D. Arbelaez

A Novel Computer Code for Modeling Quench Protection Heaters in High-Field

This paper presents a recently developed Code for Heater Delay Analysis (CoHDA), which is a tool for modeling protection heater induced quenches in superconducting Nb3Sn high-field accelerator magnets. The CoHDA thermal model numerically computes the heat diffusion from the heater to the coil and estimates the time delay to quench initiation by comparing the coil temperature with its critical surface. The model takes into account heater geometry, power, and various insulation layers and coil properties. Computational heater delays are compared with experimental data from the U.S. Large Hadron Collider Accelerator Research Program Nb3Sn High-Gradient Quadrupole magnet with good agreement. Based on the results, CoHDA provides a useful tool for quench protection design in impregnated magnets.

\hbox{Nb}_{3}\hbox{Sn}

The Canted-Cosine-Theta (CCT) magnet design offers significant reductions in conductor stress by using mandrels to prevent the accumulation of operating Lorentz forces. Each mandrel consists of a cylindrical spar with ribs guiding the conductor. These ribs intercept the turn-to-turn accumulation of forces by transferring them to the spar. Design studies of a layered CCT coil pack coupled to a shell-based structure are shown. The use of a 3-D periodic symmetry region to reduce the problem size for finite element modeling is detailed along with a discussion of axial boundary conditions. ANSYS calculation results for a two layer NbTi dipole being constructed at LBNL (CCT1) are presented. ANSYS calculations show the Lorentz force induced stress in CCT1 at the single turn level, demonstrating interception and suggesting investigation of CCT design with minimal structure external to the coil pack.

Accelerator Magnets

Cable deformation simulation and a hierarchical framework for Nb 3 Sn Rutherford cables D Arbelaez, S O Prestemon, P Ferracin, A Godeke, D R Dietderich and G Sabbi Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA E-mail: darbelaez@lbl.gov Abstract. Knowledge of the three-dimensional strain state induced in the superconducting filaments due to loads on Rutherford cables is essential to analyze the performance of Nb 3 Sn magnets. Due to the large range of length scales involved, we develop a hierarchical computational scheme that includes models at both the cable and strand levels. At the Rutherford cable level, where the strands are treated as a homogeneous medium, a three- dimensional computational model is developed to determine the deformed shape of the cable that can subsequently be used to determine the strain state under specified loading conditions, which may be of thermal, magnetic, and mechanical origins. The results can then be transferred to the model at the strand/macro-filament level for rod restack process (RRP) strands, where the geometric details of the strand are included. This hierarchical scheme can be used to estimate the three-dimensional strain state in the conductor as well as to determine the effective properties of the strands and cables from the properties of individual components. Examples of the modeling results obtained for the orthotropic mechanical properties of the Rutherford cables are presented. 1. Introduction The ability to obtain the three dimensional strain state in Nb 3 Sn filaments is of key importance in understanding the performance of Nb 3 Sn magnets under macro-scale loads. However, this is a difficult task due to the widely varying length scales in superconducting magnets. For example, some of the length scales that play an important role are the magnet, coil, cable, strand, and filament length scales, where the magnet and coil are in the m scale, the cable and strand in the mm scale, and the filaments in the µm scale. Clearly, the direct simulation of the macro-scale problem including the micro-scale details is prohibitably expensive; therefore, multi-scale tools that can be used to understand the behavior across various length scales are necessary. The development of such tools could be a significant aid in the understanding of magnet performance and for magnet design. At Lawrence Berkeley National Laboratory (LBNL) work has begun on bridging the full range of scales seen in large accelerator magnets, with specific emphasis on magnets fabricated with Rutherford cables. Since the length scales vary widely, several models, which include the relevant physics at the different length scales, must be created, and efficient techniques must be developed to bridge these scales. In this paper the main focus, within this larger framework, is on the development of models at the cable and strand scale that bridge the behavior between the coil scale and the length scale of a macro-filament in a rod restack process (RRP) strand.

Structural Design and Analysis of Canted–Cosine–Theta Dipoles

A conceptual design of curved superconducting magnet for a carbon therapy gantry has been proposed. The design can reduce the gantrys size and weight and make it more comparable with gantries used for proton therapy. In this paper we report on a combined function, 5 T, superconducting dipole magnet with a 260 mm bore diameter that is curved 90 degrees at a radius of 1269 mm. The magnet superimposes two layers of oppositely wound and skewed solenoids like windings, energized in a way that nulls the solenoid field and doubles the dipole field component. Furthermore, the combined architecture of the windings can create a selection of field terms that are off the near-pure dipole field. Combined harmonics such as a quadrupole and sextupole are needed to adjust the beam trajectory. Ways to adjust the field and beam trajectory, magnet size and assembly, structure and pre-stress are considered.

Cable deformation simulation and a hierarchical framework for Nb3Sn Rutherford cables

A high-performance superconducting undulator concept, incorporating stacked YBa2Cu3O7-δ (YBCO) tapes operating at 4.2 K, is currently under investigation at LBNL as one of many technology options for future FEL applications. The concept is particularly promising for narrow-gap, short period (<;10 mm) regimes, where traditional superconducting and permanent magnet technologies are less-suited. The current path is dictated by etching the YBCO layer using lithography techniques, resulting in a high degree of uniformity from tape to tape as well as a straightforward and highly cost-effective means of production. We describe the approaches being pursued for the tape preparation and the conceptual design of a device. We also provide an initial analysis of the impact of fabrication tolerances in terms of field errors for FEL application.

Conceptual Design of a 260 mm Bore 5 T Superconducting Curved Dipole Magnet for a Carbon Beam Therapy Gantry

The ability to correct magnetic field errors in a superconducting undulator is critical for the successful application of these devices in future and existing light sources. These field errors, which can emanate from sources such as machining and coil winding imperfections, can lead to reduced light source performance by introducing errors in both the electron trajectory and the relative phase relationship between the oscillating electrons and the emitted photons. In this work, correction schemes are presented, which use a single power supply along with a superconducting switch network to define the path for the current during undulator tuning. The basic switching concept was previously designed and successfully tested at Lawrence Berkeley National Laboratory; the approach presented here is a significant advancement in generalizing and scaling that core concept. A new fabrication method is presented here, which uses lithographic methods to produce current paths and switch heaters on a superconducting film. The effect of an example corrector current path design on the magnetic field is investigated using the Finite Element Method, and the results at various undulator and corrector energization levels are presented. Experimental results from the heater switch concept are also presented.

Development and Analysis of HTS-Undulator Components for FEL Applications

We use a recently developed quench protection heater modeling tool for an analysis of heater delays in superconducting high-field Nb3Sn accelerator magnets. The results suggest that the calculated delays are consistent with experimental data, and show how the heater delay depends on the main heater design parameters.

Magnetic Field Correction Concepts for Superconducting Undulators

(Bi2212) wire is investigated through numerical simulations. This work is part of the U.S. Very High Field Superconducting Magnet Collaboration (VHFSMC). Numerical simulations are carried out using a one-dimensional computational model of thermal transport in Bi2212 compositewires.A quench issimulated by introducing heat in a section of the wire, and the voltage and temperature are monitored as function of time and position. The quench energy, normal zone propagation velocity, and spatial distribution of temperature are calculated for varying transport current and applied magnetic field. The relevance of these simulations in defining criteria for experimental measurements is discussed. Index Terms—High temperature superconductor, quench, simulation.

Modeling heat transfer from quench protection heaters to superconducting cables in Nb3Sn magnets

A next step of energy increase of hadron colliders beyond the LHC requires high-field superconducting magnets capable of providing a dipolar field in the range of 16 T in a 50-mm aperture with accelerator quality. These characteristics could meet the requirements for an upgrade of the LHC to twice the present beam energy or for a 100-TeV center of mass energy future circular collider. This paper summarizes the activities and plans for the development of these magnets, in particular within the 16 T Magnet Technology Program, the WP5 of the EuroCirCol, and the U.S. Magnet Development Program.

Numerical Investigation of the Quench Behavior of

High-critical current density (Jc) Nb3Sn wires such as restacked-rod process wires are used in Rutherford cables for high-field superconducting magnets. However, during cabling, the wires experience strong plastic strains, which break some superconducting sub-elements and can degrade the electromagnetic performances. The damage can be reduced by forming Cu-Sn phases in the sub-elements during an annealing process prior to cabling. We found experimentally that annealing plays a significant role in reducing damage. Furthermore, we used finite-element models to validate the observations on samples and quantify the impact of annealing on damage reduction.