Symbolical Analysis of RF-Network Problems using Mason’s Rule

We briefly review Mason’s rule for the computation of RF-network problems and show its implementation into the software package freeMASON. This tool solves symbolically Mason’s rule for any wave quantity and allows to derive analytical expressions as well as their functional evaluation. We demonstrate our approach studying the effect of an unbalanced magictee on the RF power distribution to two accelerating cavities

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

Analytic Models for the Calculation of the Iron Yoke Contribution in Superconducting Accelerator Magnets

The superconducting coil of an accelerator magnet is usually surrounded by magnetic material, the iron yoke, in order to enhance the field in the aperture and to reduce the fringe field outside the magnet. For the calculation of the magnetic field of such superconducting magnets, numerical methods, typically FEM are used. Nevertheless, analytic solutions of simplified geometries are still needed in order to cross-check numerically obtained results and gain deeper understanding of the underlying principles. For the calculation of the effect of the iron yoke on the field distribution and field quality of superconducting coils as a first approximation a circular hollow cylinder of high permeable material could be used

Estimation of the Required Amount of Superconductors for High-field Accelerator Dipole Magnets

The coil size and the corresponding amount of superconducting material that is used during the design process of a magnet cross-section have direct impacts on the overall magnet cost. It is therefore of interest to estimate the minimum amount of conductors needed to reach the defined field strength before a detailed design process starts. Equally, it is useful to evaluate the efficiency of a given design by calculating the amount of superconducting cables that are used to reach the envisaged main field by simple rule. To this purpose, the minimum amount of conductors for the construction of a dipole of given main field strength and aperture size is estimated taking the actual critical current density of the used strands into account. Characteristic curves applicable for the NED Nb$_{3}$Sn strand specification are given and some of the recently studied different dipole configurations are compared. Based on these results, it is shown how the required amount of conductors changes due to the iron yoke contribution and the loss of current-transporting surface by means of insulation and cabling

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

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

Introduction of Reference Design 2 for the NED 15 t Large Aperture Dipole

In this report, the results of the electromagnetic design study for the cos θ-layer-type dipole are presented. The final configuration is referred to as Reference Design 2 for NED. The studied dipole is an 88 mm large bore, single aperture dipole surrounded by an iron yoke. It relies on the specifications for the Nb$_{3}$Sn strand and the Rutherford-type cable as well as on the material properties, the agreed dimensions and the maximum forces agreed upon by the collaboration. This design study is in the framework of CERN contributions to NED

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 Nb$_{3}$Sn conductor ( c = 1500A mm 2 @15 T, 4.2 K) in collaboration with European industry and at the design of a highfield dipole magnet making use of this conductor. In the framework of the NED collaboration which coordinates the activity of several institutes,CERNhas contributed to the electromagnetic design study of a cos , 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