Abstract. The Baryon Antibaryon Symmetry Experiment (BASE) aims at performing a stringent test of the combined charge parity and time reversal (CPT) symmetry by comparing the magnetic moments of the proton and the antiproton with high precision. Using single particles in a Penning trap, the proton/antiproton g-factors, i.e. the magnetic moment in units of the nuclear magneton, are determined by measuring the respective ratio of the spin-precession frequency to the cyclotron frequency. The spin precession frequency is measured by non-destructive detection of spin quantum transitions using the continuous Stern-Gerlach effect, and the cyclotron frequency is determined from the particle's motional eigenfrequencies in the Penning trap using the invariance theorem. By application of the double Penningtrap method we expect that in our measurements a fractional precision of δg/g 10

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.

We present recent progress with our algorithm and its implementation called SIMPA described in a previous paper. The algorithm has a new and unique approach to long-term 4D tracking of charged particles in arbitrary static electromagnetic fields. Using the improvements described in this paper, we made frequency analysis and dynamic aperture studies in ELENA. The effect of the end fields and the perturbation introduced by the magnetic system of the electron cooler on dynamic aperture is shown. A special feature of this study is that we have not introduced any multipole errors into the model. The dynamic aperture calculated in this paper is the direct consequence of the geometry of the magnetic elements. Based on the results, we make a few suggestions to reduce the losses during the deceleration of the beam.

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