- Open Access
- Access by Xinjiang University
Vortex Dynamics and Dissipation under High-Amplitude Microwave Drive
Phys. Rev. Applied 14, 044018 – Published 13 October, 2020
DOI: https://doi.org/10.1103/PhysRevApplied.14.044018
Abstract
In this paper, we describe the vortex dynamics under a high-amplitude microwave drive and its effect on the surface resistance of superconductors. The vortex surface resistance is calculated with a Monte Carlo approach, where the vortex equation of motion is solved for a collection of vortex flux lines, each oscillating within a random pinning landscape. This approach is capable of providing a detailed description of the microscopic vortex dynamics and in turn important insights into the microwave-field-amplitude dependence of the vortex surface resistance. The numerical simulations are compared against experimental data of vortex surface resistance at high microwave amplitude measured by means of bulk niobium superconducting radio-frequency cavities operating at 1.3 GHz. The good qualitative agreement of the simulations and experiments suggests that the nonlinear dependence of the trapped-flux surface resistance with the microwave field amplitude is generated by progressive microwave depinning and vortex jumps.
Physics Subject Headings (PhySH)
Article Text
References (71)
- A. A. Abrikosov, On the magnetic properties of superconductors of the second group, Zh. Eksp. Teor. Fiz. 32, 1442 (1957); A. A. Abrikosov, Soviet Phys. JETP 5, 1174 (1957).
- L. V. Shubnikov, V. I. Khotkevich, Yu. D. Shepelev, and Yu. N. Ryabinin, Magnetic properties of superconducting metals and alloys, Zh. Eksp. Teor. Fiz. 7, 221 (1937); L. V. Shubnikov, V. I. Khotkevich, Yu. D. Shepelev, and Yu. N. Ryabinin, Ukr. J. Phys. 57, 42 (2008).
- A. Romanenko, A. Grassellino, O. Melnychuk, and D. A. Sergatskov, Dependence of the residual surface resistance of superconducting radio frequency cavities on the cooling dynamics around , J. Appl. Phys. 115, 184903 (2014).
- A. Romanenko, A. Grassellino, A. C. Crawford, D. A. Sergatskov, and O. Melnychuk, Ultra-high quality factors in superconducting niobium cavities in ambient magnetic fields up to 190 mG, Appl. Phys. Lett. 105, 234103 (2014).
- S. Posen, M. Checchin, A. C. Crawford, A. Grassellino, M. Martinello, O. S. Melnychuk, A. Romanenko, D. A. Sergatskov, and Y. Trenikhina, Efficient expulsion of magnetic flux in superconducting radiofrequency cavities for high applications, J. Appl. Phys 119, 213903 (2016).
- M. Martinello, A. Grassellino, M. Checchin, A. Romanenko, O. Melnychuk, D. A. Sergatskov, S. Posen, and J. F. Zasadzinski, Effect of interstitial impurities on the field dependent microwave surface resistance of niobium, Appl. Phys. Lett. 109, 062601 (2016).
- D. C. Mattis and J. Bardeen, Theory of the anomalous skin effect in normal and superconducting metals, Phys. Rev. 111, 412 (1958).
- A. Gurevich, Theory of rf superconductivity for resonant cavities, Supercond. Sci. Technol. 30, 034004 (2017).
- T. Kubo and A. Gurevich, Field-dependent nonlinear surface resistance and its optimization by surface nanostructuring in superconductors, Phys. Rev. B 100, 064522 (2019).
- A. Romanenko, F. Barkov, L. D. Cooley, and A. Grassellino, Proximity breakdown of hydrides in superconducting niobium cavities, Supercond. Sci. Technol. 26, 035003 (2013).
- A. Romanenko and D. I. Schuster, Understanding Quality Factor Degradation in Superconducting Niobium Cavities at Low Microwave Field Amplitudes, Phys. Rev. Lett. 119, 264801 (2017).
- A. Romanenko, R. Pilipenko, S. Zorzetti, D. Frolov, M. Awida, S. Belomestnykh, S. Posen, and A. Grassellino, Three-Dimensional Superconducting Resonators at with Photon Lifetimes up to s, Phys. Rev. Appl. 13, 034032 (2020).
- M. Cardona, G. Fischer, and B. Rosenblum, Microwave Surface Impedance of Superconductors of the Second Kind: - Alloys, Phys. Rev. Lett. 12, 101 (1970).
- J. I. Gittleman and B. Rosenblum, Radio-Frequency Resistance in the Mixed State for Subcritical Currents, Phys. Rev. Lett. 16, 734 (1966).
- M. Rabinowitz, Analysis of a critical loss in a superconductor, J. Appl. Phys. 42, 88 (1971).
- H. R. Segal and W. L. McLean, Magnetic field dependence of the microwave surface resistance of pure niobium, J. Low Temp. Phys. 22, 141 (1976).
- C. C. Chin, D. E. Oates, G. Dresselhaus, and M. S. Dresselhaus, Nonlinear electrodynamics of superconducting and thin films at microwave frequencies, Phys. Rev. B 45, 4788 (1992).
- D. Janjušević, M. S. Grbić, M. Požek, A. Dulčić, D. Paar, B. Nebendahl, and T. Wagner, Microwave response of thin niobium films under perpendicular static magnetic fields, Phys. Rev. B 74, 104501 (2006).
- A. Alimenti, N. Pompeo, K. Torokhtii, T. Spina, R. Flükiger, L. Muzzi, and E. Silva, Surface impedance measurements on in high magnetic fields, IEEE Trans. Appl. Supercond. 29, 3500104 (2019).
- S. Revenaz, D. Labbé-Lavigne, D. E. Oates, G. Dresselhaus, and M. S. Dresselhaus, Frequency dependence of the surface impedance of thin films in a dc magnetic field: Investigation of vortex dynamics, Phys. Rev. B 50, 1178 (1994).
- Y. Matsuda, M. B. Gaifullin, K. Kumagai, K. Kadowaki, and T. Mochiku, Collective Josephson Plasma Resonance in the Vortex State of , Phys. Rev. Lett. 75, 4512 (1995).
- M. Golosovsky, M. Tsindlekht, and D. Davidov, High-frequency vortex dynamics in , Supercond. Sci. Technol. 9, 1 (1996).
- K. Hashimoto, T. Shibauchi, T. Kato, K. Ikada, R. Okazaki, H. Shishido, M. Ishikado, H. Kito, A. Iyo, H. Eisaki, S. Shamoto, and Y. Matsuda, Microwave Penetration Depth and Quasiparticle Conductivity of Single Crystals: Evidence for a Full-Gap Superconductor, Phys. Rev. Lett. 102, 017002 (2009).
- K. Hashimoto, T. Shibauchi, S. Kasahara, K. Ikada, S. Tonegawa, T. Kato, R. Okazaki, C. J. van der Beek, M. Konczykowski, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Microwave Surface-Impedance Measurements of the Magnetic Penetration Depth in Single Crystal Superconductors: Evidence for a Disorder-Dependent Superfluid Density, Phys. Rev. Lett. 102, 207001 (2009).
- T. Okada, H. Takahashi, Y. Imai, K. Kitagawa, K. Matsubayashi, Y. Uwatoko, and A. Maeda, Microwave surface-impedance measurements of the electronic state and dissipation of magnetic vortices in superconducting single crystals, Phys. Rev. B 86, 064516 (2012).
- M. W. Coffey and J. R. Clem, Vortex-Motion Dissipation in High- Superconductors at Microwave Frequencies, Phys. Rev. Lett. 67, 386 (1991).
- R. Marcon, R. Fastampa, M. Giura, and E. Silva, Vortex-motion dissipation in high- superconductors at microwave frequencies, Phys. Rev. B 43, 2940 (1991).
- E. B. Sonin, A. K. Tagantsev, and K. B. Traito, Two-mode electrodynamics of superconductors in the mixed state, Phys. Rev. B 43, 5830 (1992).
- A. Grassellino, A. Romanenko, D. A. Sergatskov, O. Melnychuk, Y. Trenikhina, A. C. Crawford, A. Rowe, M. Wong, T. Khabiboulline, and F. Barkov, Nitrogen and argon doping of niobium for superconducting radio frequency cavities: A pathway to highly efficient accelerating structures, Supercond. Sci. Tech. 26, 102001 (2013).
- M. Martinello, M. Checchin, A. Romanenko, A. Grassellino, S. Aderhold, S. K. Chandrasekeran, O. Melnychuk, S. Posen, and D. A. Sergatskov, Field-Enhanced Superconductivity in High-Frequency Niobium Accelerating Cavities, Phys. Rev. Lett. 121, 224801 (2018).
- B. Piosczyk, P. Kneisel, O. Stoltz, and J. Halbritter, Investigations of additional losses in superconducting niobium cavities due to frozen-in flux, IEEE Trans. Nucl. Sci. 20, 108 (1973).
- C. Benvenuti, S. Calatroni, I. E. Campisi, P. Darriulat, M. A. Peck, R. Russo, and A.-M. Valente, Study of the surface resistance of superconducting niobium films at 1.5 GHz, Physica C 316, 153 (1999).
- A. Gurevich and G. Ciovati, Effect of vortex hotspots on the radio-frequency surface resistance of superconductors, Phys. Rev. B 87, 054502 (2013).
- D. Gonnella, J. Kaufman, and M. Liepe, Impact of nitrogen doping of niobium superconducting cavities on the sensitivity of surface resistance to trapped magnetic flux, J. Appl. Phys 119, 073904 (2016).
- M. Checchin, M. Martinello, A. Grassellino, A. Romanenko, and J. F. Zasadzinski, Electron mean free path dependence of th vortex surface impedance, Supercond. Sci. Technol. 30, 034003 (2017).
- M. Checchin, M. Martinello, A. Grassellino, S. Aderhold, S. K. Chandrasekaran, O. S. Melnychuk, S. Posen, A. Romanenko, and D. A. Sergatskov, Frequency dependence of trapped flux sensitivity in SRF cavities, Appl. Phys. Lett. 112, 072601 (2018).
- S. Calatroni and R. Vaglio, Surface resistance of superconductors in the presence of a dc magnetic field: Frequency and field intensity limits, IEEE Trans. Appl. Supercond. 27, 3500506 (2017).
- S. Calatroni and R. Vaglio, Simple model for the rf field amplitude dependence of the trapped flux sensitivity in superconducting rf cavities, Phys. Rev. Accel. Beams 22, 022001 (2019).
- D. B. Liarte, D. Hall, P. N. Koufalis, A. Miyazaki, A. Senanian, M. Liepe, and J. P. Sethna, Vortex Dynamics and Losses due to Pinning: Dissipation from Trapped Magnetic Flux in Resonant Superconducting Radio-Frequency Cavities, Phys. Rev. Appl. 10, 054057 (2018).
- B. Aune, Superconducting TESLA cavities, Phys. Rev. ST Accel. Beams 3, 092001 (2000).
- J. Knobloch, H. Muller, and H. Padamsee, Design of a high speed, high resolution thermometry system for 1.5 GHz superconducting radio frequency cavities, Rev. Sci. Instrum. 65, 3521 (1994).
- O. Melnychuk, A. Grassellino, and A. Romanenko, Error analysis for intrinsic quality factor measurement in superconducting radio frequency resonators, Rev. Sci. Instrum. 85, 124705 (2014).
- F. London and H. London, The electromagnetic equations of the supraconductors, Proc. R. Soc. Lond. A 149, 71 (1935).
- E. H. Brandt, The flux-line lattice in superconductors, Rep. Prog. Phys. 58, 1465 (1995).
- Differently than our previous approach in which [35, 36], in this work we consider the line tension to describe the vortex dynamics in more general way. The microwave excitation has a large amplitude and due to the finite line tension, the vortexes oscillate much more deeply than .
- J. Bardeen and M. J. Stephen, Theory on the motion of vortices in superconductors, Phys. Rev. 140, A1197 (1965).
- M. Tinkham, Introduction to Superconductivity (Dover Publication, Inc., Mineola, New York, 2004).
- A. B. Pippard, An experimental and theoretical study of the relation between magnetic field and current in a superconductor, Proc. R. Soc. Lond. A 216, 547 (1953).
- C. J. Gorter and H. Casimir, On supraconductivity I, Physica 1, 306 (1934).
- J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
- A. Suter, E. Morenzoni, N. Garifianov, R. Khasanov, E. Kirk, H. Luetkens, T. Prokscha, and M. Horisberger, Observation of nonexponential magnetic penetration profiles in the Meissner state: A manifestation of nonlocal effects in superconductors, Phys. Rev. B 72, 024506 (2005).
- T. P. Sheehan, Rules for the energy gap and critical field of superconductors, Phys. Rev. 149, 368 (1966).
- B. W. Maxfield and W. L. McLean, Superconducting penetration depth of niobium, Phys. Rev. 139, A1515 (1965).
- V. L. Ginzburg and L. D. Landau, On the theory of superconductivity, Zh. Eksp. Teor. Fiz. 20, 1064 (1950); L. D. Landau, Collected Papers (Pergamon Press, New York, 1965).
- M. Martinello, in 19th International Conference on RF Superconductivity, Dresden, Germany, 2019, (to be published).
- C. Z. Antoine, Influence of crystalline structure on rf dissipation in superconducting niobium, Phys. Rev. Accel. Beams 22, 034801 (2019).
- Y. Trenikhina, A. Romanenko, J. Kwon, J.-M. Zuo, and J. F. Zasadzinski, Nanostructural features degrading the performance of superconducting radio frequency niobium cavities revealed by transmission electron microscopy and electron energy loss spectroscopy, J. Appl. Phys. 117, 154507 (2015).
- E. V. Thuneberg, J. Kurkijärvi, and D. Rainer, Elementary-flux-pinning potential in type-II superconductors, Phys. Rev. B 29, 3913 (1984).
- L. Embon, Y. Anahory, A. Suhov, D. Halbertal, J. Cuppens, A. Yakovenko, A. Uri, Y. Myasoedov, M. L. Rappaport, M. E. Huber, A. Gurevich, and E. Zeldov, Probing dynamics and pinning of single vortices in superconductors at nanometer scales, Sci. Rep. 5, 7598 (2015).
- R. Labusch, Calculation of the critical field gradient in type-II superconductors, Cryst. Lattice Defects 1, 1 (1969).
- A. S. Dhavale, P. Dhakal, A. A. Polyanskii, and G. Ciovati, Flux pinning characteristics in cylindrical niobium samples used for superconducting radio frequency cavity fabrication, Supercond. Sci. Technol. 25, 065014 (2012).
- L. H. Allen and J. H. Claassen, Technique for measuring the elementary pinning force in thin films, Phys. Rev. B 39, 2054 (1989).
- G. S. Park, C. E. Cunningham, B. Cabrera, and M. E. Huber, Vortex Pinning Force in a Superconducting Niobium Strip, Phys. Rev. Lett. 68, 1920 (1992).
- S. Posen, N. Valles, and M. Liepe, Radio Frequency Magnetic Field Limits of and , Phys. Rev. Lett. 115, 047001 (2015).
- P. W. Anderson, Theory of Flux Creep in Hard Superconductors, Phys. Rev. Lett. 9, 309 (1962).
- R. Prozorov, D. V. Shantsev, and R. G. Mints, Collapse of the critical state in superconducting niobium, Phys. Rev. B 74, 220511(R) (2006).
- A. Romanenko, A. Grassellino, F. Barkov, A. Suter, Z. Salman, and T. Prokscha, Strong Meissner screening change in superconducting radio frequency cavities due to mild baking, Appl. Phys. Lett. 104, 072601 (2014).
- A. I. Larkin and Yu. N. Ovchinnikov, Nonlinear conductivity of superconductors in the mixed state, Zh. Eksp. Teor. Fiz. 68, 1915 (1975); A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys.-JETP, 41, 690 (1976).
- G. Grimaldi, A. Leo, D. Zola, A. Nigro, S. Pace, F. Laviano, and E. Mezzetti, Evidence for low-field crossover in the vortex critical velocity of type-II superconducting thin films, Phys. Rev. B 82, 024512 (2010).
- A. Leo, G. Grimaldi, R. Citro, A. Nigro, S. Pace, and R. P. Hubener, Quasiparticle scattering time in niobium superconducting films, Phys. Rev. B 84, 014536 (2011).
- O. V. Dobrovolskiy, V. A. Shklovskij, M. Hanefeld, M. Zörb, L. Köhs, and M. Huth, Pinning effects on flux flow instability in epitaxial thin films, Supercond. Sci. Technol. 30, 085002 (2017).