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The application of high-temperature superconductors to accelerator magnets for future particle colliders is under study. Numerical methods are crucial for an accurate evaluation of the complex dynamical behavior of the magnets, especially concerning the magnetic field quality and thermal behavior. We present a coupled $\textbf{A}$-$\textbf{H}$ field formulation for the analysis of magneto-thermal transients in accelerator magnets. The magnetic field strength $\textbf{H}$ accounts for the eddy current problem in the source regions containing the superconducting domains, while the magnetic vector potential $\textbf{A}$ represents the magnetoquasistatic problem in the normal and non-conducting domains. Furthermore, we include a slab approximation for the source regions, making the formulation suitable for large scale models composed of thousands of tapes. In this work, the relevant equations are derived and discussed, with emphasis on the coupling conditions. The weak formulation is derived, and numerical results are provided in order to both, verify the formulation and scale it to the size of an accelerator magnet., Comment: 10 pages, 11 figures

Simulating the transient effects occurring in superconducting accelerator magnet circuits requires including the mutual electro-thermo-dynamic interaction among the circuit elements, such as power converters, magnets, and protection systems. Nevertheless, the numerical analysis is traditionally done separately for each element in the circuit, leading to possible non-consistent results. We present STEAM, a hierarchical co-simulation framework featuring the waveform relaxation method. The framework simulates a complex system as a composition of simpler, independent models that exchange information. The convergence of the coupling algorithm ensures the consistency of the solution. The modularity of the framework allows integrating models developed with both proprietary and in-house tools. The framework implements a user-customizable hierarchical algorithm to schedule how models participate to the co-simulation, for the purpose of using computational resources efficiently. As a case study, a quench scenario is co-simulated for the inner triplet circuit for the High Luminosity upgrade of the LHC at CERN., Comment: 7 pages, 14 figures

In this paper we present an algorithm for the coupling of magneto-thermal and mechanical finite element models representing superconducting accelerator magnets. The mechanical models are used during the design of the mechanical structure as well as the optimization of the magnetic field quality under nominal conditions. The magneto-thermal models allow for the analysis of transient phenomena occurring during quench initiation, propagation, and protection. Mechanical analysis of quenching magnets is of high importance considering the design of new protection systems and the study of new superconductor types. We use field/circuit coupling to determine temperature and electromagnetic force evolution during the magnet discharge. These quantities are provided as a load to existing mechanical models. The models are discretized with different meshes and, therefore, we employ a mesh-based interpolation method to exchange coupled quantities. The coupling algorithm is illustrated with a simulation of a mechanical response of a standalone high-field dipole magnet protected with CLIQ (Coupling-Loss Induced Quench) technology., Comment: 5 pages, 6 figures

This contributions discusses the simulation of magnetothermal effects in superconducting magnets as used in particle accelerators. An iterative coupling scheme using reduced order models between a magnetothermal partial differential model and an electrical lumped-element circuit is demonstrated. The multiphysics, multirate and multiscale problem requires a consistent formulation and framework to tackle the challenging transient effects occurring at both system and device level.

Superconducting accelerator magnets require sophisticated monitoring and means of protection due to the large energy stored in the magnetic field. Numerical simulations play a crucial role in understanding transient phenomena occurring within the magnet, and can, therefore, help to prevent disruptive consequences. We present a 2-D FEM model for the simulation of electro-thermal transients occurring in superconducting accelerator magnets. The magnetoquasistatic problem is solved with a modified magnetic vector potential formulation, where the cable eddy currents are resolved in terms of their equivalent magnetization. The heat balance equation is then investigated, and the relevant heat sources are discussed. The model implements a two-port component interface and is resolved, as part of an electrical circuit, in a cooperative simulation scheme with a lumped-parameter network., Comment: 4 pages, 12 figures, approved for publication, IEEE Transactions on Magnetics, 2017

In this paper we present the co-simulation of a PID class power converter controller and an electrical circuit by means of the waveform relaxation technique. The simulation of the controller model is characterized by a fixed-time stepping scheme reflecting its digital implementation, whereas a circuit simulation usually employs an adaptive time stepping scheme in order to account for a wide range of time constants within the circuit model. In order to maintain the characteristic of both models as well as to facilitate model replacement, we treat them separately by means of input/output relations and propose an application of a waveform relaxation algorithm. Furthermore, the maximum and minimum number of iterations of the proposed algorithm are mathematically analyzed. The concept of controller/circuit coupling is illustrated by an example of the co-simulation of a PI power converter controller and a model of the main dipole circuit of the Large Hadron Collider.

In this paper, we propose an optimized field/circuit coupling approach for the simulation of magnetothermal transients in superconducting magnets. The approach improves the convergence of the iterative coupling scheme between a magnetothermal partial differential model and an electrical lumped-element circuit. Such a multi-physics, multi-rate and multi-scale problem requires a consistent formulation and a dedicated framework to tackle the challenging transient effects occurring at both circuit and magnet level during normal operation and in case of faults. We derive an equivalent magnet model at the circuit side for the linear and the non-linear settings and discuss the convergence of the overall scheme in the framework of optimized Schwarz methods. The efficiency of the developed approach is illustrated by a numerical example of an accelerator dipole magnet with accompanying protection system., Comment: 8 pages, 7 figures

We study the shapes of subhalo distributions from four dark-matter-only simulations of Milky Way type haloes. Comparing the shapes derived from the subhalo distributions at high resolution to those of the underlying dark matter fields we find the former to be more triaxial if theanalysis is restricted to massive subhaloes. For three of the four analysed haloes the increased triaxiality of the distributions of massive subhaloes can be explained by a systematic effect caused by the low number of objects. Subhaloes of the fourth halo show indications for anisotropic accretion via their strong triaxial distribution and orbit alignment with respect to the dark matter field. These results are independent of the employed subhalo finder. Comparing the shape of the observed Milky Way satellite distribution to those of high-resolution subhalo samples from simulations, we find an agreement for samples of bright satellites, but significant deviations if faint satellites are included in the analysis. These deviations might result from observational incompleteness., Comment: 15 pages, 11 figures, 2 tables. 1 figure removed to reduce paper extension, shorter discussion, accepted for publication in MNRAS

The ever increasing size and complexity of data coming from simulations of cosmic structure formation demands equally sophisticated tools for their analysis. During the past decade, the art of object finding in these simulations has hence developed into an important discipline itself. A multitude of codes based upon a huge variety of methods and techniques have been spawned yet the question remained as to whether or not they will provide the same (physical) information about the structures of interest. Here we summarize and extent previous work of the "halo finder comparison project": we investigate in detail the (possible) origin of any deviations across finders. To this extent we decipher and discuss differences in halo finding methods, clearly separating them from the disparity in definitions of halo properties. We observe that different codes not only find different numbers of objects leading to a scatter of up to 20 per cent in the halo mass and Vmax function, but also that the particulars of those objects that are identified by all finders differ. The strength of the variation, however, depends on the property studied, e.g. the scatter in position, bulk velocity, mass, and the peak value of the rotation curve is practically below a few per cent, whereas derived quantities such as spin and shape show larger deviations. Our study indicates that the prime contribution to differences in halo properties across codes stems from the distinct particle collection methods and -- to a minor extent -- the particular aspects of how the procedure for removing unbound particles is implemented. We close with a discussion of the relevance and implications of the scatter across different codes for other fields such as semi-analytical galaxy formation models, gravitational lensing, and observables in general., Comment: 28 pages containing 13 figures & 4 tables + 9 pages appendix containing another 4 tables + 4 pages of references, accepted for publication in MNRAS

We present a detailed comparison of the substructure properties of a single Milky Way sized dark matter halo from the Aquarius suite at five different resolutions, as identified by a variety of different (sub-)halo finders for simulations of cosmic structure formation. These finders span a wide range of techniques and methodologies to extract and quantify substructures within a larger non-homogeneous background density (e.g. a host halo). This includes real-space, phase-space, velocity-space and time- space based finders, as well as finders employing a Voronoi tessellation, friends-of-friends techniques, or refined meshes as the starting point for locating substructure.A common post-processing pipeline was used to uniformly analyse the particle lists provided by each finder. We extract quantitative and comparable measures for the subhaloes, primarily focusing on mass and the peak of the rotation curve for this particular study. We find that all of the finders agree extremely well on the presence and location of substructure and even for properties relating to the inner part part of the subhalo (e.g. the maximum value of the rotation curve). For properties that rely on particles near the outer edge of the subhalo the agreement is at around the 20 per cent level. We find that basic properties (mass, maximum circular velocity) of a subhalo can be reliably recovered if the subhalo contains more than 100 particles although its presence can be reliably inferred for a lower particle number limit of 20. We finally note that the logarithmic slope of the subhalo cumulative number count is remarkably consistent and <1 for all the finders that reached high resolution. If correct, this would indicate that the larger and more massive, respectively, substructures are the most dynamically interesting and that higher levels of the (sub-)subhalo hierarchy become progressively less important., Comment: 16 pages, 7 figures, 2 tables, Accepted for MNRAS

[abridged] We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends (FOF), spherical-overdensity (SO) and phase-space based algorithms. We further introduce a robust (and publicly available) suite of test scenarios that allows halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large-scale structure of the universe. All the halo finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Via a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 30-40 particles. However, also here the phase space finders excelled by resolving substructure down to 10-20 particles. By comparing the halo finders using a high resolution cosmological volume we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity, and peak of the rotation curve)., Comment: 27 interesting pages, 20 beautiful figures, and 4 informative tables accepted for publication in MNRAS. The high-resolution version of the paper as well as all the test cases and analysis can be found at the web site http://popia.ft.uam.es/HaloesGoingMAD

We analyse the coarse-grained phase-space structure of the six Galaxy-scale dark matter haloes of the Aquarius Project using a state-of-the-art 6D substructure finder. Within r_50, we find that about 35% of the mass is in identifiable substructures, predominantly tidal streams, but including about 14% in self-bound subhaloes. The slope of the differential substructure mass function is close to -2, which should be compared to around -1.9 for the population of self-bound subhaloes. Near r_50 about 60% of the mass is in substructures, with about 30% in self-bound subhaloes. The inner 35 kpc of the highest resolution simulation has only 0.5% of its mass in self-bound subhaloes, but 3.3% in detected substructure, again primarily tidal streams. The densest tidal streams near the solar position have a 3-D mass density about 1% of the local mean, and populate the high velocity tail of the velocity distribution., Comment: Submitted to MNRAS on 12/10/2010, 11 pages, 10 figures