Publications

@article{perrellaExistenceGlobalSymmetries2023,

title = {Existence of Global Symmetries of Divergence-Free Fields with First Integrals},

author = {David Perrella and Nathan Duignan and David Pfefferl\'{e}},

doi = {10.1063/5.0152213},

issn = {0022-2488},

year  = {2023},

date = {2023-05-01},

urldate = {2023-05-01},

journal = {Journal of Mathematical Physics},

volume = {64},

number = {5},

pages = {052705},

keywords = {differential geometry, flux-surfaces, MHD equilibrium, noether theorem, quasi-symmetry},

pubstate = {published},

tppubtype = {article}

}

@article{perrellaRectifiabilityDivergencefreeFields2022,

title = {Rectifiability of Divergence-Free Fields along Invariant 2-Tori},

author = {David Perrella and David Pfefferl\'{e} and Luchezar Stoyanov},

doi = {10.1007/s42985-022-00182-3},

issn = {2662-2971},

year  = {2022},

date = {2022-07-01},

urldate = {2022-07-01},

journal = {Partial Differential Equations and Applications},

volume = {3},

number = {4},

pages = {50},

keywords = {cohomology, differential geometry, flux-surfaces, magnetic coordinates, MHD equilibrium, rotational transform},

pubstate = {published},

tppubtype = {article}

}

@article{jeyakumarAnalysisIsotropicAnisotropic2021,

title = {Analysis of the Isotropic and Anisotropic Grad\textendashShafranov Equation},

author = {S. Jeyakumar and D. Pfefferl\'{e} and M. J. Hole and Z. S. Qu},

doi = {10.1017/S002237782100088X},

issn = {0022-3778, 1469-7807},

year  = {2021},

date = {2021-10-01},

urldate = {2021-10-01},

journal = {Journal of Plasma Physics},

volume = {87},

number = {5},

publisher = {Cambridge University Press},

abstract = {Pressure anisotropy is a commonly observed phenomenon in tokamak plasmas, due to external heating methods such as neutral beam injection and ion-cyclotron resonance heating. Equilibrium models for tokamaks are constructed by solving the Grad\textendash Shafranov equation; such models, however, do not account for pressure anisotropy since ideal magnetohydrodynamics assumes a scalar pressure. A modified Grad\textendash Shafranov equation can be derived to include anisotropic pressure and toroidal flow by including drift-kinetic effects from the guiding-centre model of particle motion. In this work, we have studied the mathematical well-posedness of these two problems by showing the existence and uniqueness of solutions to the Grad\textendash Shafranov equation both in the standard isotropic case and when including pressure anisotropy and toroidal flow. A new fixed-point approach is used to show the existence of solutions in the Sobolev space H10H_0^1 to the Grad\textendash Shafranov equation, and sufficient criteria for their uniqueness are derived. The conditions required for the existence of solutions to the modified Grad\textendash Shafranov equation are also constructed.},

keywords = {anisotropy, grad-shafranov, mathematical analysis, MHD equilibrium, PDE},

pubstate = {published},

tppubtype = {article}

}

@article{quCoordinateParameterisationSpectral2020,

title = {Coordinate Parameterisation and Spectral Method Optimisation for Beltrami Field Solver in Stellarator Geometry},

author = {Z. S. Qu and D. Pfefferl\'{e} and S. R. Hudson and A. Baillod and A. Kumar and R. L. Dewar and M. J. Hole},

doi = {10.1088/1361-6587/abc08e},

issn = {0741-3335},

year  = {2020},

date = {2020-11-01},

urldate = {2020-11-01},

volume = {62},

number = {12},

pages = {124004},

publisher = {IOP Publishing},

abstract = {The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. In this work, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10-9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.},

keywords = {curvilinear coordinates, MHD equilibrium, numerical method, SPEC},

pubstate = {published},

tppubtype = {article}

}

@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}

}

@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{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{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}

}

@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}

}

@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{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}

}

@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}

}

@article{cooper-2016,

title = {Saturated ideal kink/peeling formations described as three-dimensional magnetohydrodynamic tokamak equilibrium states},

author = {W A Cooper and D Brunetti and B P Duval and J M Faustin and J P Graves and A Kleiner and H Patten and D Pfefferl\'{e} and L Porte and M Raghunathan and H Reimerdes and O Sauter and T M Tran},

doi = {10.1063/1.4945743},

year  = {2016},

date = {2016-04-06},

journal = {Physics of Plasmas},

volume = {23},

number = {4},

pages = {040701},

abstract = {Free boundary magnetohydrodynamic equilibrium states with spontaneous three dimensional deformations of the plasma-vacuum interface are computed for the first time. The structures obtained have the appearance of saturated ideal external kink/peeling modes. High edge pressure gradients yield toroidal mode number n = 1 corrugations for a high edge bootstrap current and larger n distortions when this current is small. Deformations in the plasma boundary region induce a nonaxisymmetric Pfirsch-Schl\"{u}ter current driving a field-aligned current ribbon consistent with reported experimental observations. A variation in the 3D equilibrium confirms that the n = 1 mode is a kink/peeling structure. We surmise that our calculated equilibrium structures constitute a viable model for the edge harmonic oscillations and outer modes associated with a quiescent H-mode operation in shaped tokamak plasmas.},

keywords = {internal kink, MHD equilibrium},

pubstate = {published},

tppubtype = {article}

}

@article{cooper-2015,

title = {Free boundary equilibrium in 3D tokamaks with toroidal rotation},

author = {W A Cooper and D Brunetti and J M Faustin and J P Graves and D Pfefferl\'{e} and M Raghunathan and O Sauter and T M Tran and I T Chapman and C J Ham and N Aiba and The MAST team and JET contributors},

url = {http://stacks.iop.org/0029-5515/55/i=6/a=063032},

doi = {10.1088/0029-5515/55/6/063032},

year  = {2015},

date = {2015-05-22},

journal = {Nuclear Fusion},

volume = {55},

number = {6},

pages = {063032},

abstract = {The three-dimensional VMEC equilibrium solver has been adapted to numerically investigate the approximate toroidal rotation model we have derived. We concentrate our applications on the simulation of JET snakes and MAST long-lived modes under free boundary conditions. Helical core solutions are triggered when 〈β〉 exceeds a threshold value, typically 2.7% in JET-like plasmas. A large plasma current and edge bootstrap current can drive helical core formations at arbitrarily small 〈β〉 in which the ideal saturated internal kink coexists with an ideal saturated external kink structure of opposite phase. The centrifugal force linked with the rotation has the effect of displacing the plasma column away from the major axis, but does not alter significantly the magnitude of the edge corrugation of the plasma. Error field correction coil currents in JET-like configurations increase the outer midplane distortions by 2 cm. The edge bootstrap current enhances the edge modulation of the plasma driven by the core snake deformations in MAST.},

keywords = {internal kink, MHD equilibrium, plasma flow},

pubstate = {published},

tppubtype = {article}

}

@article{cooper-2014,

title = {An approximate single fluid 3-dimensional magnetohydrodynamic equilibrium model with toroidal flow},

author = {W A Cooper and S P Hirshman and I T Chapman and D Brunetti and J M Faustin and J P Graves and D Pfefferl\'{e} and M Raghunathan and O Sauter and T M Tran and N Aiba},

url = {http://stacks.iop.org/0741-3335/56/i=9/a=094004},

doi = {10.1088/0741-3335/56/9/094004},

year  = {2014},

date = {2014-08-13},

journal = {Plasma Physics and Controlled Fusion},

volume = {56},

number = {9},

pages = {094004},

abstract = {An approximate model for a single fluid three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium with pure isothermal toroidal flow with imposed nested magnetic flux surfaces is proposed. It recovers the rigorous toroidal rotation equilibrium description in the axisymmetric limit. The approximation is valid under conditions of nearly rigid or vanishing toroidal rotation in regions with significant 3D deformation of the equilibrium flux surfaces. Bifurcated helical core equilibrium simulations of long-lived modes in the MAST device demonstrate that the magnetic structure is only weakly affected by the flow but that the 3D pressure distortion is important. The pressure is displaced away from the major axis and therefore is not as noticeably helically deformed as the toroidal magnetic flux under the subsonic flow conditions measured in the experiment. The model invoked fails to predict any significant screening by toroidal plasma rotation of resonant magnetic perturbations in MAST free boundary computations.},

keywords = {internal kink, MHD equilibrium, plasma flow},

pubstate = {published},

tppubtype = {article}

}

@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}

}

@article{cooper-2013,

title = {Bifurcated helical core equilibrium states in tokamaks},

author = {W A Cooper and I T Chapman and O Schmitz and A D Turnbull and B J Tobias and E A Lazarus and F Turco and M J Lanctot and T E Evans and J P Graves and D Brunetti and D Pfefferl\'{e} and H Reimerdes and O Sauter and F D Halpern and T M Tran and S Coda and B P Duval and Labit B and A Pochelon and M R Turnyanskiy and L Lao and T C Luce and R Buttery and J R Ferron and E M Hollmann and C C Petty and M van Zeeland and M E Fenstermacher and J M Hanson and H L\"{u}tjens},

url = {http://stacks.iop.org/0029-5515/53/i=7/a=073021},

doi = {10.1088/0029-5515/53/7/073021},

year  = {2013},

date = {2013-06-11},

journal = {Nuclear Fusion},

volume = {53},

number = {7},

pages = {073021},

abstract = {Tokamaks with weak to moderate reversed central shear in which the minimum inverse rotational transform (safety factor) qmin is in the neighbourhood of unity can trigger bifurcated magnetohydrodynamic equilibrium states, one of which is similar to a saturated ideal internal kink mode. Peaked prescribed pressure profiles reproduce the 'snake' structures observed in many tokamaks which has led to a novel explanation of the snake as a bifurcated equilibrium state. Snake equilibrium structures are computed in simulations of the tokamak \`{a} configuration variable (TCV), DIII-D and mega amp spherical torus (MAST) tokamaks. The internal helical deformations only weakly modulate the plasma\textendashvacuum interface which is more sensitive to ripple and resonant magnetic perturbations. On the other hand, the external perturbations do not alter the helical core deformation in a significant manner. The confinement of fast particles in MAST simulations deteriorate with the amplitude of the helical core distortion. These three-dimensional bifurcated solutions constitute a paradigm shift that motivates the applications of tools developed for stellarator research in tokamak physics investigations.},

keywords = {helical core, internal kink, MHD equilibrium},

pubstate = {published},

tppubtype = {article}

}