ENRPRD MAGT 020 CORC modelling Comenius University Institute

ENR-PRD. MAG-T 020 CORC modelling Comenius University, Institute of Electrical Engineering SAS, M. Vojenčiak, T. Kujovič, M. Mošať 1

Macroscopic model of Central Solenoid 2

Macroscopic magnetic model description • 2 D FEM based model of Central Solenoid – baseline 2018 • Hybrid model (superconductor grading + stainless steel grading) • Steel grading and superconductor grading based on latest PSI calculation • Super. Power REBCO tape with Ic = 352 A @ 4. 2 K, 12 T • Our concern is only the innermost REBCO cables Ss RE-123 rinner = 1. 528 m Nb 3 Sn Nb. Ti LTS part represents only magnetic flux contribution to whole coil router = 2. 691 m 3

Cable dimensions • Consisting of 7 CORC cables • 4 mm width Super. Power • 12 layered CORC cables • Inner 6 x 5 tapes plus outer 6 x 6 tapes • Total 66 tapes per CORC • 7 CORC subcables per cable 4

Macroscopic magnetic model description • 2 D FEM based model of Central Solenoid – baseline 2018 Dimensions - height 17. 35 m - inner radius 1. 528 m - outer radius 2. 691 m Number of conductors: Horizontally – 20 (2 x 10) Vertically – 76 (CS 3) & 37 (CS 1, 2, 4, 5) RE-123 rinner = 1. 528 m Nb 3 Sn Nb. Ti LTS part represents only magnetic flux contribution to whole coil router = 2. 691 m 5

Macroscopic magnetic model description • Magnetic flux density contribution from all five solenoidal coils • Model does not include Jc(B) dependence of HTS cables • No additional PF coil magnetic flux contribution included • Operating current constant in all turns – 46. 305 k. A Reached magnetic flux – 196. 7 Vs Number of conductors: Horizontally – 20 (2 x 10) Vertically – 76 (CS 3) & 37 (CS 1, 2, 4, 5) 6

Magnetic flux density – cross section Peak field – 13. 3 T 14 [T] 7

Magnetic flux density in cross section of CS 3 Inner radius Outer radius 8

Mechanical calculations – In progress 9

Basic model of CS coil Subcable modelled as one body. Material properties of subcable calculated from Elastic modulus of each material and their volume fraction of the subcable – Mixture approach Detailed model of single cable Subcable modelled as four main layers – Copper, Hastelloy, Copper and copper tube, each with respective Elastic modulus 10

Proposition of plan for next work • Model on the level of CORC cables • Observation of local magnetic field • Including Jc(B) dependence • Mechanical model – delayed due to error in definition of force in numerical calculation • Change in design – Stainless Steel reinforcement in the middle of copper formers of CORC cables 11