Simulation of Electrodynamics in HighTemperature Superconducting Magnets L

Simulation of Electrodynamics in High-Temperature Superconducting Magnets L. Bortot 1, 2, M. Mentink 1, S. Schoeps 2, J. Van Nugteren 1, A. Verweij 1 Special Thanks: B. Auchmann, F. Grilli (KIT), M. Maciejewski, M. Prioli, E. Ravaioli MPE Technical Meeting 28/02/2018 1 2 (*) (**) This work is supported by: (*) The ‘Excellence Initiative’ of the German Government and by the Graduate School of Computational Engineering at TU Darmstadt; (**) The Gentner program of the German Federal Ministry of Education and Research (grant no. 05 E 12 CHA).

Outline 1. Project overview 2. HTS operability 3. HTS Modeling 4. Simulation of the magnet Feather-M 2 5. Summary and Outlook

Project Overview • Protection of HTS-based high-field accelerator magnets • • • CERN Technische Universität Darmstadt Graduate School of Excellence Computational Engineering (GCE) • • Dr. Matthias Mentink (TE-MPE-PE) Prof. Dr. Sebastian Schöps (TU Darmstadt) • 05. 2018 – 05. 2021 • • • Gentner Programme at CERN (grant no. 05 E 12 CHA) ‘Excellence Initiative’ of the German Government GCE at TU Darmstadt

High-Temperature Superconductors • J_eng(T) @ 5 T J_eng(B) @ 1. 9 K 10 Nb-Ti Nb 3 Sn Re. BCO 8 6 4 2 0 0 5 10 15 20 25 30 35 40 (K) Nb-Ti Nb 3 Sn Re. BCO 8 2 0 4 (k. A mm-2) 10 0 5 10 15 20 25 (T) 30 35 40

Tapes and Cables • ■ Copper ■ Re. BCO ■Substrate Source: CDS. Coiled Roebel cable (Henry Barnard, CERN). 5

Persistent Magnetization • (-) 1. 5 T 1 0. 5 s 0 0 (-) T 1 s 0. 5 0 0 0. 005 (m) 6 0. 01 1. 5 0. 005 0. 01

Quench Protection • Quench propagation Quench resistance Hotspot temperature Minimum quench energy Accurate prediction of persistent currents crucial for both, field quality and quench issues 7 [1] Van Nugteren, Jeroen. High temperature superconductor accelerator magnets. Diss. Twente U. , Enschede, 2016.

Modeling – How? • 8

Modeling – Discrete Equations • Ampere-Maxwell Law Faraday Law Constraint on current 9

Crosscheck • (J) Ohmic loss per cycle 1 E+01 1 Hz 1 E+00 10 Hz 1 E-01 100 Hz 1 E-02 1000 Hz 1 E-03 1 E-04 1 E-05 1 E-06 10 0. 5 1. 0 1. 5 2. 0 Normalized current (-) [2] V. M. Rodriguez-Zermeno et al. , "Towards Faster FEM Simulation of Thin Film Superconductors: A Multiscale Approach, " in IEEE Transactions on Applied Superconductivity, vol. 21, no. 3, pp. 3273 -3276, June 2011. 2. 5

Benchmark Forecasts on expected computational time: Same physics… Computational time 1 tape 1 E+02 1 E+01 (hours) 5 tapes 10 tapes 8 h 1 E+00 1 E-01 H A-H 1 E-02 A-H opti 1 E-03 1 Increased computational cost 10 100 tapes (-) 10000 Optimization of: Mesh, solver, numerical implementation 11

Simulation of the Feather-M 2 Magnet 5 Tesla HTS insert-dipole, recently built at CERN [3] • Insert for the FRESCA 2 magnet • Coil based on Roebel geometry y z y x wing and central decks 2 D cross section Iron poles Courtesy of J. Van Nugteren 12 x [3] Van Nugteren, Jeroen, et al. "Powering of an HTS dipole insert-magnet operated standalone in helium gas between 5 and 85 K. " Superconductor science and technology 31. 6 (2018): 065002.

• 2 (k. A) 1. 5 1 0. 5 0 -1000 13 0 1000 (s) 2000 3000

Electrodynamics - 01 • s Total magnetic flux density (T), 1 quadrant 14 Magnetic flux density (T) due to eddy currents, 1 quadrant

Electrodynamics - 02 • s a) a) 15 b) c)

Results – 01 (Sim Vs Measurements) • 25. 0 K 4. 5 K B 1 (T) b 3 (units) 3 3 3 2 2 2 1 1 1 0 0. 00 0. 50 600 400 400 200 200 0. 50 1. 00 0 0. 00 100 100 50 50 50 0 0. 00 0. 50 t / tend 16 1. 00 0. 00 600 0 0. 00 b 5 (units) 68. 0 K 1. 00 0 0. 00 0. 50 t / tend 1. 00 0 0. 00 0. 50 1. 00 t / tend

Results – 02 (Sim Vs Measurements) • 25. 0 K 4. 5 K ΔB 1 (T) 30 30 30 10 10 10 -10 0. 0 Δb 3 (units) 2. 0 4. 0 6. 0 2. 0 4. 0 -10 50 50 30 30 30 10 10 10 -10 2. 0 4. 0 6. 0 0. 0 2. 0 4. 0 8 8 3 3 3 -2 0. 0 2. 0 4. 0 k. A 6. 0 0. 0 2. 0 k. A 4. 0 0. 0 1. 0 2. 0 -10 8 -2 17 0. 0 50 0. 0 Δb 5 (units) 68. 0 K -2 0. 0 k. A

Summary and Outlook High Temperature Superconductors • Interesting option for future accelerator magnets • Open questions related to field quality and quench protection (operability) Electrodynamics in HTS • Crucial for both field quality and quench protection • Multi rate and scale eddy-current phenomenon, nasty nonlinearities • Ad-hoc formulation implemented in FEM, for a full-size magnet (calc. time ~ 1. 5 h) • Encouraging agreement with measurements What is next • Heat balance equation and field-circuit coupling interface • Quench protection studies (e. g. Feather 2 + FRESCA 2) • Field quality improvement (Ideas from the persistent shim coil concept) • Possibly… Papers writing Thank you for your attention! 18

Backup 20

Jc (T, B, theta) • 21 lift factor [3] Fujikura, Y-based high temperature superconductor. Company leaflet at ICEC (2014). [4] Fleiter, J. , and A. Ballarino. "Parameterization of the critical surface of REBCO conductors from Fujikura. " CERN internal note, EDMS 1426239 (2014). `

Field multipoles without eddy currents Staircase Scenario at 4. 5 K • “Eddy” considers the HTS tape dynamics • “No Eddy” assumes a homogeneous current density in the tapes B 1 b 3 3 600 2 meas 400 meas 1 eddy 200 eddy 0 0. 00 no eddy 0. 50 1. 00 0 0. 00 no eddy 0. 50 b 5 b 7 80 15 60 meas 40 eddy 20 0 0. 00 22 1. 00 no eddy 0. 50 1. 00 10 meas 5 eddy 0 0. 00 no eddy 0. 50 1. 00