G. Burt, P. Ambattu, R. Carter, A. Dexter, I. Tahir, C. Beard, M. Dykes, P. Goudket, A. Kalinin, L. Ma, P. McIntosh, D. Shulte, R. M. Jones, L. Bellantoni, B. C… 展开作者
G. Burt, P. Ambattu, R. Carter, A. Dexter, I. Tahir, C. Beard, M. Dykes, P. Goudket, A. Kalinin, L. Ma, P. McIntosh, D. Shulte, R. M. Jones, L. Bellantoni, B. Chase, M. Church, T. Khabouline, A. Latina, C. Adolphsen, Z. Li, A. Seryei, L. Xiao
备注：
3 pages. To be published in proceedings of LINAC 2008, Victoria, Canada
Crab cavities have been proposed for a wide number of accelerators and interest in crab cavities has recently increased after the successful operation of a pair of crab cavities in KEK-B. In particular crab cavities are required for both the ILC and CLIC linear colliders for bunch alignment. Consideration of bunch structure and size constraints favour a 3.9 GHz superconducting, multi-cell cavity as the solution for ILC, whilst bunch structure and beam-loading considerations suggest an X-band copper travelling wave structure for CLIC. These two cavity solutions are very different in design but share complex design issues. Phase stabilisation, beam loading, wakefields and mode damping are fundamental issues for these crab cavities. Requirements and potential design solutions will be discussed for both colliders.
We studied the coupled beam motion in a storage ring between the transverse and longitudinal directions introduced by crab cavities. Analytic form of the linear decoupling transformation is derived. The equilibrium bunch distribution in an electron storage ring with a crab cavity is given, including contribution to the eigen-emittance induced by the crab cavity. Application to the short pulse generation scheme using crab cavities is considered.
KEKB was in operation from December 1988 to June 2010. The crab cavities were installed at KEKB in February 2007 and worked very stably until the end of KEKB operation. Operational experience of the crab cavities with beams is described.
The emittance growth in the HL-LHC due to beam-beam effects is examined by virtue of strong-strong computer simulations. A model of the transverse damper and the noise level have been tuned to simulate the emittance growth in the present LHC. Simulations with projected HL-LHC beam parameters and crab cavities are discussed. It is shown that with the nominal working point, the large beam-beam tune shift moves the beam into a resonance that causes substantial emittance growth. Increasing the working point slightly is demonstrated to be very beneficial.
The CLIC machine incorporates a 20 mrad crossing angle at the IP to aid the extraction of spent beams. In order to recover the luminosity lost through the crossing angle a crab cavity is proposed to rotate the bunches prior to collision. The crab cavity is chosen to have the same frequency as the main linac (11.9942 GHz) as a compromise between size, phase stability requirements and beam loading. It is proposed to use a HE11 mode travelling wave structure as the CLIC crab cavity in order to minimise beam loading and mode separation. The position of the crab cavity close to the final focus enha…
We tested the prototype DQW cavity in GERSEMI vertical test stand in FREIA. The performance met the specification, and our experimental procedure and infrastructure are qualified for testing crab cavities in the HL-LHC project. This was the critical milestone in the project and it also opens a new opportunity for testing superconducting cavities in FREIA.
In this paper, we present the effects of linear transverse-longitudinal coupling on beam size at Interaction Point (IP) of a collider with local crab crossing scheme, when time dependent transverse deflection (crab kicks) and dispersive orbit intertwine near IP. The analytic propagation formula and the closed orbit form of the crab dispersion and momentum dispersion are derived. The non-zero momentum dispersion at crab cavities and the non-ideal phase from crab cavities to IP are detailed with the derived propagation formula to predict the beam size distortion at IP with or without the beam-be…
In high energy physics, the luminosity is one useful value to characterize the performance of a particle collider. To gain more available data, we need to maximize the luminosity in most collider experiments. With the discussions of tune shift involved the beam dynamics and a recently proposed "crabbed waist" scheme of beam-beam collisions, we present some qualitative analysis to increase the luminosity. In addition, beam-beam tune shifts and luminosities of $e^{+}e^{-}$, $pp$/$p\bar{p}$, and $μ^{+}μ^{-}$ colliders are discussed.
A new concept of nonlinear focusing of colliding bunches, called Crab Waist (CW)collision scheme, has been proposed at LNF INFN. It has been successfully tested at the Italian lepton collider DAFNE in operational conditions providing luminosity for two different experimental detectors, SIDDHARTA and KLOE-2. Considering a high efficiency of the scheme for increasing collision luminosity and its relative simplicity for implementation several new collider projects have been proposed and are under development at present. These are the SuperKEKB B-factory ready to start commissioning in 2016 in Jap…
Studies of the crab cavities at KEKB revealed that the RF phase could shift by up to 50o within ~50 us during a quench; while the cavity voltage is still at approximately 75% of its nominal amplitude. If such a failure were to occur on the HL-LHC crab cavities, it is likely that the machine would sustain substantial damage to the beam line and surrounding infrastructure due to uncontrolled beam loss before the machine protection system could dump the beam. We have developed a low-level RF system model, including detuning mechanisms and beam loading, and use this to simulate the behaviour of a …
After the successful completion of the SIDDHARTA experiment run with crab waist collisions, the electron- positron collider DAΦNE has started routine operations for the KLOE-2 detector. The new interaction region also exploits the crab waist collision scheme, but features certain complications including the experimental detector solenoid, compensating anti-solenoids, and tilted quadrupole magnets. We have performed simulations of the beam-beam collisions in the collider taking into account the real DAΦNE nonlinear lattice. In particular, we have evaluated the effect of crab waist sextupoles an…
Crab crossing is essential for high-luminosity colliders. The High Luminosity Large Hadron Collider (HL-LHC) will equip one of its Interaction Points (IP1) with Double-Quarter Wave (DQW) crab cavities. A DQW cavity is a new generation of deflecting RF cavities that stands out for its compactness and broad frequency separation between fundamental and first high-order modes. The deflecting kick is provided by its fundamental mode. Each HL-LHC DQW cavity shall provide a nominal deflecting voltage of 3.4 MV, although up to 5.0 MV may be required. A Proof-of-Principle (PoP) DQW cavity was limited b…
Crab crossing scheme is an essential collision scheme to achieve high luminosity for the future colliders with large crossing angles. However, when bunch length of one or both colliding beams is comparable with the wavelength of the crab cavity voltage, the nonlinear dependence of the crabbing kick may present a challenge to the beam dynamics of the colliding beams and impact the beam quality as well as the luminosity lifetime. In this paper, the results of nonlinear dynamics in the crab crossing scheme are presented, using both analytical and numerical studies. The result indicates that highe…
Muon collider is a considerable candidate of the next-generation high-energy lepton collider machine. Operating an RF cavity in a multi-Tesla magnet is a critical requirement in a muon accelerator and a cooling channel. However, the maximum RF gradient in a vacuum RF cavity is strongly limited by an external magnetic field. Dense hydrogen gas filled RF cavity has been proposed since it is functional of generating a high RF accelerating gradient in a strong magnetic field and making an ionization cooling process at the same time. A critical issue of the cavity is a beam- induced plasma that con…
A novel design of superconducting Crab Cavity was proposed and designed at Brookhaven National Laboratory. The new cavity shape is a Double Quarter Wave or DQWCC. After fabrication and surface treatments, the niobium proof-of-principle cavity was cryogenically tested in a vertical cryostat. The cavity is extremely compact yet has a low frequency of 400 MHz, an essential property for service for the Large Hadron Collider luminosity upgrade. The electromagnetic properties of the cavity are also well matched for this demanding task. The demonstrated deflecting voltage of 4.6 MV is well above the …
The compact linear collider (CLIC) requires a crab cavity to align bunches prior to collision. The bunch structure demands tight amplitude and phase tolerances of the RF fields inside the cavity, for the minimal luminosity loss. Beam loading effects require special attention as it is one potential sources of field errors in the cavity. In order to assist the amplitude and phase control, we propose a travelling wave (TW) structure with a high group velocity allowing rapid propagation of errors out of the system. Such a design makes the cavity structure significantly different from previous ones…
The proposed linear electron-positron collider TESLA is based on 1.3 GHz superconducting niobium cavities for particle acceleration. For a centre-of-mass energy of 500 GeV, an accelerating field of 23.4 MV/m is required which is reliably achieved with a niobium surface preparation by chemical etching. An upgrade of the collider to 800 GeV requires an improved cavity preparation technique. In this paper, results are presented on single-cell cavities which demonstrate that fields of up to 40 MV/m are accessible by electrolytic polishing of the inner surface of the cavity.
In order to achieve luminosities significantly higher than in existing machines, future storage-ring based colliders will need to operate in novel parameter regimes combining ultra-low emittance, large Piwinski angle and high bunch charge; implementation of techniques such as a "crab waist" will add further challenges. Understanding the beam-beam interaction in these situations will be essential for the design of future very high luminosity colliders. Recent developments in modeling tools for studying beam-beam effects, capable of investigating the relevant regimes, will be discussed and examp…
An intense beam of muons is needed to provide a luminosity on the order of 10$^{34}$ cm$^{-2}$s$^{-1}$ for a multi-TeV collider. Because muons produced by colliding a multi-MW proton beam with a target made of carbon or mercury have a large phase space, significant six dimensional cooling is required. Through ionization cooling - the only cooling method that works within the lifetime of the muon - and emittance exchange, the desired emittances for a Higgs Factory or higher energy collider are attainable. A cooling channel utilizing gas filled radio frequency cavities has been designed to deliv…
High frequency High Order Modes can significantly affect the coupled-bunch stability in a circular accelerator. With a large enough shunt impedance they may drive a coupled-bunch transverse instability. We have developed an analytical model and implemented it in the NHT Vlasov solver. The results show that the instability is characterized by the excitation of many azimuthal intra-bunch modes, which have similar growth rates, that make the traditional remedies such as a flat resistive feedback and chromaticity inefficient in suppressing it. For the High Luminosity Large Hadron Collider this cou…
A new cavity-chain layout has been proposed for the main linac of the TESLA linear collider. This superstructure-layout is based upon four 7-cell superconducting standing-wave cavities, coupled by short beam pipes. The main advantages of the superstructure are an increase in the active accelerating length in TESLA and a saving in rf components, especially power couplers, as compared to the present 9-cell cavities. The proposed scheme allows to handle the field-flatness tuning and the HOM damping at sub-unit level, in contrast to standard multi-cell cavities. The superstructure-layout is extens…
A multi-laboratory collaboration is studying the feasibility of building a muon collider, the first phase of which maybe a neutrino factory. The phase space occupied by the muons is very large and needs to be cooled several orders of magnitude for either machine, 100,000 to 1 million for the collider and ten to 100 for the factory. Ionization cooling is the base line method for muon cooling. This scheme uses hydrogen absorbers and rf re-acceleration in a long series of magnetic focusing channels to cool the muons. At Fermilab two rf cavity types are under study to provide the required cooling …
CEPC will use 650 MHz cavities for the collider. Each collider cryomodule contains six 650 MHz 2-cell cavities, which is totally new. Therefore, new helium vessel and tuner are designed for the 650 MHz 2-cell cavity. Also, a test cryomodule, which consists of two 650 MHz 2-cell cavities, has begun as the first step to the full scale cryomodule. This paper mainly focuses on the structure design of Helium vessel and tuner for the 2-cell cavity.
RF cavity design and beam loading effects in the rectilinear cooling channel for a muon collider
European Organization for Nuclear Research (CERN)（欧洲核子研究中心）；Northern Illinois University（北伊利诺伊大学）；Argonne National Laboratory（阿贡国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Alternative Lattice Design for the STCF Collider Rings
University of Science and Technology of China（中国科学技术大学）；Budker Institute of Nuclear Physics SB RAS（布德克核物理研究所）；KEK（高能加速器研究机构）；The Graduate University for Advanced Studies (SOKENDAI)（日本高级研究院）；National Synchrotron Radiation Laboratory, University of Science and Technology of China（中国科学技术大学国家同步辐射实验室）
In view of a possible evolution of the CERN accelerator complex towards higher proton intensities, a 2.2 GeV H- linac with 4 MW beam power has been designed, for use in connection with an accumulator and compressor ring as proton driver of a muon-based Neutrino Factory. The high-energy part of this linac can use most of the RF equipment (superconducting cavities and klystrons) from the LEP collider after its decommissioning at the end of 2000. Recent results concerning low-beta superconducting cavities are presented, and the main characteristics of the linac design are described. The complete …
The conceptional design of the proposed linear electron-positron collider TESLA is based on 9-cell 1.3 GHz superconducting niobium cavities with an accelerating gradient of Eacc >= 25 MV/m at a quality factor Q0 > 5E+9. The design goal for the cavities of the TESLA Test Facility (TTF) linac was set to the more moderate value of Eacc >= 15 MV/m. In a first series of 27 industrially produced TTF cavities the average gradient at Q0 = 5E+9 was measured to be 20.1 +- 6.2 MV/m, excluding a few cavities suffering from serious fabrication or material defects. In the second production of 24 TTF cavitie…
We discuss the design of the muon capture front end for a μ+-μ- Collider. In the front end, a proton bunch on a target creates secondary pions that drift into a capture transport channel, decaying into muons. A sequence of rf cavities forms the resulting muon beams into strings of bunches of differing energies, aligns the bunches to (nearly) equal central energies, and initiates ionization cooling. The muons are then cooled and accelerated to high energy into a storage ring for high-energy high luminosity collisions. Our initial design is based on the somewhat similar front end of the Internat…
The Tera Electronvolt Superconducting Linear Accelerator TESLA is the only linear electron-positron collider project based on superconductor technology for particle acceleration. In the first stage with 500 GeV center-of-mass energy an accelerating field of 23.4 MV/m is needed in the superconducting niobium cavities which are operated at a temperature of 2 K and a quality factor Q0 of 10 to the 10. This performance has been reliably achieved in the cavities of the TESLA Test Facility (TTF) accelerator. The upgrade of TESLA to 800 GeV requires accelerating gradients of 35 MV/m. Using an improve…
A beam optics scheme has been designed for the Future Circular Collider-e+e- (FCC-ee). The main characteristics of the design are: beam energy 45 to 175 GeV, 100 km circumference with two interaction points (IPs) per ring, horizontal crossing angle of 30 mrad at the IP and the crab-waist scheme [1] with local chromaticity correction. The crab-waist scheme is implemented within the local chromaticity correction system without additional sextupoles, by reducing the strength of one of the two sextupoles for vertical chromatic correction at each side of the IP. So-called "tapering" of the magnets …
The efficiency of colliders for physics is largely determined by their luminosity, while most of the energy consumed by high-energy $e^+e^-$ colliders is proportional to the total beam current. Thus, the energy efficiency is mainly determined by the specific luminosity that needs to be maximized. One of the most effective ways to achieve this is by using the Crab waist collision scheme, which implies a large Piwinski angle (LPA). A distinctive feature of the FCC-ee is the great influence of beamstrahlung (radiation in the field of an opposite bunch) on beam dynamics. At low energies, this mani…
We outline a plan for final muon ionization cooling with quadrupole doublets focusing onto short absorbers followed by emittance exchange in vacuum to achieve the small transverse beam sizes needed by a muon collider. A flat muon beam with a series of quadrupole doublet half cells appears to provide the strong focusing required for final cooling. Each quadrupole doublet has a low beta region occupied by a dense, low Z absorber. After final cooling, normalized xyz emittances of (0.071, 0.141, 2.4) mm-rad are exchanged into (0.025, 0.025, 70) mm-rad. Thin electrostatic septa efficiently slice th…
The Future Circular Collider study is exploring possible designs of circular colliders for the post-LHC era, as recommended by the European Strategy Group for High Energy Physics. One such option is FCC-hh, a proton-proton collider with a centre-of-mass energy of 100 TeV. The experimental insertion regions are key areas defining the performance of the collider. This paper presents the first insertion region designs with a complete assessment of the main challenges, as collision debris with two orders of magnitude larger power than current colliders, beam-beam interactions in long insertions, d…
The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2 s^-1. The complex includes a polarized electron source, an undulator-based positron source, two 6.7 km circumference damping rings, two-stage bunch compressors, two 11 km long main linacs and a 4.5 km long beam delivery system. This report is Volume III (Accelerator) of the four volume Reference D…
The SuperB international team continues to optimize the design of an electron-positron collider, which will allow the enhanced study of the origins of flavor physics. The project combines the best features of a linear collider (high single-collision luminosity) and a storage-ring collider (high repetition rate), bringing together all accelerator physics aspects to make a very high luminosity of 10$^{36}$ cm$^{-2}$ sec$^{-1}$. This asymmetric-energy collider with a polarized electron beam will produce hundreds of millions of B-mesons at the $Υ$(4S) resonance. The present design is based on extr…
This Snowmass21 Contributed Paper encourages the Particle Physics community in fostering R&D in Superconducting Nb3Sn coated Copper RF Cavities instead of costly bulk Niobium. It describes the pressing need to devote effort in this direction, which would deliver higher gradient and higher temperature of operation and reduce the overall capital and operational costs of any future collider. It is unlikely that an ILC will be built in the next ten years with Nb as one of the main cost drivers of SRFs. This paper provides strong arguments on the benefits of using this time for R&D on producing Nb3…
Electrons of dark current (DC), generated in high-gradient superconducting RF cavities (SRF) due to field emission, can be accelerated up to very high energies-19 GeV in the case of the International Linear Collider (ILC) main linac-before they are removed by focusing and steering magnets. Electromagnetic and hadron showers generated by such electrons can represent a significant radiation threat to the linac equipment and personnel. In our study, an operational scenario is analysed which is believed can be considered as the worst case scenario for the main linac regarding the DC contribution t…
The international Future Circular Collider (FCC) study aims at a design of $pp$, $e^+e^-$, $ep$ colliders to be built in a new 100 km tunnel in the Geneva region. The $e^+e^-$ collider (FCC-ee) has a centre of mass energy range between 90 (Z-pole) and 375 GeV (tt_bar). To reach such unprecedented energies and luminosities, the design of the interaction region is crucial. The crab-waist collision scheme has been chosen for the design and it will be compatible with all beam energies. In this paper we will describe the machine detector interface layout including the solenoid compensation scheme. …
The International Linear Collider Technical Design Report (TDR) describes in four volumes the physics case and the design of a 500 GeV centre-of-mass energy linear electron-positron collider based on superconducting radio-frequency technology using Niobium cavities as the accelerating structures. The accelerator can be extended to 1 TeV and also run as a Higgs factory at around 250 GeV and on the Z0 pole. A comprehensive value estimate of the accelerator is give, together with associated uncertainties. It is shown that no significant technical issues remain to be solved. Once a site is selecte…
The International Linear Collider Technical Design Report (TDR) describes in four volumes the physics case and the design of a 500 GeV centre-of-mass energy linear electron-positron collider based on superconducting radio-frequency technology using Niobium cavities as the accelerating structures. The accelerator can be extended to 1 TeV and also run as a Higgs factory at around 250 GeV and on the Z0 pole. A comprehensive value estimate of the accelerator is give, together with associated uncertainties. It is shown that no significant technical issues remain to be solved. Once a site is selecte…
The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2s^-1. This report is the Executive Summary (Volume I) of the four volume Reference Design Report. It gives an overview of the physics at the ILC, the accelerator design and value estimate, the detector concepts, and the next steps towards project realization.
The International Linear Collider Technical Design Report (TDR) describes in four volumes the physics case and the design of a 500 GeV centre-of-mass energy linear electron-positron collider based on superconducting radio-frequency technology using Niobium cavities as the accelerating structures. The accelerator can be extended to 1 TeV and also run as a Higgs factory at around 250 GeV and on the Z0 pole. A comprehensive value estimate of the accelerator is give, together with associated uncertainties. It is shown that no significant technical issues remain to be solved. Once a site is selecte…
Chapter 8 in High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report. The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community of about 7,000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its luminosity (rate of collisions) by a factor of five beyond the …
Chapter 15 in High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report. The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community of about 7,000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its luminosity (rate of collisions) by a factor of five beyond the…
Chapter 9 in High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report. The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community of about 7,000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its luminosity (rate of collisions) by a factor of five beyond the …
Chapter 16 in High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report. The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community of about 7,000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its luminosity (rate of collisions) by a factor of five beyond the…
Chapter 14 in High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report. The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community of about 7,000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its luminosity (rate of collisions) by a factor of five beyond the…
Chapter 17 in High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report. The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community of about 7,000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its luminosity (rate of collisions) by a factor of five beyond the…
Chapter 12 in High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report. The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community of about 7,000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its luminosity (rate of collisions) by a factor of five beyond the…
Chapter 6 in High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report. The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community of about 7,000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its luminosity (rate of collisions) by a factor of five beyond the …
Chapter 13 in High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report. The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community of about 7,000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its luminosity (rate of collisions) by a factor of five beyond the…
