TY - JOUR

T1 - Quasi-geometric integration of guiding-center orbits in piecewise linear toroidal fields

AU - Eder, Michael

AU - Bauer, Lukas Maximilian Peter

AU - Kernbichler, Winfried

AU - Kasilov, Sergei

AU - Albert, Christopher G.

PY - 2020/12

Y1 - 2020/12

N2 - A numerical 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. The underlying formulation treats motion in piecewise linear fields exactly and, thus, preserves the non-canonical symplectic form. The algorithm itself is only quasi-geometric due to a series expansion in the orbit parameter. For practical purposes, an expansion to the fourth order retains geometric properties down to computer accuracy in typical examples. When applied to collisionless guiding-center orbits in an axisymmetric tokamak and a realistic three-dimensional stellarator configuration, the method demonstrates stable long-term orbit dynamics conserving invariants. In Monte Carlo evaluation of transport coefficients, the computational efficiency of quasi-geometric integration is an order of magnitude higher than with a standard fourth order Runge–Kutta integrator.

AB - A numerical 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. The underlying formulation treats motion in piecewise linear fields exactly and, thus, preserves the non-canonical symplectic form. The algorithm itself is only quasi-geometric due to a series expansion in the orbit parameter. For practical purposes, an expansion to the fourth order retains geometric properties down to computer accuracy in typical examples. When applied to collisionless guiding-center orbits in an axisymmetric tokamak and a realistic three-dimensional stellarator configuration, the method demonstrates stable long-term orbit dynamics conserving invariants. In Monte Carlo evaluation of transport coefficients, the computational efficiency of quasi-geometric integration is an order of magnitude higher than with a standard fourth order Runge–Kutta integrator.

UR - http://www.scopus.com/inward/record.url?scp=85099641609&partnerID=8YFLogxK

U2 - 10.1063/5.0022117

DO - 10.1063/5.0022117

M3 - Article

VL - 27

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 12

M1 - 122508

ER -