Injection of a self-consistent beam with linear space charge force into a ring

Abstract

One major concern in the design and operation of high-intensity rings is beam loss due to beam halo. Another issue of importance in applications involving fixed targets is the uniformity of the beam energy deposition on the target. Both of these issues could be favorably addressed by a hard-edged beam with uniform transverse density. This paper presents a detailed feasibility study for painting such a beam into a high-intensity proton ring. For the purposes of this paper, we define self-consistent beams to be ellipsoidal, or elliptical in 2D, distributions that have uniform density and linear space charge force and that retain these properties under all linear transformations. Because of their linear space charge forces and linear transport properties, self-consistent distributions may undergo very little halo formation if realized in practice. Because of their uniform density, they would have smaller maximum space charge tune shifts than peaked density distributions, and they would be attractive for high-intensity fixed target applications. Selfconsistent distributions involve very special relationships between the phase space coordinates, making them singular in some respects and difficult to realize experimentally. The most famous self-consistent distribution is the Kapchinsky-Vladimirsky distribution, but now many other self-consistent distributions have been discovered. One such, the 2D rotating distribution, can be painted as a coasting beam into a ring having an appropriately designed and tuned lattice. For bunched beams, if the bunch length is sufficiently long, it is expected that the coasting beam assumption will be a good approximation during painting. However, it is unknown how robust self-consistent distributions will be under real world transport in the presence of nonlinearities and collective effects. This paper studies these issues for a particular case of interest by applying realistic detailed computational models to the simulation of painting a self-consistent rotating beam into the Spallation Neutron Source (SNS) ring. As a result, we propose a case that can be carried out with only a minor modification of the SNS hardware.

Four-dimensional emittance measurement at the Spallation Neutron Source

“…In 2D emittance measurements, the phase advance from the reconstruction location to the measurement location is typically varied uniformly within a 180 • range. 4 Prat and Aiba [11] applied this strategy to the 4D emittance measurement: in the first half of the scan, the horizontal phase advance was varied while the vertical phase advance was held fixed; in the second half of the scan, the vertical phase advance was varied while the horizontal phase advance was held fixed. Since the four SNS wire-scanners are already spaced somewhat evenly in phase advance, maximal phase coverage is possible by varying the phase advances at each wire-scanner in a 30 • window; however, control of the phase advances between each wire-scanner is limited due to the shared power supplies of the RTBT quadrupoles.…”

“…A hadron beam with a uniform charge density, elliptical transverse profile, and small four-dimensional (4D) emittance could mitigate space charge effects in circular accelerators and improve collider performance [1,2,3]. A phase space painting method to generate such a distribution is being tested in the Spallation Neutron Source (SNS) accumulator ring [4,5]. A critical component of these efforts is to measure the 4D beam emittance.…”

“…Each data point corresponds to a separate beam pulse, so the measurement relies on pulse-to-pulse stability 4. Intuitively, the error is expected to be minimized when the projection angles are spread uniformly between 0 and π; however, the projection angles are only equal to the phase advances in normalized phase space[19].…”