Symplectic integration with non-canonical quadrature for guiding-center orbits in magnetic confinement devices

Abstract

We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The technique combines time-stepping in canonical coordinates with quadrature in non-canonical coordinates and is applicable in systems where a global transformation to canonical coordinates is known but its inverse is not. A fully implicit class of symplectic Runge-Kutta schemes has recently been introduced and applied to guiding-center motion by [Zhang et al., Phys. Plasmas 21, 32504 (2014)]. Here a generalization of this approach with emphasis on semi-implicit partitioned schemes is described together with methods to enhance their performance, in particular avoiding evaluation of non-canonical variables at full time steps. For application in toroidal plasma confinement configurations with nested magnetic flux surfaces a global canonicalization of coordinates for the guiding-center Lagrangian by a spatial transform is presented that allows for pre-computation of the required map in a parallel algorithm in the case of time-independent magnetic field geometry. Guiding-center orbits are studied in stationary magnetic equilibrium fields of an axisymmetric tokamak and a realistic three-dimensional stellarator configuration. Superior long-term properties of symplectic methods are demonstrated in comparison to a conventional adaptive Runge-Kutta scheme. Finally statistics of fast fusion alpha particle losses over their slowing-down time are computed in the stellarator field on a representative sample, reaching a speed-up of the symplectic Euler scheme by more than a factor three compared to usual Runge-Kutta schemes while keeping the same statistical accuracy and linear scaling with the number of computing threads.

30 pages, 14 figures, accepted version

References in corpus (7)

• Structure and structure-preserving algorithms for plasma physics
• Toroidal regularization of the guiding center Lagrangian
• Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories
• Evaluation of toroidal torque by non-resonant magnetic perturbations in tokamaks for resonant transport regimes using a Hamiltonian approach
• Gyrokinetics from variational averaging: existence and error bounds
• Projected Variational Integrators for Degenerate Lagrangian Systems
• A Second-Order Symplectic Integrator for Guiding-Center Equations

Cited by in corpus (13)

• Magnetic fields with precise quasisymmetry for plasma confinement
• Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry
• Critical gradient turbulence optimization toward a compact stellarator reactor concept
• Symplectic Gaussian Process Regression of Hamiltonian Flow Maps
• Direct Optimization of Fast-Ion Confinement in Stellarators
• A compact stellarator-tokamak hybrid
• Faithful guiding-center orbits in an axisymmetric magnetic field
• Quasi-geometric integration of guiding-center orbits in piecewise linear toroidal fields
• Physics-regularized neural network of the ideal-MHD solution operator in Wendelstein 7-X configurations
• Energetic Particle Tracing in Optimized Quasisymmetric Stellarator Equilibria
• Poisson Integrators based on splitting method for Poisson systems
• Efficient Computation of Stellarator Coils with an Augmented Lagrangian Optimization Method
• Efficient calculation of magnetic fields from ferromagnetic materials near strong electromagnets, and application to stellarator coil optimization