2020
4.
Pfefferlé, David; Noakes, Lyle; Zhou, Yao
Rigidity of MHD equilibria to smooth incompressible ideal motion near resonant surfaces Journal Article
In: Plasma Physics and Controlled Fusion, vol. 62, no. 7, pp. 074004, 2020.
Abstract | Links | BibTeX | Tags: Hamiltonian, MHD, MHD equilibrium, perturbation theory, resonant surfaces
@article{pfefferle-rigidityb,
title = {Rigidity of MHD equilibria to smooth incompressible ideal motion near resonant surfaces},
author = {David Pfefferl\'{e} and Lyle Noakes and Yao Zhou},
url = {https://doi.org/10.1088%2F1361-6587%2Fab8ca3},
doi = {10.1088/1361-6587/ab8ca3},
year = {2020},
date = {2020-06-01},
journal = {Plasma Physics and Controlled Fusion},
volume = {62},
number = {7},
pages = {074004},
publisher = {IOP Publishing},
abstract = {In ideal MHD, the magnetic flux is advected by the plasma motion, freezing flux-surfaces into the flow. An MHD equilibrium is reached when the flow relaxes and force balance is achieved. We ask what classes of MHD equilibria can be accessed from a given initial state via smooth incompressible ideal motion. It is found that certain boundary displacements are formally not supported. This follows from yet another investigation of the Hahm\textendashKulsrud\textendashTaylor (HKT) problem, which highlights the resonant behaviour near a rational layer formed by a set of degenerate critical points in the flux-function. When trying to retain the mirror symmetry of the flux-function with respect to the resonant layer, the vector field that generates the volume-preserving diffeomorphism vanishes at the identity to all order in the time-like path parameter.},
keywords = {Hamiltonian, MHD, MHD equilibrium, perturbation theory, resonant surfaces},
pubstate = {published},
tppubtype = {article}
}
In ideal MHD, the magnetic flux is advected by the plasma motion, freezing flux-surfaces into the flow. An MHD equilibrium is reached when the flow relaxes and force balance is achieved. We ask what classes of MHD equilibria can be accessed from a given initial state via smooth incompressible ideal motion. It is found that certain boundary displacements are formally not supported. This follows from yet another investigation of the Hahm–Kulsrud–Taylor (HKT) problem, which highlights the resonant behaviour near a rational layer formed by a set of degenerate critical points in the flux-function. When trying to retain the mirror symmetry of the flux-function with respect to the resonant layer, the vector field that generates the volume-preserving diffeomorphism vanishes at the identity to all order in the time-like path parameter.
2017
3.
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.
2.
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
1.
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.