Collective weak pinning model of vortex dissipation in SRF cavities - PowerPoint PPT Presentation

Collective weak pinning model of vortex dissipation in SRF cavities Danilo Liarte, James Sethna, Daniel Hall, Matthias Liepe TTC Topical Cornell University Workshop - RF Superconductivity: Pushing Cavity Performance Limits

5.5 a) Experimental data 5 Gurevich theory, ℓ p = 75 ℓ Outline 4.5 4 R 0,B /B trapped (n Ω /mG) 3.5 3 2.5 2 a) Introduction 1.5 1 b) Collective weak pinning 0.5 0 10 0 10 1 10 2 10 3 c) Results Mean free path (nm) d) Final remarks c) b) Pinning centers H RF Vortex line Superconductor interface

5.5 a) Experimental data 5 Gurevich theory, ℓ p = 75 ℓ Outline 4.5 4 R 0,B /B trapped (n Ω /mG) 3.5 3 2.5 2 a) Introduction 1.5 1 b) Collective weak pinning 0.5 0 10 0 10 1 10 2 10 3 c) Results Mean free path (nm) d) Final remarks c) b) Pinning centers H RF Vortex line Superconductor interface

�� � Gaining insight on trapped flux Introduction and flux expulsion measurements on fine grain cavities Sam POSEN IARC Auditorium, Fermilab 08:30 - 08:55 Flux expulsion measurements in large grain cavities Dr. Pashupati DHAKAL IARC Auditorium, Fermilab 08:55 - 09:20 Variations in bulk flux trapping by MO imaging in Nb Shreyas BALACHANDRAN Gurevich & Ciovati IARC Auditorium, Fermilab 09:20 - 09:45 PRB 2013 Theoretical insights on pinning Ivan SADOVSKI H(t) u(z,t) IARC Auditorium, Fermilab 09:45 - 10:05 Point pinning versus grain boundary pinning – physics and techniques Zuhawn SUNG IARC Auditorium, Fermilab 10:05 - 10:25 Coffee Break IARC Auditorium, Fermilab 10:25 - 10:45 Theoretical models of flux expulsion and dissipation Dr. Mattia CHECCHIN 2 � IARC Auditorium, Fermilab 10:45 - 11:10 Flux losses due to weak collective pinning Dr. Danilo LIARTE IARC Auditorium, Fermilab 11:10 - 11:35 Vortex dissipation in Nb/Cu films Dr. Akira MIYAZAKI IARC Auditorium, Fermilab 11:35 - 12:00 Flux dissipation in Nb3Sn Films Ryan PORTER IARC Auditorium, Fermilab 12:00 - 12:25

Sensitivity of 𝑆 " to trapped flux Dependence on MFP (Gonnella) Dependence on RF field (Hall) 5.5 Experimental data 5 Gurevich theory, ℓ p = 75 ℓ 4.5 4 R 0,B /B trapped (n Ω /mG) 3.5 3 2.5 2 1.5 1 0.5 0 10 0 10 1 10 2 10 3 Mean free path (nm) Gonnella et al. J. Appl. Phys. 2016 Hall et al. IPAC 2017

5.5 a) Experimental data 5 Gurevich theory, ℓ p = 75 ℓ Outline 4.5 4 R 0,B /B trapped (n Ω /mG) 3.5 3 2.5 2 a) Introduction 1.5 1 b) Collective weak pinning 0.5 0 10 0 10 1 10 2 10 3 c) Results Mean free path (nm) d) Final remarks c) b) Pinning centers H RF Vortex line Superconductor interface

� � 𝑂 fluctuations and collective weak pinning viscous Magnus pinning 𝑁𝑣̈ = 𝑔 < + 𝑔 > + 𝑔 & + 𝑔 3 + 𝑔 ? inertial Lorentz elastic Pinning f orces add up randomly; only fluctuations can pin the line. + 𝑜 𝜊 + 𝑀 𝐺 &'( ≅ 𝑔 accumulated pinning force &'( ℇ &'( 𝑀 1 = ℇ 34567'1 𝑀 1 For 𝑀 > 𝑀 1 , a vortex can bend to find a favorable position in the pinning potential, cutting off the square-root growth of 𝐺 &'( .

� 𝑂 fluctuations and collective weak pinning viscous Magnus pinning 𝑁𝑣̈ = 𝑔 < + 𝑔 > + 𝑔 & + 𝑔 3 + 𝑔 ? inertial Lorentz elastic A vortex breaks up into segments of size 𝑀 1 ; each will compete with the Lorentz force. Pinning force & depinning current… ℇ &'( 𝑀 1 = ℇ 34567'1 𝑀 1 𝐺 &'( 𝑀 1 = 𝐺 >@A3(7B (𝑘 E , 𝑀 1 ) 𝐺 + 𝜊 𝑘 E &'( = 𝐼 1 (cgs units) 𝑀 1 𝑘 @

5.5 a) Experimental data 5 Gurevich theory, ℓ p = 75 ℓ Outline 4.5 4 R 0,B /B trapped (n Ω /mG) 3.5 3 2.5 2 a) Introduction 1.5 1 b) Collective weak pinning 0.5 0 10 0 10 1 10 2 10 3 c) Results Mean free path (nm) d) Final remarks c) b) Pinning centers H RF Vortex line Superconductor interface

Collective weak pinning at low frequency Derivation and analytical solution MF pinning ?J + 𝑔 Solution for Nb 3 Sn at 20mT RF field and 0 = 𝑔 > + 𝑔 1mA/µm 2 depinning current & 3 Lorentz elastic ● 4 𝑧 ∗ (𝑢) 𝑧 LL = 𝛽 − 𝛾 sin 𝑢 𝜀(𝑨) 𝑧 \ (𝑨) 2 𝑧 V (𝑨) ● y [ μ m ] 𝑧 V 𝑨 = 𝑏 𝑢 − 𝛾 sin 𝑢 𝑨 − |𝛽| 0 ● ● 2 𝑨 + - 2 𝑧 < 𝑧 ∗ for - 4 𝑧 \ 𝑨 = |𝛽| + 𝑨 − 𝛾 0 1 2 3 4 5 6 ] |𝛽| 2 z [ μ m ] 𝑧 > 𝑧 ∗ for

Collective weak pinning at low frequency ‘Sanity’ tests Point-like force, collective weak pinning, BC… Viscous dissipation term Amplitudes in y and z 100 100 At 1.3GHz Curvature radius 50 10 at the surface η | v max | / | f pin | Lengths [ λ ] 10 1 5 Pinning length 0.100 At 10 MHz 1 ‘Curvature radius’ 0.5 0.010 at the surface 0.001 0.1 0 10 20 30 40 0 10 20 30 40 B rf [ mT ] B [ mT ]

Dependence on RF field 𝑆 " = 𝑏 𝐶 A_ + 𝑐 𝐶 7A5&&3E • The linear behavior is consistent with collective weak pinning (but not accurate) U sing 𝑘 E ~3 ×10 jk 𝑘 @ • There is a factor of 100 off in comparison with the experimental results. Viscous dissipation is needed. 𝑔𝜇 + 𝜈 " 𝑏 = 4 𝑘 @ ; + 𝜊 3 𝑘 E 𝐶 1 𝑐 = 0 DBL, Hall, Liepe, Sethna, in progress

� � Collective weak pinning at low frequency ‘Sanity’ tests 𝑜 l/k = 𝜊 𝑚 Estimate density of impurities assuming ] 10 𝑏 + experimental value for 𝑘 E ~3 ×10 jk 𝑘 @ 𝜊 𝑚 = 0.738 𝜊 " r 1 + 0.882 𝜊 " 𝑚 + 𝑜 𝜊 + 𝑀 1 ] 𝐺 &'( ≅ 𝑔 &'( Atomic scale 𝐺 + 𝜊 𝑘 E &'( 𝑏 = 1Å = 𝐼 1 10 25 𝑀 1 𝑘 @ 10 24 𝑏 = 2Å n [ cm - 3 ] + &'( ≅ 𝜊 jl 𝑏 k 𝐼 1 10 23 Individual 𝑏 = 3Å 𝑔 8𝜌 pinning force 10 22 𝑏 = 4Å 10 21 k 𝜊 x 𝑘 @ = 256 𝜌 w 1 5 10 50 100 500 1000 𝑜 l+ 𝑏 l+ 𝑘 E ℓ

Collective weak pinning at high frequency Simulated solution viscous MF pinning ?J + 𝑔 0 = 𝑔 < + 𝑔 > + 𝑔 & 3 Lorentz elastic At 𝐶 A_ = 20 mT At 𝐶 A_ = 50 mT

Sensitivity of 𝑆 " to trapped flux as a function of the RF field • Simulation • Experiment (Hall) At 𝑘 E = 1 (black), 2 (red), 3 (blue), and 4mA/µm 2 (green)

Sensitivity of 𝑆 " to trapped flux as a function of frequency • Simulation • Experiment (Oseroff) Square-root Plateau Analytical curve

5.5 a) Experimental data 5 Gurevich theory, ℓ p = 75 ℓ Outline 4.5 4 R 0,B /B trapped (n Ω /mG) 3.5 3 2.5 2 a) Introduction 1.5 1 b) Collective weak pinning 0.5 0 10 0 10 1 10 2 10 3 c) Results Mean free path (nm) d) Final remarks c) b) Pinning centers H RF Vortex line Superconductor interface

Conclusions and future work • Hysteretic losses might explain the dependence of the residual resistance sensitivity to trapped flux on the RF field. • Our approximations are consistent, though we predict dissipations larger than the experimental ones by a factor of about eight. • The collective weak-pinning model predicts three distinct regimes for the dissipation as a function of frequency: linear, square-root, and a plateau. • Simulations with explicit inclusion of impurities. • Large amplitudes, grain boundaries, and mixed (strong and weak pinning) scenarios. • Experimental check: do most trapped vortices lie perpendicular to the interface? (We have assumed vortices that are normally aligned with respect to the interface.)

Acknowledgments • TTC Topical Workshop Committee, for the invitation. • The Sethna and the Liepe groups in Cornell. • The Center for Bright Beams SRF team. • Prof. Alex Gurevich, for useful consultation. • Financial support from the Center for Bright Beams. TTC Topical Workshop - RF Superconductivity: Pushing Cavity Performance Limits