2023
5.
Benjamin, Stuart; Järleblad, Henrik; Salewski, Mirko; Stagner, Luke; Hole, Matthew; Pfefferlé, David
Distribution Transforms for Guiding Center Orbit Coordinates in Axisymmetric Tokamak Equilibria Journal Article
In: Computer Physics Communications, vol. 292, pp. 108893, 2023, ISSN: 0010-4655.
Links | BibTeX | Tags: diagnostics, fast particles, numerical method, orbit tomography
@article{benjaminDistributionTransformsGuiding2023,
title = {Distribution Transforms for Guiding Center Orbit Coordinates in Axisymmetric Tokamak Equilibria},
author = {Stuart Benjamin and Henrik J\"{a}rleblad and Mirko Salewski and Luke Stagner and Matthew Hole and David Pfefferl\'{e}},
doi = {10.1016/j.cpc.2023.108893},
issn = {0010-4655},
year = {2023},
date = {2023-11-01},
urldate = {2023-11-01},
journal = {Computer Physics Communications},
volume = {292},
pages = {108893},
keywords = {diagnostics, fast particles, numerical method, orbit tomography},
pubstate = {published},
tppubtype = {article}
}
2022
4.
Muir, Dean; Pfefferlé, David; Qu, Zhisong; Hole, Matthew; Hegland, Markus
Numerical Integration of Particle Orbits in Discontinuous Fields Using VENUS-LEVIS and SPEC Journal Article
In: Computer Physics Communications, vol. 271, pp. 108191, 2022, ISSN: 0010-4655.
Abstract | Links | BibTeX | Tags: discontinuous fields, full-orbit, numerical method, SPEC, VENUS-LEVIS
@article{muirNumericalIntegrationParticle2022,
title = {Numerical Integration of Particle Orbits in Discontinuous Fields Using VENUS-LEVIS and SPEC},
author = {Dean Muir and David Pfefferl\'{e} and Zhisong Qu and Matthew Hole and Markus Hegland},
doi = {10.1016/j.cpc.2021.108191},
issn = {0010-4655},
year = {2022},
date = {2022-02-01},
urldate = {2022-02-01},
journal = {Computer Physics Communications},
volume = {271},
pages = {108191},
abstract = {The orbit code VENUS-LEVIS is adapted to follow particles in plasma equilibria with discontinuous fields generated by the Stepped Pressure Equilibrium Code (SPEC). The latter is an implementation of the Multi-Region relaxed MHD model, which efficiently computes Taylor states in a series of nested toroidal volumes and supports the formation of magnetic islands and chaotic field regions. To adapt VENUS-LEVIS, an event location procedure is implemented in the existing numerical integrator, which ensures the particle sees the correct field along its trajectory, regardless of the discontinuities present in the Stepped Pressure Equilibrium model. The algorithm is tested in the case where the magnetic field is uniform in the upper and lower half-spaces but has a discontinuity in its direction (shear) on the plane z=0. Particle drifts due to the discontinuity are studied. The convergence properties of the numerical scheme are highlighted by the numerical accuracy, and conservation of the system's invariants, such as energy and momentum. Simulations and convergence studies using the SPEC-LEVIS interface in axisymmetric geometry are then presented. Finally, illustrative particle drifts due to the discontinuity are studied and explained: we examine drifts associated with the change in Larmor radius of passing particles with small excursion from flux surfaces.},
keywords = {discontinuous fields, full-orbit, numerical method, SPEC, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
The orbit code VENUS-LEVIS is adapted to follow particles in plasma equilibria with discontinuous fields generated by the Stepped Pressure Equilibrium Code (SPEC). The latter is an implementation of the Multi-Region relaxed MHD model, which efficiently computes Taylor states in a series of nested toroidal volumes and supports the formation of magnetic islands and chaotic field regions. To adapt VENUS-LEVIS, an event location procedure is implemented in the existing numerical integrator, which ensures the particle sees the correct field along its trajectory, regardless of the discontinuities present in the Stepped Pressure Equilibrium model. The algorithm is tested in the case where the magnetic field is uniform in the upper and lower half-spaces but has a discontinuity in its direction (shear) on the plane z=0. Particle drifts due to the discontinuity are studied. The convergence properties of the numerical scheme are highlighted by the numerical accuracy, and conservation of the system's invariants, such as energy and momentum. Simulations and convergence studies using the SPEC-LEVIS interface in axisymmetric geometry are then presented. Finally, illustrative particle drifts due to the discontinuity are studied and explained: we examine drifts associated with the change in Larmor radius of passing particles with small excursion from flux surfaces.
2021
3.
Lazerson, Samuel A.; Pfefferlé, David; Drevlak, Michael; Smith, Håkan; Geiger, Joachim; Äkäslompolo, Simppa; Xanthopoulos, Pavlos; Dinklage, Andreas; Ford, Oliver; McNeely, Paul; Rust, Norbert; Bozhenkov, Sergey; Hartmann, Dirk; Rahbarnia, Kian; Andreeva, Tamara; Schilling, Jonathan; Brandt, Christian; Neuner, Ulrich; Thomsen, Henning; Wolf, Robert C.; Team, The W7-X.
Modeling and Measurement of Energetic Particle Slowing down in Wendelstein 7-X Journal Article
In: vol. 61, no. 9, pp. 096005, 2021, ISSN: 0029-5515.
Abstract | Links | BibTeX | Tags: benchmark, fast particles, numerical method, slowing-down distribution, stellarator, VENUS-LEVISLEVIS
@article{lazersonModelingMeasurementEnergetic2021,
title = {Modeling and Measurement of Energetic Particle Slowing down in Wendelstein 7-X},
author = {Samuel A. Lazerson and David Pfefferl\'{e} and Michael Drevlak and Hr{a}kan Smith and Joachim Geiger and Simppa \"{A}k\"{a}slompolo and Pavlos Xanthopoulos and Andreas Dinklage and Oliver Ford and Paul McNeely and Norbert Rust and Sergey Bozhenkov and Dirk Hartmann and Kian Rahbarnia and Tamara Andreeva and Jonathan Schilling and Christian Brandt and Ulrich Neuner and Henning Thomsen and Robert C. Wolf and The W7-X. Team},
doi = {10.1088/1741-4326/ac0771},
issn = {0029-5515},
year = {2021},
date = {2021-07-01},
urldate = {2021-07-01},
volume = {61},
number = {9},
pages = {096005},
publisher = {IOP Publishing},
abstract = {The energetic particle slowing down model in the BEAMS3D stellarator neutral beam code is compared to analytic models and experimental data from the Wendelstein 7-X experiment (W7-X). Recently, the first neutral beam experiments were performed in W7-X, providing validation of neutral beam deposition codes (Lazerson S.A. et al 2020 Nucl. Fusion 60 076020). This work builds upon that work, and follows the gyro-center orbits of the neutral-beam-generated fast ions to the plasma boundary. Slowing down times based on measurements of diamagnetic energy changes are compared to simulation data. A discharge solely heated by neutral beam injection is used to compare neoclassical heat flux estimates to neutral beam fueling, heating, and current drive. Experimental estimates of electron heat diffusivity suggest that electron turbulence is destabilized by density peaking in the discharge. Neutral beam current drive dominates over bootstrap current, resulting in a reversal of the toroidal current, as seen experimentally. Particle losses and heat flux through the equilibrium boundary are described. The effects of the magnetic configuration and plasma density on such parameters are also assessed. Benchmarking based on analytic estimates and other energetic particle codes is presented.},
keywords = {benchmark, fast particles, numerical method, slowing-down distribution, stellarator, VENUS-LEVISLEVIS},
pubstate = {published},
tppubtype = {article}
}
The energetic particle slowing down model in the BEAMS3D stellarator neutral beam code is compared to analytic models and experimental data from the Wendelstein 7-X experiment (W7-X). Recently, the first neutral beam experiments were performed in W7-X, providing validation of neutral beam deposition codes (Lazerson S.A. et al 2020 Nucl. Fusion 60 076020). This work builds upon that work, and follows the gyro-center orbits of the neutral-beam-generated fast ions to the plasma boundary. Slowing down times based on measurements of diamagnetic energy changes are compared to simulation data. A discharge solely heated by neutral beam injection is used to compare neoclassical heat flux estimates to neutral beam fueling, heating, and current drive. Experimental estimates of electron heat diffusivity suggest that electron turbulence is destabilized by density peaking in the discharge. Neutral beam current drive dominates over bootstrap current, resulting in a reversal of the toroidal current, as seen experimentally. Particle losses and heat flux through the equilibrium boundary are described. The effects of the magnetic configuration and plasma density on such parameters are also assessed. Benchmarking based on analytic estimates and other energetic particle codes is presented.
2020
2.
Qu, Z. S.; Pfefferlé, D.; Hudson, S. R.; Baillod, A.; Kumar, A.; Dewar, R. L.; Hole, M. J.
Coordinate Parameterisation and Spectral Method Optimisation for Beltrami Field Solver in Stellarator Geometry Journal Article
In: vol. 62, no. 12, pp. 124004, 2020, ISSN: 0741-3335.
Abstract | Links | BibTeX | Tags: curvilinear coordinates, MHD equilibrium, numerical method, SPEC
@article{quCoordinateParameterisationSpectral2020,
title = {Coordinate Parameterisation and Spectral Method Optimisation for Beltrami Field Solver in Stellarator Geometry},
author = {Z. S. Qu and D. Pfefferl\'{e} and S. R. Hudson and A. Baillod and A. Kumar and R. L. Dewar and M. J. Hole},
doi = {10.1088/1361-6587/abc08e},
issn = {0741-3335},
year = {2020},
date = {2020-11-01},
urldate = {2020-11-01},
volume = {62},
number = {12},
pages = {124004},
publisher = {IOP Publishing},
abstract = {The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. In this work, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10-9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.},
keywords = {curvilinear coordinates, MHD equilibrium, numerical method, SPEC},
pubstate = {published},
tppubtype = {article}
}
The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. In this work, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10-9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.
2014
1.
Pfefferlé, D; Cooper, W A; Graves, J P; Misev, C
In: Computer Physics Communications, vol. 185, no. 12, pp. 3127 - 3140, 2014, ISSN: 0010-4655.
Abstract | Links | BibTeX | Tags: cubic spline, curvilinear coordinates, fast particles, numerical method, VENUS-LEVIS
@article{pfefferle-levis,
title = {VENUS-LEVIS and its spline-Fourier interpolation of 3D toroidal magnetic field representation for guiding-centre and full-orbit simulations of charged energetic particles},
author = {D Pfefferl\'{e} and W A Cooper and J P Graves and C Misev},
doi = {10.1016/j.cpc.2014.08.007},
issn = {0010-4655},
year = {2014},
date = {2014-08-16},
journal = {Computer Physics Communications},
volume = {185},
number = {12},
pages = {3127 - 3140},
abstract = {Curvilinear guiding-centre drift and full-orbit equations of motion are presented as implemented in the VENUS-LEVIS code. A dedicated interpolation scheme based on Fourier reconstruction in the toroidal and poloidal directions and cubic spline in the radial direction of flux coordinate systems is detailed. This interpolation method exactly preserves the order of the RK4 integrating scheme which is crucial for the investigation of fast particle trajectories in 3D magnetic structures such as helical saturated tokamak plasma states, stellarator geometry and resonant magnetic perturbations (RMP). The initialisation of particles with respect to the guiding-centre is discussed. Two approaches to implement RMPs in orbit simulations are presented, one where the vacuum field is added to the 2D equilibrium, creating islands and stochastic regions, the other considering 3D nested flux-surfaces equilibrium including the RMPs.},
keywords = {cubic spline, curvilinear coordinates, fast particles, numerical method, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
Curvilinear guiding-centre drift and full-orbit equations of motion are presented as implemented in the VENUS-LEVIS code. A dedicated interpolation scheme based on Fourier reconstruction in the toroidal and poloidal directions and cubic spline in the radial direction of flux coordinate systems is detailed. This interpolation method exactly preserves the order of the RK4 integrating scheme which is crucial for the investigation of fast particle trajectories in 3D magnetic structures such as helical saturated tokamak plasma states, stellarator geometry and resonant magnetic perturbations (RMP). The initialisation of particles with respect to the guiding-centre is discussed. Two approaches to implement RMPs in orbit simulations are presented, one where the vacuum field is added to the 2D equilibrium, creating islands and stochastic regions, the other considering 3D nested flux-surfaces equilibrium including the RMPs.