An Algorithm to Calculate the Magnetic Field in a Helical Magnetic Trap

In this paper, we present an algorithm for calculating the magnetic field inside a helical magnetic trap. An important feature of the proposed algorithm is that it automatically fulfills both the finite-difference Gauss law for the magnetic field, which is ensured by the use of staggered grids for the vector potential components, and the condition of divergence-free vector potential imposed by the Coulomb gauge. The latter is achieved by a special method for calculating the spiral electric current on the computational grid. The created algorithm can be applied to any configuration of time-independent currents. In particular, it can be used to calculate the initial field in an axisymmetric multimirror magnetic trap as well.