2021
11.
Neto, E. Lascas; Graves, J. P.; Raghunathan, M.; Sommariva, C.; Pfefferlé, D.; Contributors, J. E. T.
Heavy Impurity Transport in Tokamaks Subject to Plasma Rotation, NTV and the Influence of Saturated Ideal MHD Perturbations Journal Article
In: Plasma Physics and Controlled Fusion, vol. 64, no. 1, pp. 014002, 2021, ISSN: 0741-3335.
Links | BibTeX | Tags: impurities, internal kink, neoclassical transport, plasma flow, VENUS-LEVIS
@article{netoHeavyImpurityTransport2021,
title = {Heavy Impurity Transport in Tokamaks Subject to Plasma Rotation, NTV and the Influence of Saturated Ideal MHD Perturbations},
author = {E. Lascas Neto and J. P. Graves and M. Raghunathan and C. Sommariva and D. Pfefferl\'{e} and J. E. T. Contributors},
doi = {10.1088/1361-6587/ac3964},
issn = {0741-3335},
year = {2021},
date = {2021-11-01},
urldate = {2021-11-01},
journal = {Plasma Physics and Controlled Fusion},
volume = {64},
number = {1},
pages = {014002},
publisher = {IOP Publishing},
keywords = {impurities, internal kink, neoclassical transport, plasma flow, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
2020
10.
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.
2017
9.
Raghunathan, M; Graves, J P; Nicolas, T; Cooper, W A; Garbet, X; Pfefferlé, D
Heavy impurity confinement in hybrid operation scenario plasmas with a rotating 1/1 continuous mode Journal Article
In: Plasma Physics and Controlled Fusion, vol. 59, no. 12, pp. 124002, 2017.
Abstract | Links | BibTeX | Tags: fast particles, impurities, neoclassical transport, plasma flow, VENUS-LEVIS
@article{raghunathan-2017,
title = {Heavy impurity confinement in hybrid operation scenario plasmas with a rotating 1/1 continuous mode},
author = {M Raghunathan and J P Graves and T Nicolas and W A Cooper and X Garbet and D Pfefferl\'{e}},
url = {https://iopscience.iop.org/article/10.1088/1361-6587/aa896f},
doi = {10.1088/1361-6587/aa896f},
year = {2017},
date = {2017-10-09},
journal = {Plasma Physics and Controlled Fusion},
volume = {59},
number = {12},
pages = {124002},
abstract = {In future tokamaks like ITER with tungsten walls, it is imperative to control tungsten accumulation in the core of operational plasmas, especially since tungsten accumulation can lead to radiative collapse and disruption. We investigate the behavior of tungsten trace impurities in a JET-like hybrid scenario with both axisymmetric and saturated 1/1 ideal helical core in the presence of strong plasma rotation. For this purpose, we obtain the equilibria from VMEC and use VENUS-LEVIS, a guiding-center orbit-following code, to follow heavy impurity particles. In this work, VENUS-LEVIS has been modified to account for strong plasma flows with associated neoclassical effects arising from such flows. We find that the combination of helical core and plasma rotation augments the standard neoclassical inward pinch compared to axisymmetry, and leads to a strong inward pinch of impurities towards the magnetic axis despite the strong outward diffusion provided by the centrifugal force, as frequently observed in experiments.},
keywords = {fast particles, impurities, neoclassical transport, plasma flow, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
In future tokamaks like ITER with tungsten walls, it is imperative to control tungsten accumulation in the core of operational plasmas, especially since tungsten accumulation can lead to radiative collapse and disruption. We investigate the behavior of tungsten trace impurities in a JET-like hybrid scenario with both axisymmetric and saturated 1/1 ideal helical core in the presence of strong plasma rotation. For this purpose, we obtain the equilibria from VMEC and use VENUS-LEVIS, a guiding-center orbit-following code, to follow heavy impurity particles. In this work, VENUS-LEVIS has been modified to account for strong plasma flows with associated neoclassical effects arising from such flows. We find that the combination of helical core and plasma rotation augments the standard neoclassical inward pinch compared to axisymmetry, and leads to a strong inward pinch of impurities towards the magnetic axis despite the strong outward diffusion provided by the centrifugal force, as frequently observed in experiments.
8.
Faustin, J M; Graves, J P; Cooper, W A; Lanthaler, S; Villard, L; Pfefferlé, D; Geiger, J; Kazakov, Ye O; Eester, Van D
Modelling of advanced three-ion ICRF heating and fast ion generation scheme for tokamaks and stellarators Journal Article
In: Plasma Physics and Controlled Fusion, vol. 59, no. 8, pp. 084001, 2017.
Abstract | Links | BibTeX | Tags: fast particles, heating, ion cyclotron resonance, neoclassical transport, stellarator
@article{faustin-2017,
title = {Modelling of advanced three-ion ICRF heating and fast ion generation scheme for tokamaks and stellarators},
author = {J M Faustin and J P Graves and W A Cooper and S Lanthaler and L Villard and D Pfefferl\'{e} and J Geiger and Ye O Kazakov and Van D Eester},
doi = {10.1088/1361-6587/aa72a4},
year = {2017},
date = {2017-06-13},
journal = {Plasma Physics and Controlled Fusion},
volume = {59},
number = {8},
pages = {084001},
abstract = {Absorption of ion-cyclotron range of frequencies waves at the fundamental resonance is an efficient source of plasma heating and fast ion generation in tokamaks and stellarators. This heating method is planned to be exploited as a fast ion source in the Wendelstein 7-X stellarator. The work presented here assesses the possibility of using the newly developed three-ion species scheme (Kazakov et al (2015) Nucl. Fusion 55 032001) in tokamak and stellarator plasmas, which could offer the capability of generating more energetic ions than the traditional minority heating scheme with moderate input power. Using the SCENIC code, it is found that fast ions in the MeV range of energy can be produced in JET-like plasmas. The RF-induced particle pinch is seen to strongly impact the fast ion pressure profile in particular. Our results show that in typical high-density W7-X plasmas, the three-ion species scheme generates more energetic ions than the more traditional minority heating scheme, which makes three-ion scenario promising for fast-ion confinement studies in W7-X.},
keywords = {fast particles, heating, ion cyclotron resonance, neoclassical transport, stellarator},
pubstate = {published},
tppubtype = {article}
}
Absorption of ion-cyclotron range of frequencies waves at the fundamental resonance is an efficient source of plasma heating and fast ion generation in tokamaks and stellarators. This heating method is planned to be exploited as a fast ion source in the Wendelstein 7-X stellarator. The work presented here assesses the possibility of using the newly developed three-ion species scheme (Kazakov et al (2015) Nucl. Fusion 55 032001) in tokamak and stellarator plasmas, which could offer the capability of generating more energetic ions than the traditional minority heating scheme with moderate input power. Using the SCENIC code, it is found that fast ions in the MeV range of energy can be produced in JET-like plasmas. The RF-induced particle pinch is seen to strongly impact the fast ion pressure profile in particular. Our results show that in typical high-density W7-X plasmas, the three-ion species scheme generates more energetic ions than the more traditional minority heating scheme, which makes three-ion scenario promising for fast-ion confinement studies in W7-X.
7.
Wenninger, R; al.,
The DEMO wall load challenge Journal Article
In: Nuclear Fusion, vol. 57, no. 4, pp. 046002, 2017.
Abstract | Links | BibTeX | Tags: confinement, DEMO, fast particles, magnetic ripple, MHD equilibrium, neoclassical transport, perturbation theory, VENUS-LEVIS, wall load
@article{wenninger-2017,
title = {The DEMO wall load challenge},
author = {R Wenninger and al.},
url = {https://iopscience.iop.org/article/10.1088/1741-4326/aa4fb4},
doi = {10.1088/1741-4326/aa4fb4},
year = {2017},
date = {2017-02-09},
journal = {Nuclear Fusion},
volume = {57},
number = {4},
pages = {046002},
abstract = {For several reasons the challenge to keep the loads to the first wall within engineering limits is substantially higher in DEMO compared to ITER. Therefore the pre-conceptual design development for DEMO that is currently ongoing in Europe needs to be based on load estimates that are derived employing the most recent plasma edge physics knowledge.
An initial assessment of the static wall heat load limit in DEMO infers that the steady state peak heat flux limit on the majority of the DEMO first wall should not be assumed to be higher than 1.0 MW m−2. This compares to an average wall heat load of 0.29 MW m−2 for the design EU-DEMO1 2015 assuming a perfect homogeneous distribution. The main part of this publication concentrates on the development of first DEMO estimates for charged particle, radiation, fast particle (all static) and disruption heat loads. Employing an initial engineering wall design with clear optimization potential in combination with parameters for the flat-top phase (x-point configuration), loads up to 7 MW m−2 (penalty factor for tolerances etc not applied) have been calculated. Assuming a fraction of power radiated from the x-point region between 1/5 and 1/3, peaks of the total power flux density due to radiation of 0.6\textendash0.8 MW m−2 are found in the outer baffle region.
This first review of wall loads, and the associated limits in DEMO clearly underlines a significant challenge that necessitates substantial engineering efforts as well as a considerable consolidation of the associated physics basis.},
keywords = {confinement, DEMO, fast particles, magnetic ripple, MHD equilibrium, neoclassical transport, perturbation theory, VENUS-LEVIS, wall load},
pubstate = {published},
tppubtype = {article}
}
For several reasons the challenge to keep the loads to the first wall within engineering limits is substantially higher in DEMO compared to ITER. Therefore the pre-conceptual design development for DEMO that is currently ongoing in Europe needs to be based on load estimates that are derived employing the most recent plasma edge physics knowledge.
An initial assessment of the static wall heat load limit in DEMO infers that the steady state peak heat flux limit on the majority of the DEMO first wall should not be assumed to be higher than 1.0 MW m−2. This compares to an average wall heat load of 0.29 MW m−2 for the design EU-DEMO1 2015 assuming a perfect homogeneous distribution. The main part of this publication concentrates on the development of first DEMO estimates for charged particle, radiation, fast particle (all static) and disruption heat loads. Employing an initial engineering wall design with clear optimization potential in combination with parameters for the flat-top phase (x-point configuration), loads up to 7 MW m−2 (penalty factor for tolerances etc not applied) have been calculated. Assuming a fraction of power radiated from the x-point region between 1/5 and 1/3, peaks of the total power flux density due to radiation of 0.6–0.8 MW m−2 are found in the outer baffle region.
This first review of wall loads, and the associated limits in DEMO clearly underlines a significant challenge that necessitates substantial engineering efforts as well as a considerable consolidation of the associated physics basis.
An initial assessment of the static wall heat load limit in DEMO infers that the steady state peak heat flux limit on the majority of the DEMO first wall should not be assumed to be higher than 1.0 MW m−2. This compares to an average wall heat load of 0.29 MW m−2 for the design EU-DEMO1 2015 assuming a perfect homogeneous distribution. The main part of this publication concentrates on the development of first DEMO estimates for charged particle, radiation, fast particle (all static) and disruption heat loads. Employing an initial engineering wall design with clear optimization potential in combination with parameters for the flat-top phase (x-point configuration), loads up to 7 MW m−2 (penalty factor for tolerances etc not applied) have been calculated. Assuming a fraction of power radiated from the x-point region between 1/5 and 1/3, peaks of the total power flux density due to radiation of 0.6–0.8 MW m−2 are found in the outer baffle region.
This first review of wall loads, and the associated limits in DEMO clearly underlines a significant challenge that necessitates substantial engineering efforts as well as a considerable consolidation of the associated physics basis.
2016
6.
Faustin, J M; Cooper, W A; Graves, J P; Pfefferlé, D; Geiger, J
Fast particle loss channels in Wendelstein 7-X Journal Article
In: Nuclear Fusion, vol. 56, no. 9, pp. 092006, 2016.
Abstract | Links | BibTeX | Tags: fast particles, heating, ion cyclotron resonance, MHD equilibrium, neoclassical transport, neutral beam injection, stellarator
@article{faustin-2016a,
title = {Fast particle loss channels in Wendelstein 7-X},
author = {J M Faustin and W A Cooper and J P Graves and D Pfefferl\'{e} and J Geiger},
url = {https://iopscience.iop.org/article/10.1088/0029-5515/56/9/092006},
doi = {10.1088/0029-5515/56/9/092006},
year = {2016},
date = {2016-07-29},
journal = {Nuclear Fusion},
volume = {56},
number = {9},
pages = {092006},
abstract = {One of the main goals of Wendelstein 7-X (W7-X) is to demonstrate the fast particle confinement properties of the quasi-isodynamic stellarator concept. Fast particle populations will be produced either by Neutral Beam Injection (NBI) or by minority Ion Cyclotron Resonant Heating (ICRH). A fraction of these particles are expected to be lost (even without collisions), despite the optimisation procedure used for the W7-X design. Confinement properties of NBI particles in W7-X were presented in the paper of Drevlak et al (2014 Nucl. Fusion 54 073002). A detailed study is presented here where the loss patterns of an NBI population are described. In particular, focussing on a high-mirror equilibrium, the confinement of fast ions with varying energy injection is studied under collisional conditions. It is found that collisions are not only responsible for classical transport losses but also enhance drift induced losses caused by trapped particles. Moreover, an asymmetry is found in the toroidal position of particle losses which can be explained by local variation in the equilibrium field. The effects of a neoclassically resolved radial electric field are also investigated. Fast particle confinement is significantly improved by the associated ExB drift. In particular, an increasing radial electric field helps to reduce and even stop the losses due to the 3D equilibrium structure for times comparable to slowing down time.},
keywords = {fast particles, heating, ion cyclotron resonance, MHD equilibrium, neoclassical transport, neutral beam injection, stellarator},
pubstate = {published},
tppubtype = {article}
}
One of the main goals of Wendelstein 7-X (W7-X) is to demonstrate the fast particle confinement properties of the quasi-isodynamic stellarator concept. Fast particle populations will be produced either by Neutral Beam Injection (NBI) or by minority Ion Cyclotron Resonant Heating (ICRH). A fraction of these particles are expected to be lost (even without collisions), despite the optimisation procedure used for the W7-X design. Confinement properties of NBI particles in W7-X were presented in the paper of Drevlak et al (2014 Nucl. Fusion 54 073002). A detailed study is presented here where the loss patterns of an NBI population are described. In particular, focussing on a high-mirror equilibrium, the confinement of fast ions with varying energy injection is studied under collisional conditions. It is found that collisions are not only responsible for classical transport losses but also enhance drift induced losses caused by trapped particles. Moreover, an asymmetry is found in the toroidal position of particle losses which can be explained by local variation in the equilibrium field. The effects of a neoclassically resolved radial electric field are also investigated. Fast particle confinement is significantly improved by the associated ExB drift. In particular, an increasing radial electric field helps to reduce and even stop the losses due to the 3D equilibrium structure for times comparable to slowing down time.
5.
Pfefferlé, D; Cooper, W A; Fasoli, A; Graves, J P
Effects of magnetic ripple on 3D equilibrium and alpha particle confinement in the European DEMO Journal Article
In: Nuclear Fusion, vol. 56, no. 11, pp. 112002, 2016.
Abstract | Links | BibTeX | Tags: confinement, DEMO, fast particles, magnetic ripple, MHD equilibrium, neoclassical transport, perturbation theory
@article{pfefferle-demo,
title = {Effects of magnetic ripple on 3D equilibrium and alpha particle confinement in the European DEMO},
author = {D Pfefferl\'{e} and W A Cooper and A Fasoli and J P Graves},
url = {https://iopscience.iop.org/article/10.1088/0029-5515/56/11/112002},
doi = {10.1088/0029-5515/56/11/112002},
year = {2016},
date = {2016-07-22},
journal = {Nuclear Fusion},
volume = {56},
number = {11},
pages = {112002},
abstract = {An assessment of alpha particle confinement is performed in the European DEMO reference design. 3D MHD equilibria with nested flux-surfaces and single magnetic axis are obtained with the VMEC free-boundary code, thereby including the plasma response to the magnetic ripple created by the finite number of TF coils. Populations of fusion alphas that are consistent with the equilibrium profiles are evolved until slowing-down with the VENUS-LEVIS orbit code in the guiding-centre approximation. Fast ion losses through the last-closed flux-surface are numerically evaluated with two ripple models: (1) using the 3D equilibrium and (2) algebraically adding the non-axisymmetric ripple perturbation to the 2D equilibrium. By virtue of the small ripple field and its non-resonant nature, both models quantitatively agree. Differences are however noted in the toroidal location of particles losses on the last-closed flux-surface, which in the first case is 3D and in the second not. Superbanana transport, i.e. ripple-well trapping and separatrix crossing, is expected to be the dominant loss mechanism, the strongest effect on alphas being between 100\textendash200 KeV. Above this, stochastic ripple diffusion is responsible for a rather weak loss rate, as the stochastisation threshold is observed numerically to be higher than analytic estimates. The level of ripple in the current 18 TF coil design of the European DEMO is not found to be detrimental to fusion alpha confinement.},
keywords = {confinement, DEMO, fast particles, magnetic ripple, MHD equilibrium, neoclassical transport, perturbation theory},
pubstate = {published},
tppubtype = {article}
}
An assessment of alpha particle confinement is performed in the European DEMO reference design. 3D MHD equilibria with nested flux-surfaces and single magnetic axis are obtained with the VMEC free-boundary code, thereby including the plasma response to the magnetic ripple created by the finite number of TF coils. Populations of fusion alphas that are consistent with the equilibrium profiles are evolved until slowing-down with the VENUS-LEVIS orbit code in the guiding-centre approximation. Fast ion losses through the last-closed flux-surface are numerically evaluated with two ripple models: (1) using the 3D equilibrium and (2) algebraically adding the non-axisymmetric ripple perturbation to the 2D equilibrium. By virtue of the small ripple field and its non-resonant nature, both models quantitatively agree. Differences are however noted in the toroidal location of particles losses on the last-closed flux-surface, which in the first case is 3D and in the second not. Superbanana transport, i.e. ripple-well trapping and separatrix crossing, is expected to be the dominant loss mechanism, the strongest effect on alphas being between 100–200 KeV. Above this, stochastic ripple diffusion is responsible for a rather weak loss rate, as the stochastisation threshold is observed numerically to be higher than analytic estimates. The level of ripple in the current 18 TF coil design of the European DEMO is not found to be detrimental to fusion alpha confinement.
2015
4.
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.
3.
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
2.
Faustin, J M; Cooper, W A; Graves, J P; Pfefferlé, D
Modeling of ion-cyclotron resonant heating in Wendelstein 7-X equilibrium Proceedings Article
In: Journal of Physics: Conference Series, pp. 012006, 2014.
Abstract | Links | BibTeX | Tags: confinement, fast particles, ion cyclotron resonance, neoclassical transport, stellarator, VENUS-LEVIS
@inproceedings{faustin-2014,
title = {Modeling of ion-cyclotron resonant heating in Wendelstein 7-X equilibrium},
author = {J M Faustin and W A Cooper and J P Graves and D Pfefferl\'{e}},
url = {http://stacks.iop.org/1742-6596/561/i=1/a=012006},
doi = {10.1088/1742-6596/561/1/012006},
year = {2014},
date = {2014-11-27},
booktitle = {Journal of Physics: Conference Series},
journal = {Journal of Physics: Conference Series},
volume = {561},
number = {1},
pages = {012006},
abstract = {W7X stellarator 3D equilibrium has been computed with the equilibrium code ANIMEC (Anisotropic Neumann Inverse Moments Equilibrium Code). This equilibrium was used to model ICRH minority heating in 4He(H) plasma with the 3D full-wave code LEMan (Low frequency ElectroMagnetic wave propagation). The coupled power spatial distribution is shown for different resonance positions within the range of frequencies foreseen for the ICRH antenna. It is found that for the high mirror equilibrium examined, the antenna frequency can be chosen to optimise the power deposition in the plasma core while limiting the absorption at the edge.},
keywords = {confinement, fast particles, ion cyclotron resonance, neoclassical transport, stellarator, VENUS-LEVIS},
pubstate = {published},
tppubtype = {inproceedings}
}
W7X stellarator 3D equilibrium has been computed with the equilibrium code ANIMEC (Anisotropic Neumann Inverse Moments Equilibrium Code). This equilibrium was used to model ICRH minority heating in 4He(H) plasma with the 3D full-wave code LEMan (Low frequency ElectroMagnetic wave propagation). The coupled power spatial distribution is shown for different resonance positions within the range of frequencies foreseen for the ICRH antenna. It is found that for the high mirror equilibrium examined, the antenna frequency can be chosen to optimise the power deposition in the plasma core while limiting the absorption at the edge.
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.