies under uncertain values of the objective function coefficients is described. Finally, the method is applied to a simple uncertainty case of the MESSAGE model

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

Enhanced Preconditioner for JOREK MHD Solver

The JOREK extended magneto-hydrodynamic (MHD) code is a widely used simulation code for studying the non-linear dynamics of large-scale instabilities in divertor tokamak plasmas. Due to the large scale-separation intrinsic to these phenomena both in space and time, the computational costs for simulations in realistic geometry and with realistic parameters can be very high, motivating the investment of considerable effort for optimization. In this article, a set of developments regarding the JOREK solver and preconditioner is described, which lead to overall significant benefits for large production simulations. This comprises in particular enhanced convergence in highly non-linear scenarios and a general reduction of memory consumption and computational costs. The developments include faster construction of preconditioner matrices, a domain decomposition of preconditioning matrices for solver libraries that can handle distributed matrices, interfaces for additional solver libraries, an option to use matrix compression methods, and the implementation of a complex solver interface for the preconditioner. The most significant development presented consists in a generalization of the physics based preconditioner to "mode groups", which allows to account for the dominant interactions between toroidal Fourier modes in highly non-linear simulations. At the cost of a moderate increase of memory consumption, the technique can strongly enhance convergence in suitable cases allowing to use significantly larger time steps. For all developments, benchmarks based on typical simulation cases demonstrate the resulting improvements

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

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

Seeing the smart city on Twitter: Colour and the affective territories of becoming smart

This paper pays attention to the immense and febrile field of digital image files which picture the smart city as they circulate on the social media platform Twitter. The paper considers tweeted images as an affective field in which flow and colour are especially generative. This luminescent field is territorialised into different, emergent forms of becoming ‘smart’. The paper identifies these territorialisations in two ways: firstly, by using the data visualisation software ImagePlot to create a visualisation of 9030 tweeted images related to smart cities; and secondly, by responding to the affective pushes of the image files thus visualised. It identifies two colours and three ways of affectively becoming smart: participating in smart, learning about smart, and anticipating smart, which are enacted with different distributions of mostly orange and blue images. The paper thus argues that debates about the power relations embedded in the smart city should consider the particular affective enactment of being smart that happens via social media. More generally, the paper concludes that geographers must pay more attention to the diverse and productive vitalities of social media platforms in urban life and that this will require experiment with methods that are responsive to specific digital qualities

Fast-ion redistribution and loss due to edge perturbations in the ASDEX Upgrade, DIII-D and KSTAR tokamaks

The impact of edge localized modes (ELMs) and externally applied resonant and non-resonant magnetic perturbations (MPs) on fast-ion confinement/transport have been investigated in the ASDEX Upgrade (AUG), DIII-D and KSTAR tokamaks. Two phases with respect to the ELM cycle can be clearly distinguished in ELM-induced fast-ion losses. Inter-ELM losses are characterized by a coherent modulation of the plasma density around the separatrix while intra-ELM losses appear as well-defined bursts. In high collisionality plasmas with mitigated ELMs, externally applied MPs have little effect on kinetic profiles, including fast-ions, while a strong impact on kinetic profiles is observed in low-collisionality, low q 95 plasmas with resonant and non-resonant MPs. In low-collisionality H-mode plasmas, the large fast-ion filaments observed during ELMs are replaced by a loss of fast-ions with a broad-band frequency and an amplitude of up to an order of magnitude higher than the neutral beam injection prompt loss signal without MPs. A clear synergy in the overall fast-ion transport is observed between MPs and neoclassical tearing modes. Measured fast-ion losses are typically on banana orbits that explore the entire pedestal/scrape-off layer. The fast-ion response to externally applied MPs presented here may be of general interest for the community to better understand the MP field penetration and overall plasma response.Ministerio de Economía y Empresa ((RYC-2011-09152 y ENE2012-31087)Marie Curie (Grant PCIG11-GA-2012-321455)US Department of Energy (DE-FC02-04ER54698, SC-G903402, DE-FG02-04ER54761, DE-AC02-09CH11466 and DE-FG02- 08ER54984)NRF Korea contract 2009-0082012MEST under the KSTAR projec