On solving the Thomas Bargman-Michel-Telegdi equation using the Bogoliubov Krylov method of averages and the calculation of the Berry phases

Several proposals aimed at measuring the Electric Dipole Moment (EDM) for charged particles require very precise simulations and understanding of the systematic errors that can contribute to a spin buildup mimicking the EDM signal to be detected. In what follows, one used the Bogoliubov-Krylov-Mitropolski method of averages to solve the T-BMT equation and calculate the Berry phases arising for a proton EDM storage ring. The formalism employed proved to be particularly useful to determine the evolution of the spin at the observation point, i.e. at the location of the polarimeter. Several selected cases of lattice imperfections were simulated and benchmarked with the analytical estimates. This allowed the proof of the convergence of the numerical simulations and helped gain better understanding of the systematic errors

Creation of Hollow Bunches using a Double Harmonic RF system

The main motivation for the creation of hollow bunches in the PSB is to increase the bunching factor at transfer to the PS. Due to the reduction of the peak current and direct transverse space charge forces, one expects less blow up and losses at low energy in the PS. Thus, it does not matter when the hollow distribution in longitudinal phase space is created in the PSB cycle. We propose methods involving the h=1 and h=2 RF systems available in the PSB. The first method is based on controlled blow up by recombination of the bunch in one bucket, with another empty bucket. By appropriate adjustment of the phase between the two RF systems, more empty phase space can be inserted close to the centre creating a hollow distribution. The second method is based on a redistribution of phase space. The beam is transferred from one h=2 sub-bucket to the other and, during that process, regions from the centre with high density and from the periphery are exchanged. Simulations of both methods, based on tracking of particles in he longitudinal phase space, are presented. The second method has been set up successfully at the PS Booster. A significant decrease of the peak current has been achieved, while keeping the bunch length approximately constant

Transverse Electron Cooling from the Time Evolution of the Profiles to Drift Velocities of the Oscillation Amplitudes

When a beam in a synchrotron is subjected to transverse cooling, the betatron oscillation amplitudes of the individual particles are reduced. A method to establish the velocity of the amplitude reduction as a function of the amplitude itself has been developed. The beam profile can be measured along the cooling process with for example beam ionisation monitors. From successive profiles one computes the time evolution of the amplitude distribution, which in turn allows the determination of the amplitude reduction velocity. This method could be applied to investigate the influence of the transverse electron temperature on electron cooling performance

New Methods to Create Hollow Bunches

New methods to create hollow distributions in longitudinal phase space based on manipulations with a double harmonic RF system at high energy are presented with application to the PS Booster synchrotron (PSB). Whereas the first tenatative to create hollow bunches at the PSB aimed to improve the performance of the PSB itself, these new methods are expected to reduce the limitations due to direct space charge forces in the receiving PS (where no double harmonic RF system is available) after transfer. One method aims to introduce empty phase space in the centre of the phase space by recombination of the beam in one bucket with another empty bucket. The second method is based on redistribution of phase space surfaces during the transfer of the beam from one second harmonic sub-bucket to another. During that process, phase space surfaces are exchanged and low density from the periphery ends up in the centre, whereas the high density surfaces from the centre are transferred to the periphery. Both methods have been simulated by particle tracking. The second method has been applied in practice at the PSB. The set-up turned out to be simple and fast, and to yield hollow distributions with good reproducibility

Matching to gantries for medical synchrotrons

Treatment of tumours by hadron-therapy is greatly improved if the patient can be irradiated from different directions. This task is performed by a gantry, i.e. a section of beam line that can be rotated around the patient. The gantry optics have to be designed in such a way that the beam at the patient is independent of the rotation angle. The various matching techniques are briefly reviewed in the light of the current development in medical synchrotrons towards active scanning, which requires a small, high-precision beam spot at the patient. In particular, beam delivery systems with rotators are discussed

Stochastic Cooling at the CERN Antiproton Decelerator

When transforming the CERN Antiproton Collector (AC) into the Antiproton Decelerator (AD), the stochastic cooling systems were rebuilt to cope with the new requirements. Instead of using the original three frequency bands, (0.9-1.6 GHz, 1.6-2.45 GHz and 2.4-3.2 GHz) only the first of these was used due to lattice limitations and other constraints. The same pick-ups and kickers are in use at two different energies. As in the AC, simultaneous cooling in all three phase planes is required. Switching between two transmission paths (at 3.5 GeV/c and 2.0 GeV/c) became necessary, including separate notch filters and delay compensation for the kicker sections. The tanks has to be rendered bakeable (150 C) to make the vacuum properties (<10-10 Torr) compatible with deceleration to low energies. Further improvements included programmable, phase-invariant electronic attenuators and amplitude-invariant delays. Experience during commissioning showed that careful optimization (depth and periodicity) of the notch filters, as well as efficient suppression of the common mode response in the transverse cooling systems, were essential to reach and even exceed design performance. The systems were operated with protons (about 109) as well as pbars (2-3x107)

A Comparative Study of Profile and Scraping Methods for Emittance Measurements in the PS Booster

It is important to have a clear understanding of the transverse emittance in a circular accelerator in order to achieve optimum brilliance. Experience with comparing emittance data from different instruments has shown that systematic errors can be important. In an attempt to detect such errors in the PS Booster, the emittance measurements are made according to two different principles: measurement of density distribution and measurement of amplitude distribution. In this paper we i) discuss these two principles and the theory behind them; ii) show how the data can be compared; iii) describe the instrumentation used for these measurements; and iv) present results for the typical PS Booster beams

Combined longitudinal and transverse multiturn injection in a heavy ion accumulator

After the completion of the antiproton programme, the Low-Energy Antiproton Ring (LEAR) will be able to serve as an accumulator ring for heavy ions in the injector chain of the Large Hadron Collider (LHC). For injection and accumulation, a scheme is proposed, which exploits both the longitudinal and the transverse acceptances of LEAR. Compared to a classical multiturn injection, a factor 3 to 5 in intensity is gained for the set of parameters pertaining to this case; furthermore emittances, which are more favorable for electron cooling, result. The principle is outlined and computer simulations are presented

Reduction of the Impedance Created by the Insulated Vacuum Flanges in the PS Booster

The original vacuum flange assembly in the PS Booster (PSB) was designed to present insulation at low frequency and conduction to the beam image current above 2 MHz. However, in order to satisfy the needs for the LHC, the RF harmonic in the PSB had to be changed from h=5 to h=1, leading to a reduction of the lowest accelerating frequency to 600 kHz. The RF component of the beam was therefore passing through the main resonance of these flanges giving a total (integrated around the ring) longitudinal coupling impedance of 1000 W at 750 kHz, taking into account some additional RF bypasses. The voltage generated by the beam current was coupling to various electronic devices which therefore had to be equipped with common-mode rejection circuits. After some non-essential insulated flanges had been replaced by conducting ones during the 1998-99 shutdown, the total impedance was lowered to about 200 ohms (still higher than the maximum value for h=5 which was 130 ohms). This was one of the improvements that made it possible to reach a new intensity record in September 1999. New RF decoupling flanges introduced in 2000 to further reduce the impedance are described here, together with the results obtained