2020
6.
Lazerson, Samuel A; Ford, Oliver P; Nuehrenberg, Carolin; Äkäslompolo, Simppa; Poloskei, Peter Zs.; Machielsen, Mike; McNeely, Paul; Vanó, Lilla; Rust, Norbert; Bozhenkov, Sergey; Neelis, Tristan W C; Graves, Jonathan P; Pfefferlé, David; Spanier, Annabelle; Hartmann, Dirk; Marushchenko, Nikolai; Turkin, Yuriy; Hirsch, Matthias; Chaudhary, Neha; Hoefel, Udo; Stange, Torsten; Weir, Gavin; Pablant, Novimir; Langenberg, Andreas; Traverso, Peter; Valson, Pranay; Knauer, Jens; Brunner, Kai Jakob; Pasch, Ekkehard; Beurskens, Marc; Damm, Hannes; Fuchert, Golo; Nelde, Philipp; Scott, Evan; Hergenhahn, Uwe; Pavone, Andrea; Rahbarnia, Kian; Andreeva, Tamara; Schilling, Jonathan; Brandt, Christian; Neuner, Ulrich; Thomsen, Henning; Jakubowski, Marcin; Ali, Adnan; Gao, Yu; Niemann, Holger; Sitjes, Aleix Puig; Koenig, Ralf; and, Robert Wolf C
Validation of the BEAMS3D neutral beam deposition model on Wendelstein 7-X Journal Article
In: Nuclear Fusion, vol. 60, no. 7, pp. 076020, 2020.
Abstract | Links | BibTeX | Tags: fast particles, full-orbit, guiding-centre, neoclassical transport, stellarator
@article{lazerson-2020,
title = {Validation of the BEAMS3D neutral beam deposition model on Wendelstein 7-X},
author = {Samuel A Lazerson and Oliver P Ford and Carolin Nuehrenberg and Simppa \"{A}k\"{a}slompolo and Peter Zs. Poloskei and Mike Machielsen and Paul McNeely and Lilla Van\'{o} and Norbert Rust and Sergey Bozhenkov and Tristan W C Neelis and Jonathan P Graves and David Pfefferl\'{e} and Annabelle Spanier and Dirk Hartmann and Nikolai Marushchenko and Yuriy Turkin and Matthias Hirsch and Neha Chaudhary and Udo Hoefel and Torsten Stange and Gavin Weir and Novimir Pablant and Andreas Langenberg and Peter Traverso and Pranay Valson and Jens Knauer and Kai Jakob Brunner and Ekkehard Pasch and Marc Beurskens and Hannes Damm and Golo Fuchert and Philipp Nelde and Evan Scott and Uwe Hergenhahn and Andrea Pavone and Kian Rahbarnia and Tamara Andreeva and Jonathan Schilling and Christian Brandt and Ulrich Neuner and Henning Thomsen and Marcin Jakubowski and Adnan Ali and Yu Gao and Holger Niemann and Aleix Puig Sitjes and Ralf Koenig and Robert Wolf C and},
url = {https://doi.org/10.1088%2F1741-4326%2Fab8e61},
doi = {10.1088/1741-4326/ab8e61},
year = {2020},
date = {2020-06-01},
journal = {Nuclear Fusion},
volume = {60},
number = {7},
pages = {076020},
publisher = {IOP Publishing},
abstract = {The neutral beam deposition model in the BEAMS3D code is validated against neutral beam attenuation data from Wendelstein 7-X (W7-X). A set of experimental discharges where the neutral beam injection system of W7-X was utilized were reconstructed. These discharges scanned the magnetic configurations and plasma densities of W7-X. The equilibrium reconstructions were performed using STELLOPT which calculates three-dimensional self-consistent ideal magnetohydrodynamic equilibria and kinetic profiles. These reconstructions leveraged new capabilities to incorporate electron cyclotron emission and x-ray imaging diagnostics in the STELLOPT code. The reconstructed equilibria and profiles served as inputs for BEAMS3D calculations of neutral beam deposition in W7-X. It is found that if reconstructed kinetic profiles are utilized, good agreement between measured and simulated beam attenuation is found. As deposition models provide initial conditions for fast-ion slowing down calculations, this work provides a first step towards validating our ability to predict fast ion confinement in stellarators.},
keywords = {fast particles, full-orbit, guiding-centre, neoclassical transport, stellarator},
pubstate = {published},
tppubtype = {article}
}
The neutral beam deposition model in the BEAMS3D code is validated against neutral beam attenuation data from Wendelstein 7-X (W7-X). A set of experimental discharges where the neutral beam injection system of W7-X was utilized were reconstructed. These discharges scanned the magnetic configurations and plasma densities of W7-X. The equilibrium reconstructions were performed using STELLOPT which calculates three-dimensional self-consistent ideal magnetohydrodynamic equilibria and kinetic profiles. These reconstructions leveraged new capabilities to incorporate electron cyclotron emission and x-ray imaging diagnostics in the STELLOPT code. The reconstructed equilibria and profiles served as inputs for BEAMS3D calculations of neutral beam deposition in W7-X. It is found that if reconstructed kinetic profiles are utilized, good agreement between measured and simulated beam attenuation is found. As deposition models provide initial conditions for fast-ion slowing down calculations, this work provides a first step towards validating our ability to predict fast ion confinement in stellarators.
2019
5.
Lanthaler, S; Graves, J P; Pfefferlé, D; Cooper, W A
Guiding-centre theory for kinetic-magnetohydrodynamic modes in strongly flowing plasmas Journal Article
In: Plasma Physics and Controlled Fusion, vol. 61, no. 7, pp. 074006, 2019.
Abstract | Links | BibTeX | Tags: drift-kinetic, guiding-centre, MHD, plasma flow
@article{lanthaler-2019,
title = {Guiding-centre theory for kinetic-magnetohydrodynamic modes in strongly flowing plasmas},
author = {S Lanthaler and J P Graves and D Pfefferl\'{e} and W A Cooper},
url = {https://doi.org/10.1088%2F1361-6587%2Fab1d21},
doi = {10.1088/1361-6587/ab1d21},
year = {2019},
date = {2019-05-01},
journal = {Plasma Physics and Controlled Fusion},
volume = {61},
number = {7},
pages = {074006},
publisher = {IOP Publishing},
abstract = {A kinetic-magnetohydrodynamic model with kinetic pressure closure is derived from a consistent guiding-centre framework. Higher-order (gyroviscous) corrections to the pressure tensor are derived in complex geometry from a reduced kinetic equation. The proposed model allows for flows of the order of the thermal ion velocity, taking into account important centrifugal effects due to the ExB flow, as well as the effects of diamagnetic flows associated with finite Larmor radius corrections to both ion fluid inertia and long mean-free path contributions. Wave\textendashparticle interactions, such as toroidal drift-resonance, are retained. Furthermore, the linearised model includes a quasi-neutrality equation, allowing the effects of a parallel electric field to be studied in fast rotating tokamak plasmas.},
keywords = {drift-kinetic, guiding-centre, MHD, plasma flow},
pubstate = {published},
tppubtype = {article}
}
A kinetic-magnetohydrodynamic model with kinetic pressure closure is derived from a consistent guiding-centre framework. Higher-order (gyroviscous) corrections to the pressure tensor are derived in complex geometry from a reduced kinetic equation. The proposed model allows for flows of the order of the thermal ion velocity, taking into account important centrifugal effects due to the ExB flow, as well as the effects of diamagnetic flows associated with finite Larmor radius corrections to both ion fluid inertia and long mean-free path contributions. Wave–particle interactions, such as toroidal drift-resonance, are retained. Furthermore, the linearised model includes a quasi-neutrality equation, allowing the effects of a parallel electric field to be studied in fast rotating tokamak plasmas.
2017
4.
Lanthaler, S; Pfefferlé, D; Graves, J P; Cooper, W A
Higher order Larmor radius corrections to guiding-centre equations and application to fast ion equilibrium distributions Journal Article
In: Plasma Physics and Controlled Fusion, vol. 59, no. 4, pp. 044014, 2017.
Abstract | Links | BibTeX | Tags: drift-kinetic, guiding-centre, MHD equilibrium, perturbation theory, VENUS-LEVIS
@article{lanthaler-2017,
title = {Higher order Larmor radius corrections to guiding-centre equations and application to fast ion equilibrium distributions},
author = {S Lanthaler and D Pfefferl\'{e} and J P Graves and W A Cooper},
url = {https://iopscience.iop.org/article/10.1088/1361-6587/aa5e70},
doi = {10.1088/1361-6587/aa5e70},
year = {2017},
date = {2017-03-15},
journal = {Plasma Physics and Controlled Fusion},
volume = {59},
number = {4},
pages = {044014},
abstract = {An improved set of guiding-centre equations, expanded to one order higher in Larmor radius than usually written for guiding-centre codes, are derived for curvilinear flux coordinates and implemented into the orbit following code VENUS-LEVIS. Aside from greatly improving the correspondence between guiding-centre and full particle trajectories, the most important effect of the additional Larmor radius corrections is to modify the definition of the guiding-centre's parallel velocity via the so-called Ba\~{n}os drift. The correct treatment of the guiding-centre push-forward with the Ba\~{n}os term leads to an anisotropic shift in the phase-space distribution of guiding-centres, consistent with the well-known magnetization term. The consequence of these higher order terms are quantified in three cases where energetic ions are usually followed with standard guiding-centre equations: (1) neutral beam injection in a MAST-like low aspect-ratio spherical equilibrium where the fast ion driven current is significantly larger with respect to previous calculations, (2) fast ion losses due to resonant magnetic perturbations where a lower lost fraction and a better confinement is confirmed, (3) alpha particles in the ripple field of the European DEMO where the effect is found to be marginal.},
keywords = {drift-kinetic, guiding-centre, MHD equilibrium, perturbation theory, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
An improved set of guiding-centre equations, expanded to one order higher in Larmor radius than usually written for guiding-centre codes, are derived for curvilinear flux coordinates and implemented into the orbit following code VENUS-LEVIS. Aside from greatly improving the correspondence between guiding-centre and full particle trajectories, the most important effect of the additional Larmor radius corrections is to modify the definition of the guiding-centre's parallel velocity via the so-called Baños drift. The correct treatment of the guiding-centre push-forward with the Baños term leads to an anisotropic shift in the phase-space distribution of guiding-centres, consistent with the well-known magnetization term. The consequence of these higher order terms are quantified in three cases where energetic ions are usually followed with standard guiding-centre equations: (1) neutral beam injection in a MAST-like low aspect-ratio spherical equilibrium where the fast ion driven current is significantly larger with respect to previous calculations, (2) fast ion losses due to resonant magnetic perturbations where a lower lost fraction and a better confinement is confirmed, (3) alpha particles in the ripple field of the European DEMO where the effect is found to be marginal.
2015
3.
Pfefferlé, D
Energetic ion dynamics and confinement in 3D saturated MHD configurations PhD Thesis
Swiss Institute of Technology Lausanne (EPFL), 2015.
Abstract | Links | BibTeX | Tags: drift-kinetic, fast particles, guiding-centre, Hamiltonian, internal kink, magnetic ripple, MHD equilibrium, neoclassical transport, neutral beam injection, stellarator, VENUS-LEVIS
@phdthesis{pfefferle-thesis,
title = {Energetic ion dynamics and confinement in 3D saturated MHD configurations},
author = {D Pfefferl\'{e}},
url = {https://infoscience.epfl.ch/record/207958},
doi = {10.5075/epfl-thesis-6561},
year = {2015},
date = {2015-05-04},
publisher = {EPFL},
school = {Swiss Institute of Technology Lausanne (EPFL)},
abstract = {In the following theoretical and numerically oriented work, a number of findings have been assembled. The newly devised VENUS-LEVIS code, designed to accurately solve the motion of energetic particles in the presence of 3D magnetic fields, relies on a non-canonical general coordinate Lagrangian formulation of the guiding-centre and full-orbit equations of motion. VENUS-LEVIS can switch between guiding-centre and full-orbit equations with minimal discrepancy at first order in Larmor radius by verifying the perpendicular variation of magnetic vector field, not only including gradients and curvature terms but also parallel currents and the shearing of field-lines. By virtue of a Fourier representation of the fields in poloidal and toroidal coordinates and a cubic spline in the radial variable, the order of the Runge-Kutta integrating scheme is preserved and convergence of Hamiltonian properties is obtained. This interpolation scheme is crucial to compute orbits over slowing-down times, as well as to mitigate the singularity of the magnetic axis in toroidal flux coordinate systems. Three-dimensional saturated MHD states are associated with many tokamak phenomena including snakes and LLMs in spherical or more conventional tokamaks, and are inherent to stellarator devices. The VMEC equilibrium code conveniently reproduces such 3D magnetic configurations. Slowing-down simulations of energetic ions from NBI predict off-axis deposition of particles during LLM MHD activity in hybrid-like plasmas of the MAST. Co-passing particles helically align in the opposite side of the plasma deformation, whereas counter-passing and trapped particles are less affected by the presence of a helical core. Qualitative agreement is found against experimental measurements of the neutron emission. Two opposing approaches to include RMPs in fast ion simulations are compared, one where the vacuum field caused by the RMP current coils is added to the axisymmetric MHD equilibrium, the other where the MHD equilibrium includes the plasma response within the 3D deformation of its flux-surfaces. The first model admits large regions of stochastic field-lines that penetrate the plasma without alteration. The second assumes nested flux-surfaces with a single magnetic axis, embedding the RMPs in a 3D saturated ideal MHD state but excluding stochastic field-lines within the last closed flux-surface. Simulations of fast ion populations from NBI are applied to MAST n=3 RMP coil configuration with 4 different activation patterns. At low beam energies, particle losses are dominated by parallel transport due to the stochasticity of the field-lines, whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma as well as drift resonances.},
keywords = {drift-kinetic, fast particles, guiding-centre, Hamiltonian, internal kink, magnetic ripple, MHD equilibrium, neoclassical transport, neutral beam injection, stellarator, VENUS-LEVIS},
pubstate = {published},
tppubtype = {phdthesis}
}
In the following theoretical and numerically oriented work, a number of findings have been assembled. The newly devised VENUS-LEVIS code, designed to accurately solve the motion of energetic particles in the presence of 3D magnetic fields, relies on a non-canonical general coordinate Lagrangian formulation of the guiding-centre and full-orbit equations of motion. VENUS-LEVIS can switch between guiding-centre and full-orbit equations with minimal discrepancy at first order in Larmor radius by verifying the perpendicular variation of magnetic vector field, not only including gradients and curvature terms but also parallel currents and the shearing of field-lines. By virtue of a Fourier representation of the fields in poloidal and toroidal coordinates and a cubic spline in the radial variable, the order of the Runge-Kutta integrating scheme is preserved and convergence of Hamiltonian properties is obtained. This interpolation scheme is crucial to compute orbits over slowing-down times, as well as to mitigate the singularity of the magnetic axis in toroidal flux coordinate systems. Three-dimensional saturated MHD states are associated with many tokamak phenomena including snakes and LLMs in spherical or more conventional tokamaks, and are inherent to stellarator devices. The VMEC equilibrium code conveniently reproduces such 3D magnetic configurations. Slowing-down simulations of energetic ions from NBI predict off-axis deposition of particles during LLM MHD activity in hybrid-like plasmas of the MAST. Co-passing particles helically align in the opposite side of the plasma deformation, whereas counter-passing and trapped particles are less affected by the presence of a helical core. Qualitative agreement is found against experimental measurements of the neutron emission. Two opposing approaches to include RMPs in fast ion simulations are compared, one where the vacuum field caused by the RMP current coils is added to the axisymmetric MHD equilibrium, the other where the MHD equilibrium includes the plasma response within the 3D deformation of its flux-surfaces. The first model admits large regions of stochastic field-lines that penetrate the plasma without alteration. The second assumes nested flux-surfaces with a single magnetic axis, embedding the RMPs in a 3D saturated ideal MHD state but excluding stochastic field-lines within the last closed flux-surface. Simulations of fast ion populations from NBI are applied to MAST n=3 RMP coil configuration with 4 different activation patterns. At low beam energies, particle losses are dominated by parallel transport due to the stochasticity of the field-lines, whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma as well as drift resonances.
2.
Pfefferlé, D; Graves, J P; Cooper, W A
Hybrid guiding-centre/full-orbit simulations in non-axisymmetric magnetic geometry exploiting general criterion for guiding-centre accuracy Journal Article
In: Plasma Physics and Controlled Fusion, vol. 57, no. 5, pp. 054017, 2015.
Abstract | Links | BibTeX | Tags: fast particles, full-orbit, guiding-centre, neoclassical transport, neutral beam injection, VENUS-LEVIS
@article{pfefferle-hybrid,
title = {Hybrid guiding-centre/full-orbit simulations in non-axisymmetric magnetic geometry exploiting general criterion for guiding-centre accuracy},
author = {D Pfefferl\'{e} and J P Graves and W A Cooper},
url = {http://stacks.iop.org/0741-3335/57/i=5/a=054017},
doi = {10.1088/0741-3335/57/5/054017},
year = {2015},
date = {2015-04-15},
journal = {Plasma Physics and Controlled Fusion},
volume = {57},
number = {5},
pages = {054017},
abstract = {To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM).},
keywords = {fast particles, full-orbit, guiding-centre, neoclassical transport, neutral beam injection, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM).
2014
1.
Pfefferlé, D; Graves, J P; Cooper, W A; Misev, C; Chapman, I T; Turnyanskiy, M; Sangaroon, S
NBI fast ion confinement in the helical core of MAST hybrid-like plasmas Journal Article
In: Nuclear Fusion, vol. 54, no. 6, pp. 064020, 2014.
Abstract | Links | BibTeX | Tags: confinement, fast particles, guiding-centre, internal kink, MHD equilibrium, neoclassical transport, neutral beam injection, VENUS-LEVIS
@article{pfefferle-nbi,
title = {NBI fast ion confinement in the helical core of MAST hybrid-like plasmas},
author = {D Pfefferl\'{e} and J P Graves and W A Cooper and C Misev and I T Chapman and M Turnyanskiy and S Sangaroon},
url = {https://iopscience.iop.org/article/10.1088/0029-5515/54/6/064020},
doi = {10.1088/0029-5515/54/6/064020},
year = {2014},
date = {2014-05-23},
journal = {Nuclear Fusion},
volume = {54},
number = {6},
pages = {064020},
abstract = {Energetic ions are found to be transported strongly from the core of MAST hybrid-like plasmas during long-lived mode (LLM) magnetohydrodynamic activity. The resulting impact on the neutral beam ion deposition and concurrent current drive is modelled using the guiding-centre approximation in the internal kinked magnetic topology. General coordinate guiding-centre equations are extended for this purpose. It is found that the kinked core spirals around the position of strongest ionization, which remains geometrically centred, so that a large fraction of the population is deposited in the high shear external region where the plasma is almost axisymmetric. Those particles ionized in the low shear region exhibit exotic drift motion due to the strongly non-axisymmetric equilibrium, periodically passing near the magnetic axis and then reflected by the boundary of the kinked equilibrium, which in this respect acts as a confining pinch. Broad agreement is found against experimental measurement of fast ion particle confinement degradation as the MAST LLM amplitude varies.},
keywords = {confinement, fast particles, guiding-centre, internal kink, MHD equilibrium, neoclassical transport, neutral beam injection, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
Energetic ions are found to be transported strongly from the core of MAST hybrid-like plasmas during long-lived mode (LLM) magnetohydrodynamic activity. The resulting impact on the neutral beam ion deposition and concurrent current drive is modelled using the guiding-centre approximation in the internal kinked magnetic topology. General coordinate guiding-centre equations are extended for this purpose. It is found that the kinked core spirals around the position of strongest ionization, which remains geometrically centred, so that a large fraction of the population is deposited in the high shear external region where the plasma is almost axisymmetric. Those particles ionized in the low shear region exhibit exotic drift motion due to the strongly non-axisymmetric equilibrium, periodically passing near the magnetic axis and then reflected by the boundary of the kinked equilibrium, which in this respect acts as a confining pinch. Broad agreement is found against experimental measurement of fast ion particle confinement degradation as the MAST LLM amplitude varies.