Efficient evaluation of arbitrary static electromagnetic fields with applications for symplectic particle tracking

Abstract

This article describes a method devised for efficient evaluation of arbitrary static magnetic and electric fields in a source free region needed for long time tracking of charged particles. Field values given on the boundary of the region of interest are reproduced inside by an arrangement of hypothetical magnetic or electric monopoles surrounding the boundary surface. The vector and scalar potentials are obtained by summing the contributions of each monopole. The second step of the method improves the evaluation speed of the potentials and their derivatives by orders of magnitude. This comprises covering the region of interest by overlapping spheres, then calculating the spherical harmonic expansion of the potentials on each sphere. During tracking, field values are evaluated by calculating the solid harmonics and their derivatives inside a sphere containing the particle. Software has been developed to test and demonstrate the method on a small particle accelerator. To our knowledge, there is no other method of this kind, allowing long time symplectic integration in general static fields, without simplification.I.

Frequency analysis and dynamic aperture studies in a low energy antiproton ring with realistic 3D magnetic fields

“…The importance of fringe fields in small rings is well known and it has been taken into account for multipole magnets at various degrees for decades [1][2][3][4]. The approach to particle tracking we described in [5] naturally includes the end fields for all kinds of elements with the same treatment. The aim of this paper is two-fold.…”

“…The aim of this paper is two-fold. One is to apply our algorithm described in [5] on the extra low energy antiproton (ELENA) ring [6], the 30.4 meters circumference machine built at CERN to decelerate antiprotons. Another aim is to gain insight into the beam dynamics of ELENA by frequency analysis and dynamic aperture studies.…”

“…Long-term tracking of charged particles is a fundamental problem of accelerator physics, plasma physics and it is important in astrophysics. In a recent paper [5] we described a new algorithm allowing long-term symplectic integration of charged particle trajectories in arbitrary static magnetic and electric fields. We introduced several new ideas and pointed out the importance of two requirements for a physically valid description of the electromagnetic fields.…”

“…This triggered the author to devise the algorithm [5] and implement it. The name of the software is SIMPA, an abbreviation of symplectic integration through monopole arrangements.…”

“…The algorithm described in [5] was applied to a simple test machine with a beam region having a constant circular profile. This was covered with a single line of overlapping spheres.…”