The Muon (g-2) Experiment, E989 at Fermilab, will measure the muon anomalous magnetic moment a factor-of-four more precisely than was done in E821 at the Brookhaven National Laboratory AGS. The E821 result appears to be greater than the Standard-Model prediction by more than three standard deviations. When combined with expected improvement in the Standard-Model hadronic contributions, E989 should be able to determine definitively whether or not the E821 result is evidence for physics beyond the Standard Model. After a review of the physics motivation and the basic technique, which will use the muon storage ring built at BNL and now relocated to Fermilab, the design of the new experiment is presented. This document was created in partial fulfillment of the requirements necessary to obtain DOE CD-2/3 approval.

Beam-beam forces and collision optics can strongly affect beam lifetime, dynamic aperture, and halo formation in particle colliders. Extensive analytical and numerical simulations are carried out in the design and operational stage of a machine to quantify these effects, but experimental data is scarce. The technique of small-step collimator scans was applied to the Fermilab Tevatron collider and to the CERN Large Hadron Collider to study the effect of collisions on transverse beam halo dynamics. We describe the technique and present a summary of the first results on the dependence of the halo diffusion coefficient on betatron amplitude in the Tevatron and in the LHC.

Experimental measurements of beam halo diffusion dynamics with collimator scans are reviewed. The concept of halo control with a hollow electron beam collimator, its demonstration at the Tevatron, and its possible applications at the LHC are discussed.

The T980 crystal collimation experiment is underway at the Tevatron to determine if this technique could increase 980 GeV beam-halo collimation efficiency at high-energy hadron colliders such as the Tevatron and the LHC. T980 also studies various crystal types and parameters. The setup has been substantially enhanced during the Summer 2009 shutdown by installing a new O-shaped crystal in the horizontal goniometer, as well as adding a vertical goniometer with two alternating crystals (O-shaped and multi-strip) and additional beam diagnostics. First measurements with the new system are quite encouraging, with channeled and volume-reflected beams observed on the secondary collimators as predicted. Investigation of crystal collimation efficiencies with crystals in volume reflection and channeling modes are described in comparison with an amorphous primary collimator. Results on the system performance are presented for the end-of-store studies and for entire collider stores. The first investigation of colliding beam collimation simultaneously using crystals in both the vertical and horizontal plane has been made in the regime with horizontally channeled and vertically volume-reflected beams. Planning is underway for significant hardware improvements during the FY10 summer shutdown and for dedicated studies during the final year of Tevatron operation and also for a "post-collider beam physics running" period.

During the first 20 years of operation, the Fermilab Tevatron developed strong coupling between the two transverse degrees of freedom. The required strength of the circuit of skew quadrupole magnets used to correct for coupling, though capable, had increased by an order of magnitude since 1983. Changes made to the Tevatron for colliding beams operation had altered the skew quadrupole corrector distribution and strong coupling became evident, often encumbering routine operation during the colliding beam physics run. It was discovered that the superconducting coils of the main dipole magnets had become vertically displaced relative to their yokes since their construction. The ensuing systematic skew quadrupole field introduced by this displacement accounts for the required corrector settings and observed beam behavior. The magnets were adjusted in situ over the course of several long maintenance periods and the Tevatron performance improved as a result.

The T-980 bent crystal collimation experiment at the Tevatron has recently acquired substantial enhancements. First, two new crystals - a 16-strip one manufactured and characterized by the INFN Ferrara group and a quasi-mosaic crystal manufactured and characterized by the PNPI group. Second, a two plane telescope with 3 high-resolution pixel detectors per plane along with corresponding mechanics, electronics, control and software has been manufactured, tested and installed in the E0 crystal region. The purpose of the pixel telescope is to measure and image channeled (CH), volume-reflected (VR) and multiple volume-reflected (MVR) beam profiles produced by bent crystals. Third, an ORIGIN-based system has been developed for thorough analysis of experimental and simulation data. Results of analysis are presented for different types of crystals used from 2005 to present for channeling and volume reflection including pioneering tests of two-plane crystal collimation at the collider, all in comparison with detailed simulations.

The transverse beam diffusion rate vs. particle oscillation amplitude was measured in the Tevatron using collimator scans. All collimator jaws except one were retracted. As the jaw of interest was moved in small steps, the local shower rates were recorded as a function of time. By using a diffusion model, the time evolution of losses could be related to the diffusion rate at the collimator position. Preliminary results of these measurements are presented.

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.

Recent experimental studies at the Fermilab Tevatron collider have shown that magnetically confined hollow electron beams can act as a new kind of collimator for high-intensity beams in storage rings. In a hollow electron beam collimator, electrons enclose the circulating beam. Their electric charge kicks halo particles transversely. If their distribution is axially symmetric, the beam core is unaffected. This device is complementary to conventional two-stage collimation systems: the electron beam can be placed arbitrarily close to the circulating beam; and particle removal is smooth, so that the device is a diffusion enhancer rather than a hard aperture limitation. The concept was tested in the Tevatron collider using a hollow electron gun installed in one of the existing electron lenses. We describe some of the technical aspects of hollow-beam scraping and the results of recent measurements.

Correction of the second order betatron tune chromatic - ity is essential for operation at the working point near half integer resonance which is proposed as one of the ways to improve performance of the Tevatron. In this report the new chromaticity correction scheme with split sextupole families is described. Details of implementation and commissioning at the present working point are discussed.

During the beginning of Run II of the Tevatron Collider it became apparent that a large skew quadrupole source, or sources, had developed in the superconducting synchrotron. Efforts to locate the current source of coupling were undertaken, with the eventual discovery that the main magnets had developed a systematic skew quadrupole moment over their lifetime. Over the past year, the magnets have been altered in place in an attempt to restore the systematic skew quadrupole moment to zero. Beam observations and their interpretations are presented, and remedial measures are discussed.

Chromaticity drift during injection is a well-known phenomenon in superconducting colliders, such as the Tevatron, HERA and RHIC. Imperfect compensation of the drift effects can contribute to beam loss and emittance growth. It is caused by the drift of the sextupole component in the dipole magnets due to current redistribution in its superconducting coils. Recently extensive studies of chromaticity drift were conducted at the Tevatron, aiming at the improvement of the luminosity performance in the ongoing run II. These studies included not only beam experiments, but also extensive off-line magnetic measurements on spare Tevatron dipoles. Less known, until recently, is that chromaticity drift is often accompanied by tune and coupling drift. This was recently discovered in the Tevatron. We believe that these effects are the product of systematic beam offset in conjunction with the sextupole drifts (and their compensation in the chromaticity correctors). These discoveries are most relevant to the upcoming LHC, where the drift effects will have even more dramatic consequences given the high beam current. It is therefore not a surprise that CERN has been the source of major advances in the understanding of dynamic effects during the LHC superconducting magnet development. The following will briefly review the CERN results as well as those of the recent Fermilab studies. A new result, which will be presented here also, is related to fast drifts occurring in the first few seconds of the injection plateau.

porch can be correlated with a total of ~100 units (of 10-4 times the dipole field at injection) of quadrupolar field over the entire ring. This indicates a small effect, which can be produced by one (normal -b1- or skew -a1-) corrector quad running at ~7 A. The time-dependence of the tune and coupling drift is logarithmic, similar to that of the sextupole (b2) drift in the main dipoles. It is therefore suspected that the cause of the problem lies within the main superconducting magnets of the Tevatron. The following note discusses the tune drift issue in the Tevatron, and explores possible avenues of explanation. These are a) feed-down effects from the sextupole fields in the main dipoles and sextupole correctors due to beam-offset and/or systematic magnet mis- alignment and geometric errors; b) possible wiring errors in the corrector circuits, c) possible decaying main fields in quadrupoles and d) decaying skew and normal quadrupole components in the main dipoles.

Beam loss and emittance dilution during ramping from injection to collision energy is observed in the Tevatron, now in its collider run-II stage. Imperfect control of the machine chromaticity during the injection porch and the ensuing ramp to collision could contribute to the beam loss. Dipole magnets are the main source of chromaticity in the Tevatron. Sextupole correctors are distributed around the ring to compensate for the sextupole from the dipole magnets. Furthermore, the sextupole component in the superconducting Tevatron dipole magnets decays during the injection plateau and snaps back to the value before the start of the decay at the start of the ramp. The chromaticity correctors also correct for this so-called dynamic sextupole behavior. To determine if the sextupole compensation is working successfully in the Tevatron a thorough investigation of the sextupole (b2) in Tevatron dipole magnets was recently conducted. This included an extensive series of off-line magnetic measurements on several Tevatron dipole magnets from the spare pool. Traditionally one differentiates between three different b2 components, geometric, hysteretic and dynamic. This note discusses the results of these measurements. The experiments were also complemented with magnetic field calculations and analysis of data from the Tevatron magnetic measurement archive. On the basis of this document it is hoped that the chromaticity correction scheme in the Tevatron can be improved. Such improvements, however, are discussed in a separate note on the Tevatron chromaticity compensation (TD-03-008 - Revision I). This work is essentially a continuation of a similar study conducted in 1996 (1), on the basis of which the chromaticity correction scheme for the Tevatron run II was devised.

To help optimize the performance of the Fermilab Tevatron accelerator in Collider Run II, we have undertaken a systematic study of the drift and subsequent snapback of dipole magnet harmonics. The study has mostly focused on the dynamic behavior of the normal sextupole component, b2, as measured on a sample of spare Tevatron dipoles at the Fermilab Magnet Test Facility. We measured the dependence of the decay amplitude and the snapback time on Tevatron ramp parameters and magnet operational history. A series of beam studies was also performed (1). This paper summarizes the magnetic measurement results and concludes with proposals for an optimization of the b2 correction scheme which is derived from these measurements.