  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.
