A limit on the permanent electric dipole moment (EDM) of the positive muon is presented based on data from the Fermilab Muon g-2 Experiment taken between 2019 and 2020. The tracking detectors measure the average vertical decay angle of positrons from muon decays, enabling a search for an interaction between a possible muon EDM d_μ and the lab-frame magnetic field. The result, d_μ= (-0.35 ± 0.19_stat± 0.34_sys) ×10^-19 e·cm, is consistent with zero and sets a new direct limit on the muon EDM of |d_μ|<1.10×10^-19 e·cm at the 95 percent confidence level.

This report details the final measurement of the muon magnetic anomaly, a_μ=(g_μ-2)/2, by the Muon g-2 experiment at Fermi National Accelerator Laboratory (FNAL), using positive muons collected from 2021 to 2023. The value of a_μ is determined from the ratio of the anomalous spin precession frequency to the shielded proton precession frequency in the muon storage ring magnetic field, combined with external constants known at the 22 ppb level. The new dataset, containing over 2.5 times the statistics of our previous results, yields a_μ=116 592 0710(162)× 10^-12 (139 ppb), or a_μ=116 592 0705(148)× 10^-12 (127 ppb) when combined with our previous results. The new experimental world average, dominated by the measurements at FNAL, is a_μ^Exp=116 592 0715(145)× 10^-12 (124 ppb).

A new measurement of the magnetic anomaly a_{μ} of the positive muon is presented based on data taken from 2020 to 2023 by the Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL). This dataset contains over 2.5 times the total statistics of our previous results. From the ratio of the precession frequencies for muons and protons in our storage ring magnetic field, together with precisely known ratios of fundamental constants, we determine a_{μ}=1 165 920 710(162)×10^{-12} (139 ppb) for the new datasets, and a_{μ}=1 165 920 705(148)×10^{-12} (127 ppb) when combined with our previous results. The new experimental world average, dominated by the measurements at FNAL, is a_{μ}(exp)=1 165 920 715(145)×10^{-12} (124 ppb). The measurements at FNAL have improved the precision on the world average by over a factor of 4.

This paper is not a proposal for a CERN future project but provides information on the International Linear Collider (ILC) considered for Japan in order to facilitate the European Strategy discussion in a global context. It describes progress to date, ongoing engineering studies, updated cost estimate for the machine at √(s)=250 GeV and the situation in Japan. The physics of the ILC is not presented here, but jointly for all Linear Collider projects in a separate document “A Linear Collider Vision for the Future of Particle Physics” submitted for the forthcoming European Strategy deliberations.

We present a new measurement of the positive muon magnetic anomaly, a_{μ}≡(g_{μ}-2)/2, from the Fermilab Muon g-2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω[over ˜]_{p}^{'}, and of the anomalous precession frequency corrected for beam dynamics effects, ω_{a}. From the ratio ω_{a}/ω[over ˜]_{p}^{'}, together with precisely determined external parameters, we determine a_{μ}=116 592 057(25)×10^{-11} (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a_{μ}(FNAL)=116 592 055(24)×10^{-11} (0.20 ppm). The new experimental world average is a_{μ}(exp)=116 592 059(22)×10^{-11} (0.19 ppm), which represents a factor of 2 improvement in precision.

The Fermi National Accelerator Laboratory has measured the anomalous precession frequency $a^{}_\mu = (g^{}_\mu-2)/2$ of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7$^\circ$C. The measured field is weighted by the muon distribution resulting in $\tilde{\omega}'^{}_p$, the denominator in the ratio $\omega^{}_a$/$\tilde{\omega}'^{}_p$ that together with known fundamental constants yields $a^{}_\mu$. The reported uncertainty on $\tilde{\omega}'^{}_p$ for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb.

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon g-2 Experiment for the positive muon magnetic anomaly a_{μ}≡(g_{μ}-2)/2. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ω_{a} between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ω[over ˜]_{p}^{'} in a spherical water sample at 34.7 °C. The ratio ω_{a}/ω[over ˜]_{p}^{'}, together with known fundamental constants, determines a_{μ}(FNAL)=116 592 040(54)×10^{-11} (0.46 ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both μ^{+} and μ^{-}, the new experimental average of a_{μ}(Exp)=116 592 061(41)×10^{-11} (0.35 ppm) increases the tension between experiment and theory to 4.2 standard deviations.

In preparation for a demonstration of optical stochastic cooling in the Cornell Electron Storage Ring (CESR) we have developed a particle tracking simulation to study the relevant beam dynamics. Optical radiation emitted in the pickup undulator gives a momentum kick to that same particle in the kicker undulator. The optics of the electron bypass from pickup to kicker couples betatron amplitude and momentum offset to path length so that the momentum kick reduces emittance and momentum spread. Nearby electrons contribute an incoherent noise. Layout of the bypass line is presented that accommodates optics with a range of transverse and longitudinal cooling parameters. The simulation is used to determine cooling rates and their dependence on bunch and lattice parameters for bypass optics with distinct emittance and momentum acceptance.

This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 dataset of the Fermilab Muon g - 2 Experiment. Two corrections to the measured muon precession frequency omega(m)(a) are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary, because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to omega(m)(a) is 0.50 +/- 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of omega(m)(a).

The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has measured the muon anomalous precession frequency $\omega_a$ to an uncertainty of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data collected in four storage ring configurations during its first physics run in 2018. When combined with a precision measurement of the magnetic field of the experiment's muon storage ring, the precession frequency measurement determines a muon magnetic anomaly of $a_{\mu}({\rm FNAL}) = 116\,592\,040(54) \times 10^{-11}$ (0.46 ppm). This article describes the multiple techniques employed in the reconstruction, analysis and fitting of the data to measure the precession frequency. It also presents the averaging of the results from the eleven separate determinations of \omega_a, and the systematic uncertainties on the result.

A proposed experiment to demonstrate Optical Stochastic Cooling (OSC) in the Cornell Electron Storage Ring (CESR) based on an arc-bypass design is presented. This arc-bypass provides significantly longer optical delay than the dog-leg style chicane, opening up the possibility of a multi-pass or staged optical amplifier that can achieve the gains required for effective cooling of hadron or heavy-ions. Beyond introducing the arc-bypass, in this paper we study the stability requirements for the dipoles comprising it and investigate the use of an optical feedback system to relax the dipole and light-path stability tolerances.

We report here the first experimental result for the anisotropy of the one-way maximum attainable speed of the electron, Delta(c) over right arrow (1,e), obtained via the study of a sidereal time dependence of the difference between momenta of the counterrotating electron and positron beams in the Cornell Electron Storage Ring at Cornell University. At 95% confidence, an upper limit for the component of Delta(c) over right arrow (1,e)/c perpendicular to Earth's rotational axis is found to be 5.5 x 10(-15).

In order to test the process of Optical Stochastic Cooling (OSC) at the Cornell Electron Storage Ring (CESR), we plan to use helical wigglers as both the pickup and kicker, since the required radiation wavelength of 800nm can be achieved with lower magnetic field strength in helical as compared to planar wigglers. In order to simulate the lattice with such wigglers, it is useful to be able to model the effect of the wiggler on the optics without resorting to direct tracking, which is time-consuming and so ill-suited for the repeated evaluations necessary in running an optimizer. We generate a Taylor map to third order for this element using analytic field expressions, enabling easy determination of the effects of such an element on linear and nonlinear optics. This model is compared with the results of direct tracking and shows good agreement.

During the summer and fall of 2018 the Cornell High Energy Synchrotron Source (CHESS) is undergoing an upgrade to increase high-energy flux for x-ray users. The upgrade requires replacing one-sixth of the Cornell Electron Storage Ring (CESR), inverting the polarity of half of the CHESS beam lines, and switching to single-beam on-axis operation. The new sextant is comprised of six double-bend achromats (DBAs) with combined-function dipole-quadrupoles. Although the DBA design is widely utilized and well understood, the constraints for the CESR modifications make the CHESS-U lattice unique. This paper describes the design objectives, constraints, and implementation for the CESR accelerator upgrade for CHESS-U.

We report on extensive measurements at the Cornell Electron-positron Storage Ring of electron-cloud-induced betatron tune shifts for trains of positron bunches at 2.1 and 5.3 GeV with bunch populations ranging between 0.64x10^10 and 9.6x10^10. Measurements using a witness bunch with variable distance from the end of the train and variable bunch population provide information on cloud decay and cloud pinching during the bunch passage. We employ Monte Carlo simulations of the reflection and absorption of synchrotron radiation photons to determine the pattern of absorption sites around the circumference of the storage ring. The Geant4 simulation toolkit is used to model the interactions of the photons with the beampipe wall and determine the production energy and location distributions of the photoelectrons which seed the electron cloud. An electron cloud buildup model based on fitted ring-averaged secondary-yield properties of the vacuum chamber predicts tune shifts in good agreement with the measurements.

Short range transverse wake fields are excited by charged particles passing through a vacuum chamber. The wake fields can act back on a bunch of particles and alter its trajectory. We have measured the distortion of the closed orbit due to transverse wake fields in the Cornell Electron–positron Storage Ring. A transverse monopole wake field is induced by an asymmetric impedance associated with the insertion of a single vertical scraper. A transverse dipole wake field is generated by displacing the bunch from the symmetry axis of the chamber. The orbit is offset vertically through the gap of a pair of symmetrically inserted scrapers and also in a narrow-gap undulator chamber. A fit to the distorted orbits yields the average kick of the transverse monopole wake of the asymmetric scrapers and the kick factor of the symmetric scrapers; the scraper results are in reasonable agreement with the values from numerical simulation of the wake fields. The kick factor extracted from the closed orbit distortion of the dipole wake induced by the narrow-gap undulator chamber is significantly greater than that predicted by the numerical simulation. Possible sources of the discrepancy are discussed.

Particle storage rings are a rich application domain for online optimization algorithms. The Cornell Electron Storage Ring (CESR) has hundreds of independently powered magnets, making it a high-dimensional test-problem for algorithmic tuning. We investigate algorithms that restrict the search space to a small number of linear combinations of parameters ("knobs") which contain most of the effect on our chosen objective (the vertical emittance), thus enabling efficient tuning. We report experimental tests at CESR that use dimension-reduction techniques to transform an 81-dimensional space to an 8-dimensional one which may be efficiently minimized using one-dimensional parameter scans. We also report an experimental test of a multi-objective genetic algorithm using these knobs that results in emittance improvements comparable to state-of-the-art algorithms, but with increased control over orbit errors.

Particle accelerators contain hundreds ofmagnets, making dimension-reduction techniques attractive when attempting to tune them. We apply this procedure to two different problems: correcting the orbit in the Cornell synchrotron and maximizing the dynamic aperture in the Cornell Electron Storage Ring (CESR). Cornell’s rapid cycling synchrotron accepts a 200 MeV beam from the linac and accelerates it to 6 GeV for injection into the CESR. ‘Kicker coils’ (dipole correctors) are used to correct for residual fields which would otherwise cause beam loss at the low energies. In such cases, it is usually advisable to measure and correct the orbit. However, one cannot measure the orbit without first getting the beam to circulate a few hundred times, by which point the low-energy orbit would already be mostly corrected. In order to speed up the process of empirical orbit tuning, we form knobs which have the largest effect on the global orbit error, so that the dimensionality of the space which must be searched may be greatly reduced. A small dynamic aperture in CESR will have adverse effects on beam lifetime and injection efficiency, and so ought to be maximized by tuning sextupoles. However, it is often unclear which sextupoles one ought to tune to alleviate the problem. Moreover, once the chromaticity is properly adjusted, it should not be changed. Since we expect resonance driving terms (RDTs) to have a large impact on the dynamic aperture, we develop sextupole knobs which change the RDTs as much as possible while leaving the chromaticity fixed.

Transverse vertical wakefields can increase the vertical emittance and distort the phase space of a bunch in a storage ring. Recently, we observed charge-dependent vertical beam size growth with a single scraper inserted through the top of the storage ring vacuum chamber. This apparent growth was due in large part to the yz coupling (vertical crabbing) induced by the wake field from the asymmetric scraper configuration. Here, we report a direct measurement of a small beam yz tilt (crabbing) using a streak camera. The recorded images (projected beam profiles in yz plane) are analyzed with three different methods, which yield consistent beam yz tilts. We found the directly-measured current-dependent beam tilts by the streak camera are consistent with the beam tilts calculated from a wakefield model.

Transverse vertical wakefields can increase vertical emittance and distort the phase space of a bunch in a storage ring. Here we report recent measurements and simulations of these effects from wakefields from movable scrapers at the Cornell electron-positron storage ring test accelerator. Charge-dependent vertical beam size growth was observed with a single scraper inserted through the top of the storage ring vacuum chamber. No change in the beam size was observed with top and bottom scrapers inserted symmetrically. The apparent growth in the vertical beam size was due in large part to the yz coupling (vertical crabbing) induced by the transverse monopole wake of the asymmetric scraper configuration. We explored this yz coupling and thus the orientation at the observation point by varying the vertical betatron phase advance between the vertical beam size monitor and the scrapers. In addition, we found that existing residual, current-independent yz coupling, perhaps due to nonzero vertical dispersion in the rf cavities, could be compensated by the scraper wake. Predictions from tracking simulations are in good agreement with the measurements. Moreover, the vertical beam size as a function of vertical displacement at narrow-gap chambers (closed scrapers and undulator chamber) was measured. We found the transverse wakefield produced by the off-axis beam could also introduce a yz tilt as well as dilute the beam emittance.