Beam transport optics of dipole fringe field in the framework of third-order matrix theory

Sagalovsky, L.

doi:10.1016/0168-9002(90)90618-g

Cited by 6 publications

(2 citation statements)

References 4 publications

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“…However, in the perturbative order-by-order approach the divergence can occur at different orders depending on the specific fields involved. For the case of the homogeneous dipole it has been derived [28] that the lowest order map element that causes divergence is ͑b j yyy͒; that is the element that shows how the final angle in the vertical phase plane depends on the initial position in the vertical direction. For multipoles with straight optical axes, the divergences occur at higher orders.…”

Section: The Sharp Cutoff Limitmentioning

confidence: 99%

Fringe field effects in small rings of large acceptance

Berz

Erdélyi

Makino

2000

Phys. Rev. ST Accel. Beams

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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.

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Section: The Sharp Cutoff Limitmentioning

confidence: 99%

Fringe field effects in small rings of large acceptance

Berz

Erdélyi

Makino

2000

Phys. Rev. ST Accel. Beams

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“…Numerous works have been carried out to obtain the higher order matrix elements for different types of magnetic elements. All these works concentrate on the solution of equation of motion using differential equations or Hamiltonian approach [7][8][9][10][11][12]. In these approaches, one derives the driving terms for the next desired order of solution and then, using Green's function, the equation is solved or one frames the appropriate Lie operators for the magnets.…”

Section: Introductionmentioning

confidence: 99%

Analytical expressions of transfer functions for a hard edge dipole magnet using a basic geometrical approach

Sharma

Singh

Abdurrahim

et al. 2013

Phys. Rev. ST Accel. Beams

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In charged particle accelerators, higher order optics studies become important from various points of view, such as dynamic aperture, emittance dilution, beam loss, etc. For some new applications, nonlinear study has become important in single pass optics also. For studying the higher order optics, each magnetic element is represented by a higher order transfer function (map, i.e., a function that relates output coordinates of a trajectory with initial coordinates and momentum deviation). Here in this paper we have provided an alternate method to obtain the analytical formulation of the transfer function for a dipole magnet. This formulation is obtained on the basis of basic geometrical analysis and is exact up to all orders under hard edge approximation. Being an analytical expression, the estimation of higher order effects of dipole magnet can be studied quickly. For checking the correctness of this formulation, we separated terms up to third order, which can be used to obtain the standard transfer matrices up to same order. An example of emittance growth and bunch length modification for a C-chicane-type electron beam bunch compressor is provided using the analytical expression.

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