2020
7.
Patten, H W; Graves, J P; Cooper, W A; Eriksson, J; Pfefferlé, D
Identification of an Optimized Heating and Fast Ion Generation Scheme for the Wendelstein 7-X Stellarator Journal Article
In: Phys. Rev. Lett., vol. 124, pp. 155001, 2020.
Abstract | Links | BibTeX | Tags: fast particles, ion cyclotron resonance, neutral beam injection, stellarator
@article{PhysRevLett.124.155001,
title = {Identification of an Optimized Heating and Fast Ion Generation Scheme for the Wendelstein 7-X Stellarator},
author = {H W Patten and J P Graves and W A Cooper and J Eriksson and D Pfefferl\'{e}},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.155001},
doi = {10.1103/PhysRevLett.124.155001},
year = {2020},
date = {2020-04-01},
journal = {Phys. Rev. Lett.},
volume = {124},
pages = {155001},
publisher = {American Physical Society},
abstract = {A Doppler shifted resonance minority species ion cyclotron range of frequency (ICRF) scheme for heating neutral beam ions has been identified and optimized for the Wendelstein 7-X stellarator. Compared with more conventional methods, the synergetic scheme increases the normalized core collisional power transfer to the background plasma, and induces larger concentrations of energetic ions. Simulations in the intricate 3D magnetic stellarator geometry reveal an energetic distribution function that is only weakly anisotropic, and is thus relevant to fast ion and alpha particle driven Alfv\'{e}n eigenmode experimental preparation. Quasilinear theory and simulations of the Joint European Torus indicate that the excellent confinement properties are due to increased velocity diffusion from ICRF interaction along the magnetic field lines. Agreement is found between SCENIC simulations and Joint European Torus experimental measurements for the total neutron rate and the energy distribution of the fast ions.},
keywords = {fast particles, ion cyclotron resonance, neutral beam injection, stellarator},
pubstate = {published},
tppubtype = {article}
}
A Doppler shifted resonance minority species ion cyclotron range of frequency (ICRF) scheme for heating neutral beam ions has been identified and optimized for the Wendelstein 7-X stellarator. Compared with more conventional methods, the synergetic scheme increases the normalized core collisional power transfer to the background plasma, and induces larger concentrations of energetic ions. Simulations in the intricate 3D magnetic stellarator geometry reveal an energetic distribution function that is only weakly anisotropic, and is thus relevant to fast ion and alpha particle driven Alfvén eigenmode experimental preparation. Quasilinear theory and simulations of the Joint European Torus indicate that the excellent confinement properties are due to increased velocity diffusion from ICRF interaction along the magnetic field lines. Agreement is found between SCENIC simulations and Joint European Torus experimental measurements for the total neutron rate and the energy distribution of the fast ions.
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.
Faustin, J M; Cooper, W A; Graves, J P; Pfefferlé, D; Geiger, J
ICRH induced particle losses in Wendelstein 7-X Journal Article
In: Plasma Physics and Controlled Fusion, vol. 58, no. 7, pp. 074004, 2016.
Abstract | Links | BibTeX | Tags: fast particles, ion cyclotron resonance, MHD equilibrium, neutral beam injection, stellarator, VENUS-LEVIS
@article{faustin-2016b,
title = {ICRH induced particle losses 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/10.1088/0741-3335/58/7/074004},
doi = {10.1088/0741-3335/58/7/074004},
year = {2016},
date = {2016-05-31},
journal = {Plasma Physics and Controlled Fusion},
volume = {58},
number = {7},
pages = {074004},
abstract = {Fast ions in W7-X will be produced either by neutral beam injection (NBI) or by ion-cyclotron resonant heating (ICRH). The latter presents the advantage of depositing power locally and does not suffer from core accessibility issues (Drevlak et al 2014 Nucl. Fusion 54 073002). This work assesses the possibility of using ICRH as a fast ion source in W7-X relevant conditions. The SCENIC package is used to resolve the full wave propagation and absorption in a three-dimensional plasma equilibrium. The source of the ion-cyclotron range of frequency (ICRF) wave is modelled in this work by an antenna formulation allowing its localisation in both the poloidal and toroidal directions. The actual antenna dimension and localization is therefore approximated with good agreement. The local wave deposition breaks the five-fold periodicity of W7-X. It appears that generation of fast ions is hindered by high collisionality and significant particle losses. The particle trapping mechanism induced by ICRH is found to enhance drift induced losses caused by the finite orbit width of trapped particles. The inclusion of a neoclassically resolved radial electric field is also investigated and shows a significant reduction of particle losses.},
keywords = {fast particles, ion cyclotron resonance, MHD equilibrium, neutral beam injection, stellarator, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
Fast ions in W7-X will be produced either by neutral beam injection (NBI) or by ion-cyclotron resonant heating (ICRH). The latter presents the advantage of depositing power locally and does not suffer from core accessibility issues (Drevlak et al 2014 Nucl. Fusion 54 073002). This work assesses the possibility of using ICRH as a fast ion source in W7-X relevant conditions. The SCENIC package is used to resolve the full wave propagation and absorption in a three-dimensional plasma equilibrium. The source of the ion-cyclotron range of frequency (ICRF) wave is modelled in this work by an antenna formulation allowing its localisation in both the poloidal and toroidal directions. The actual antenna dimension and localization is therefore approximated with good agreement. The local wave deposition breaks the five-fold periodicity of W7-X. It appears that generation of fast ions is hindered by high collisionality and significant particle losses. The particle trapping mechanism induced by ICRH is found to enhance drift induced losses caused by the finite orbit width of trapped particles. The inclusion of a neoclassically resolved radial electric field is also investigated and shows a significant reduction of particle losses.
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.
Pfefferlé, D; Misev, C; Cooper, W A; Graves, J P
Impact of RMP magnetic field simulation models on fast ion losses Journal Article
In: Nuclear Fusion, vol. 55, no. 1, pp. 012001, 2014.
Abstract | Links | BibTeX | Tags: fast particles, neutral beam injection, resonant magnetic perturbations, VENUS-LEVIS
@article{pfefferle-rmp,
title = {Impact of RMP magnetic field simulation models on fast ion losses},
author = {D Pfefferl\'{e} and C Misev and W A Cooper and J P Graves},
url = {https://iopscience.iop.org/article/10.1088/0029-5515/55/1/012001},
doi = {10.1088/0029-5515/55/1/012001},
year = {2014},
date = {2014-12-19},
journal = {Nuclear Fusion},
volume = {55},
number = {1},
pages = {012001},
abstract = {Two opposing approaches to include resonant magnetic perturbations (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, which excludes stochastic field-lines, and embeds the RMPs within a 3D saturated ideal MHD state. The two descriptions of RMPs have been implemented in the VENUS-LEVIS guiding-centre orbit code. Simulations of fast ion populations resulting from MAST neutral beam injection have been applied to MAST n = 3 RMP coil configuration. At low beam energies, particle losses are dominated by parallel transport due to the stochasticity of the field-lines (vacuum-RMP model), whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma and the resulting drifts (equilibrium-RMP model).},
keywords = {fast particles, neutral beam injection, resonant magnetic perturbations, VENUS-LEVIS},
pubstate = {published},
tppubtype = {article}
}
Two opposing approaches to include resonant magnetic perturbations (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, which excludes stochastic field-lines, and embeds the RMPs within a 3D saturated ideal MHD state. The two descriptions of RMPs have been implemented in the VENUS-LEVIS guiding-centre orbit code. Simulations of fast ion populations resulting from MAST neutral beam injection have been applied to MAST n = 3 RMP coil configuration. At low beam energies, particle losses are dominated by parallel transport due to the stochasticity of the field-lines (vacuum-RMP model), whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma and the resulting drifts (equilibrium-RMP model).
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.