The Pairing Matrix in Discrete Electromagnetism On the Geometry of Discrete de Rham Currents

We introduce pairing matrices on simplicial cell complexes in discrete electromagnetism as a means to avoid the explicit construction of a topologically dual complex. Interestingly, the Finite Element Method with first-order Whitney elements â when it is looked upon from a cell-method perspective â features pairing matrices and thus an implicitly defined dual mesh. We show that the pairing matrix can be used to construct discrete energy products. In this exercise we find that different formalisms lead to equivalent matrix representations. Discrete de Rham currents are an elegant way to subsume these geometrically equivalent but formally distinct ways of defining energy-products

Experimental results and analysis from the 11 T Nb3Sn DS dipole

FNAL and CERN are developing a 5.5-m-long twin-aperture Nb3Sn dipole suitable for installation in the LHC. A 2-m-long single-aperture demonstrator dipole with 60 mm bore, a nominal field of 11 T at the LHC nominal current of 11.85 kA and 20% margin has been developed and tested. This paper presents the results of quench protection analysis and protection heater study for the Nb3Sn demonstrator dipole. Extrapolations of the results for long magnet and operation in LHC are also presented.Comment: 10 pages, Contribution to WAMSDO 2013: Workshop on Accelerator Magnet, Superconductor, Design and Optimization; 15 - 16 Jan 2013, CERN, Geneva, Switzerlan

Validation of a Coupled Thermal-Electromagnetic Quench model for Accelerator Magnets

Quench simulation in superconducting magnets is a challenging task due to the interdependence of thermal, electrical, and magnetic phenomena. We present a new quench-simulation module in the CERN magnet-design program ROXIE. Thermal, electrical, and magnetic models are solved simultaneously. The integrated model helps to single out the impact of different phenomena. We can thus reach a deeper understanding of measured quench behavior. Moreover, the magnet-design process is improved due to the implementation within an integrated design and optimization environment. We compare simulations and measurements of the LHC main dipole magnet

Quench Simulation in an Integrated Design Environment for Superconducting Magnets

The electrical integrity of superconducting magnets that go through a resistive transition (quench) is an important consideration in magnet design. Numerical quench simulation leads to a coupled thermodynamic and electromagnetic problem, due to the mutual dependence of material parameters. While many tools treat the electromagnetic field problem and the thermodynamic one independently, more recent developments adopt a strongly coupled approach in a 3-D finite-element environment. We introduce a computationally efficient weak electromagnetic-thermodynamic coupling within an integrated design environment for superconducting magnet

Discrete Differential Geometry Applied to the Coil-End Design of Superconducting Magnets

Coil-end design for superconducting accelerator magnets, based on the continuous strip theory of differential geometry, has been introduced by Cook in 1991. A similar method has later been coupled to numerical field calculation and used in an integrated design process for LHC magnets within the CERN field computation program ROXIE. In this paper we present a discrete analog on to the continuous theory of strips. Its inherent simplicity enhances the computational performance, while reproducing the accuracy of the continuous model. The method has been applied to the desig

Calculation of Field Quality in Fast-Ramping Superconducting Magnets

Fast-ramping superconducting (SC) accelerator magnets are the subject of R&D efforts at various laboratories. The simulation of field quality in fast-ramping magnets requires modifications of magnet design tools such as the CERN field computation program ROXIE. In this paper we present the efforts towards dynamic 2-D simulations of fast-ramping SC magnets. Models for persistent currents, inter-strand coupling currents, inter-filament coupling currents, and for eddy-currents in conducting coil-wedges are described and validated

2-D Electromagnetic Model of Fast-Ramping Superconducting Magnets

Fast-ramping superconducting (SC) accelerator magnets are the subject of R&D efforts by magnet designers at various laboratories. They require modifications of magnet design tools such as the ROXIE program at CERN, i.e. models of dynamic effects in superconductors need to be implemented and validated. In this paper we present the efforts towards a dynamic 2-D simulation of fast-ramping SC magnets with the ROXIE tool. Models are introduced and simulation results are compared to measurements of the GSI001 magnet of a GSI test magnet constructed and measured at BNL

Fast Ramping Superconducting Magnet Design Issues for Future Injector Upgrades at CERN

An upgrade of the LHC injection chain, and especially the sequence of PS and SPS, up to an extraction energy of 1 TeV, is one of the steps considered to improve the performance of the whole accelerator complex. The magnets for this upgrade require central magnetic field from 2 T (for a PS upgrade) to 4.5 T (for an SPS upgrade), for which superconducting magnets are a candidate. Due to the fast field sweep rate of the magnets (from about 1.5 T/s to 2.5 T/s), internal heating from eddy and persistent current effects (AC loss) must be minimized. In this paper we discuss a rationale for the design and optimization of fast ramped superconducting accelerator magnets, specifically aimed at the LHC injectors. We introduce a design parameter, the product of bore field and field ramp-rate, providing a measure of the magnet performance, and we apply it to choose the design range for a technology demonstration magnet. We finally discuss the dependence of key design parameters on the bore field and the bore diameter, to provide an approximate scaling and guidelines for critical R&D

Impact of CMS Stray Field on the Large Hadron Collider Beam Dynamics and Thin Solenoid in the SixTrack Code

The impact of the CMS main solenoid field and stray field on the coupling and on the dynamic aperture is evaluated for both LHC collision (7 TeV) and injection optics (450 GeV). To study the impact of CMS solenoid field on the LHC dynamic aperture, a new element ‘solenoid’ has been added in the SixTrack code and debugged. In Appendix B and C the analytical formulae applied on the solenoid are presented

Testing Beam-Induced Quench Levels of LHC Superconducting Magnets

In the years 2009-2013 the Large Hadron Collider (LHC) has been operated with the top beam energies of 3.5 TeV and 4 TeV per proton (from 2012) instead of the nominal 7 TeV. The currents in the superconducting magnets were reduced accordingly. To date only seventeen beam-induced quenches have occurred; eight of them during specially designed quench tests, the others during injection. There has not been a single beam- induced quench during normal collider operation with stored beam. The conditions, however, are expected to become much more challenging after the long LHC shutdown. The magnets will be operating at near nominal currents, and in the presence of high energy and high intensity beams with a stored energy of up to 362 MJ per beam. In this paper we summarize our efforts to understand the quench levels of LHC superconducting magnets. We describe beam-loss events and dedicated experiments with beam, as well as the simulation methods used to reproduce the observable signals. The simulated energy deposition in the coils is compared to the quench levels predicted by electro-thermal models, thus allowing to validate and improve the models which are used to set beam-dump thresholds on beam-loss monitors for Run 2.Comment: 19 page