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 niedermayer@temf.tu-darmstadt.de 19 April 2018 | 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

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 2

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 3

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, 032001, 2015 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 4

Multi layer surface impedance iteratively Vacuum Copper Titanium 6.4kHz 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 5

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 6

Overview NC vs. SC       W.Buckel, Supraleitung Grundlagen und Anwendung, Wiley-VCH Verlag GmbH & Co. KGaA 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 7

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, https://arxiv.org/abs/1108.1643 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 8

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 9

Magnetoresistance for HTS 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 10

Impedance for 1m beam pipe   Copper Stripes YBCO                                           19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 11

Impedance for 1m beam pipe @ 16T       NC magnetoresistance, cond. Factor 0.155 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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 12

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 13

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 14

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 15

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 16

Diagonal vorices distort the magnetic field stronger! ?? 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 17

Outlook: HTC magnetization  complicated hysteretic behavior PhD thesis C. Völlinger Treatment with the critical current model… (Bean‘s model) 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 18

Thank you for your attention! The End Thank you for your attention! 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 19

  77K     Buckel, Werner: Supraleitung, Grundlagen und Anwendungen, 7.Auflage, Wiley-VHC Verlag GmbH & Co.KGaA, 2013 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 20

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 21

Imaginary 0T 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 22

Imaginary 16T 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 23

Different shapes of stripes HTS Carbon 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 24

Different shapes of stripes HTS Carbon 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 25

Very thin stripes HTS Carbon 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 26

HTS Carbon 19 April 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 27

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 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 28