James MacLachlan

Optimization of electron cooling for a medium energy accumulator ring

Abstract The binary collision model of electron cooling is used to discuss the principal issues in the use of electron cooling for accumulating ions at medium energies, where “medium energy” is defined by a beam velocity >0.8 c . Some new general results are developed which are important in this context. Longitudinal and transverse cooling rates are calculated analytically for a particle executing betatron oscillations in a storage ring. The formulas obtained are compared with numerical results. Particular attention is paid to the case in which the transverse components of the relative velocities substantially exceed the longitudinal components. The exact analytical results for finite electron temperatures are presented. The time for longitudinal cooling of a Gaussian beam is calculated as a function of the acceptable fraction of uncooled particles; the optimum electron beam size is calculated and an optimum electron density distribution is found. The results obtained are applied to an electron cooling system for the Fermilab Recycler (Jackson, FERMILAB-TM-1991, Unpublished Internal Note, November 1999); the cooling time, optimum parameters and tolerances are calculated.

Scenario for electron cooling of antiprotons in the Recycler

Abstract A system of electron cooling of antiprotons in the Recycler must satisfy certain conditions. Analytic and numeric calculations of the cooling process allow to specify these requirements.

Fermilab R&D program in medium energy electron cooling

Abstract Fermilab began an R&D program in medium energy electron cooling in April 1995 with the object of cooling 8 GeV antiprotons in a new 3.3 km permanent magnet storage ring (Recycler) to be built in the same tunnel as the Main Injector (MI). The MI is to be completed in 1998, and it is planned to install the Recycler by the end of 1997 to reduce interference during the final rush of MI installation. Although the Recycler will employ stochastic cooling initially, its potential for contributing and order of magnitude to Tevatron collider luminosity is tied to electron cooling. The short time scale and Fermilabs limited familiarity with low energy electron beams has given rise to a two-phase development plan. The first phase is to build a cooling system based on an electron beam of ≥200 mA before the year 2000. The second phase of about three years is planned to reach an electron current of 2 A or more. This report describes the general scheme for high luminosity collider operation as well as the R&D plan and progress to date.

Applying synchrotron phase measurement to the estimation of maximum beam intensity in the Fermilab Booster

It is important to have experimental methods to estimate the maximum beam intensity for the Fermilab Booster as objective input into long term program commitments. An important existing limit is set by the available rf power. This limit is difficult to set a priori, because the real longitudinal impedance is not well known. The synchrotron phase at transition crossing was measured using both the mountain range plot and the direct phase measurement of the RF accelerating voltage relative to the beam, and results were consistent. They were applied to predict 6 x 10{sup 12} maximum Booster beam intensity with present running conditions.

Implications of beam phase and RFSUM measured near transition

A technique using RF bucket reduction for acquiring information about the particle distribution in longitudinal phase space has been applied in the Fermilab Booster. Data sets were obtained at six important time intervals of a Booster cycle for three different beam intensities. Controlled RF bucket reduction also provides other opportunities for beam manipulation.

Multiparticle Dynamics in the E‐φ Tracking Code ESME

ESME has developed over a twenty year period from its origins as a program for modeling rf gymnastics to a rather general facility for that fraction of beam dynamics of synchrotrons and storage rings which can be properly treated in the two dimensional longitudinal phase space. The features of this program which serve particularly for multiparticle calculations are described, some uderlying principles are noted, and illustrative results are given.

A proposed transition scheme for the longitudinal emittance control in the Fermilab Booster

Instead of applying the {gamma}{sub T} jump at the designed value of 1.0, which never can be used in the operation due to the quad steering, the combination of the rf manipulation and a 0.2-unit {gamma}{sub T} jump can reduce the longitudinal emittance growth nearly 40% during transition. Especially, a 0.2-unit {gamma}{sub T} jump can help in reducing the rf manipulating voltage from 1000 kV to 850 kV, and makes the transition scheme operationally feasible.

Beam-based determination of the offset of Booster {gamma}{sub T} quads

Twelve pulsed {gamma}{sub T} quads have been installed in the Booster to provide fast transition crossing. The less time the beam stays in the non-adiabatic period near transition, the less the longitudinal emittance grows. From the past experience, the {gamma}{sub T} quads are not well aligned relative to the usual closed orbit. Quad steering can cause beam loss and a dispersion wave after transition. To make the {gamma}{sub T} quads routinely operational, procedures for finding the center of the beam relative to the quads and centering the beam through all of them are very important. A program, which uses the difference in the closed orbits when {gamma}{sub T} quads are on and off and calculates the offsets of the beam relative to {gamma}{sub T} quads, has been developed and tested. A radial orbit offset (ROF) of about 3 mm has been experimentally determined to be nearly the optimal radial position for centering the beam through all the {gamma}{sub T} quads, thereby eliminating the immediate need for repositioning the quads.

Indicators of the energy error in the Linac to Booster transfer

The match between the Linac beam energy and the energy determined by the bending field of the Booster magnets is crucial for rf capture, beam quality, and the transmission efficiency in a Booster cycle. The observation of the injection energy match is important for injection tuning. Several signals, such as phase shift drive (PSD), radial position error (RPOS), synchrotron phase (SPD), and fast phase error (FPERR), provide consistent information on the energy match and can be used for an injection match tuning.

Measurement of {gamma}{sub T} with the {gamma}{sub T} quads on and off

An experimental procedure for measuring {gamma}{sub T} has been developed and tested in two different measurements, with the {gamma}{sub T} quads on and off. The results were compared to MAD calculations. The discrepancy between the measured {gamma}{sub T} and the calculated {gamma}{sub T} is less than 5%.