Nikolai Schwerg

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 magnets.

Comparison of 2-D Magnetic Designs of Selected Coil Configurations for the Next European Dipole (NED)

The next European dipole (NED) activity is developing a high-performance Nb3Sn wire (aiming at a non-copper critical current density of 1500 A/mm2 at 4.2 K and 15 T), within the framework of the Coordinated Accelerator Research in Europe (CARE) project. This activity is expected to lead to the fabrication of a large aperture, high field dipole magnet. In preparation for this phase, a working group on magnet design and optimization (MDO) has been established to propose an optimal design. Other parallel work packages are concentrating on relevant topics, such as quench propagation simulation, innovative insulation techniques, and heat transfer measurements. In a first stage, the MDO working group has selected a number of coil configurations to be studied, together with salient parameters and features to be considered during the evaluation: the field quality, the superconductor efficiency, the conductor peak field, the stored magnetic energy, the Lorentz forces and the fabrication difficulties. 2-D magnetic calculations have been performed, and the results of this comparison between the different topologies are presented in this paper. The 2-D mechanical computations are ongoing and the final stage will be 3-D magnetic and mechanical studies.

Design Challenges for a Wide-Aperture Insertion Quadrupole Magnet

The design and development of a superconducting (Nb-Ti) quadrupole with 120-mm aperture, for an upgrade of the LHC insertion region, faces challenges arising from the LHC beam optics requirements and the heat-deposition. The first triggered extensive studies of coil alternatives with four and six coil-blocks in view of field quality and operation margins. The latter requires more porous insulation schemes for both the cables and the ground-plane. This in turn necessitates extensive heat propagation and quench-velocity studies, as well as more efficient quench heaters. The engineering design of the magnet includes innovative features such as self-locking collars, which will enable the collaring to be performed with the coils on a horizontal assembly bench, a spring-loaded and collapsible assembly mandrel, tuning-shims for field quality, porous collaring-shoes, and coil end-spacer design based on differential geometry methods. The project also initiated code extensions in the quench-simulation and CAD/CAM modules of the CERN field computation program ROXIE.

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 design of coil ends for the SIS300 dipole magnets of the FAIR project.

Challenges in the Thermal Modeling of Quenches With ROXIE

The simulation of thermal processes in a superconducting coil during resistive transition is an intricate problem. A detailed thermo-hydraulic modeling comes at a high computational cost and suffers from the large number of empirical parameters. We present a macroscopical approach, covering the most relevant features while providing enough flexibility to gauge the material parameters with measurements. By combining the thermal model with numerical field computation, effects can be simulated that are otherwise difficult to measure, e.g., turn-to-turn voltages, quench propagation and recovery. The thermal model recently implemented in the CERN field computation program ROXIE is validated by means of measurements on model and prototype magnets, as well as data taken during the hardware commissioning of the LHC.

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.

Trends in cable magnetization and persistent currents during the production of the main dipoles of the Large Hadron Collider

The production of more than 60% of superconducting cables for the main dipoles of the Large Hadron Collider has been completed. The results of the measurements of cable magnetization and the dependence on the manufacturers are presented. The strand magnetization produces field errors that have been measured in a large number of dipoles (approximately 100 to date) tested in cold conditions. We examine here the correlation between the available magnetic measurements and the large database of cable magnetization. The analysis is based on models documented elsewhere in the literature. Finally, a forecast of the persistent current effects to be expected in the LHC main dipoles is presented, and the more critical parameters for beam dynamics are singled out.

Estimation of the Instantaneously Dissipated Hysteresis Losses in Superconductors

Cables in superconducting magnets are subjected to field-dependent losses, i.e., induced interstrand and interfilament coupling losses, and superconductor hysteresis losses. For the two kinds of induced eddy currents, analytical and numerical models are available, allowing calculating the dissipated power under various operating conditions. For the losses stemming from the superconductor magnetization, the literature only gives formulas for the dissipated energy over closed excitation cycles. We derive an expression for the instantaneously dissipated hysteresis losses during an arbitrary ramp profile using a simplified geometry and hysteresis model. This allows estimating the losses dissipated in nonclosed excitation loops.

2D Magnetic Design and Optimization of a 88-mm Aperture 15 T Dipole for NED

The Next European Dipole (NED) activity supported by the European Union aims at the development of a high-performance Nb3Sn conductor (Jc = 1500 A/mm2 @ 15 T, 4.2 K) in collaboration with European industry and at the design of a high- field dipole magnet making use of this conductor. In the framework of the NED collaboration which coordinates the activity of several institutes, CERN has contributed to the electromagnetic design study of a cos - thetas, layer-type superconducting dipole with an 88 mm aperture that is able to reach 15 T at 4.2 K. Part of the optimization process was dedicated to the reduction of the multipole coefficients so as to improve field quality while keeping an efficient peak-field to main-field ratio. In this paper, we present the optimization of the coil cross-section and of the shape of the iron yoke to reduce saturation-induced field errors during ramp. The effects of persistent magnetization currents are also estimated and different methods to compensate persistent-current-induced field distortions are presented.

Development of a Current Fit Function for NbTi to be Used for Calculation of Persistent Current Induced Field Errors in the LHC Main Dipoles

A new fit function for the critical current density of superconducting NbTi cables for the LHC main dipoles is presented. Existing fit functions usually show a good matching of the very low field range, but produce a current density which is significantly too small for the intermediate and high field range. Consequently the multipole range measured at cold is only partially reproduced and loops from current cycling do not match. The presented function is used as input for the field quality calculation of a complete magnet cross-section including arbitrary current cycling and all hysteresis effects. This way allows to trace a so-called finger-print of the cable combination used in the LHC main bending magnets. The finger-print pattern is a consequence of the differences of the measured superconductor magnetization of cables from different manufacturers. The simulation results have been compared with measurements at cold obtained from LHC main dipoles and a very good agreement for low and intermediate field values could be observed