Publications

@article{lazersonModelingMeasurementEnergetic2021,

title = {Modeling and Measurement of Energetic Particle Slowing down in Wendelstein 7-X},

author = {Samuel A. Lazerson and David Pfefferl\'{e} and Michael Drevlak and Hr{a}kan Smith and Joachim Geiger and Simppa \"{A}k\"{a}slompolo and Pavlos Xanthopoulos and Andreas Dinklage and Oliver Ford and Paul McNeely and Norbert Rust and Sergey Bozhenkov and Dirk Hartmann and Kian Rahbarnia and Tamara Andreeva and Jonathan Schilling and Christian Brandt and Ulrich Neuner and Henning Thomsen and Robert C. Wolf and The W7-X. Team},

doi = {10.1088/1741-4326/ac0771},

issn = {0029-5515},

year  = {2021},

date = {2021-07-01},

urldate = {2021-07-01},

volume = {61},

number = {9},

pages = {096005},

publisher = {IOP Publishing},

abstract = {The energetic particle slowing down model in the BEAMS3D stellarator neutral beam code is compared to analytic models and experimental data from the Wendelstein 7-X experiment (W7-X). Recently, the first neutral beam experiments were performed in W7-X, providing validation of neutral beam deposition codes (Lazerson S.A. et al 2020 Nucl. Fusion 60 076020). This work builds upon that work, and follows the gyro-center orbits of the neutral-beam-generated fast ions to the plasma boundary. Slowing down times based on measurements of diamagnetic energy changes are compared to simulation data. A discharge solely heated by neutral beam injection is used to compare neoclassical heat flux estimates to neutral beam fueling, heating, and current drive. Experimental estimates of electron heat diffusivity suggest that electron turbulence is destabilized by density peaking in the discharge. Neutral beam current drive dominates over bootstrap current, resulting in a reversal of the toroidal current, as seen experimentally. Particle losses and heat flux through the equilibrium boundary are described. The effects of the magnetic configuration and plasma density on such parameters are also assessed. Benchmarking based on analytic estimates and other energetic particle codes is presented.},

keywords = {benchmark, fast particles, numerical method, slowing-down distribution, stellarator, VENUS-LEVISLEVIS},

pubstate = {published},

tppubtype = {article}

}

@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}

}

@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}

}

@article{hudson-2018,

title = {Differentiating the shape of stellarator coils with respect to the plasma boundary},

author = {S R Hudson and C Zhu and D Pfefferl\'{e} and L Gunderson},

doi = {https://doi.org/10.1016/j.physleta.2018.07.016},

issn = {0375-9601},

year  = {2018},

date = {2018-09-29},

journal = {Physics Letters A},

volume = {382},

number = {38},

pages = {2732 - 2737},

abstract = {The task of designing the geometry of a set of current-carrying coils that produce the magnetic field required to confine a given plasma equilibrium in stellarators is expressed as a minimization principle, namely that the coils minimize a suitably defined error expressed as a surface integral, which is recognized as the quadratic-flux. A penalty on the coil length is included to avoid pathological solutions. A simple expression for how the quadratic-flux and coil length vary as the coil geometry varies is derived, and an expression describing how this varies with variations in the surface geometry is derived. These expressions allow efficient coil-design algorithms to be implemented, and also enable efficient algorithms for varying the shape of the plasma surface in order to simplify the coil geometry, and a numerical illustration of this is given.},

keywords = {coil design, MHD equilibrium, stellarator},

pubstate = {published},

tppubtype = {article}

}

@article{pfefferle-elastica,

title = {Non-planar elasticae as optimal curves for the magnetic axis of stellarators},

author = {D Pfefferl\'{e} and L Gunderson and S R Hudson and L Noakes},

doi = {10.1063/1.5040894},

year  = {2018},

date = {2018-09-26},

journal = {Physics of Plasmas},

volume = {25},

number = {9},

pages = {092508},

abstract = {The problem of finding an optimal curve for the target magnetic axis of a stellarator is addressed. Euler-Lagrange equations are derived for finite length three-dimensional curves that extremise their bending energy while yielding fixed integrated torsion. The obvious translational and rotational symmetries are exploited to express solutions in a preferred cylindrical coordinate system in terms of elliptic Jacobi functions. These solution curves, which, up to similarity transformations, depend on three dimensionless parameters, do not necessarily close. Two closure conditions are obtained for the vertical and toroidal displacement (the radial coordinate being trivially periodic) to yield a countably infinite set of one-parameter families of closed non-planar curves. The behaviour of the integrated torsion (Twist of the Frenet frame), the Linking of the Frenet frame, and the Writhe of the solution curves are studied in light of the C\u{a}lug\u{a}reanu theorem. A refreshed interpretation of Mercier's formula for the on-axis rotational transform of stellarator magnetic field-lines is proposed.},

keywords = {elastica, euler-lagrange equations, linking number, magnetic axis, non-planar curves, rotational transform, stellarator, twist, variational problem, writhe},

pubstate = {published},

tppubtype = {article}

}

@article{patten-2018,

title = {The effect of magnetic equilibrium on auxiliary heating schemes and fast particle confinement in Wendelstein 7-X},

author = {H Patten and J P Graves and J Faustin and W A Cooper and J Geiger and D Pfefferl\'{e} and Y Turkin},

doi = {10.1088/1361-6587/aac9ee},

year  = {2018},

date = {2018-06-01},

journal = {Plasma Physics and Controlled Fusion},

volume = {60},

number = {8},

pages = {085009},

publisher = {IOP Publishing},

abstract = {The performance of the auxiliary heating systems ion cyclotron resonance heating and neutral beam injection is calculated in three different magnetic mirror configurations foreseen to be used in future experiments in the Wendelstein 7-X stellarator: low, standard and high mirror. This numerical work is implemented with the SCENIC code package, which is designed to model three-dimensional magnetic equilibria whilst retaining effects such as anisotropy and the influence of including a finite orbit width of the particles. The ability to simulate NBI deposition in three-dimensional equilibria, the implementation of the realistic beam injector geometry, and the modification of the SCENIC package to permit the investigation of the 3-ion species heating scheme, are recent developments. Using these modifications, an assessment of the advantages and disadvantages of these two fast-ion producing auxiliary heating systems is made in the three different magnetic mirror equilibria. For NBI heating, the high mirror configuration displays the best global confinement properties, resulting in a larger collisional power transfer to the background plasma. The standard mirror has the best particle confinement in the core region, but the worst towards the edge of the plasma. The low mirror has the largest lost power and thus the lowest total collisional power. For ICRH, the displacement of the RF-resonant surface significantly impacts the heating performance. Due to the large toroidal magnetic mirror in the high mirror equilibrium, resonant particles easily become trapped and cannot remain in resonance, generating only small energetic particle populations. Despite this, global confinement is still the strongest in this equilibrium. The low mirror is the only equilibrium to produce peaked on-axis collisional power deposition, with associated peaked on-axis fast ion pressure profiles. A highly energetic particle population is then produced but this results in larger lost power as this equilibrium is not sufficiently optimised for fast ion confinement. A comparison between the two heating methods concludes that NBI produces a smaller fraction of lost to input power, and a reduced sensitivity of the performance to variations of the toroidal magnetic mirror. The main limit of NBI which does not apply to ICRH is the production of highly energetic particle populations, with predictions of energetic particles of E ~ 0.45 MeV.},

keywords = {fast particles, heating, MHD equilibrium, stellarator},

pubstate = {published},

tppubtype = {article}

}

@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}

}

@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}

}

@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}

}