High Temperature Superconductor Coating for the FCC-hh Beam Pipe

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 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 1

Contents • FCC-hh Beam Pipe • Beam Impedance 2D, iterative surfaceimpedanemodel • High TemperatureSuperconductors • Surface impedance in thepresenceof strong magneticfield • Transverse impedanceofthe FCC-hhpipe • An Ideatomeasuresurfaceimpedance • Outlook: Superconductormagnetizationandeffects on fieldquality 04 January 2020 | 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 04 January 2020 | 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 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 4

High Temperature Superconductors(HTS) • Rare earth copper oxides • Strongly anisotropic • Various technical applications Magnetic field penetrates the HTS by forming quantized flux vortices! 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 6

Magnetoresistance and T-dependencefor normal conductors • Residual Resistivity Ratio • Kohler‘slaw Plateau is determined by impurities! See also: E. Metral, Beam Screen Issues, https://arxiv.org/abs/1108.1643 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 8

Magnetoresistance for HTSSergio 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 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 9

Impedance for 1m beam pipe @ 16T NC magnetoresistance, cond. Factor 0.155 at 50 K Depinningfrequency* Copper Stripes YBCO Note that the SC impedance is always a surface impedance! (the skin depth can never exceed the London depth) 04 January 2020 | 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 Loop Coupler  Polarization VNA 04 January 2020 | 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 Loop Coupler  Polarization VNA 04 January 2020 | 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 Loop Coupler  Polarization VNA 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 15

Static magnetic field perturbation Shubnikov phase Meissner phase MagneticInduction Normal Conductor Vortex solid Vortex fluid Very coarse estimate: Field perturbation is being investigated in detail… Temperature 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 16

Outlook: HTC magnetization complicated hysteretic behavior PhD thesis C. Völlinger Treatment with the critical current model… (Bean‘s model) 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 18

Combined surface impedance • Single surfaceimpedancealreadyimplemented • Split boundary such that • whereuis a parameterizationoftheboundary • is a Dirichlet and is a Neumann boundarycondition • Evaluate at surface • Include as boundary integral in weak formulation for FEM 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 21

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 04 January 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 28

High Temperature Superconductor Coating for the FCC-hh Beam Pipe