1. QXF Magnetization VERY preliminary analysis Susana Izquierdo Bermudez 07/05/2013

2. QXF. Main Parameters 2 Napa Cross-Section Iron yoke updated (remove bus-bar slot) Jc fit https://plone.uslarp.org/MagnetRD/DesignStudies/QX- CD/Magnetic/Study%20of%20the%20QXF%20cross-section/folder.2013-04-15.9119834501/ 2650A/mm2 at 12T, 4.2K 1400A/mm2 at 15T, 4.2K Degradation: 5 %

3. QXF. Cable parameters XF150HTA (ref. 1, nov 2012) XF150HTA1 (ref. 2, march 2013) XF150HTA2 (ref. 3, may 2013) Bare Cable after reaction Width (mm) 18.63818.3 Thickness in (mm) 1.4591.454 Thickness out (mm) 1.6761.66 Other cable parameters # strands 40 transposition pitch (mm) --109 Degradation (%) 555 Insulation thickness Radial (mm) 0.150.125 Azimuthal (mm) 0.150.125 Jc Summers fit (sf no included) Data 2650A/mm2 at 12T, 4.2K 1400A/mm2 at 15T, 4.2K 2650A/mm2 at 12T, 4.2K 1400A/mm2 at 15T, 4.2K 2650A/mm2 at 12T, 4.2K 1400A/mm2 at 15T, 4.2K C 3.82E+10 Bc20 28.075 Tc0 18 Filament Name OST RRP 108/127 Outer diameter (um) 50 56 Inner diameter (um) 000 Strand Diameter (mm) 0.85 Cu/SC 1.13 1.15 RRR 150 3 Parameters used for all the calculations shown in this presentation WRONG! Reference?

4. Magnetization models implemented in ROXIE Scalar model (nested ellipse model) 4 Identical to the scalar model, but takes into account that, in the case of an applied rotating field, the orientation of the magnetization that is produced by a filament de- couples from the direction of the source field. It has never been validated experimentally Critical state model (beam model) Vector model REFERENCES: 1.Superconductor Magnetization Modelling for the Numerical Calculation of Field Errors in Accelerator Magnets 2.Magnetization Measurements of High-Jc Nb3Sn strands

5. Strand Magnetization 5 Significant differences at low field Analysis for 11T Magnet (Bernhard Auchmann) First Guess for QXF Summers fit Deff = 50 µm (should be 56 µm!)

6. Impact of Strand Magnetization in b6 6 Persistent Currents not Considered Persistent Currents Considered Δb6 Δb6 Iron yoke not considered -5.86-7.10 -1.24 Non-linear iron yoke0.36-0.52-0.88 b6 @ Rref = 50 mm, I = Inom (17 kA) 0.01I nom -> I nom ->0.001I nom ->I nom Current cycle: Data for second up-ramp: -0.62 for Deff = 56 µm Scalar magnetization model zoom

7. Proposals and Open Questions Compare magnetization calculations between Opera and Roxie Reference design? Should we incorporate the impact of coil deformation in the design of QXF cross section? Would be very nice to do the analysis in HQ and see how magnetic measurements correlate with ROXIE calculations 7

9. Nested ellipse model 9 Superconductor Magnetization Modelling for the Numerical Calculation of Field Errors in Accelerator Magnets

10.  ROXIE magnetization model o Summers fit, o Deff = 55 µm, o Aleksa/Russenschuck/Völlinger scalar model.  Strand magnetization model consistent with measurements at CERN and FNAL. Strand magnetization model Aug. 31, 2012 10 B. Auchmann TE-MSC-MDT Courtesy E. Barzi

11. Algorithm for the calculation of persistent currents as incorporated in the field computation program ROXIE. 11 1.Superconductor Magnetization Modelling for the Numerical Calculation of Field Errors in Accelerator Magnets

12. 12

13. I=Inom