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- Sprache: Englisch
Superconducting Radiofrequency Technology for Accelerators
Single source reference enabling readers to understand and master state-of-the-art accelerator technology
Superconducting Radiofrequency Technology for Accelerators provides a quick yet thorough overview of the key technologies for current and future accelerators, including those projected to enable breakthrough developments in materials science, nuclear and astrophysics, high energy physics, neutrino research and quantum computing.
The work is divided into three sections. The first part provides a review of RF superconductivity basics, the second covers new techniques such as nitrogen doping, nitrogen infusion, oxide-free niobium, new surface treatments, and magnetic flux expulsion, high field Q slope, complemented by discussions of the physics of the improvements stemming from diagnostic techniques and surface analysis as well as from theory. The third part reviews the on-going applications of RF superconductivity in already operational facilities and those under construction such as light sources, proton accelerators, neutron and neutrino sources, ion accelerators, and crab cavity facilities. The third part discusses planned accelerator projects such as the International Linear Collider, the Future Circular Collider, the Chinese Electron Positron Collider, and the Proton Improvement Plan-III facility at Fermilab as well as exciting new developments in quantum computing using superconducting niobium cavities.
Written by the leading expert in the field of radiofrequency superconductivity, Superconducting Radiofrequency Technology for Accelerators covers other sample topics such as:
- Fabrication and processing on Nb-based SRF structures, covering cavity fabrication, preparation, and a decade of progress in the field
- SRF physics, covering zero DC resistance, the Meissner effect, surface resistance and surface impedance in RF fields, and non-local response of supercurrent
- N-doping and residual resistance, covering trapped DC flux losses, hydride losses, and tunneling measurements
- Theories for anti-Q-slope, covering the Xiao theory, the Gurevich theory, non-equilibrium superconductivity, and two fluid model based on weak defects
Superconducting Radiofrequency Technology for Accelerators is an essential reference for high energy physicists, power engineers, and electrical engineers who want to understand the latest developments of accelerator technology and be able to harness it to further research interest and practical applications.
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Superconducting Radiofrequency Technology for Accelerators
State of the Art and Emerging Trends
Hasan Padamsee
Author
Dr. Hasan Padamsee Cornell University Newman Laboratory Cornell University NY United States
Cover Image: Courtesy of Fermi National Accelerator Laboratory
All books published by WILEY-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
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Print ISBN: 978-3-527-41409-3ePDF ISBN: 978-3-527-83629-1ePub ISBN: 978-3-527-83630-7oBook ISBN: 978-3-527-83631-4
Preface
It has been more than 20 years since Wiley's 1998 publication and enthusiastic reception of RF Superconductivity for Accelerators [1] and now more than 10 years since the sequel in 2009: RF Superconductivity – Science, Technology, and Applications [2]. Many aspects of superconducting RF (SRF) development are thoroughly covered in these two books, plus many review papers [3–6], and most completely in the proceedings of international SRF conferences (1980–2021) published on JACoW.org [7].
Over the period 2010–2022 there has been spectacular progress in terms of the performance of SRF structures, scientific understanding of the improvements, innovative cavity designs for new applications, and wide exploration of new material avenues to take us beyond the capabilities of the popular standard of niobium, as well as the large scale, worldwide implementation of the mature technology to many new accelerators. Exciting new prospects are on the horizon.
It is time for a new volume on RF Superconductivity to provide a comprehensive update for more than a decade of advances carried out by enthusiastic researchers all over the world. A large fraction of the progress in SRF performance reported here is a testament to the creativity and success of imaginative researchers who have worked on innovative treatments, pursued efforts to gain understanding, and opened the door to new applications. Our review of the field covers progress till January 2022. No doubt there will be much additional progress reported in upcoming coming meetings such as Tesla Technology Collaboration (TTC) Meetings, as well as Thin Film SRF Conferences. We look forward to many new results by the time of the next SRF Conference in 2023.
Experts as well as newcomers to the field, including students, will benefit from the discussion of progress, as well as recent and forthcoming applications. Researchers in accelerator physics may also find much that is relevant to their discipline. There are now more than a thousand practitioners of the SRF field at more than 150 institutions and industries worldwide.
The book has four parts. Part I is the introduction and update of SRF fundamentals. Many of the SRF basics covered in the first two books will only be briefly touched, although essentials will be summarized for the sake of completeness. Part II covers performance advances and understanding at the high Q frontier. Part III covers performance advances and understanding at the high gradient frontier. Part IV covers new cavity and new treatment developments, as well as ongoing applications and future prospects.
An exciting new development discussed briefly in Part IV is the use of SRF cavities for quantum computing. Nb cavities offer a transformative vehicle for increasing the coherence times of qubits from sub-milliseconds to seconds, promising to bring the quantum computing field to quantum advantage over classical computers.
October 26, 2022
Hasan Padamsee
References
1
Padamsee, H., Knobloch, J., and Hays, T. (1998).
RF Superconductivity for Accelerators
, 2e, 2008 Wiley.
2
Padamsee, H. (2009). RF Superconductivity: Science, Technology, and Applications, 2e 2008. Wiley.
3
Kelly, M. (2012). Superconducting radio-frequency cavities for low-beta particle accelerators.
Rev. Accel. Sci. Technol.
5: 185–203.
https://doi.org/10.1142/9789814449953_0007
.
4
Belomestnykh, S. (2012). Superconducting radio-frequency systems for high-ß particle accelerators. In:
Reviews of Accelerator Science and Technology: Applications of Superconducting Technology to Accelerators
(eds. A. Choa and W. Chou) vol. 5, 147–184. World Scientific.
https://doi.org/10.1142/S179362681230006X
.
5
Reece, C.E. and Ciovati, G. (2012). Superconducting radio-frequency technology R&D for future accelerator applications. In:
Reviews of Accelerator Science and Technology: Applications of Superconducting Technology to Accelerators
, vol. 5 (ed. A. Chao and W. Chou), 285–312. World Scientific.
https://doi.org/10.1142/S1793626812300113
.
6
Gurevich, A. (2012). Superconducting radio-frequency fundamentals for particle accelerators.
Rev. Accel. Sci. Technol.
5: 119–146.
https://doi.org/10.1142/S1793626812300058
.
7
SRF Conference Proceedings.
Part IUpdate of SRF Fundamentals
1Introduction
Discovered in 1911, superconductivity is a fascinating phenomena of modern physics with marvelous scientific and technological applications, such as powerful magnets for medical imaging (magnetic resonance imaging [MRI]), for high energy physics, in particular, the large hadron collider (LHC), for nuclear fusion, and a wide range of modern applications.
The first major milestone in the history of superconductivity was the discovery by Kamerlingh Onnes [1, 2] that the electrical resistance of various metals, such as mercury, lead, and tin disappears when the temperature is lowered below some critical temperature value, Tc. Zero electrical resistance allows persistent currents in superconducting rings. These currents flow without any measurable decrease up to one year, allowing a lower bound of 105 years on their decay time. Compared to good conductors, such as copper, which have a residual resistivity at low temperature of the order of 10−6 Ω-cm, the resistivity of a superconductor is lower than 10−23 Ω-cm.
Subsequently, Meissner and Ochsenfeld [3] discovered perfect diamagnetism in superconductors. Magnetic fields are excluded from superconductors. Any field originally present in the metal is expelled from the metal when lowering the temperature below its critical value. Expulsion of magnetic field from walls of superconducting cavities via the Meissner effect will be an important topic in Chapter 4.
Starting with pioneering efforts in the 1960's, RF superconductivity (SRF) finally catapulted to an enabling technology since the 1980's. SRF has since equipped frontier accelerators in high energy physics, nuclear astrophysics, nuclear physics, as well as light sources and neutron sources for materials and life sciences. New applications are coming on line to intense proton sources for neutrino beams, and transmutation of nuclear waste, as well as for deflecting cavities for beam tilts for higher luminosity at LHC.
The primary advantages of the SRF technology have been discussed in the two previous books [4, 5]. The most attractive features of applying SRF to particle accelerators lie in the high accelerating gradient, Eacc, possible in continuous wave (cw) and long-pulse operating modes, along with extremely low RF losses in the cavity walls at cryogenic temperatures. There is another important advantage. The presence of accelerating structures has a disruptive effect on the beam, limiting the quality of the beam in aspects such as energy spread, beam halo, or the maximum current. SRF systems can be shorter, and thereby impose less disruption to the beam. By virtue of low wall losses, SRF cavities can be designed with large beam holes (apertures) to further reduce beam disruption and allow higher beam currents desirable.
Figure 1.1 Superconducting cavities spanning the full range of particle velocities.
Source: [6]/M. Kelly, Argonne National Lab/with permission from World Scientific Publishing.
There are two distinct types of superconducting cavities. The first type, TM-mode cavities, is for accelerating charged particles that move at nearly the speed of light, such as electrons in a high-energy linear accelerator (linac) or a storage ring. The second type, TEM-mode cavities, is for particles that move at a small fraction (e.g. 0.01–0.5) of the speed of light, such as the heavy ions. Structures for these applications are the quarter wave resonator (QWR), the half wave resonator (HWR) and the single spoke resonator (SSR), or one with multiple spokes. At intermediate velocities, both TM and TEM types could be used, depending on the application. Figure 1.1 [6] shows practical geometry sketches, and typical RF frequencies for each cavity type, depending on the velocity of the particles spanning the full velocity range of particles.
The QWR is the compact choice for low-β applications (β < 0.15) requiring ∼50% less structure with less overall RF dissipation compared to the HWR for the same frequency and β. (Here β = v/c, where v is the speed of the particle under acceleration, and c is the speed of light.) But the asymmetric field pattern in the accelerating gaps produces vertical steering that increases with velocity. The QWR is less mechanically stable than the HWR due to the unsupported end at the bottom in Figure 1.1. Hence the HWR is more suitable in the mid-velocity range (β > 0.15) or where steering must be eliminated (i.e. for high intensity). It has a symmetric field pattern and provides higher mechanical rigidity. But the HWR is larger, requires a larger cryomodule (CM), and has roughly twice the dissipation for the same β and frequency. The SSR is a more compact variant of the HWR. It opens a path to extension to several accelerating gaps along the beam in a single resonator, using multiple spokes. It provides a higher effective voltage, but with a narrower transit time acceptance.
This book will mostly focus on a review for the near velocity-of-light, or high-β accelerating cavities, and to particle accelerators that use these structures. We only briefly cover some of the latest applications of low-β structures to major facilities. For in-depth coverage of low-β cavities, we refer the reader to excellent articles [6], and tutorials at International SRF conferences [7, 8].
This book will not cover many important topics in SRF, such as input couplers, higher-order-mode couplers, tuners, and cryomodules. For latest developments in these areas, we refer the reader to many papers published in the Proceedings of the International SRF Conferences. The proceedings are available on the JACoW website [9].
2SRF Fundamentals Review
2.1 SRF Basics
We briefly review the key figures of merit that characterize the performance of an SRF cavity or structure, referring the reader to [4, 5] for in-depth coverage. The first important parameter – the accelerating voltageVc– is the ratio of the maximum energy gain that a particle moving along the cavity axis can achieve, to the charge of that particle. As all existing high-β multicell SRF structures operate in a π standing-wave mode, the optimal length (active length) of the cavity cells is βλ/2. Here λ is the rf wavelength. Next, the accelerating gradient is the ratio of the accelerating voltage per cell to the cell length, or Eacc = Vc/(βλ/2). The cavity quality factor Q0 determines the number of rf cycles (multiplied by 2π) required to dissipate the energy stored in the cavity. The key performance factor of an SRF cavity is typically given by the Q0 versus E curve, showing how rf losses change as the gradient (Eacc) rises. The quality factor (Q0) is derived as a ratio of two values via Rs = G/Q0, where G is the geometry factor, and Rs is the surface resistivity. As the name suggests, the geometry factor is determined only by the shape of the cavity. Surface resistivity (often referred to as surface resistance, Rs) depends only on material properties and the rf frequency. The physics of surface resistance is dominated by the physics of superconductors, and so will be a major topic of the book. The cavity’s shunt impedance, Rsh, determines how much acceleration a particle can derive from a cavity for a given power dissipation, Pc in the cavity walls. Hence Rsh = Vc2/Pc. A related quantity is the geometric shunt impedance Rsh/Q0, or simply R/Q, which depends only on the cavity shape. Two other important figures of merit are the ratios Epk/Eacc and Bpk/Eacc of the peak surface electric field Epk and magnetic field Bpk to the accelerating gradient Eacc. The typical distributions of the electric and magnetic field in a single cell β = 1 cavity are shown in Figure 2.1a,b, as well as for a low-β QWR in Figure 2.1c. Note that for the single cell β = 1 cavity, the magnetic field is maximum near the equator, whereas the electric field is at a peak near the iris. Maximum electric field locations for the QWR are shown in red.
For a given accelerating field, both Epk and Hpk need to be minimized for a good design. A high surface electric field can cause field emission of electrons, which impact and heat the cavity wall, often leading to a premature breakdown of superconductivity (called “quench”). Field emission electrons also generate undesirable “dark current” in the accelerator. A high surface magnetic field may limit the cavity’s performance at high gradients if rf heating from a high resistance region (such as a defect) triggers a quench of superconductivity, or if the local field approaches the critical rf magnetic field, discussed in more detail in later chapters.
Figure 2.1 (a) Electric and magnetic field distributions for a single-cell TM010 cavity.
Source: [10] Courtesy of J. Knobloch, Cornell University. (b) Microwave Studio®[11] simulations of the electric field (left) and magnetic field (right) in a TM010 mode [12] Courtesy of D. Bafia, Illinois Institute of Technology. The phase of the magnetic field is 90° shifted relative to the phase of the electric field. (c) Electric field (left) and magnetic field (right) simulation for the QWR [13]. Zhang and Venturini Delsolaro/JACoW/CC BY 3.0.
Figure 2.2 Typical Q versus E curves obtained for cavities exhibiting various performance limiting phenomena such as: hydrogen-Q-disease, multipacting, thermal instability (or quench), field emission, or high field Q-slope (HFQS). The flat curve depicting ideal performance is rarely (or never) achieved. The X-axis for gradient is not to scale [14].
The key performance of an SRF cavity is expressed by measuring the Q0 versus Eacc curve. As shown in Figure 2.2, the Q0 departs from the ideal flat curve due to limitations arising from various phenomena such as the hydrogen-related Q-disease, multipacting, breakdown from a defect, field emission, high field Q-slope (HFQS), and medium field Q-slope (MFQS). Each of these phenomena has been extensively studied with great progress in understanding the fundamental causes. Remedies have been developed to overcome the limitations and to return cavity behavior toward the ideal, flat Q0 versus Eacc curve.
Temperature mapping of the outer wall of the cavity has played a crucial role in understanding and curing many of these limitations. Figures 2.3 and 2.4 show the earliest system [15] for rapid mapping the outer-wall temperature below the lambda point of liquid He (2.2 K). Figure 2.4 also shows a temperature map when there is heating at a defect that eventually leads to a quench at a higher field. The thermometry system shown here has been improved [16] and adopted by many labs [17–19].
The performance of an SRF cavity depends on the maximum values of the peak surface fields that can be tolerated without increasing the microwave surface resistance substantially, or without causing a breakdown of superconductivity. A high surface electric field can cause field emission of electrons, degrading the Q0. A high surface magnetic field may limit the gradient of the cavity through heating at a defect followed by thermal runaway (Figure 2.4), or through a magnetic transition to the normal state at the local critical magnetic field. The ultimate accelerating field achievable for an ideal Nb cavity is set by the rf critical magnetic field, theoretically equal to the superheating critical magnetic field [21], Hsh. For ideal niobium, Hsh at 2 K is about 0.22 T, which translates to a maximum accelerating field of about 52 MV/m for a typical shape β = 1 niobium structure, and roughly 30 MV/m for a typical β < 1 Nb structure.
Figure 2.3 (a) A single thermometer board holding 21 carbon-resistor thermometers. The shape of the board matches the contour of a 1-cell cavity [10] Courtesy of J. Knobloch, Cornell University. (b) A single thermometer encased in epoxy. The sensing element is a 100 Ω Allen–Bradley carbon resistor the surface of which is ground down to just expose the carbon element for higher sensitivity.
Source: Courtesy of J. Knobloch, Cornell University. (c) Schematic of the thermometer housing showing the spring-loaded pogo stick that helps to keep contact with the cavity wall, and the leads of manganin wire to limit the stray heat input. The face of the thermometer is painted with insulation.
Source: [10, 16]/with permission of AIP Publishing LLC.
Other important design features for an SRF structure discussed further in [22] are cell-to-cell coupling for multicell structures, Lorentz-force (LF) detuning coefficient, input power required for beam power (Pb), coupling strength of input coupler (Qext), higher order mode (HOM) frequencies, HOM shunt impedances and HOM Q values. Mechanical properties also play a role in ensuring stability under atmospheric loading and temperature differentials, to minimize Lorentz-force detuning, and to keep microphonics detuning under control.
Figure 2.4 (a) Thermometers positioned on a cavity wall. Apiezon-N grease promotes thermal contact between the thermometer and the cavity wall. Some boards are removed to expose the cavity. [10, 16]. Courtesy of J. Knobloch, Cornell University & with permission of AIP through CCC. (b) Sample temperature map showing heating at a sub-mm defect site that leads to quench at higher fields. (c) At higher RF field, the defect heating grows to cause a quench of superconductivity, and a large region of the cavity surface around the defect shows high temperatures.
Source: [20]/H. Padamsee, Cornell University.
2.2 Fabrication and Processing on Nb-Based SRF Structures
To appreciate the latest progress in the performance and applications of SRF cavities it is helpful to briefly review the main features of customary fabrication and processing methods. The short review will help understand how the evolution of fabrication and surface treatment practices couple to the solution of the performance difficulties mentioned above, such as the hydrogen Q-disease, field emission and quench. More detail information about the fabrication and processing is available in [4, 5, 22].
2.2.1 Cavity Fabrication
Several industries provide niobium sheets with well-defined cavity specifications [23]. The sheets are inspected for flatness, uniform grain size (typically 50 μm), near-complete and uniform recrystallization, RRR value (>300), and good surface quality (absence of scratches). Here RRR stands for Residual Resistivity Ratio, and is a measure of the purity of Nb. Since the many fabrication stages can embed “defects,” such as impurity inclusions, pits, bumps, or scratches, each sheet from industry is scanned with eddy-current scanning [24, 25] to weed out defective sheets. Defects can lead to breakdown of superconductivity (quench) either by overheating, or by lowering the local critical field, resulting in a magnetic quench. The high RRR Nb helps to stabilize defect heating due to the high thermal conductivity that accompanies the high RRR.
For a β ∼ 1 structures, half-cells are stamped, spun, or hydro-formed, checked with the coordinate measuring machine (CMM) for the correct shape, then trimmed for weld preparations. Cavity parts are given a light (20 μm) (Buffered Chemical Polish) BCP etch to prepare for electron beam welding. Electron beam welding is a critical process with carefully developed parameters. A smooth weld under bead with complete absence of spatter is essential for high field performance. This can be achieved with defocused electron-beam welding [26], or by using a raster with a rhombic or circular pattern as described in [27]. To avoid RRR degradation, the vacuum in the electron-beam welder should be better than 2 × 10−5 Torr. All welds are inspected for complete, smooth under bead, flat on the inside, and no weld spatter. After completing a single-cell or multicell structure, the inside surface is inspected optically. A special optical inspection apparatus has been developed and widely adopted [28]. Mechanical measurements ensure straightness and correct dimensions. The electric field profile along the beam axis is checked and adjusted. The goal is usually 98% field flatness. A “flat” field profile is achieved by tuning the cells relative to each other by squeezing or stretching the cells mechanically to adjust and properly match the frequency of each cell.
Most low-β resonators are made from bulk niobium with high RRR (150–300). Fabrication of parts include machining, forming, rolling, and welding. Recently, wire electric discharge machining (EDM) has been developed together with industry [6] which has little possibility for foreign material inclusions as compared to traditional machining. Parts are joined together by electron beam welding in high vacuum.
2.2.2 Preparation
Niobium cavities undergo a first stage etching (100–150 μm) to remove the “surface damage” layer. Methods used for material removal are standard buffered chemical polishing(BCP), electropolishing (EP) [29], and centrifugal barrel polishing (CBP) [30]. By far the best method proven is EP [31], giving the smoothest surface (roughness <0.3 μm) and leading eventually to highest gradients.
BCP is a technically simpler process and used for pre-etching parts for cleaning and welding. BCP is chemical etching with a mixture of HF (40% concentration), HNO3 (65%), and H3PO4 (85%) acids in a volumetric ratio of 1 : 1 : 2. The process is exothermic so that good heat exchange and stirring are necessary for uniform material removal, and to keep the acid temperature below 15 °C to prevent excess hydrogen take-up (Section 6.11). BCP yields sharp grain boundary steps of 1–2 μm, and several μm at the weld because the etch rate depends on the crystal grain orientation. Such sharp steps are undesirable due to local field enhancement and lower quench fields.
EP is carried out with an acid mix of HF (40%) and H2SO4 (98%) in a ratio of 1 : 9 as the electrolyte. The niobium cavity serves as the anode and a high-purity aluminum cathode is inserted into the cavity. A typical arrangement has the cavity and the cathode in horizontal orientation with electrolyte filling about 60% of the cavity. The assembly is slowly rotated to allow uniform etching and polishing of the surface. The acid is circulated to an external reservoir where it is also cooled. Nitrogen gas is circulated via the cathode structure to expel hydrogen produced. Steps at the grain boundaries are reduced to below 0.2 μm (Figure 2.5). After EP, removal of sulfur residues [32] must be carried out with ultrasonic degreasing for a couple of hours in ethanol [33] or in detergent and water [34].
Figure 2.5 Comparison of surface roughness Nb surface treated with (a) BCP and (b) EP.
Source: [35]/Courtesy of L. Popielarski, FRIB, MSU/U.S. Department of Energy, Office of Science.
Tumbling or CBP is used to remove irregularities at welds, as well as pits, and scratches. The slow rate of material removal is highly dependent on the tumbling medium and rotation speeds. The final finish can be mirror-like, with 10 nm roughness, but the mirror quality by itself has not been shown to yield higher performance than EP. A final stage of light (5–20 μm) chemical etching via EP is still necessary to remove the tumbling abrasive embedded in the surface [36]. CBP has successfully been used to repair cavities with mechanical defects, such as pits, and bring them to high field performance [36, 37]. All chemical treatment or mechanical abrasion admits hydrogen into the bulk, leading to a Q-disease (Section 6.11).
After chemical etching and rinsing, high pressure water rinsing (HPR) is carried out at 100 atm water pressure for several hours to remove chemical residues and attached particles to avoid field emission or thermal breakdown. HPR is effective in scrubbing the surface free of impurities from chemical processing. The water must be particulate-free (using 0.1 μm or better filters) deionized water at a nozzle pressure of ∼100 bar to remove chemical residues [38, 39]. HPR is performed in an ISO5 (Class 100) or better clean room to prevent dust contamination during the process. Dust particles and chemical surface contamination results is heavy field emission, so both HPR and clean room environments are essential for good performance.
All preparation procedures for bulk material removal (BCP, EP, CBP) carry a risk of H evolution and absorption so that a furnace treatment at 600–800 °C is necessary to remove the H and to avoid the Q-disease. As shown in Figure 2.2, Q-disease will cause the Q to fall at low fields due to the formation of niobium hydrides during cool-down (Section 6.11). After furnace treatment, the cell-to-cell field profile is remeasured and readjusted. The final chemical treatment is a light etch (about 20 μm material removal) by EP to reach the highest field levels.
After final EP, the cavity is transported to the clean room where the inside surface is once again given a high-pressure rinse with high purity water jets for many hours. The cavity dries in the clean room.
A final HPR takes place after assembly of the necessary flanges, and the field monitor probe. The cavity is then ready for evacuation for rf tests. Great care must be exercised to avoid recontamination during the subsequent cavity handling, component assembly, and installation [40].
To reach the highest fields, an electropolished cavity needs to be baked at 120 °C for 48 hours [17, 41]. The mild baking step provides several benefits: first and foremost to remove the HFQS (Section 6.4). Chapter 6 discusses new research to understand the origins of HFQS and physics of the 120 °C bake benefits. Additional benefits of baking are to reduce the processing time for multipacting by degassing water from the surface, and lowering the secondary electron emission coefficient, as well as to reduce the BCS surface resistance for higher Q values by lowering the electron mean free path (Section 2.3.5). The bake is normally carried out with the inside of the cavity in a good vacuum (∼10−8 Torr).
2.2.3 A Decade of Progress
The decade 2010–2020 has brought enormous progress to the physics, technology, and applications of SRF cavities, the major rationale for this book. Here we summarize some of the highlights. Typical Q versus E curves for niobium cavities shows three distinct regions of Q-slope changes (Figure 2.6 [a]): low, medium, and high field Q-slopes [5], abbreviated as low-field Q-slope (LFQS), MFQS, and HFQS. The book reviews progress in understanding these Q-slope regimes.
Unprecedented Q values (>2 × 1011 at 1.3 GHz and 1.5 K) have been attained up to Eacc = 20–30 MV/m. These advances were achieved by novel surface preparation techniques, such as nitrogen doping (Chapter 3), and 300 °C (mid-T) baking (Chapter 4), along with special cavity cool-down procedures to eliminate the residual resistance contribution from trapped dc magnetic flux (Chapter 5). These recent accomplishments have translated into significant increases (factors >2–3) in the efficiency of cw particle accelerators (e.g. LCLS-II at SLAC) operated at medium accelerating fields of about 20 MV/m.
On the high gradient frontier, new treatments of nitrogen infusion (Section 7.3) and two-step baking (75/120C) (Section 7.1) have paved the way for gradients near 50 MV/m. The benefits of these new discoveries are collected in a Q versus E collage shown in Figure 2.6b. The proximity effect, nano-hydride model (Section 6.13) for the HFQS, and the 120 °C mild baking cure, which inhibits the formation of the harmful hydrides, have gained much experimental support. The model provides a platform to account for the gradient improvements with new techniques.
Another mystery from the past, the LFQS, is now fully understood as originating from two-level states (TLS) in the niobium pentoxide (Section 4.6). A technique (340 °C baking) has been found to substantially remove the oxide and reduce the TLS losses to achieve record low residual resistance values under one nano-Ohm. A very important benefit of the advances in the low field arena is to improve the lifetime of qubits (Section 13.9) opening the door to higher coherence times for quantum computing (Chapter 13).
2.3 SRF Physics
2.3.1 Zero DC Resistance
The two-hallmark features of superconductivity are zero resistance for dc currents and the Meissner effect. An early treatment for superconductivity comes from the London equations [43, 44] that account for these two salient properties. The London brothers provided a phenomenological description of superconductivity based on a two-fluid type concept proposed by Gorter and Casimir [45]. Here the superfluid and normal fluid densities ns and nn are associated with velocities vs and vn. The densities satisfy
Figure 2.6 (a) Low field, medium field, and high field Q-slopes observed after standard treatment of EP. 120 C bake removes the HFQS, leaving an extended region of MFQS [42] Courtesy of A. Grassellino, Fermilab. (b) Q0 versus Eacc at 2 K of 1.3 GHz Nb SRF cavities treated at FNAL with state-of-the-art surface treatments, such as nitrogen-doping, two-step baking, and nitrogen infusion, compared to standard treatments of EP or EP followed by 120 C baking [12] Courtesy of D. Bafia, Fermilab.
where n is the average electron number per unit volume. The two current densities satisfy
We can think of the first and second London equation pair below (2.3) as describing the electric and magnetic fields inside a superconductor
The electric field equation of the pair accounts for zero resistivity in superconductors that carry a direct current (dc) because using the supercurrent component of Eq. (2.2), it can be re-expressed as:
Equation (2.4) implies that in the presence of an electric field, E, the electrons in an ideally perfect conductor are accelerated freely, with zero resistance. The first London equation also implies that when the current is constant in time, as in the case of dc, there is no electric field inside the superconductor, and conduction takes place without losses.
Equation (2.5) should be contrasted with the conductivity equation for a normal metal or Ohm’s Law. In the Drude formulation [46, 47]
where τ is the average time between collisions or the electron relaxation time, m the electron mass, ℓ is the electron mean free path, and vF is the Fermi velocity.
2.3.2 Meissner Effect
Using Maxwell’s equations with the London equations, we derive the Meissner effect. Starting with Maxwell’s equation
Apply the curl
Using the second London equation for B,
Since ∇ · B = 0, this leads to a wave – type differential equation
where
λL is defined as the London penetration depth. (The value is 39 nm for high-purity niobium.) In the case of a semi-infinite superconducting slab that occupies the space z > 0, the solution to Eq. (2.11) is
which states that the parallel component of the B field decays exponentially with distance from the surface, to satisfy B = 0 inside the superconductor. This is the Meissner effect.
There are several consequences of the Meissner effect – important for Chapter 4. When a superconducting material is cooled through its transition temperature, Tc
