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. Self-consistent 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.
Highlights
Our motivation in pursuing the work described in this paper is to assess the possibility of injecting a uniform elliptical beam distribution with linear space charge forces into a high-intensity ring
We mean the coordinates of a collection of particles in 2N-dimensional phase space which evolve according to the Boltzmann equation, which in turn reduces to the Vlasov equation in the Hamiltonian limit when collisions are neglected [1]
This paper has presented the results of extensive computational studies performed to demonstrate the feasibility of painting a rotating uniform-density self-consistent beam into a high-intensity ring, using the Spallation Neutron Source (SNS) accumulator as an example
Summary
Our motivation in pursuing the work described in this paper is to assess the possibility of injecting a uniform elliptical beam distribution with linear space charge forces into a high-intensity ring. The KV distribution depends on only one invariant function of coordinates and momenta, which corresponds to a single Hamiltonian when the focusing is time independent, and it takes the form of a uniformly populated constant energy shell in phase space. It was shown in Appendix A in Ref. There is no distribution function in three dimensions that depends on only one invariant (the Hamiltonian in the time-independent case) and produces linear space charge forces This paper did not analyze the stability of the newly described self-consistent distributions, but it did pave the way for such studies and for the consideration of practical applications of self-consistent beams in existing or planned accelerators
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