2910:
lossy material attached to the interior surface, as shown in the adjacent image. This "beamline load" approach can be more technically challenging, since the load must absorb high RF power while preserving a high-vacuum beamline environment in close proximity to a contamination-sensitive SRF cavity. Further, such loads must sometimes operate at cryogenic temperatures to avoid large thermal gradients along the beampipe from the cold SRF cavity. The benefit of the beamline HOM load configuration, however, is a greater absorptive bandwidth and HOM attenuation as compared to antenna coupling. This benefit can be the difference between a stable vs. an unstable particle beam for high current accelerators.
221:
306:" superconducting materials are suitable for RF applications. Shortcomings of these materials arise due to their underlying physics as well as their bulk mechanical properties not being amenable to fabricating accelerator cavities. However, depositing films of promising materials onto other mechanically amenable cavity materials may provide a viable option for exotic materials serving SRF applications. At present, the de facto choice for SRF material is still pure niobium, which has a critical temperature of 9.3 K and functions as a superconductor nicely in a liquid helium bath of 4.2 K or lower, and has excellent mechanical properties.
213:
2948:
transition from internal cryogenic temperatures to room temperature at the vacuum vessel boundary. The thermal conductivity of these parts is minimized by having small cross sectional area and being composed of low thermal conductivity material, such as stainless steel for the vacuum beampipe and fiber reinforced epoxies (G10) for mechanical support. The vacuum beampipe also requires good electrical conductivity on its interior surface to propagate the image currents of the beam, which is accomplished by about 100 μm of copper plating on the interior surface.
258:. The low electrical loss in an SRF cavity allows their geometry to have large beampipe apertures while still maintaining a high accelerating field along the beam axis. Normal-conducting cavities need small beam apertures to concentrate the electric field as compensation for power losses in wall currents. However, the small apertures can be deleterious to a particle beam due to their spawning of larger wakefields, which are quantified by the accelerator parameters termed "beam impedance" and "loss parameter".
1712:
sudden increase of the conducting wall diameter in the transition from the small-diameter beampipe to the large hollow RF cavity. A portion of the particle's radiation field is then "clipped off" upon re-entrance into the beampipe and left behind as wakefields in the cavity. The wakefields are simply superimposed upon the externally driven accelerating fields in the cavity. The spawning of electromagnetic cavity modes as wakefields from the passing beam is analogous to a
156:
perturbations. An antenna is needed in the setup to couple RF power to the cavity fields and, in turn, any passing particle beam. The cold portions of the setup need to be extremely well insulated, which is best accomplished by a vacuum vessel surrounding the helium vessel and all ancillary cold components. The full SRF cavity containment system, including the vacuum vessel and many details not discussed here, is a
264:. The RF source driving the cavity need only provide the RF power that is absorbed by the particle beam being accelerated, since the RF power dissipated in the SRF cavity walls is negligible. This is in contrast to normal-conducting cavities where the wall power loss can easily equal or exceed the beam power consumption. The RF power budget is important since the RF source technologies, such as a
2447:
1978:
3177:
1418:) translates to a magnetic field of 0.5 Oe (40 A/m) and would produce a residual surface resistance in a superconductor that is orders of magnitude greater than the BCS resistance, rendering the superconductor too lossy for practical use. For this reason, superconducting cavities are surrounded by
2893:
as possible. The damping is accomplished by preferentially allowing dipole and all HOMs to leak out of the SRF cavity, and then coupling them to resistive RF loads. The leaking out of undesired RF modes occurs along the beampipe, and results from a careful design of the cavity aperture shapes. The
2909:
The resistive load for HOMs can be implemented by having loop antennas located at apertures on the side of the beampipe, with coaxial lines routing the RF to outside of the cryostat to standard RF loads. Another approach is to place the HOM loads directly on the beampipe as hollow cylinders with RF
2947:
mechanical connections between the cold mass and the room temperature vacuum vessel. These connections are required, for example, to support the mass of the helium vessel inside the vacuum vessel and to connect the apertures in the SRF cavity to the accelerator beamline. Both types of connections
2802:
mode in accelerators show that there are specific regions of phase between the beam bunches and the driven RF mode that allow stable operation at the highest possible beam currents. At some point of increasing beam current, though, just about any accelerator configuration will become unstable. As
806:
The geometry factor is quoted for cavity designs to allow comparison to other designs independent of wall loss, since wall loss for SRF cavities can vary substantially depending on material preparation, cryogenic bath temperature, electromagnetic field level, and other highly variable parameters.
618:
The integrals of the electromagnetic field in the above expressions are generally not solved analytically, since the cavity boundaries rarely lie along axes of common coordinate systems. Instead, the calculations are performed by any of a variety of computer programs that solve for the fields for
3221:
150 K the Carnot efficiency is unity. The practical efficiency is a catch-all term that accounts for the many mechanical non-idealities that come into play in a refrigeration system aside from the fundamental physics of the Carnot efficiency. For a large refrigeration installation there is
1702:
In 2012, the Q(E) dependence on SRF cavities discovered for the first time in such a way that the Q-rise phenomenon was observed in Ti doped SRF cavity. The quality factor increases with increase in accelerating field and was explained by the presence of sharper peaks in the electronic density of
231:
A large variety of RF cavities are used in particle accelerators. Historically most have been made of copper – a good electrical conductor – and operated near room temperature with exterior water cooling to remove the heat generated by the electrical loss in the cavity. In the past two decades,
126:
formed from or coated with superconducting materials. Electromagnetic fields are excited in the cavity by coupling in an RF source with an antenna. When the RF fed by the antenna is the same as that of a cavity mode, the resonant fields build to high amplitudes. Charged particles passing through
2924:
A significant part of SRF technology is cryogenic engineering. The SRF cavities tend to be thin-walled structures immersed in a bath of liquid helium having temperature 1.6 K to 4.5 K. Careful engineering is then required to insulate the helium bath from the room-temperature external
1711:
One of the main reasons for using SRF cavities in particle accelerators is that their large apertures result in low beam impedance and higher thresholds of deleterious beam instabilities. As a charged particle beam passes through a cavity, its electromagnetic radiation field is perturbed by the
2905:
inside of the cavity and allow HOMs to propagate away. The propagation of HOMs is sometimes facilitated by having a larger diameter beampipe on one side of the cavity, beyond the smaller diameter cavity iris, as seen in the SRF cavity CAD cross-section at the top of this wiki page. The larger
3398:
The temperature of operation of an SRF cavity is typically selected as a minimization of wall-plug power for the entire SRF system. The plot to the right then shows the pressure to which the helium vessel must be pumped to obtain the desired liquid helium temperature. Atmospheric pressure is
2952:
The major cryogenic engineering challenge is the refrigeration plant for the liquid helium. The small power that is dissipated in an SRF cavity and the heat leak to the vacuum vessel are both heat loads at very low temperature. The refrigerator must replenish this loss with an inherent poor
2885:
mode of an RF cavity, numerous higher frequency modes and a few lower-frequency dipole modes are excited by charged particle beam wakefields, all generally denoted higher order modes (HOMs). These modes serve no useful purpose for accelerator particle beam dynamics, only giving rise to beam
236:
to achieve a net power saving, but rather to increase the quality of the particle beam being accelerated. Though superconductors have little AC electrical resistance, the little power they do dissipate is radiated at very low temperatures, typically in a liquid helium bath at 1.6 K to
155:
to take advantage of the superfluid's thermal properties. Because superfluid has very high thermal conductivity, it makes an excellent coolant. In addition, superfluids boil only at free surfaces, preventing the formation of bubbles on the surface of the cavity, which would cause mechanical
1041:, which have zero resistance for DC current, have finite mass and momentum which has to alternate sinusoidally for the AC currents of RF fields, thus giving rise to a small energy loss. The BCS resistance for niobium can be approximated when the temperature is less than half of niobium's
1231:
arises from several sources, such as random material defects, hydrides that can form on the surface due to hot chemistry and slow cool-down, and others that are yet to be identified. One of the quantifiable residual resistance contributions is due to an external magnetic field pinning
2248:
3407:
point occurs at about 38 Torr (5.1 kPa), corresponding to 2.18 K helium. Most SRF systems either operate at atmospheric pressure, 4.2 K, or below the λ point at a system efficiency optimum usually around 1.8 K, corresponding to about 12 Torr (1.6 kPa).
1606:
performance, such as impurities in the niobium, hydrogen contamination due to excessive heat during chemistry, and a rough surface finish. After a couple decades of development, a necessary prescription for successful SRF cavity production is emerging. This includes:
2490:
The calculation of electromagnetic field buildup in a cavity due to wakefields can be complex and depends strongly on the specific accelerator mode of operation. For the straightforward case of a storage ring with repetitive particle bunches spaced by time interval
744:
1180:
294:
between the cavity and the surrounding environment could yield a significant net power savings by SRF over the normal conducting approach to RF cavities. Other issues will need to be considered with a higher bath temperature, though, such as the fact that
127:
apertures in the cavity are then accelerated by the electric fields and deflected by the magnetic fields. The resonant frequency driven in SRF cavities typically ranges from 200 MHz to 3 GHz, depending on the particle species to be accelerated.
2104:
1486:
just described can be further improved by up to a factor of 2 by performing a mild vacuum bake of the cavity. Empirically, the bake seems to reduce the BCS resistance by 50%, but increases the residual resistance by 30%. The plot below shows the ideal
1224:. For this reason, the majority of superconducting cavity applications favor lower frequencies, <3 GHz, and normal-conducting cavity applications favor higher frequencies, >0.5 GHz, there being some overlap depending on the application.
2833:
for a 500 MHz superconducting cavity and a 500 MHz normal-conducting cavity is shown below. The accelerating voltage provided by both cavities is comparable for a given net power consumption when including refrigeration power for SRF. The
2939:
wrapped around cold components. This insulation is composed of dozens of alternating layers of aluminized mylar and thin fiberglass sheet, which reflects infrared radiation that shines through the vacuum insulation from the 300 K exterior
2630:
1586:
would remain constant as the accelerating field is increased all the way up to the point of a magnetic quench field, as indicated by the "ideal" dashed line in the plot below. In reality, though, even a well prepared niobium cavity will have a
3765:
Grassellino, A; Romanenko, A; Sergatskov, D; Melnychuk, O; Trenikhina, Y; et al. (22 August 2013). "Nitrogen and argon doping of niobium for superconducting radio frequency cavities: a pathway to highly efficient accelerating structures".
622:
An RF cavity parameter known as the
Geometry Factor ranks the cavity's effectiveness of providing accelerating electric field due to the influence of its shape alone, which excludes specific material wall loss. The Geometry Factor is given by
1752:
1368:
1703:
states at the gap edges in doped cavities and such peaks being broadened by the rf current. Later the similar phenomenon was observed with nitrogen doping and which has been the current state-of-art cavity preparation for high performance.
232:
however, accelerator facilities have increasingly found superconducting cavities to be more suitable (or necessary) for their accelerators than normal-conducting copper versions. The motivation for using superconductors in RF cavities is
2977:
237:
4.5 K, and maintaining such low temperatures takes a lot of energy. The refrigeration power required to maintain the cryogenic bath at low temperature in the presence of heat from small RF power dissipation is dictated by the
2464:
is then a parameter that factors out cavity dissipation and is viewed as measure of the cavity geometry's effectiveness of producing accelerating voltage per stored energy in its volume. The wakefield being proportional to
1534:
limit. Few cavities make it to the magnetic field quench limit since residual losses and vanishingly small defects heat up localized spots, which eventually exceed the superconducting critical temperature and lead to a
598:
3830:
P. Wilson, "High Energy
Electron Linacs: Applications to Storage Ring RF Systems and Linear Colliders", SLAC-PUB-2884 (Rev) November 1991. See Section 6 of this excellent treatment of particle accelerator RF and beam
486:
930:
1692: slope phenomena is the subject of ongoing fundamental SRF research. The insight gained could lead to simpler cavity fabrication processes as well as benefit future material development efforts to find higher
2845:
for the SRF cavity is 15 times less than the normal-conducting version, and thus less beam-instability susceptible. This one of the main reasons such SRF cavities are chosen for use in high-current storage rings.
2775:
that can be orders of magnitude larger than used in this example. In this case, the buildup of wakefields of the trapped mode would likely cause a beam instability. The beam instability implications due to the
2442:{\displaystyle {\frac {R}{Q_{o}}}={\frac {V^{2}}{\omega _{o}U}}={\frac {2\left(\int {{\overrightarrow {E}}\cdot dl}\right)^{2}}{\omega _{o}\mu _{o}\int {|{\overrightarrow {H}}|^{2}dV}}}={\frac {2k}{\omega _{o}}}}
171:
Entry into superconducting RF technology can incur more complexity, expense, and time than normal-conducting RF cavity strategies. SRF requires chemical facilities for harsh cavity treatments, a low-particulate
1236:
in a Type II superconductor. The pinned fluxon cores create small normal-conducting regions in the niobium that can be summed to estimate their net resistance. For niobium, the magnetic field contribution to
176:
for high-pressure water rinsing and assembly of components, and complex engineering for the cryomodule vessel and cryogenics. A vexing aspect of SRF is the as-yet elusive ability to consistently produce high
3321:
314:
The physics of
Superconducting RF can be complex and lengthy. A few simple approximations derived from the complex theories, though, can serve to provide some of the important parameters of SRF cavities.
2729:) gives the worse-case wakefield build-up, where successive bunches are maximally decelerated by previous bunches' wakefields and give up even more energy than with only their "self wake". Then, taking
1553:
When using superconducting RF cavities in particle accelerators, the field level in the cavity should generally be as high as possible to most efficiently accelerate the beam passing through it. The
2701:
1731:
mode. There are then a host of beam instabilities that can occur as the repetitive particle beam passes through the RF cavity, each time adding to the wakefield energy in a collection of modes.
2210:
1669:
There remains some uncertainty as to the root cause of why some of these steps lead to success, such as the electropolish and vacuum bake. However, if this prescription is not followed, the
371:
801:
115:
typical of today's SRF cavities and left it swinging in an entombed lab since the early 17th century, that pendulum would still be swinging today with about half of its original amplitude.
629:
1425:
Using the above approximations for a niobium a SRF cavity at 1.8 K, 1.3 GHz, and assuming a magnetic field of 10 mOe (0.8 A/m), the surface resistance components would be
1062:
2242:
serves as a good comparative measure of wakefield amplitude for various cavity shapes, since the other terms are typically dictated by the application and are fixed. Mathematically,
2004:
241:, and can easily be comparable to the normal-conductor power dissipation of a room-temperature copper cavity. The principle motivations for using superconducting RF cavities, are:
1023:
2768:. A pitfall for any accelerator cavity would be the presence of what is termed a "trapped mode". This is an HOM that does not leak out of the cavity and consequently has a
2504:
1973:{\displaystyle V_{wake}={\frac {q\omega _{o}R}{2Q_{o}}}\ e^{j\omega _{o}t}\ e^{-{\frac {\omega _{o}t}{2Q_{L}}}}=kq\ e^{j\omega _{o}t}\ e^{-{\frac {\omega _{o}t}{2Q_{L}}}}}
1250:
3172:{\displaystyle \eta _{C}={\begin{cases}{\frac {T_{cold}}{T_{warm}-T_{cold}}},&{\mbox{if }}T_{cold}<T_{warm}-T_{cold}\\1,&{\mbox{otherwise}}\end{cases}}}
196:, bi-annual International Conferences on RF Superconductivity held at varying global locations in odd numbered years, and tutorials presented at the conferences.
248:. SRF cavities allow the excitation of high electromagnetic fields at high duty cycle, or even cw, in such regimes that a copper cavity's electrical loss could
2498:
and a bunch length much shorter than the wavelength of a given mode, the long term steady state wakefield voltage presented to the beam by the mode is given by
2224:
can be calculated from the solution of the electromagnetic fields of a mode, typically by a computer program that solves for the fields. In the equation for
3387:=5.5 kW. Of course, most accelerator facilities have numerous SRF cavities, so the refrigeration plants can get to be very large installations.
130:
The most common fabrication technology for such SRF cavities is to form thin walled (1–3 mm) shell components from high purity niobium sheets by
185:. Nevertheless, for many applications the capabilities of SRF cavities provide the only solution for a host of demanding performance requirements.
220:
518:
56:
1498:
413:
188:
Several extensive treatments of SRF physics and technology are available, many of them free of charge and online. There are the proceedings of
855:
148:
bath. Pumping removes helium vapor boil-off and controls the bath temperature. The helium vessel is often pumped to a pressure below helium's
33:
2850:
164:
1644:
810:
As an example of the above parameters, a typical 9-cell SRF cavity for the
International Linear Collider (a.k.a. a TESLA cavity) would have
318:
By way of background, some of the pertinent parameters of RF cavities are itemized as follows. A resonator's quality factor is defined by
299:(which is presently exploited with liquid helium) would not be present with (for example) liquid nitrogen. At present, none of the "high
205:
3239:
2874:
3391:
216:
A niobium-based 1.3 GHz nine-cell superconducting radio frequency to be used at the main linac of the
International Linear Collider
3641:"Effect of high temperature heat treatments on the quality factor of a large-grain superconducting radio-frequency niobium cavity"
1519:
degradation due to RF losses in ancillary components, such as stainless steel vacuum flanges that are too close to the cavity's
3422:
1512:
In general, much care and attention to detail must be exercised in the experimental setup of SRF cavities so that there is not
3451:
Nuclear
Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
2642:
212:
192:
accelerator schools, a scientific paper giving a thorough presentation of the many aspects of an SRF cavity to be used in the
3417:
1560:
values described by the above calculations tend to degrade as the fields increase, which is plotted for a given cavity as a "
3615:
838:, and is where the complex physics comes into play. For normal-conducting copper cavities operating near room temperature,
807:
The
Geometry Factor is also independent of cavity size, it is constant as a cavity shape is scaled to change its frequency.
1626:
High pressure rinsing (HPR) of the cavity interior in a clean room with filtered water to remove particulate contamination,
193:
182:
88:
3848:
2968:
1724:
1573:
2476:
can be seen intuitively since a cavity with small beam apertures concentrates the electric field on axis and has high
2158:
739:{\displaystyle G={\frac {\omega \mu _{0}\int {|{\overrightarrow {H}}|^{2}dV}}{\int {|{\overrightarrow {H}}|^{2}dS}}}}
324:
1175:{\displaystyle R_{BCS}\simeq 2\times 10^{-4}\left({\frac {f}{1.5\times 10^{9}}}\right)^{2}{\frac {e^{-17.67/T}}{T}}}
756:
103:
The amount of loss in an SRF resonant cavity is so minute that it is often explained with the following comparison:
3853:
2906:
beampipe diameter allows the HOMs to easily propagate away from the cavity to an HOM antenna or beamline absorber.
957:
can be viewed as the sum of the superconducting BCS resistance and temperature-independent "residual resistances",
1508:
vs external DC magnetic field for the same cavity frequency, temperature, and geometry factor as used in the text.
91:. These properties can be exploited for a variety of applications, including the construction of high-performance
1419:
273:
2099:{\displaystyle R={\frac {\left(\int {{\overrightarrow {E}}\cdot dl}\right)^{2}}{P_{d}}}={\frac {V^{2}}{P_{d}}}}
141:
A simplified diagram of the key elements of an SRF cavity setup is shown below. The cavity is immersed in a
3700:"Reduction of Dissipative Nonlinear Conductivity of Superconductors by Static and Microwave Magnetic Fields"
131:
3603:
963:
2936:
1536:
1523:
fields. However, careful SRF cavity preparation and experimental configuration have achieved the ideal
269:
135:
2625:{\displaystyle V_{ss\ wake}=V_{wake}\left({\frac {1}{1-e^{-\tau }e^{j\delta }}}-{\frac {1}{2}}\right)}
1738:, a length much shorter than the wavelength of a given cavity mode, and traversing the cavity at time
1393:
is the Type II superconductor magnetic quench field, which is 2400 Oe (190 kA/m) for niobium, and
3785:
3721:
3662:
3557:
3458:
3230:
2944:
119:
92:
2999:
167:
A simplified diagram of an SRF cavity in a helium bath with RF coupling and a passing particle beam.
3517:
1220: , whereas for normal conductors the surface resistance increases as the root of frequency, ~√
1363:{\displaystyle R_{H}={\frac {H_{ext}}{2H_{c2}}}R_{n}\approx 9.49\times 10^{-12}H_{ext}{\sqrt {f}}}
407:
The energy stored in the cavity is given by the integral of field energy density over its volume,
3829:
3809:
3775:
3711:
3652:
3547:
37:
107:(1564–1642) was one of the first investigators of pendulous motion, a simple form of mechanical
3534:
Aune, B.; Bandelmann, R.; Bloess, D.; Bonin, B.; Bosotti, A.; et al. (22 September 2000).
3491:
3443:
1629:
Careful assembly of the cavity and other vacuum apparatus in a clean room with clean practices,
17:
3801:
3747:
3739:
3680:
3575:
3474:
1531:
1042:
281:
48:
3639:
Dhakal, P.; Ciovati, G.; Myneni, G. R.; Gray, K. E.; Groll, N.; et al. (10 April 2013).
3493:
2002 CERN Accelerator School: Superconductivity and cryogenics for accelerators and detectors
2487:, but also clips off more of the particle bunch's radiation field as deleterious wakefields.
3793:
3729:
3670:
3565:
3466:
1620:
1216:
Note that for superconductors, the BCS resistance increases quadratically with frequency, ~
1992:
1617:
Maintaining low cavity temperatures during acid chemistry to avoid hydrogen contamination,
1520:
1497:
142:
104:
72:
52:
36:
An SRF technology single-cell
Niobium cavity CAD image with cross section, as used in the
3797:
3504:
1530:
not only for low field amplitudes, but up to cavity fields that are typically 75% of the
831:
The critical parameter for SRF cavities in the above equations is the surface resistance
512:
The power dissipated is given by the integral of resistive wall losses over its surface,
3789:
3725:
3666:
3561:
3462:
2803:
pointed out above, the beam wakefield amplitude is proportional to the cavity parameter
32:
3470:
3394:
Plot of helium-4 temperature vs. pressure, with the superfluid λ point indicated.
3842:
2138:" of the cavity, which takes into account energy leakage out of the coupling antenna,
296:
145:
3813:
2849:
163:
3734:
3699:
2709:
is the phase shift of the wakefield mode between bunch passages through the cavity.
1643:
1411:
1037:. One way to view the nature of the BCS RF resistance is that the superconducting
152:
3675:
3640:
1422:
to reduce the field permeating the cavity to typically <10 mOe (0.8 A/m).
3592:
3570:
3535:
3192:
is the temperature of the cold load, which is the helium vessel in this case, and
2783:
wakefields is thus addressed differently for the fundamental accelerating mode TM
1632:
A vacuum bake of the cavity at 120 °C for 48 hours; this typically improves
59:
of a superconducting material allows an RF resonator to obtain an extremely high
1723:
The beam wakefields in an RF cavity excite a subset of the spectrum of the many
1038:
619:
non-simple cavity shapes, and then numerically integrate the above expressions.
291:
238:
2853:
Comparison of superconducting and normal-conducting RF cavity shapes and their
3349:
2930:
2919:
2153:
the real exponential term quantifies the decay of the wakefield with time, and
1713:
1494:
values for a range of residual magnetic field for a baked and unbaked cavity.
1415:
1403:
1034:
845:
is simply determined by the empirically measured bulk electrical conductivity
224:
A cross section view of the niobium superconducting radio frequency cavity at
204:
157:
149:
3805:
3743:
3684:
3579:
3478:
2798:
The complex calculations treating wakefield-related beam stability for the TM
1595:
curve that lies beneath the ideal, as shown by the "good" curve in the plot.
3201:
is the temperature of the refrigeration heat sink, usually room temperature.
2814:, so this is typically used as a comparative measure of the likelihood of TM
593:{\displaystyle P_{d}={\frac {R_{s}}{2}}\int {|{\overrightarrow {H}}|^{2}dS}}
173:
123:
111:. Had Galileo experimented with a 1 Hz resonator with a quality factor
108:
3751:
2873:
481:{\displaystyle U={\frac {\mu _{0}}{2}}\int {|{\overrightarrow {H}}|^{2}dV}}
3442:
Akai, K; Akasaka, N; Ebihara, K; Ezura, E; Furuya, T; et al. (2003).
3390:
2721:
mode by design and unfortunately likely to occur for a few HOM's. Having
1717:
925:{\displaystyle R_{s\ normal}={\sqrt {\frac {\omega \mu _{0}}{2\sigma }}}}
265:
225:
60:
3552:
3519:
1988 CERN Accelerator School: Superconductivity in particle accelerators
3506:
1995 CERN Accelerator School: Superconductivity in particle accelerators
1598:
There are many phenomena that can occur in an SRF cavity to degrade its
181:
cavities in high volume production, which would be required for a large
276:
amplifier, have costs that increase dramatically with increasing power.
68:
280:
When future advances in superconducting material science allow higher
3348:
As an example, if the refrigerator delivers 1.8 K helium to the
1742:=0, the amplitude of the wakefield voltage left behind in the cavity
1233:
208:
An SRF technology 9-cell
Niobium cavity CAD image with cross section.
76:
2121:
is the power dissipated in the cavity to produce the electric field
3403:(101.325 kPa), corresponding to 4.2 K helium. The superfluid
27:
Technique used to attain a high quality factor in resonant cavities
3780:
3716:
3657:
2848:
2150:
the imaginary exponential is the mode's sinusoidal time variation,
1688: slope" curve in the plot below. Finding the root causes of
219:
211:
3316:{\displaystyle P_{warm}={\frac {P_{cold}}{\eta _{C}\ \eta _{p}}}}
399:
is the power dissipated in in the cavity to maintain the energy
3400:
290:
and consequently higher SRF bath temperatures, then the reduced
189:
3617:
2929:
A vacuum chamber surrounding the cold components to eliminate
1611:
Eddy-current scanning of the raw niobium sheet for impurities,
1466: = 270 Ω then the ideal quality factor would be
47:
science and technology involves the application of electrical
3604:
SRF Tutorials at the 2009 Conference on RF Superconductivity
2886:
instabilities, and are best heavily damped to have as low a
1208:=9.3 K for niobium, so this approximation is valid for
3165:
2953:
efficiency, given by the product of the Carnot efficiency
1451: = 3.42 nΩ, giving a net surface resistance
1614:
Good quality control of electron beam welding parameters,
2877:
An SRF technology HOM load CAD image with cross section.
2696:{\displaystyle \tau ={\frac {\omega _{o}T_{b}}{2Q_{L}}}}
1623:
of the cavity interior to achieve a very smooth surface,
614:
is the surface resistance which will be discussed below.
118:
The most common application of superconducting RF is in
3645:
Physical Review Special Topics: Accelerators and Beams
3540:
Physical Review Special Topics: Accelerators and Beams
3156:
3074:
87:
resonator stores energy with very low loss and narrow
3242:
3222:
some economy of scale, and it is possible to achieve
2980:
2645:
2507:
2251:
2161:
2007:
1755:
1253:
1065:
966:
858:
759:
632:
521:
416:
327:
67:. For example, it is commonplace for a 1.3 GHz
1572:" refers to the accelerating electric field of the
3315:
3171:
2703:is the decay of the wakefield between bunches, and
2695:
2624:
2441:
2204:
2098:
1972:
1402:is the normal-conducting resistance of niobium in
1362:
1174:
1017:
924:
795:
738:
592:
480:
365:
2725:(or an integer multiple of an RF mode's period,
2205:{\displaystyle k={\frac {\omega _{o}R}{2Q_{o}}}}
2713:As an example calculation, let the phase shift
2453:where relations defined above have been used.
366:{\displaystyle Q_{o}={\frac {\omega U}{P_{d}}}}
200:SRF cavity application in particle accelerators
3651:(4). American Physical Society (APS): 042001.
2881:In addition to the fundamental accelerating TM
1677:curve often shows an excessive degradation of
1460: = 7.97 nΩ. If for this cavity
1410:The Earth's nominal magnetic flux of 0.5
796:{\displaystyle Q_{o}={\frac {G}{R_{s}}}\cdot }
2818:related beam instabilities. A comparison of
2717:, which would be close to the case for the TM
1720:and exciting many resonant mechanical modes.
8:
3233:power consumed by the refrigerator is then
2894:aperture shapes are tailored to keep the TM
2787:and all other RF modes, as described next.
252:the copper, even with robust water cooling.
3825:
3823:
2967:. The Carnot efficiency derives from the
950:For Type II superconductors in RF fields,
3779:
3733:
3715:
3674:
3656:
3569:
3551:
3359:=10 W, then the refrigerator having
3352:where the cavity and heat leak dissipate
3304:
3291:
3271:
3265:
3247:
3241:
3155:
3128:
3106:
3084:
3073:
3050:
3028:
3008:
3002:
2994:
2985:
2979:
2684:
2669:
2659:
2652:
2644:
2607:
2592:
2579:
2563:
2543:
2512:
2506:
2431:
2417:
2398:
2393:
2382:
2377:
2376:
2367:
2357:
2345:
2320:
2319:
2304:
2289:
2278:
2272:
2261:
2252:
2250:
2193:
2175:
2168:
2160:
2088:
2078:
2072:
2061:
2051:
2026:
2025:
2014:
2006:
1959:
1941:
1934:
1930:
1912:
1904:
1877:
1859:
1852:
1848:
1830:
1822:
1806:
1788:
1778:
1760:
1754:
1353:
1341:
1328:
1309:
1293:
1273:
1267:
1258:
1252:
1157:
1150:
1144:
1138:
1125:
1109:
1095:
1070:
1064:
1003:
984:
971:
965:
904:
893:
863:
857:
782:
773:
764:
758:
720:
715:
704:
699:
698:
680:
675:
664:
659:
658:
649:
639:
631:
577:
572:
561:
556:
555:
541:
535:
526:
520:
465:
460:
449:
444:
443:
429:
423:
415:
355:
341:
332:
326:
3389:
2872:
2754:=10, the buildup of wakefields would be
1707:Wakefields and higher order modes (HOMs)
1684:with increasing field, as shown by the "
1642:
1496:
940:=5.8×10 (Ω·m) and at 1.3 GHz,
203:
162:
31:
3593:2009 Conference on RF Superconductivity
3434:
3337:is the power dissipated at temperature
2925:environment. This is accomplished by:
499:is the magnetic field in the cavity and
3529:
3527:
2971:and can be quite low. It is given by
3768:Superconductor Science and Technology
3620:. International Linear Collider. 2013
2147:is the angular frequency of the mode,
2112:is the electric field of the RF mode,
1018:{\displaystyle R_{s}=R_{BCS}+R_{res}}
282:superconducting critical temperatures
45:Superconducting radio frequency (SRF)
7:
3229:in the range of 0.2–0.3. The
1727:, including the externally driven TM
1043:superconducting critical temperature
262:Nearly all RF power goes to the beam
1654:vs the accelerating electric field
1384:is any external magnetic field in ,
3444:"RF systems for the KEK B-Factory"
508:is the permeability of free space.
134:. These shell components are then
25:
1734:For a particle bunch with charge
1661:and peak magnetic field of the TM
3536:"Superconducting TESLA cavities"
3380:=0.006 and a wall-plug power of
2791:Fundamental accelerating mode TM
3698:Gurevich, A. (18 August 2014).
3423:Circuit quantum electrodynamics
246:High duty cycle or cw operation
18:Superconducting Radio Frequency
3798:10.1088/0953-2048/26/10/102001
3774:(10). IOP Publishing: 102001.
3735:10.1103/physrevlett.113.087001
3418:Cavity quantum electrodynamics
2394:
2378:
716:
700:
676:
660:
573:
557:
461:
445:
384:is the resonant frequency in ,
79:to obtain a quality factor of
1:
3676:10.1103/physrevstab.16.042001
3471:10.1016/s0168-9002(02)01773-4
2960:and a "practical" efficiency
1435: = 4.55 nΩ and
390:is the energy stored in , and
194:International Linear Collider
122:. Accelerators typically use
3571:10.1103/physrevstab.3.092001
2969:second law of thermodynamics
1647:Example plots of SRF cavity
1579:mode. Ideally, the cavity
1199:is the temperature in , and
138:together to form cavities.
3870:
2917:
936:For copper at 300 K,
3457:(1). Elsevier BV: 45–65.
2898:mode "trapped" with high
2869:Higher order modes (HOMs)
1699:alternatives to niobium.
1501:Plot of SRF cavity ideal
83:=5×10. Such a very high
55:devices. The ultra-low
3704:Physical Review Letters
2933:heat transfer by gases.
1244:can be approximated by
310:Physics of SRF cavities
3395:
3317:
3173:
2937:Multi-layer insulation
2878:
2865:
2697:
2626:
2443:
2206:
2100:
1974:
1666:
1509:
1364:
1176:
1019:
926:
797:
740:
594:
482:
367:
228:
217:
209:
168:
57:electrical resistivity
41:
3393:
3318:
3174:
2876:
2852:
2698:
2627:
2444:
2207:
2101:
1975:
1725:electromagnetic modes
1646:
1532:magnetic field quench
1500:
1365:
1227:The superconductor's
1193:is the frequency in ,
1177:
1020:
927:
798:
741:
595:
483:
368:
270:Inductive output tube
223:
215:
207:
166:
120:particle accelerators
35:
3240:
2978:
2945:thermal conductivity
2740: 500 MHz,
2643:
2505:
2249:
2220:The shunt impedance
2159:
2005:
1753:
1475: = 3.4×10.
1251:
1063:
964:
856:
757:
630:
519:
414:
325:
124:resonant RF cavities
93:particle accelerator
3849:Accelerator physics
3790:2013SuScT..26j2001G
3726:2014PhRvL.113h7001G
3667:2013PhRvS..16d2001D
3562:2000PhRvS...3i2001A
3463:2003NIMPA.499...45A
3213:300 K, so for
1229:residual resistance
3396:
3313:
3169:
3164:
3160:
3078:
2879:
2866:
2693:
2622:
2439:
2202:
2096:
1970:
1667:
1510:
1420:magnetic shielding
1360:
1172:
1015:
922:
793:
736:
590:
478:
363:
256:Low beam impedance
229:
218:
210:
169:
42:
3854:Superconductivity
3311:
3299:
3159:
3077:
3066:
2691:
2615:
2602:
2521:
2437:
2412:
2390:
2328:
2299:
2267:
2200:
2094:
2067:
2034:
1966:
1925:
1899:
1884:
1843:
1817:
1813:
1639:by a factor of 2.
1358:
1303:
1170:
1132:
920:
919:
869:
788:
734:
712:
672:
569:
550:
457:
438:
361:
239:Carnot efficiency
16:(Redirected from
3861:
3833:
3827:
3818:
3817:
3783:
3762:
3756:
3755:
3737:
3719:
3695:
3689:
3688:
3678:
3660:
3636:
3630:
3629:
3627:
3625:
3612:
3606:
3601:
3595:
3590:
3584:
3583:
3573:
3555:
3531:
3522:
3515:
3509:
3502:
3496:
3489:
3483:
3482:
3448:
3439:
3373:=0.3 would have
3366:=300 K and
3322:
3320:
3319:
3314:
3312:
3310:
3309:
3308:
3297:
3296:
3295:
3285:
3284:
3266:
3261:
3260:
3178:
3176:
3175:
3170:
3168:
3167:
3161:
3157:
3142:
3141:
3120:
3119:
3098:
3097:
3079:
3075:
3067:
3065:
3064:
3063:
3042:
3041:
3022:
3021:
3003:
2990:
2989:
2747:=1 μs, and
2702:
2700:
2699:
2694:
2692:
2690:
2689:
2688:
2675:
2674:
2673:
2664:
2663:
2653:
2631:
2629:
2628:
2623:
2621:
2617:
2616:
2608:
2603:
2601:
2600:
2599:
2587:
2586:
2564:
2557:
2556:
2535:
2534:
2519:
2448:
2446:
2445:
2440:
2438:
2436:
2435:
2426:
2418:
2413:
2411:
2410:
2403:
2402:
2397:
2391:
2383:
2381:
2372:
2371:
2362:
2361:
2351:
2350:
2349:
2344:
2340:
2339:
2329:
2321:
2305:
2300:
2298:
2294:
2293:
2283:
2282:
2273:
2268:
2266:
2265:
2253:
2211:
2209:
2208:
2203:
2201:
2199:
2198:
2197:
2184:
2180:
2179:
2169:
2105:
2103:
2102:
2097:
2095:
2093:
2092:
2083:
2082:
2073:
2068:
2066:
2065:
2056:
2055:
2050:
2046:
2045:
2035:
2027:
2015:
1979:
1977:
1976:
1971:
1969:
1968:
1967:
1965:
1964:
1963:
1950:
1946:
1945:
1935:
1923:
1922:
1921:
1917:
1916:
1897:
1887:
1886:
1885:
1883:
1882:
1881:
1868:
1864:
1863:
1853:
1841:
1840:
1839:
1835:
1834:
1815:
1814:
1812:
1811:
1810:
1797:
1793:
1792:
1779:
1774:
1773:
1621:Electropolishing
1568:" curve, where "
1369:
1367:
1366:
1361:
1359:
1354:
1352:
1351:
1336:
1335:
1314:
1313:
1304:
1302:
1301:
1300:
1284:
1283:
1268:
1263:
1262:
1234:magnetic fluxons
1212:<4.65 K.
1181:
1179:
1178:
1173:
1171:
1166:
1165:
1161:
1145:
1143:
1142:
1137:
1133:
1131:
1130:
1129:
1110:
1103:
1102:
1081:
1080:
1024:
1022:
1021:
1016:
1014:
1013:
995:
994:
976:
975:
931:
929:
928:
923:
921:
918:
910:
909:
908:
895:
894:
889:
888:
867:
821:= 10 nΩ, giving
802:
800:
799:
794:
789:
787:
786:
774:
769:
768:
745:
743:
742:
737:
735:
733:
732:
725:
724:
719:
713:
705:
703:
693:
692:
685:
684:
679:
673:
665:
663:
654:
653:
640:
599:
597:
596:
591:
589:
582:
581:
576:
570:
562:
560:
551:
546:
545:
536:
531:
530:
487:
485:
484:
479:
477:
470:
469:
464:
458:
450:
448:
439:
434:
433:
424:
372:
370:
369:
364:
362:
360:
359:
350:
342:
337:
336:
21:
3869:
3868:
3864:
3863:
3862:
3860:
3859:
3858:
3839:
3838:
3837:
3836:
3828:
3821:
3764:
3763:
3759:
3697:
3696:
3692:
3638:
3637:
3633:
3623:
3621:
3614:
3613:
3609:
3602:
3598:
3591:
3587:
3553:physics/0003011
3533:
3532:
3525:
3516:
3512:
3503:
3499:
3490:
3486:
3446:
3441:
3440:
3436:
3431:
3414:
3385:
3378:
3371:
3364:
3357:
3342:
3335:
3300:
3287:
3286:
3267:
3243:
3238:
3237:
3227:
3218:
3210:
3199:
3190:
3163:
3162:
3153:
3144:
3143:
3124:
3102:
3080:
3071:
3046:
3024:
3023:
3004:
2995:
2981:
2976:
2975:
2965:
2958:
2922:
2916:
2903:
2897:
2891:
2884:
2871:
2862:
2843:
2827:
2817:
2812:
2801:
2796:
2794:
2786:
2781:
2773:
2766:
2759:
2752:
2745:
2734:
2727:δ=n2π
2720:
2680:
2676:
2665:
2655:
2654:
2641:
2640:
2588:
2575:
2568:
2562:
2558:
2539:
2508:
2503:
2502:
2496:
2485:
2474:
2462:
2427:
2419:
2392:
2363:
2353:
2352:
2315:
2311:
2310:
2306:
2285:
2284:
2274:
2257:
2247:
2246:
2240:
2229:
2216:of the RF mode.
2189:
2185:
2171:
2170:
2157:
2156:
2145:
2134:is the "loaded
2132:
2119:
2084:
2074:
2057:
2021:
2017:
2016:
2003:
2002:
1993:shunt impedance
1955:
1951:
1937:
1936:
1926:
1908:
1900:
1873:
1869:
1855:
1854:
1844:
1826:
1818:
1802:
1798:
1784:
1780:
1756:
1751:
1750:
1744:in a given mode
1730:
1709:
1697:
1682:
1664:
1659:
1652:
1637:
1584:
1577:
1558:
1551:
1528:
1517:
1506:
1492:
1484:
1473:
1458:
1449:
1442:
1433:
1400:
1391:
1382:
1337:
1324:
1305:
1289:
1285:
1269:
1254:
1249:
1248:
1242:
1206:
1146:
1121:
1114:
1105:
1104:
1091:
1066:
1061:
1060:
1054:
999:
980:
967:
962:
961:
955:
947:= 9.4 mΩ.
945:
911:
900:
896:
859:
854:
853:
843:
836:
826:
819:
778:
760:
755:
754:
714:
694:
674:
645:
641:
628:
627:
612:
571:
537:
522:
517:
516:
506:
459:
425:
412:
411:
397:
351:
343:
328:
323:
322:
312:
304:
288:
202:
183:linear collider
105:Galileo Galilei
101:
73:resonant cavity
53:radio frequency
49:superconductors
28:
23:
22:
15:
12:
11:
5:
3867:
3865:
3857:
3856:
3851:
3841:
3840:
3835:
3834:
3819:
3757:
3690:
3631:
3607:
3596:
3585:
3523:
3510:
3497:
3484:
3433:
3432:
3430:
3427:
3426:
3425:
3420:
3413:
3410:
3383:
3376:
3369:
3362:
3355:
3346:
3345:
3340:
3333:
3325:
3324:
3307:
3303:
3294:
3290:
3283:
3280:
3277:
3274:
3270:
3264:
3259:
3256:
3253:
3250:
3246:
3225:
3216:
3208:
3205:In most cases
3203:
3202:
3197:
3193:
3188:
3180:
3179:
3166:
3154:
3152:
3149:
3146:
3145:
3140:
3137:
3134:
3131:
3127:
3123:
3118:
3115:
3112:
3109:
3105:
3101:
3096:
3093:
3090:
3087:
3083:
3072:
3070:
3062:
3059:
3056:
3053:
3049:
3045:
3040:
3037:
3034:
3031:
3027:
3020:
3017:
3014:
3011:
3007:
3001:
3000:
2998:
2993:
2988:
2984:
2963:
2956:
2950:
2949:
2941:
2934:
2918:Main article:
2915:
2912:
2901:
2895:
2889:
2882:
2870:
2867:
2860:
2841:
2825:
2815:
2810:
2799:
2795:
2792:
2789:
2784:
2779:
2771:
2764:
2757:
2750:
2743:
2732:
2718:
2711:
2710:
2704:
2687:
2683:
2679:
2672:
2668:
2662:
2658:
2651:
2648:
2634:
2633:
2620:
2614:
2611:
2606:
2598:
2595:
2591:
2585:
2582:
2578:
2574:
2571:
2567:
2561:
2555:
2552:
2549:
2546:
2542:
2538:
2533:
2530:
2527:
2524:
2518:
2515:
2511:
2494:
2483:
2472:
2460:
2451:
2450:
2434:
2430:
2425:
2422:
2416:
2409:
2406:
2401:
2396:
2389:
2386:
2380:
2375:
2370:
2366:
2360:
2356:
2348:
2343:
2338:
2335:
2332:
2327:
2324:
2318:
2314:
2309:
2303:
2297:
2292:
2288:
2281:
2277:
2271:
2264:
2260:
2256:
2238:
2227:
2218:
2217:
2214:loss parameter
2212:is termed the
2196:
2192:
2188:
2183:
2178:
2174:
2167:
2164:
2154:
2151:
2148:
2143:
2139:
2130:
2126:
2117:
2113:
2107:
2091:
2087:
2081:
2077:
2071:
2064:
2060:
2054:
2049:
2044:
2041:
2038:
2033:
2030:
2024:
2020:
2013:
2010:
2000:
1995:of the cavity
1982:
1981:
1962:
1958:
1954:
1949:
1944:
1940:
1933:
1929:
1920:
1915:
1911:
1907:
1903:
1896:
1893:
1890:
1880:
1876:
1872:
1867:
1862:
1858:
1851:
1847:
1838:
1833:
1829:
1825:
1821:
1809:
1805:
1801:
1796:
1791:
1787:
1783:
1777:
1772:
1769:
1766:
1763:
1759:
1728:
1708:
1705:
1695:
1680:
1673: vs
1662:
1657:
1650:
1641:
1640:
1635:
1630:
1627:
1624:
1618:
1615:
1612:
1602: vs
1591: vs
1582:
1575:
1564: vs
1556:
1550:
1541:
1537:thermal quench
1526:
1515:
1504:
1490:
1482:
1477:
1476:
1471:
1467:
1461:
1456:
1452:
1447:
1440:
1436:
1431:
1408:
1407:
1398:
1394:
1389:
1385:
1380:
1372:
1371:
1357:
1350:
1347:
1344:
1340:
1334:
1331:
1327:
1323:
1320:
1317:
1312:
1308:
1299:
1296:
1292:
1288:
1282:
1279:
1276:
1272:
1266:
1261:
1257:
1240:
1214:
1213:
1204:
1200:
1194:
1184:
1183:
1169:
1164:
1160:
1156:
1153:
1149:
1141:
1136:
1128:
1124:
1120:
1117:
1113:
1108:
1101:
1098:
1094:
1090:
1087:
1084:
1079:
1076:
1073:
1069:
1052:
1031:BCS resistance
1027:
1026:
1012:
1009:
1006:
1002:
998:
993:
990:
987:
983:
979:
974:
970:
953:
943:
934:
933:
917:
914:
907:
903:
899:
892:
887:
884:
881:
878:
875:
872:
866:
862:
841:
834:
824:
817:
804:
803:
792:
785:
781:
777:
772:
767:
763:
748:
747:
731:
728:
723:
718:
711:
708:
702:
697:
691:
688:
683:
678:
671:
668:
662:
657:
652:
648:
644:
638:
635:
616:
615:
610:
602:
601:
588:
585:
580:
575:
568:
565:
559:
554:
549:
544:
540:
534:
529:
525:
510:
509:
504:
500:
490:
489:
476:
473:
468:
463:
456:
453:
447:
442:
437:
432:
428:
422:
419:
405:
404:
395:
391:
385:
375:
374:
358:
354:
349:
346:
340:
335:
331:
311:
308:
302:
286:
278:
277:
259:
253:
201:
198:
100:
97:
61:quality factor
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3866:
3855:
3852:
3850:
3847:
3846:
3844:
3832:
3826:
3824:
3820:
3815:
3811:
3807:
3803:
3799:
3795:
3791:
3787:
3782:
3777:
3773:
3769:
3761:
3758:
3753:
3749:
3745:
3741:
3736:
3731:
3727:
3723:
3718:
3713:
3710:(8): 087001.
3709:
3705:
3701:
3694:
3691:
3686:
3682:
3677:
3672:
3668:
3664:
3659:
3654:
3650:
3646:
3642:
3635:
3632:
3619:
3618:
3611:
3608:
3605:
3600:
3597:
3594:
3589:
3586:
3581:
3577:
3572:
3567:
3563:
3559:
3554:
3549:
3546:(9): 092001.
3545:
3541:
3537:
3530:
3528:
3524:
3521:
3520:
3514:
3511:
3508:
3507:
3501:
3498:
3495:
3494:
3488:
3485:
3480:
3476:
3472:
3468:
3464:
3460:
3456:
3452:
3445:
3438:
3435:
3428:
3424:
3421:
3419:
3416:
3415:
3411:
3409:
3406:
3402:
3392:
3388:
3386:
3379:
3372:
3365:
3358:
3351:
3343:
3336:
3330:
3329:
3328:
3305:
3301:
3292:
3288:
3281:
3278:
3275:
3272:
3268:
3262:
3257:
3254:
3251:
3248:
3244:
3236:
3235:
3234:
3232:
3228:
3220:
3212:
3200:
3194:
3191:
3185:
3184:
3183:
3150:
3147:
3138:
3135:
3132:
3129:
3125:
3121:
3116:
3113:
3110:
3107:
3103:
3099:
3094:
3091:
3088:
3085:
3081:
3068:
3060:
3057:
3054:
3051:
3047:
3043:
3038:
3035:
3032:
3029:
3025:
3018:
3015:
3012:
3009:
3005:
2996:
2991:
2986:
2982:
2974:
2973:
2972:
2970:
2966:
2959:
2946:
2942:
2938:
2935:
2932:
2928:
2927:
2926:
2921:
2913:
2911:
2907:
2904:
2892:
2875:
2868:
2863:
2856:
2851:
2847:
2844:
2837:
2832:
2828:
2821:
2813:
2806:
2790:
2788:
2782:
2774:
2767:
2760:
2753:
2746:
2739:
2735:
2728:
2724:
2716:
2708:
2705:
2685:
2681:
2677:
2670:
2666:
2660:
2656:
2649:
2646:
2639:
2638:
2637:
2618:
2612:
2609:
2604:
2596:
2593:
2589:
2583:
2580:
2576:
2572:
2569:
2565:
2559:
2553:
2550:
2547:
2544:
2540:
2536:
2531:
2528:
2525:
2522:
2516:
2513:
2509:
2501:
2500:
2499:
2497:
2488:
2486:
2479:
2475:
2468:
2463:
2456:
2432:
2428:
2423:
2420:
2414:
2407:
2404:
2399:
2387:
2384:
2373:
2368:
2364:
2358:
2354:
2346:
2341:
2336:
2333:
2330:
2325:
2322:
2316:
2312:
2307:
2301:
2295:
2290:
2286:
2279:
2275:
2269:
2262:
2258:
2254:
2245:
2244:
2243:
2241:
2234:
2230:
2223:
2215:
2194:
2190:
2186:
2181:
2176:
2172:
2165:
2162:
2155:
2152:
2149:
2146:
2140:
2137:
2133:
2127:
2124:
2120:
2114:
2111:
2108:
2089:
2085:
2079:
2075:
2069:
2062:
2058:
2052:
2047:
2042:
2039:
2036:
2031:
2028:
2022:
2018:
2011:
2008:
2001:
1998:
1994:
1990:
1987:
1986:
1985:
1960:
1956:
1952:
1947:
1942:
1938:
1931:
1927:
1918:
1913:
1909:
1905:
1901:
1894:
1891:
1888:
1878:
1874:
1870:
1865:
1860:
1856:
1849:
1845:
1836:
1831:
1827:
1823:
1819:
1807:
1803:
1799:
1794:
1789:
1785:
1781:
1775:
1770:
1767:
1764:
1761:
1757:
1749:
1748:
1747:
1746:is given by
1745:
1741:
1737:
1732:
1726:
1721:
1719:
1715:
1706:
1704:
1700:
1698:
1691:
1687:
1683:
1676:
1672:
1660:
1653:
1645:
1638:
1631:
1628:
1625:
1622:
1619:
1616:
1613:
1610:
1609:
1608:
1605:
1601:
1596:
1594:
1590:
1585:
1578:
1571:
1567:
1563:
1559:
1549:
1545:
1542:
1540:
1538:
1533:
1529:
1522:
1518:
1507:
1499:
1495:
1493:
1485:
1474:
1468:
1465:
1462:
1459:
1453:
1450:
1444: =
1443:
1437:
1434:
1428:
1427:
1426:
1423:
1421:
1417:
1413:
1405:
1401:
1395:
1392:
1386:
1383:
1377:
1376:
1375:
1355:
1348:
1345:
1342:
1338:
1332:
1329:
1325:
1321:
1318:
1315:
1310:
1306:
1297:
1294:
1290:
1286:
1280:
1277:
1274:
1270:
1264:
1259:
1255:
1247:
1246:
1245:
1243:
1235:
1230:
1225:
1223:
1219:
1211:
1207:
1201:
1198:
1195:
1192:
1189:
1188:
1187:
1167:
1162:
1158:
1154:
1151:
1147:
1139:
1134:
1126:
1122:
1118:
1115:
1111:
1106:
1099:
1096:
1092:
1088:
1085:
1082:
1077:
1074:
1071:
1067:
1059:
1058:
1057:
1055:
1048:
1044:
1040:
1036:
1033:derives from
1032:
1010:
1007:
1004:
1000:
996:
991:
988:
985:
981:
977:
972:
968:
960:
959:
958:
956:
948:
946:
944:s copper
939:
915:
912:
905:
901:
897:
890:
885:
882:
879:
876:
873:
870:
864:
860:
852:
851:
850:
848:
844:
837:
829:
827:
820:
813:
808:
790:
783:
779:
775:
770:
765:
761:
753:
752:
751:
729:
726:
721:
709:
706:
695:
689:
686:
681:
669:
666:
655:
650:
646:
642:
636:
633:
626:
625:
624:
620:
613:
607:
606:
605:
586:
583:
578:
566:
563:
552:
547:
542:
538:
532:
527:
523:
515:
514:
513:
507:
501:
498:
495:
494:
493:
474:
471:
466:
454:
451:
440:
435:
430:
426:
420:
417:
410:
409:
408:
402:
398:
392:
389:
386:
383:
380:
379:
378:
356:
352:
347:
344:
338:
333:
329:
321:
320:
319:
316:
309:
307:
305:
298:
297:superfluidity
293:
289:
283:
275:
271:
267:
263:
260:
257:
254:
251:
247:
244:
243:
242:
240:
235:
227:
222:
214:
206:
199:
197:
195:
191:
186:
184:
180:
175:
165:
161:
159:
154:
151:
147:
146:liquid helium
144:
139:
137:
133:
128:
125:
121:
116:
114:
110:
106:
98:
96:
94:
90:
86:
82:
78:
74:
70:
66:
62:
58:
54:
50:
46:
39:
34:
30:
19:
3771:
3767:
3760:
3707:
3703:
3693:
3648:
3644:
3634:
3622:. Retrieved
3616:
3610:
3599:
3588:
3543:
3539:
3518:
3513:
3505:
3500:
3492:
3487:
3454:
3450:
3437:
3404:
3397:
3381:
3374:
3367:
3360:
3353:
3347:
3338:
3331:
3326:
3223:
3214:
3206:
3204:
3195:
3186:
3181:
2961:
2954:
2951:
2923:
2908:
2899:
2887:
2880:
2858:
2854:
2839:
2835:
2830:
2823:
2819:
2808:
2804:
2797:
2777:
2769:
2762:
2755:
2748:
2741:
2737:
2730:
2726:
2722:
2714:
2712:
2706:
2635:
2492:
2489:
2481:
2477:
2470:
2466:
2458:
2454:
2452:
2236:
2232:
2231:, the ratio
2225:
2221:
2219:
2213:
2141:
2135:
2128:
2122:
2115:
2109:
1996:
1988:
1983:
1743:
1739:
1735:
1733:
1722:
1710:
1701:
1693:
1689:
1685:
1678:
1674:
1670:
1668:
1655:
1648:
1633:
1603:
1599:
1597:
1592:
1588:
1580:
1569:
1565:
1561:
1554:
1552:
1547:
1543:
1524:
1513:
1511:
1502:
1488:
1480:
1478:
1469:
1463:
1454:
1445:
1438:
1429:
1424:
1409:
1396:
1387:
1378:
1373:
1238:
1228:
1226:
1221:
1217:
1215:
1209:
1202:
1196:
1190:
1185:
1050:
1046:
1039:Cooper pairs
1030:
1028:
951:
949:
941:
937:
935:
846:
839:
832:
830:
822:
815:
811:
809:
805:
749:
621:
617:
608:
603:
511:
502:
496:
491:
406:
400:
393:
387:
381:
376:
317:
313:
300:
284:
279:
261:
255:
249:
245:
233:
230:
187:
178:
170:
153:lambda point
140:
129:
117:
112:
102:
99:Introduction
95:structures.
84:
80:
75:at 1.8
64:
44:
43:
40:accelerator.
29:
1716:striking a
814:=270 Ω and
292:thermocline
274:solid state
3843:Categories
3429:References
3350:cryomodule
2931:convective
2920:Cryomodule
2914:Cryogenics
1999:defined by
1521:evanescent
1035:BCS theory
272:(IOT), or
158:cryomodule
150:superfluid
3806:0953-2048
3781:1306.0288
3744:0031-9007
3717:1408.4476
3685:1098-4402
3658:1210.6875
3624:14 August
3580:1098-4402
3479:0168-9002
3399:760
3302:η
3289:η
3231:wall-plug
3158:otherwise
3122:−
3044:−
2983:η
2736: = 2
2657:ω
2647:τ
2605:−
2597:δ
2584:τ
2581:−
2573:−
2429:ω
2388:→
2374:∫
2365:μ
2355:ω
2331:⋅
2326:→
2317:∫
2287:ω
2173:ω
2037:⋅
2032:→
2023:∫
1939:ω
1932:−
1910:ω
1857:ω
1850:−
1828:ω
1786:ω
1714:drumstick
1330:−
1322:×
1316:≈
1152:−
1119:×
1097:−
1089:×
1083:≃
916:σ
902:μ
898:ω
828:=2.7×10.
791:⋅
750:and then
710:→
696:∫
670:→
656:∫
647:μ
643:ω
567:→
553:∫
455:→
441:∫
427:μ
345:ω
174:cleanroom
143:saturated
109:resonance
89:bandwidth
3831:loading.
3814:14055828
3752:25192119
3412:See also
3076:if
2723:δ=0
2715:δ=0
1718:drumhead
266:Klystron
226:Fermilab
132:stamping
3786:Bibcode
3722:Bibcode
3663:Bibcode
3558:Bibcode
3459:Bibcode
3219:≥
2780:ss wake
2758:ss wake
2636:where:
1991:is the
1984:where:
1374:where:
1186:where:
1056:/2, by
604:where:
492:where:
377:where:
77:kelvins
69:niobium
3812:
3804:
3750:
3742:
3683:
3578:
3477:
3405:λ
3375:η
3368:η
3327:where
3298:
3224:η
3182:where
2962:η
2955:η
2940:walls.
2738:π
2731:ω
2707:δ
2520:
2142:ω
1924:
1898:
1842:
1816:
938:σ
868:
847:σ
503:μ
382:ω
136:welded
3810:S2CID
3776:arXiv
3712:arXiv
3653:arXiv
3548:arXiv
3447:(PDF)
2761:=637×
1665:mode.
1412:gauss
1155:17.67
38:KEK-B
3802:ISSN
3748:PMID
3740:ISSN
3681:ISSN
3626:2015
3576:ISSN
3475:ISSN
3401:Torr
3384:warm
3363:warm
3356:cold
3341:cold
3334:cold
3217:cold
3209:warm
3198:warm
3189:cold
3100:<
2943:Low
2829:and
2765:wake
2228:wake
1997:mode
1479:The
1414:(50
1404:ohms
1319:9.49
1049:<
1029:The
250:melt
190:CERN
71:SRF
3794:doi
3730:doi
3708:113
3671:doi
3566:doi
3467:doi
3455:499
2883:010
2800:010
2793:010
1546:vs
1441:res
1432:BCS
1381:ext
1116:1.5
849:by
234:not
51:to
3845::
3822:^
3808:.
3800:.
3792:.
3784:.
3772:26
3770:.
3746:.
3738:.
3728:.
3720:.
3706:.
3702:.
3679:.
3669:.
3661:.
3649:16
3647:.
3643:.
3574:.
3564:.
3556:.
3542:.
3538:.
3526:^
3473:.
3465:.
3453:.
3449:.
2896:01
2816:01
2785:01
2719:01
1729:01
1663:01
1576:01
1574:TM
1544:Q
1539:.
1416:μT
1390:c2
1333:12
1326:10
1123:10
1093:10
1045:,
268:,
160:.
63:,
3816:.
3796::
3788::
3778::
3754:.
3732::
3724::
3714::
3687:.
3673::
3665::
3655::
3628:.
3582:.
3568::
3560::
3550::
3544:3
3481:.
3469::
3461::
3382:P
3377:C
3370:p
3361:T
3354:P
3344:.
3339:T
3332:P
3323:,
3306:p
3293:C
3282:d
3279:l
3276:o
3273:c
3269:P
3263:=
3258:m
3255:r
3252:a
3249:w
3245:P
3226:p
3215:T
3211:=
3207:T
3196:T
3187:T
3151:,
3148:1
3139:d
3136:l
3133:o
3130:c
3126:T
3117:m
3114:r
3111:a
3108:w
3104:T
3095:d
3092:l
3089:o
3086:c
3082:T
3069:,
3061:d
3058:l
3055:o
3052:c
3048:T
3039:m
3036:r
3033:a
3030:w
3026:T
3019:d
3016:l
3013:o
3010:c
3006:T
2997:{
2992:=
2987:C
2964:p
2957:C
2902:o
2900:Q
2890:L
2888:Q
2864:.
2861:o
2859:Q
2857:/
2855:R
2842:o
2840:Q
2838:/
2836:R
2831:R
2826:o
2824:Q
2822:/
2820:R
2811:o
2809:Q
2807:/
2805:R
2778:V
2772:L
2770:Q
2763:V
2756:V
2751:L
2749:Q
2744:b
2742:T
2733:o
2686:L
2682:Q
2678:2
2671:b
2667:T
2661:o
2650:=
2632:,
2619:)
2613:2
2610:1
2594:j
2590:e
2577:e
2570:1
2566:1
2560:(
2554:e
2551:k
2548:a
2545:w
2541:V
2537:=
2532:e
2529:k
2526:a
2523:w
2517:s
2514:s
2510:V
2495:b
2493:T
2484:o
2482:Q
2480:/
2478:R
2473:o
2471:Q
2469:/
2467:R
2461:o
2459:Q
2457:/
2455:R
2449:,
2433:o
2424:k
2421:2
2415:=
2408:V
2405:d
2400:2
2395:|
2385:H
2379:|
2369:o
2359:o
2347:2
2342:)
2337:l
2334:d
2323:E
2313:(
2308:2
2302:=
2296:U
2291:o
2280:2
2276:V
2270:=
2263:o
2259:Q
2255:R
2239:o
2237:Q
2235:/
2233:R
2226:V
2222:R
2195:o
2191:Q
2187:2
2182:R
2177:o
2166:=
2163:k
2144:o
2136:Q
2131:L
2129:Q
2125:,
2123:E
2118:d
2116:P
2110:E
2106:,
2090:d
2086:P
2080:2
2076:V
2070:=
2063:d
2059:P
2053:2
2048:)
2043:l
2040:d
2029:E
2019:(
2012:=
2009:R
1989:R
1980:,
1961:L
1957:Q
1953:2
1948:t
1943:o
1928:e
1919:t
1914:o
1906:j
1902:e
1895:q
1892:k
1889:=
1879:L
1875:Q
1871:2
1866:t
1861:o
1846:e
1837:t
1832:o
1824:j
1820:e
1808:o
1804:Q
1800:2
1795:R
1790:o
1782:q
1776:=
1771:e
1768:k
1765:a
1762:w
1758:V
1740:t
1736:q
1696:c
1694:T
1690:Q
1686:Q
1681:o
1679:Q
1675:E
1671:Q
1658:a
1656:E
1651:o
1649:Q
1636:o
1634:Q
1604:E
1600:Q
1593:E
1589:Q
1583:o
1581:Q
1570:E
1566:E
1562:Q
1557:o
1555:Q
1548:E
1527:o
1525:Q
1516:o
1514:Q
1505:o
1503:Q
1491:o
1489:Q
1483:o
1481:Q
1472:o
1470:Q
1464:G
1457:s
1455:R
1448:H
1446:R
1439:R
1430:R
1406:.
1399:n
1397:R
1388:H
1379:H
1370:,
1356:f
1349:t
1346:x
1343:e
1339:H
1311:n
1307:R
1298:2
1295:c
1291:H
1287:2
1281:t
1278:x
1275:e
1271:H
1265:=
1260:H
1256:R
1241:s
1239:R
1222:f
1218:f
1210:T
1205:c
1203:T
1197:T
1191:f
1182:,
1168:T
1163:T
1159:/
1148:e
1140:2
1135:)
1127:9
1112:f
1107:(
1100:4
1086:2
1078:S
1075:C
1072:B
1068:R
1053:c
1051:T
1047:T
1025:.
1011:s
1008:e
1005:r
1001:R
997:+
992:S
989:C
986:B
982:R
978:=
973:s
969:R
954:s
952:R
942:R
932:.
913:2
906:0
891:=
886:l
883:a
880:m
877:r
874:o
871:n
865:s
861:R
842:s
840:R
835:s
833:R
825:o
823:Q
818:s
816:R
812:G
784:s
780:R
776:G
771:=
766:o
762:Q
746:,
730:S
727:d
722:2
717:|
707:H
701:|
690:V
687:d
682:2
677:|
667:H
661:|
651:0
637:=
634:G
611:s
609:R
600:,
587:S
584:d
579:2
574:|
564:H
558:|
548:2
543:s
539:R
533:=
528:d
524:P
505:0
497:H
488:,
475:V
472:d
467:2
462:|
452:H
446:|
436:2
431:0
421:=
418:U
403:.
401:U
396:d
394:P
388:U
373:,
357:d
353:P
348:U
339:=
334:o
330:Q
303:c
301:T
287:c
285:T
179:Q
113:Q
85:Q
81:Q
65:Q
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
