Discrete electromagnetism (DEM)-in the authors' view-should be a self-consistent theory, mirroring the properties of the continuous electromagnetic theory in a discrete setting. Any recursion to ...continuous techniques can be interpreted as an inconsistency in the discrete theory. Recently, discrete Hodge operators on tetrahedra and triangles have been introduced that avoid the concepts of interpolation and integration of fields. In this paper we introduce a geometrical definition of a discrete Hodge operator for general dimension n and degree p,0lesnles3,0lesplesn. The definition generalizes previously published definitions. The increased level of abstraction allows for a short definition and a concise discussion of the properties of this operator
During 2016, one-quarter of the LHC main dipoles have has been powered above the 7.7 T operational field, to reach a field of 8.1 T. These tests were done to confirm the extrapolation of the training ...behavior based on a Gaussian tail of the quench distribution. In this paper, it is shown that a modified Gaussian distribution can be used to better model the quench distributions. We then present the data above 6.5 TeV, showing that they are compatible with the previous expectations. We present the data of retraining of sector 12, which was warmed up in 2016 to replace a magnet, and training of individual magnets that went through several thermal cycles: there is an indication that training campaigns during successive warm-ups and cool-downs could become shorter. We finally show that a significant correlation is found between the training of the installed magnet and individual test after a thermal cycle (second cool-down). On the other hand, no correlation is found with individual test under virgin conditions (first cool-down).
The Large Hadron Collider (LHC) contains eight main dipole circuits, each of them with 154 dipole magnets powered in series. These 15-m-long magnets are wound from Nb-Ti superconducting Rutherford ...cables, and have active quench detection triggering heaters to quickly force the transition of the coil to the normal conducting state in case of a quench, and hence reduce the hot spot temperature. During the reception tests in 2002-2007, all these magnets have been trained up to at least 12 kA, corresponding to a beam energy of 7.1 TeV. After installation in the accelerator, the circuits have been operated at reduced currents of up to 6.8 kA, from 2010 to 2013, corresponding to a beam energy of 4 TeV. After the first long shutdown of 2013-2014, the LHC runs at 6.5 TeV, requiring a dipole magnet current of 11.0 kA. A significant number of training quenches were needed to bring the 1232 magnets up to this current. In this paper, the circuit behavior in case of a quench is presented, as well as the quench training as compared to the initial training during the reception tests of the individual magnets.
The goal of the High Luminosity LHC project is upgrading the LHC in order to increase its luminosity by a factor of five. To achieve this, 24 150-mm-aperture 12-T Nb 3 Sn quadrupole magnets are to be ...installed close to the two interaction regions at ATLAS and CMS. This new generation of high-field magnets poses a significant challenge concerning the protection of the coils in the case of a quench. The very high stored energy per unit volume requires a fast and effective quench heating system in order to limit the hot-spot temperature and hence avoid damage due to overheating. Conventional protection systems based on quench heaters have a limited response time due to the thermal insulation between the heater and the coil. An advanced solution for the protection of high-field magnets is the coupling-loss induced quench (CLIQ) system, recently developed at CERN. Due to its fast intrawire energy-deposition mechanism, CLIQ is a very effective, yet electrically robust, quench protection system. Various protection scenarios, including quench heaters, CLIQ, or combinations of the two methods, are analyzed and discussed, with the aim of minimizing the coil's hot-spot temperature and thermal gradients during the discharge. The proposed design assures a fully redundant system.
The design and construction of a wide-aperture, superconducting quadrupole magnet for the LHC insertion region is part of a study towards a luminosity upgrade of the LHC at CERN. The engineering ...design of components and tooling, the procurement, and the construction work presented in this paper includes innovative features such as more porous cable insulation, a new collar structure allowing horizontal assembly with a hydraulic collaring press, tuning shims for the adjustment of field quality, a fishbone like structure for the ground-plane insulation, and an improved quench-heater design. Rapid prototyping of coil-end spacers and trial-coil winding led to improved shapes, thus avoiding the need to impregnate the ends with epoxy resin, which would block the circulation of helium. The magnet construction follows established procedures for the curing and assembly of the coils, in order to match the workflow established in CERN's "large magnet facility." This requirement led to the design and procurement of a hydraulic press allowing for both a vertical and a horizontal position of the coil-collar pack, as well as a collapsible assembly mandrel, which guarantees the pack's four-fold symmetry during collaring. The assembly process has been validated with the construction of two short models, instrumented with strain gauges and capacitive pressure transducers. This also determines the final parameters for coil curing and shim sizes.
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 magnets.
We present a comparison between the electromagnetic model of the main LHC magnets and the magnetic measurements carried out during production. The goal of this study is to test the validity range of ...the model and to uncover discrepancies between models and reality. We de-compose the field computation into several parts: geometry (coils, collars, and yoke), persistent currents in the superconducting cables, and saturation of the iron yoke. For each component we give the agreement between model and measurements. This gives an indication about the precision one can expect to obtain from a simulation code-this information is particularly relevant for future upgrades of the LHC.
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