We present a new measurement of the positive muon magnetic anomaly, a µ ≡ (gµ − 2)/2, from the Fermilab Muon g −2 Experiment based on data collected in 2019 and 2020. We have analyzed more than four 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 two due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω′ p , and of the anomalous precession frequency corrected for beam dynamics effects, ωa. From the ratio ωa/ω ′ 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 aµ(Exp) = 116 592 059(22) × 10 −11 (0.19 ppm), which represents a factor of two improvement in precision.

A novel concept of controlled halo removal for intense high-energy beams in storage rings and colliders is presented. It is based on the interaction of the circulating beam with a 5-keV, magnetically confined, pulsed hollow electron beam in a 2-m-long section of the ring. The electrons enclose the circulating beam, kicking halo particles transversely and leaving the beam core unperturbed. By acting as a tunable diffusion enhancer and not as a hard aperture limitation, the hollow electron beam collimator extends conventional collimation systems beyond the intensity limits imposed by tolerable losses. The concept was tested experimentally at the Fermilab Tevatron proton-antiproton collider. The first results on the collimation of 980-GeV antiprotons are presented. PACS numbers: 29.20.db, 41.85.Si Keywords: storage rings and colliders; beam collimation; magnetically confined electron beams; beam diffusion In high-energy particle accelerators and storage rings, the collimation system must protect equipment from intentional and accidental beam aborts by intercepting particle losses [1][2][3]. Its functions include controlling and reducing the beam halo, which is continually replenished by various processes such as beam-gas scattering, intrabeam scattering, electrical noise in the accelerating cavities, ground motion, betatron resonances, and beam-beam collisions. Uncontrolled losses of even a small fraction of the circulating beam can damage components, quench superconducting magnets, or produce intolerable experimental backgrounds. Collimators also serve as a diagnostic tool for fundamental machine measurements, such as transverse admittances, beam vibrations, and diffusion rates.Conventional collimation schemes are based on scatterers and absorbers, possibly incorporating several stages. The primary collimators (or targets) are the devices closest to the beam. They generate random transverse kicks mainly via multiple Coulomb scattering. In the Tevatron, the primary collimators are 5-mm tungsten plates positioned about 5 standard deviations (σ ) away from the beam axis. The random multiple-scattering kick has a root mean square (r.m.s.) of 17 µrad for 980-GeV protons. The betatron oscillation amplitude of the affected particles increases, and a large fraction of them is captured by the secondary collimators (or absorbers), suitably placed around the ring. In the Tevatron, the absorbers are 1.5-m steel blocks at 6σ .The conventional two-stage system offers robust shielding of sensitive components and it is very efficient in reducing beam-related backgrounds at the experiments. However, it has limitations. In high-power accelerators, the minimum distance between the collimator and the beam axis is limited by instantaneous loss rates, radiation damage, and by the electromagnetic impedance of the device. Moreover, beam jitter, caused by ground motion and other vibrations and partly mitigated by active orbit feedback, can cause periodic bursts of losses at aperture restrictions.

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The volume reflection phenomenon was detected while investigating 400 GeV proton interactions with bent silicon crystals in the external beam H8 of the CERN Super Proton Synchrotron. Such a process was observed for a wide interval of crystal orientations relative to the beam axis, and its efficiency exceeds 95%, thereby surpassing any previously observed value. These observations suggest new perspectives for the manipulation of high-energy beams, e.g., for collimation and extraction in new-generation hadron colliders, such as the CERN Large Hadron Collider.

Collimation of proton and antiproton beams in the Tevatron collider is required to protect CDF and D0 detectors and minimize their background rates, to keep irradiation of superconducting magnets under control, to maintain long-term operational reliability, and to reduce the impact of beam-induced radiation on the environment. In this article we briefly describe the design, practical implementation and performance of the collider collimation system, methods to control transverse and longitudinal beam halo and two novel collimation techniques tested in the Tevatron.