Geometric integration of guiding-center orbits in piecewise linear toroidal fields

A geometric integration method for guiding-center orbits of charged particles in toroidal fusion devices with three-dimensional field geometry is described. Here, high order interpolation of electromagnetic fields in space is replaced by a special linear interpolation, leading to locally linear Hamiltonian equations of motion with piecewise constant coefficients. This approach reduces computational effort and noise sensitivity while the conservation of total energy, magnetic moment and phase space volume is retained. When applied to collisionless guiding-center orbits in an axisymmetric tokamak and a realistic three-dimensional stellarator configuration, the method demonstrates correct long-term orbit dynamics. Within Monte Carlo evaluation of transport coefficients, the computational efficiency of geometric integration is an order of magnitude higher than with a standard adaptive Runge-Kutta integrator.