Fringe field effects in small rings of large acceptance

Abstract

Recently there has been renewed interest in the influence of fringe fields on particle dynamics, due to studies that revealed their importance in some cases, as, for example, the proposed Neutrino Factory and muon colliders. In this paper, we present a systematic study of generic fringe field effects. Using as an example a lattice of the proposed Neutrino Factory, we show that fringe fields influence the dynamics of particles at all orders, starting with the linear motion. It is found that the widely used sharp cutoff approximation leads to divergences regardless of the specific fall-off shape of the fields. The results suggest that a careful consideration of fringe field effects in the design stage of small machines for large emittances is always recommended.

Deflections in magnet fringe fields

“…Since the straight line approximation has been used throughout, these formulas are only precise for magnetic fields that are well-approximated by step functions (the "hard-edge" approximation). Thus, the formulas contain no parameters associated with the fringe shape (for example, see [11,12]). Also, as stated previously, only those fringe fields matching, and therefore required by, the nominal body multipolarity are accounted for.…”

Dipole fringe field thin map for compact synchrotrons

“…Conventionally, the dipole vertical gap and magnet aperture are used to represent the fringe field extent [1,7], because the fringe field extent is generally about the size of the magnet aperture. Throughout the paper, we will use the vertical gap g to represent the fringe field extent.…”

“…In order to verify the differential, we exploit the automatic differentiation technique [17] similar to the differential algebra [7]. The theoretical and simulated values of the differential ∂ …”

“…It is worth mentioning that the hard-edge model is ill defined if one goes beyond a quadrupole, and the fact that the detuning term by an octupolelike potential is infinite in the hard-edge model has already been known [7,19].…”

“…[5,6]. The numerical method was used to extract the Taylor map or Lie map out of the 3D field data [7,8]. However, there is still a demand for an analytic expression of the fringe field map, particularly when the 3D field data are not available at the design stage.…”