Efficient Representation of Realistic 3D Static Magnetic Fields for Symplectic Tracking and First Applications for Frequency Analysis and Dynamic Aperture Studies in ELENA

The algorithm called SIMPA has a new and unique approach to long-term 4D tracking of charged particles in arbitrary static electromagnetic fields. Field values given on the boundary of the region of interest are reproduced by an arrangement of hypothetical magnetic or electric point sources surrounding the boundary surface. The vector and scalar potentials are obtained by summing the contributions of each source. 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. Frequency analysis and dynamic aperture studies in ELENA is presented. The effect of the end fields and the perturbation introduced by the magnetic system of the electron cooler on dynamic aperture is shown. The dynamic aperture calculated is the direct consequence of the geometry of the magnetic elements, no multipole errors have been added to the model.