Orbit and optics distortion in fixed field alternating gradient muon accelerators

Abstract

In a linear nonscaling fixed field alternating gradient (FFAG) accelerator, betatron tunes vary over a wide range and a beam has to cross integer and half-integer tunes several times. Although it is plausible to say that integer and half-integer resonances are not harmful if the crossing speed is fast, no quantitative argument exists. With tracking simulation, we studied orbit and optics distortion due to alignment and magnet errors. It was found that the concept of integer and half-integer resonance crossing is irrelevant to explain beam behavior in a nonscaling FFAG when acceleration is fast and betatron tunes change quickly. In a muon FFAG accelerator, it takes 17 turns for acceleration and the betatron tunes change more than 10, for example. Instead, the orbit and optics distortion is excited by random dipole and quadrupole kicks. The latter causes beam size growth because the beam starts tumbling in phase space, but not necessarily with emittance growth.

The EMMA Main Ring Lattice.

“…The driving of the resonances is minimized by constructing a lattice consisting entirely of identical, compact cells, and by using linear magnets which should reduce the driving of nonlinear magnets. Any breaking of the perfect symmetry can lead to emittance growth and orbit distortion [18]. In addition, some authors have found significant effects due to nonlinearities when realistic magnets are used in a linear non-scaling FFAG [19,4,18].…”

“…Any breaking of the perfect symmetry can lead to emittance growth and orbit distortion [18]. In addition, some authors have found significant effects due to nonlinearities when realistic magnets are used in a linear non-scaling FFAG [19,4,18]. To study imperfections, we plan to vary the position and gradient in some individual magnets.…”

“…The second effect of interest is resonances (though "resonance" may not be precisely the right term [18]). Because the machine tune varies with energy, one expects to cross a number of resonances.…”

“…A higher value for this quantity reduces the discretization in the acceleration process (which is an important effect [18]) and reduces the rate of resonance crossing (which we would like to be small so that the effect can be studied). Since muon accelerators typically have that value in the range of 500-1500, and since the size of the ring increases with that number, 500 was chosen for the goal for that quantity.…”

“…It was chosen to have a relatively high horizontal tune, which reduces the time of flight variation with energy and therefore increases increases the number of turns over which one can accelerate [31], and to avoid the ν x − 2ν y = 0 resonance line, which was found to give significant nonlinear coupling between the transverse planes in some circumstances [18]. In the design of this lattice, there are 6 parameters that can be varied: two magnet lengths, two quadrupole strengths, and two quadrupole displacements.…”