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This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $\omega_a^m$ 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 $\omega_a^m$ is 0.50 $\pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $\omega_a^m$., Comment: 35 pages, 29 figures. Accepted by Phys. Rev. Accel. Beams

In the following years the Fermilab Muon Campus will deliver highly polarized muon beams to the storage ring of the Muon g-2 Experiment. The transmission fraction of the storage ring has been shown to depend strongly on the transverse optics of the injected beam. Unfortunately, the current diagnostics in the Muon Campus allow only measurement of the beam configuration space which limits how well propagation can be predicted. This paper demonstrates an experimental technique based on a conventional magnet scan to obtain the Twiss parameters at a point, using only beam profiles such that installation of new equipment is not required. A proof-of-principle experiment is presented which shows that this new method is applicable to the Muon Campus, offering a viable approach to optimization of injection in the Muon g-2 Experiment.

The Muon g-2 experiment seeks to measure the anomalous magnetic moment (g-2) of muons to a 0.14 ppm uncertainty. In order to accomplish this, the experiment’s storage ring must be supplied with the largest number of muons with energies within 0.2% of 3.094 GeV/c possible. In this work we perform a parametric analysis for enhancing the experiment’s stored beam intensity. From the accelerator technology side, we discuss the impact in muon flux of both, a passive absorber for tailoring the momentum distribution of the injected beam, and a magnetic inflector for shielding it from the storage ring fringe fields. From the beam parameter side, we examine the interplay between beam energy and momentum spread in maximizing muon storage. We show that with a proper choice of injection beam parameters in conjunction with a wedge-shaped absorber and an open-ended inflector design, the yield of the experiment could increase by over 50% as compared to the current performance. We also find that although the wedge can enhance the stored muon yield, most of the improvement originates from the open-ended inflector design.

A scheme is discussed for momentum selection and momentum-spread reduction for muon-based experiments. The concept relies on placing a wedge absorber at a point along a beam transport system with nonzero dispersion. The technique has direct relevance to precision-science experiments such as the Fermilab Muon g-2 Experiment as it can enhance the muon beam intensity and therefore minimize the statistical uncertainty of the anomalous magnetic moment measurement. This paper presents a theoretical and numerical study about the orientation, material, geometrical parameters, and performance of this wedge. Results suggest a considerable increase in muon intensity for the Muon g-2 Experiment, when the optimal wedge is introduced along the beam path.

The goal of the Muon g-2 Experiment is to measure the anomalous magnetic moment of the muon with a precision of 140 ppb; this is achieved by observing the polarization of muon decays in a precisely designed storage ring. Unfortunately, 90% of the injected beam is lost in apertures since it has a rms momentum spread that is an order of magnitude larger than the ring’s acceptance. In this study, we investigate the use of a wedge absorber for reducing the momentum spread of a muon beam. This technique relies on an interplay between ionization cooling and emittance exchange. We present the outcomes of tracking simulations and examine in detail the impact of the absorber length in reducing the momentum spread of the beam. Overall, we illustrate that the wedge has a positive impact on the Muon g-2 Experiment as it can increase the intensity of the storable beam. The technique discussed here may serve as an important a tool for momentum control of next generation secondary-beam-based experiments.

Ionization cooling is the preferred method for producing bright muon beams. This cooling technique requires the operation of normal conducting, radio-frequency (RF) accelerating cavities within the multi-tesla fields of DC solenoid magnets. Under these conditions, cavities exhibit increased susceptibility to RF breakdown, which can damage channel components and imposes limits on channel length and transmission efficiency. We present a solution to the problem of breakdown in strong magnetic fields. We report, for the first time, stable high-vacuum, copper cavity operation at gradients above 50 MV/m and in an external magnetic field of three tesla. This eliminates a significant technical risk that has previously been inherent in ionization cooling channel designs., Comment: 7 pages, 7 figures

Fermilab is dedicated to hosting world-class experiments in search of new physics that will operate in the coming years. The Muon g-2 Experiment is one such experiment that will determine with unprecedented precision the muon anomalous magnetic moment, which offers an important test of the Standard Model. We describe in this study the accelerator facility that will deliver a muon beam to this experiment. We first present the lattice design that allows for efficient capture, transport, and delivery of polarized muon beams. We then numerically examine its performance by simulating pion production in the target, muon collection by the downstream beam line optics, as well as transport of muon polarization. We finally establish the conditions required for the safe removal of unwanted secondary particles that minimizes contamination of the final beam., 10 pp

Small muon beams increase the luminosity of a muon collider. Reducing the momentum and position spreads of muons reduces emittance and leads to small, cool beams. Ionization cooling has been observed at the Muon Ionization Cooling Experiment. 6D emittance reduction by a factor of 100, 000 has been achieved in simulation. Another factor of 5 in cooling would meet the basic requirements of a high luminosity muon collider. In this paper we compare, for the first time, the amount of RF needed in a cooling channel to previous linacs. We also outline three methods aimed to help achieve a final factor of 5 in 6D cooling., Comment: 18 pages, 5 figures, explanations added

It is believed that a neutrino factory would deliver unparalleled performance in studying neutrino mixing and would provide tremendous sensitivity to new physics in the neutrino sector. A neutrino factory employs muons which are produced, collected, accelerated and then stored so that their eventual decay produces an intense neutrino beam. A key challenge is that the initial muon beam occupies a region in phase space that vastly exceeds the acceptance of the downstream accelerators. Here we study a novel method to manipulate the longitudinal and transverse phase space with the purpose of collecting and cooling a muon beam. In this method, a set of properly tuned rf cavities captures the muon beams into strings of bunches and aligns them to nearly equal central energies, and a following set of rf cavities with absorbers cools them by a factor of three in transverse emittance. The sensitivity in performance of the channel against key parameters such as the number of cavities, accelerating gradient and magnetic field is analyzed. Finally, the lattice tolerance to positioning errors of various lattice components is systematically examined.

A fast cooling technique is described that simultaneously reduces all six phase-space dimensions of a muon beam. In this process, cooling is accomplished by reducing the beam momentum through ionization energy loss in wedge absorbers and replenishing the momentum loss only in the longitudinal direction by using gas-filled rf cavities. With the aid of numerical simulations we show that the transmission is comparable to that of an equivalent channel with vacuum rf cavities. Furthermore, the final emittances achieved satisfy the cooling criteria for a Muon Collider. Finally, we discuss the sensitivity in performance for various gas pressures.

In this study, obtaining muon beams with high-density in 6D phase-space is essential for realization of muon colliders, neutrino factories based on accelerated muons beams and other experiments involving muons. While several schemes to compress the beam phase-space by means of muon cooling having been proposed, very little is known about the impact of particle-particle interactions in the whole design. In this paper, we examine the influence of space-change fields on the cooling process of muon beams. We show that the cooling efficiency decreases with the degree of intensity, leading to emittance growth and particle loss for beams with large intensities. We further show that the emittance growth is only longitudinal and present a space-charge compensation solution by means of increasing the rf gradient. With the aid of numerical simulations, we obtain a quantitative relationship between the required compensation gradient and bunch charge and compare our results to earlier theoretical findings.

The relative immunity of muons to synchrotron radiation suggests that they might be used in place of electrons as probes in fundamental high-energy physics experiments. Muons are commonly produced indirectly through pion decay by interaction of a charged particle beam with a target. However, the large angle and energy dispersion of the initial beams as well as the short muon lifetime limits many potential applications. Here, we describe a fast method for manipulating the longitudinal and transverse phase-space of a divergent pion-muon beam to enable efficient capture and downstream transport with minimum losses. We also discuss the design of a handling system for the removal of unwanted secondary particles from the target region and thus reduce activation of the machine. The compact muon source we describe can be used for fundamental physics research in neutrino experiments., Comment: 27 pp

An ionization cooling channel is a tightly spaced lattice containing absorbers for reducing the momentum of the muon beam, rf cavities for restoring the longitudinal momentum, and strong solenoids for focusing. Such a lattice can be an essential feature for fundamental high-energy physics applications. In this paper we design, simulate, and compare four individual cooling schemes that rely on ionization cooling. We establish a scaling characterizing the impact of rf gradient limitations on the overall performance and systematically compare important lattice parameters such as the required magnetic fields and the number of cavities and absorber lengths for each cooling scenario. We discuss approaches for reducing the peak magnetic field inside the rf cavities by either increasing the lattice cell length or adopting a novel bucked-coil configuration. We numerically examine the performance of our proposed channels with two independent codes that fully incorporate all basic particle-matter-interaction physical processes. An ionization cooling channel is a tightly spaced lattice containing absorbers for reducing the momentum of the muon beam, rf cavities for restoring the longitudinal momentum, and strong solenoids for focusing. Such a lattice can be an essential feature for fundamental high-energy physics applications. In this paper we design, simulate, and compare four individual cooling schemes that rely on ionization cooling. We establish a scaling characterizing the impact of rf gradient limitations on the overall performance and systematically compare important lattice parameters such as the required magnetic fields and the number of cavities and absorber lengths for each cooling scenario. We discuss approaches for reducing the peak magnetic field inside the rf cavities by either increasing the lattice cell length or adopting a novel bucked-coil configuration. We numerically examine the performance of our proposed channels with two independent codes that fully incorporate all basic particle-matter-interaction physical processes.

In the neutrino factory, muons are produced by firing high-energy protons onto a target to produce pions. The pions decay to muons and pass through a capture channel known as the muon front end, before acceleration to 12.6 GeV. The muon front end comprises a variable frequency rf system for longitudinal capture and an ionization cooling channel. In this paper we detail recent improvements in the design of the muon front end.

A Neutrino Factory, which can deliver an intense flux of ∼1021 neutrinos per year from a multi-GeV stored muon-beam is seemingly the ideal tool for studying neutrino oscillations and CP-violations for leptons. The front-end of this facility plays a critical role in determining the number of muons that can be accepted by the downstream accelerators. Delivering peak performance requires transporting the muon beams through long sections of a beam channel containing high-gradient rf cavities and strong focusing solenoids. Here, we propose a novel scheme to improve the performance of the cavities, thereby increasing the number of muons within the acceptance of the accelerator chain. The key element of our new scheme is to apply a set of bucked coils along the lattice, thus forcing the external magnetic field to drop substantially within the cavity. We incorporate this idea into a new lattice design for a Neutrino Factory, and detail its performance numerically.

A neutrino factory, which can deliver an intense flux of $\ensuremath{\sim}{10}^{21}$ neutrinos per year from a multi-GeV stored muon beam, is seemingly the ideal tool for studying neutrino oscillations and $CP$ violations for leptons. The front end of this facility plays a critical role in determining the number of muons that can be accepted by the downstream accelerators. Delivering peak performance requires transporting the muon beams through long sections of a beam channel containing high-gradient rf cavities and strong focusing solenoids. Here, we propose a novel scheme to improve the performance of the cavities, thereby increasing the number of muons within the acceptance of the accelerator chain. The key element of our new scheme is to apply a tangential magnetic field to the rf surfaces, thus forcing any field-emitted electrons to return to the surface before gaining enough energy to damage the cavity. We incorporate this idea into a new lattice design for a neutrino factory, and detail its performance numerically. Although our proposed front-end channel requires more rf power than conventional pillbox designs, it provides enough beam cooling and muon production to be a feasible option for a neutrino factory.

Unwanted field emission is a well known problem for high‐gradient accelerating structures as it can cause damage and initiate breakdown. Recent experiments indicated that the deleterious effects of field‐emission are greatly enhanced in the presence of external magnetic fields. In the context of designing a muon accelerator this imposes numerous constraints since rf cavities need to operate within strong magnetic fields in order to successfully transport the beam. Here, a novel design of a magnetically insulated cavity in which the walls are parallel to the magnetic field lines is presented. We show that with magnetic insulation, damage from field emission can be significantly suppressed. Effects of coil positioning errors on the cavity performance are discussed and the required magnetic field strength to achieve insulation is estimated. We present a conceptual design of a muon collider cooling lattice with magnetic insulated cavities and cross‐check its performance to the one with pillbox cavities. Final...

Reduction of the available accelerating gradient in cavities exposed to external magnetic fields is a longstanding problem which limits the performance of many systems, especially muon accelerators. We propose a novel idea for improving the cavity's gradient by suppressing breakdown events caused by field emissions on its surfaces. The concept involves designing an rf cavity wherein its walls are parallel to the contour lines of the external magnetic fields, thereby preventing field-emitted electrons from leaving the surface, and subsequently picking up energy from the rf electric field. We present a conceptual design of a muon accelerator cooling lattice with magnetically insulated cavities and detail its expected performance. Our results suggest that the magnetically insulated cooling channel we describe, although demanding in rf power, can produce enough initial beam cooling to be a feasible option for a muon collider or a neutrino factory.