High Temperature Superconductor Coating for the FCC-hh Beam Pipe

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1 High Temperature Superconductor Coating for the FCC-hh Beam Pipe
Uwe Niedermayer, Patrick Krkotic, Daria Astapovich, Oliver Boine-Frankenheim Institut für Theorie Elektromagnetischer Felder Technische Universität Darmstadt, Germany 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 1 19 April 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

2 Contents FCC-hh Beam Pipe
Beam Impedance 2D, iterative surface impedane model High Temperature Superconductors Surface impedance in the presence of strong magnetic field Transverse impedance of the FCC-hh pipe An Idea to measure surface impedance Outlook: Superconductor magnetization and effects on field quality 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 2

3 FCC-hh beam pipe design
Slit for synchrotron radiation dissipation Pumping holes  Bernhard Aperture: Z_tr ~ 1/b3 Coating for impedance reduction Copper (300µm) HTS (1µm, stripes) Coating for SEY reduction Carbon (thin layer) Surface treatment for SEY reduction Mechanical treatment Laser treatment (c) CERN 2016 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 3

4 FEM 2D impedance solver based on Helmholtz-split
De Rham diagram for the 2D and 3D Sobolev Spaces and Operators Nédélec edge elements Surface Impedance Boundary Condition (SIBC): Any bulk frequency domain material properties or any surface impedance can be converted into longitudinal or transverse beam impedance! U. Niedermayer et al., Space charge and resistive wall impedance computation in the frequency domain using the finite element method, Phys. Rev. –STAB 18, , 2015 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 4

5 Multi layer surface impedance iteratively
Vacuum Copper Titanium 6.4kHz 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 5

6 High Temperature Superconductors (HTS)
Rare earth copper oxides Strongly anisotropic Various technical applications Magnetic field penetrates the HTS by forming quantized flux vortices! 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 6

7 Overview NC vs. SC W.Buckel, Supraleitung Grundlagen und Anwendung, Wiley-VCH Verlag GmbH & Co. KGaA 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 7

8 Magnetoresistance and T-dependence for normal conductors
Residual Resistivity Ratio Kohler‘s law Plateau is determined by impurities! See also: E. Metral, Beam Screen Issues, 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 8

9 Magnetoresistance for HTS Sergio Calatroni – (submitted to PR-AB )
Fluxon equation of motion under J x B drive: Depinning Frequency: Viscosity: Pinning force: 2-fluid model resistivity Flux flow resistivity F J 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 9

10 Magnetoresistance for HTS
19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 10

11 Impedance for 1m beam pipe
Copper Stripes YBCO 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 11

12 Impedance for 1m beam pipe @ 16T
NC magnetoresistance, cond. Factor at 50 K Depinning frequency* Copper Stripes YBCO Note that the SC impedance is always a surface impedance! (the skin depth can never exceed the London depth) 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 12

13 Proposal: Experimental X-check of surface impedance of YBCO
9K Cryostat Iron Shielding Nb3Sn Solenoids Substrate coated with YBCO Magnetic field (normal to sample) Pure Niobium Cavity VNA Loop Coupler  Polarization 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 13

14 Proposal: Experimental X-check of surface impedance of YBCO
9K Cryostat Iron Shielding Nb3Sn Solenoids Substrate coated with YBCO Magnetic field (parallel to sample) Pure Niobium Cavity VNA Loop Coupler  Polarization 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 14

15 Proposal: Experimental X-check of surface impedance of YBCO
9K Cryostat Iron Shielding Nb3Sn Solenoids Niobium plate (ref measurement) Pure Niobium Cavity VNA Loop Coupler  Polarization 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 15

16 Static magnetic field perturbation
Vortex solid Vortex fluid Normal Conductor Magnetic Induction Temperature Meissner phase Shubnikov phase Very coarse estimate: Field perturbation is being investigated in detail… 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 16

17 Diagonal vorices distort the magnetic field stronger!
?? 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 17

18 Outlook: HTC magnetization  complicated hysteretic behavior
PhD thesis C. Völlinger Treatment with the critical current model… (Bean‘s model) 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 18

19 Thank you for your attention!
The End Thank you for your attention! 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 19

20 77K Buckel, Werner: Supraleitung, Grundlagen und Anwendungen, 7.Auflage, Wiley-VHC Verlag GmbH & Co.KGaA, 2013 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 20

21 Combined surface impedance
Single surface impedance already implemented Split boundary such that where u is a parameterization of the boundary is a Dirichlet and is a Neumann boundary condition Evaluate at surface Include as boundary integral in weak formulation for FEM 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 21

22 Imaginary 0T 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 22

23 Imaginary 16T 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 23

24 Different shapes of stripes
HTS Carbon 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 24

25 Different shapes of stripes
HTS Carbon 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 25

26 Very thin stripes HTS Carbon
19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 26

27 HTS Carbon 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 27

28 Coupled bunch resistive instability
Most critical at injection due to less stiff beam! most unstable coupled-bunch mode at lowest frequency=2kHz Pipe only, solid Cu 50K E=3TeV Growth rate by factor 1.6 higher for 80 um coating Required thickness for “thick wall“ 150 um for 50K 450 um for 140K N. Mounet, EPFL Lausanne, formerly CERN 19 April | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 28