TY - JOUR

T1 - Distribution transforms for guiding center orbit coordinates in axisymmetric tokamak equilibria

AU - Benjamin, Stuart

AU - Järleblad, Henrik

AU - Salewski, Mirko

AU - Stagner, Luke

AU - Hole, Matthew

AU - Pfefferlé, David

N1 - Funding Information:
This paper would not have been possible without the support of the National Computational Infrastructure Australia, on which all computing was completed, and the Mathematical Sciences Institute. We also thank the ITPA Energetic Particle Physics Topical Group, and the ANU Plasma Theory and Modelling group.
Publisher Copyright:
© 2023 The Author(s)

PY - 2023/11

Y1 - 2023/11

N2 - Accurate distribution transforms between common 4D axisymmetric tokamak guiding center coordinates {energy,pitch,R,Z}, and orbit-space coordinates (made up of a particle's kinetic energy E, maximum radius in the tokamak Rm, pitch at the point of maximum radius pm, and time-normalised phase τ=t/torbit) are vital for the verification and implementation of orbit tomography. These transforms have proven difficult in the past due to discontinuities across topological boundaries in orbit-space. In this work we exhaustively investigate these transforms, comparing existing and novel transform methods in speed, accuracy and specific sources of error. A distribution transform that samples {energy,pitch,R,Z}-space along pre-computed orbit paths, and relies on Jacobians calculated with autodifferentiation, is benchmarked against a Monte Carlo sampling and binning algorithm. Our new transform demonstrates a hundredfold increase in speed, and better preserves natural discontinuities across the orbit trapped-passing boundary. A potentially damaging source of transform error caused by a Jacobian singularity that occurs for vanishingly small orbits is addressed, ensuring repeated transforms are well-behaved. The application of smoothing splines in {energy,pitch,R,Z}-space and orbit-space is also discussed. A Jacobian-based transform utilising thin-plate polyharmonic splines restricted to subdomains of similar orbit class is presented and benchmarked against its equivalent non-splined transform. This new smoothing transform correctly avoids interpolating across the trapped/passing boundary, doing so without the prohibitively slow computation and hyperparameter tuning required by previous orbit-space splines.

AB - Accurate distribution transforms between common 4D axisymmetric tokamak guiding center coordinates {energy,pitch,R,Z}, and orbit-space coordinates (made up of a particle's kinetic energy E, maximum radius in the tokamak Rm, pitch at the point of maximum radius pm, and time-normalised phase τ=t/torbit) are vital for the verification and implementation of orbit tomography. These transforms have proven difficult in the past due to discontinuities across topological boundaries in orbit-space. In this work we exhaustively investigate these transforms, comparing existing and novel transform methods in speed, accuracy and specific sources of error. A distribution transform that samples {energy,pitch,R,Z}-space along pre-computed orbit paths, and relies on Jacobians calculated with autodifferentiation, is benchmarked against a Monte Carlo sampling and binning algorithm. Our new transform demonstrates a hundredfold increase in speed, and better preserves natural discontinuities across the orbit trapped-passing boundary. A potentially damaging source of transform error caused by a Jacobian singularity that occurs for vanishingly small orbits is addressed, ensuring repeated transforms are well-behaved. The application of smoothing splines in {energy,pitch,R,Z}-space and orbit-space is also discussed. A Jacobian-based transform utilising thin-plate polyharmonic splines restricted to subdomains of similar orbit class is presented and benchmarked against its equivalent non-splined transform. This new smoothing transform correctly avoids interpolating across the trapped/passing boundary, doing so without the prohibitively slow computation and hyperparameter tuning required by previous orbit-space splines.

KW - Constant of motion coordinates

KW - Distribution transforms

KW - Energetic particles

KW - Fast ion orbits

KW - Orbit tomography

UR - http://www.scopus.com/inward/record.url?scp=85168993571&partnerID=8YFLogxK

U2 - 10.1016/j.cpc.2023.108893

DO - 10.1016/j.cpc.2023.108893

M3 - Article

AN - SCOPUS:85168993571

SN - 0010-4655

VL - 292

JO - Computer Physics Communications

JF - Computer Physics Communications

M1 - 108893

ER -