Work

Symplecticity of the GORILLA guiding-centre tracer and its implications for edge transport modelling

Year: 2025

Type: article

Abstract: We demonstrate symplecticity of the flow map generated by the guiding-centre tracer Guiding centre ORbit Integrator with Local Linearisation Approach. Since the underlying algorithm relies on a piecewise linear interpolation of the Hamiltonian on a tetrahedral grid, usual proofs based on a twice continuously differentiable Hamiltonian are not applicable. The analysis is pinned down to the critical section near the boundaries of tetrahedral elements, where the Hamiltonian vector field is non-smooth. We show that it is possible to retain symplecticity of the piecewise linear system as a limiting case of a parameterised family of smooth Hamiltonian systems nearly everywhere in phase-space. Limitations are discussed for the case of the X- and O-point in the magnetic field topology. The connection to Hdiv-conforming finite element discretisations and their interface conditions is pointed out. Finally, the practical implications for edge transport modelling are elaborated. For this purpose, we analyse the footprints of magnetic field lines intersecting the divertor plates of a tokamak with resonant magnetic perturbations. These footprints are shown to be in line with the expected behaviour of invariant manifolds of the underlying Hamiltonian system. This demonstration of physical consistency at low-order discretisation lays the basis for further developments of highly efficient edge transport solvers.

Source: Plasma Physics and Controlled Fusion

DOI: 10.1088/1361-6587/add0df