2019 

35.  Pfefferlé, D; Noakes, L; Zhou, Y Rigidity of MHD equilibria to smooth incompressible ideal motion near resonant surfaces Journal Article Forthcoming Forthcoming. Abstract  Links  BibTeX  Tags: Hamiltonian, MHD equilibrium, resonant surfaces @article{pfefferlerigidity, title = {Rigidity of MHD equilibria to smooth incompressible ideal motion near resonant surfaces}, author = {D Pfefferlé and L Noakes and Y Zhou}, url = {https://arxiv.org/abs/1910.01767}, year = {2019}, date = {20191004}, abstract = {In ideal MHD, the magnetic flux is advected by the plasma motion, freezing fluxsurfaces 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 HahmKulsrudTaylor (HKT) problem, which highlights the resonant behaviour near a rational layer formed by a set of degenerate critical points in the fluxfunction. When trying to retain the mirror symmetry of the fluxfunction with respect to the resonant layer, the vector field that generates the volumepreserving diffeomorphism vanishes at the identity to all order in the timelike path parameter.}, keywords = {Hamiltonian, MHD equilibrium, resonant surfaces}, pubstate = {forthcoming}, tppubtype = {article} } In ideal MHD, the magnetic flux is advected by the plasma motion, freezing fluxsurfaces 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 HahmKulsrudTaylor (HKT) problem, which highlights the resonant behaviour near a rational layer formed by a set of degenerate critical points in the fluxfunction. When trying to retain the mirror symmetry of the fluxfunction with respect to the resonant layer, the vector field that generates the volumepreserving diffeomorphism vanishes at the identity to all order in the timelike path parameter. 
34.  Pfefferlé, D; Noakes, L Gauge freedom in magnetostatics and the effect on helicity in toroidal volumes Journal Article Forthcoming Forthcoming. Abstract  Links  BibTeX  Tags: cohomology, gauge freedom, helicity, MHD equilibrium @article{pfefferlehelicity, title = {Gauge freedom in magnetostatics and the effect on helicity in toroidal volumes}, author = {D Pfefferlé and L Noakes}, url = {https://arxiv.org/abs/1909.02723}, year = {2019}, date = {20190909}, publisher = {Cornell University, Ithaca, NY}, abstract = {Magnetostatics defines a class of boundary value problems in which the topology of the domain plays a subtle role. For example, representability of a divergencefree field as the curl of a vector potential comes about because of homological considerations. With this in mind, we study gaugefreedom in magnetostatics and its effect on the comparison between magnetic configurations through key quantities such as the magnetic helicity. For this, we apply the Hodge decomposition of kforms on compact orientable Riemaniann manifolds with smooth boundary, as well as de Rham cohomology, to the representation of magnetic fields through potential 1forms in toroidal volumes. An advantage of the homological approach is the recovery of classical results without explicit coordinates and assumptions about the fields on the exterior of the domain. In particular, a detailed construction of a minimal gauge and a formal proof of relative helicity formulae are presented.}, keywords = {cohomology, gauge freedom, helicity, MHD equilibrium}, pubstate = {forthcoming}, tppubtype = {article} } Magnetostatics defines a class of boundary value problems in which the topology of the domain plays a subtle role. For example, representability of a divergencefree field as the curl of a vector potential comes about because of homological considerations. With this in mind, we study gaugefreedom in magnetostatics and its effect on the comparison between magnetic configurations through key quantities such as the magnetic helicity. For this, we apply the Hodge decomposition of kforms on compact orientable Riemaniann manifolds with smooth boundary, as well as de Rham cohomology, to the representation of magnetic fields through potential 1forms in toroidal volumes. An advantage of the homological approach is the recovery of classical results without explicit coordinates and assumptions about the fields on the exterior of the domain. In particular, a detailed construction of a minimal gauge and a formal proof of relative helicity formulae are presented. 
33.  Pfefferlé, D; Ranjan, D; Abarzhi, S I Whittle Maximum Likelihood Estimate of spectral properties of RayleighTaylor interfacial mixing using hotwire anemometry experimental data Journal Article Forthcoming Forthcoming. Abstract  Links  BibTeX  Tags: data analysis, maximum likelihood estimator, power spectrum, RayleighTaylor flow, whittle approximation @article{pfefferlewhittle, title = {Whittle Maximum Likelihood Estimate of spectral properties of RayleighTaylor interfacial mixing using hotwire anemometry experimental data}, author = {D Pfefferlé and D Ranjan and S I Abarzhi}, url = {https://arxiv.org/abs/1908.03977}, year = {2019}, date = {20190812}, publisher = {ACOUSTICAL SOC AMER AMER INST PHYSICS}, abstract = {The RayleighTaylor instability (RTI) occurs in a broad range of processes in nature and technology. Analysing the power density spectrum of fluctuations in RayleighTaylor (RT) flow is a means of highlighting characteristic length and timescales, anisotropies and anomalous processes. Raw time series from hotwire anemometry measurements of RayleighTaylor interfacial mixing experiment by Akula et al., JFM 816, 619660 (2017) are considered as a sample case to adjust the parameters of a model power density spectrum. The results suggest that the power density spectrum of one of the flow components can be confidently modelled as the product of a power law and an exponential. The data analysis is based on Whittle's approximation of the power density spectrum for independent zeromean nearGaussian signals to construct a Maximum likelihood Estimator (MLE) of the parameters. Those that maximise the loglikelihood are computed numerically through NewtonRaphson iteration. The Hessian of the loglikelihood is used to evaluate the Fisher information matrix and provide an estimate of the statistical error on the obtained parameters. The KolmogorovSmirnov test is used to verify the hypothesis that the ratio between the observed periodogram and the estimated power density spectrum follows a chisquared probability distribution. This step is performed to show goodnessoffit. We also study the dependence of the model parameters on the range of mode numbers over which the fit is performed.}, keywords = {data analysis, maximum likelihood estimator, power spectrum, RayleighTaylor flow, whittle approximation}, pubstate = {forthcoming}, tppubtype = {article} } The RayleighTaylor instability (RTI) occurs in a broad range of processes in nature and technology. Analysing the power density spectrum of fluctuations in RayleighTaylor (RT) flow is a means of highlighting characteristic length and timescales, anisotropies and anomalous processes. Raw time series from hotwire anemometry measurements of RayleighTaylor interfacial mixing experiment by Akula et al., JFM 816, 619660 (2017) are considered as a sample case to adjust the parameters of a model power density spectrum. The results suggest that the power density spectrum of one of the flow components can be confidently modelled as the product of a power law and an exponential. The data analysis is based on Whittle's approximation of the power density spectrum for independent zeromean nearGaussian signals to construct a Maximum likelihood Estimator (MLE) of the parameters. Those that maximise the loglikelihood are computed numerically through NewtonRaphson iteration. The Hessian of the loglikelihood is used to evaluate the Fisher information matrix and provide an estimate of the statistical error on the obtained parameters. The KolmogorovSmirnov test is used to verify the hypothesis that the ratio between the observed periodogram and the estimated power density spectrum follows a chisquared probability distribution. This step is performed to show goodnessoffit. We also study the dependence of the model parameters on the range of mode numbers over which the fit is performed. 
32.  Lanthaler, S; Graves, J P; Pfefferlé, D; Cooper, W A Guidingcentre theory for kineticmagnetohydrodynamic modes in strongly flowing plasmas Journal Article Plasma Physics and Controlled Fusion, 61 (7), pp. 074006, 2019. Abstract  Links  BibTeX  Tags: driftkinetic, guidingcentre, MHD, plasma flow @article{lanthaler2019, title = {Guidingcentre theory for kineticmagnetohydrodynamic modes in strongly flowing plasmas}, author = {S Lanthaler and J P Graves and D Pfefferlé and W A Cooper}, url = {https://doi.org/10.1088%2F13616587%2Fab1d21}, doi = {10.1088/13616587/ab1d21}, year = {2019}, date = {20190501}, journal = {Plasma Physics and Controlled Fusion}, volume = {61}, number = {7}, pages = {074006}, publisher = {IOP Publishing}, abstract = {A kineticmagnetohydrodynamic model with kinetic pressure closure is derived from a consistent guidingcentre framework. Higherorder (gyroviscous) corrections to the pressure tensor are derived in complex geometry from a reduced kinetic equation. The proposed model allows for flows of the order of the thermal ion velocity, taking into account important centrifugal effects due to the ExB flow, as well as the effects of diamagnetic flows associated with finite Larmor radius corrections to both ion fluid inertia and long meanfree path contributions. Wave–particle interactions, such as toroidal driftresonance, are retained. Furthermore, the linearised model includes a quasineutrality equation, allowing the effects of a parallel electric field to be studied in fast rotating tokamak plasmas.}, keywords = {driftkinetic, guidingcentre, MHD, plasma flow}, pubstate = {published}, tppubtype = {article} } A kineticmagnetohydrodynamic model with kinetic pressure closure is derived from a consistent guidingcentre framework. Higherorder (gyroviscous) corrections to the pressure tensor are derived in complex geometry from a reduced kinetic equation. The proposed model allows for flows of the order of the thermal ion velocity, taking into account important centrifugal effects due to the ExB flow, as well as the effects of diamagnetic flows associated with finite Larmor radius corrections to both ion fluid inertia and long meanfree path contributions. Wave–particle interactions, such as toroidal driftresonance, are retained. Furthermore, the linearised model includes a quasineutrality equation, allowing the effects of a parallel electric field to be studied in fast rotating tokamak plasmas. 
2018 

31.  Hudson, S R; Zhu, C; Pfefferlé, D; Gunderson, L Differentiating the shape of stellarator coils with respect to the plasma boundary Journal Article Physics Letters A, 382 (38), pp. 2732  2737, 2018, ISSN: 03759601. Abstract  Links  BibTeX  Tags: coil design, MHD equilibrium, stellarator @article{hudson2018, title = {Differentiating the shape of stellarator coils with respect to the plasma boundary}, author = {S R Hudson and C Zhu and D Pfefferlé and L Gunderson}, doi = {https://doi.org/10.1016/j.physleta.2018.07.016}, issn = {03759601}, year = {2018}, date = {20180929}, journal = {Physics Letters A}, volume = {382}, number = {38}, pages = {2732  2737}, abstract = {The task of designing the geometry of a set of currentcarrying 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 quadraticflux. A penalty on the coil length is included to avoid pathological solutions. A simple expression for how the quadraticflux 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 coildesign 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} } The task of designing the geometry of a set of currentcarrying 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 quadraticflux. A penalty on the coil length is included to avoid pathological solutions. A simple expression for how the quadraticflux 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 coildesign 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. 
30.  Pfefferlé, D; Gunderson, L; Hudson, S R; Noakes, L Nonplanar elasticae as optimal curves for the magnetic axis of stellarators Journal Article Physics of Plasmas, 25 (9), pp. 092508, 2018. Abstract  Links  BibTeX  Tags: elastica, eulerlagrange equations, linking number, magnetic axis, nonplanar curves, rotational transform, stellarator, twist, variational problem, writhe @article{pfefferleelastica, title = {Nonplanar elasticae as optimal curves for the magnetic axis of stellarators}, author = {D Pfefferlé and L Gunderson and S R Hudson and L Noakes}, doi = {10.1063/1.5040894}, year = {2018}, date = {20180926}, 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. EulerLagrange equations are derived for finite length threedimensional 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 oneparameter families of closed nonplanar 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 Călugăreanu theorem. A refreshed interpretation of Mercier's formula for the onaxis rotational transform of stellarator magnetic fieldlines is proposed.}, keywords = {elastica, eulerlagrange equations, linking number, magnetic axis, nonplanar curves, rotational transform, stellarator, twist, variational problem, writhe}, pubstate = {published}, tppubtype = {article} } The problem of finding an optimal curve for the target magnetic axis of a stellarator is addressed. EulerLagrange equations are derived for finite length threedimensional 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 oneparameter families of closed nonplanar 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 Călugăreanu theorem. A refreshed interpretation of Mercier's formula for the onaxis rotational transform of stellarator magnetic fieldlines is proposed. 
29.  Patten, H; Graves, J P; Faustin, J; Cooper, W A; Geiger, J; Pfefferlé, D; Turkin, Y The effect of magnetic equilibrium on auxiliary heating schemes and fast particle confinement in Wendelstein 7X Journal Article Plasma Physics and Controlled Fusion, 60 (8), pp. 085009, 2018. Abstract  Links  BibTeX  Tags: fast particles, heating, MHD equilibrium, stellarator @article{patten2018, title = {The effect of magnetic equilibrium on auxiliary heating schemes and fast particle confinement in Wendelstein 7X}, author = {H Patten and J P Graves and J Faustin and W A Cooper and J Geiger and D Pfefferlé and Y Turkin}, doi = {10.1088/13616587/aac9ee}, year = {2018}, date = {20180601}, 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 7X stellarator: low, standard and high mirror. This numerical work is implemented with the SCENIC code package, which is designed to model threedimensional 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 threedimensional equilibria, the implementation of the realistic beam injector geometry, and the modification of the SCENIC package to permit the investigation of the 3ion species heating scheme, are recent developments. Using these modifications, an assessment of the advantages and disadvantages of these two fastion 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 RFresonant 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 onaxis collisional power deposition, with associated peaked onaxis 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} } 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 7X stellarator: low, standard and high mirror. This numerical work is implemented with the SCENIC code package, which is designed to model threedimensional 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 threedimensional equilibria, the implementation of the realistic beam injector geometry, and the modification of the SCENIC package to permit the investigation of the 3ion species heating scheme, are recent developments. Using these modifications, an assessment of the advantages and disadvantages of these two fastion 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 RFresonant 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 onaxis collisional power deposition, with associated peaked onaxis 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. 
28.  Pfefferlé, D; Ferraro, N; Jardin, S C; Krebs, I; Bhattacharjee, A Modelling of NSTX hot vertical displacement events using M3DC1 Journal Article Physics of Plasmas, 25 (5), pp. 056106, 2018. Abstract  Links  BibTeX  Tags: disruption, M3DC1, resistive MHD, vertical displacement event @article{pfefferlem3dc1, title = {Modelling of NSTX hot vertical displacement events using M3DC1}, author = {D Pfefferlé and N Ferraro and S C Jardin and I Krebs and A Bhattacharjee}, doi = {10.1063/1.5016348}, year = {2018}, date = {20180403}, journal = {Physics of Plasmas}, volume = {25}, number = {5}, pages = {056106}, abstract = {The main results of an intense vertical displacement event (VDE) modelling activity using the implicit 3D extended MHD code M3DC1 are presented. A pair of nonlinear 3D simulations are performed using realistic transport coefficients based on the reconstruction of a socalled NSTX frozen VDE where the feedback control was purposely switched off to trigger a vertical instability. The vertical drift phase is solved assuming axisymmetry until the plasma contacts the first wall, at which point the intricate evolution of the plasma, decaying to large extent in forcebalance with induced halo/wall currents, is carefully resolved via 3D nonlinear simulations. The faster 2D nonlinear runs allow to assess the sensitivity of the simulations to parameter changes. In the limit of perfectly conducting wall, the expected linear relation between vertical growth rate and wall resistivity is recovered. For intermediate wall resistivities, the halo region contributes to slowing the plasma down, and the characteristic VDE time depends on the choice of halo temperature. The evolution of the current quench and the onset of 3D halo/eddy currents are diagnosed in detail. The 3D simulations highlight a rich structure of toroidal modes, penetrating inwards from edge to core and cascading from highn to lown mode numbers. The breakup of fluxsurfaces results in a progressive stochastisation of fieldlines precipitating the thermalisation of the plasma with the wall. The plasma current then decays rapidly, inducing large currents in the halo region and the wall. Analysis of normal currents flowing in and out of the divertor plate reveals rich timevarying patterns.}, keywords = {disruption, M3DC1, resistive MHD, vertical displacement event}, pubstate = {published}, tppubtype = {article} } The main results of an intense vertical displacement event (VDE) modelling activity using the implicit 3D extended MHD code M3DC1 are presented. A pair of nonlinear 3D simulations are performed using realistic transport coefficients based on the reconstruction of a socalled NSTX frozen VDE where the feedback control was purposely switched off to trigger a vertical instability. The vertical drift phase is solved assuming axisymmetry until the plasma contacts the first wall, at which point the intricate evolution of the plasma, decaying to large extent in forcebalance with induced halo/wall currents, is carefully resolved via 3D nonlinear simulations. The faster 2D nonlinear runs allow to assess the sensitivity of the simulations to parameter changes. In the limit of perfectly conducting wall, the expected linear relation between vertical growth rate and wall resistivity is recovered. For intermediate wall resistivities, the halo region contributes to slowing the plasma down, and the characteristic VDE time depends on the choice of halo temperature. The evolution of the current quench and the onset of 3D halo/eddy currents are diagnosed in detail. The 3D simulations highlight a rich structure of toroidal modes, penetrating inwards from edge to core and cascading from highn to lown mode numbers. The breakup of fluxsurfaces results in a progressive stochastisation of fieldlines precipitating the thermalisation of the plasma with the wall. The plasma current then decays rapidly, inducing large currents in the halo region and the wall. Analysis of normal currents flowing in and out of the divertor plate reveals rich timevarying patterns. 
27.  Pfefferlé, D; Bhattacharjee, A Algebraic motion of vertically displacing plasmas Journal Article Physics of Plasmas, 25 (2), pp. 022516, 2018. Abstract  Links  BibTeX  Tags: eddy current, inductance, vertical displacement event @article{pfefferlevdemagneto, title = {Algebraic motion of vertically displacing plasmas}, author = {D Pfefferlé and A Bhattacharjee}, doi = {10.1063/1.5011176}, year = {2018}, date = {20180127}, journal = {Physics of Plasmas}, volume = {25}, number = {2}, pages = {022516}, abstract = {The vertical motion of a tokamak plasma is analytically modelled during its nonlinear phase by a freemoving currentcarrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a nonlinear “sinking” behaviour shown to be algebraic and decelerating. The acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quench dynamics precipitating loss of plasma current.}, keywords = {eddy current, inductance, vertical displacement event}, pubstate = {published}, tppubtype = {article} } The vertical motion of a tokamak plasma is analytically modelled during its nonlinear phase by a freemoving currentcarrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a nonlinear “sinking” behaviour shown to be algebraic and decelerating. The acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quench dynamics precipitating loss of plasma current. 
2017 

26.  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 Plasma Physics and Controlled Fusion, 59 (12), pp. 124002, 2017. Abstract  Links  BibTeX  Tags: fast particles, impurities, neoclassical transport, plasma flow, VENUSLEVIS @article{raghunathan2017, 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 Pfefferlé}, url = {https://iopscience.iop.org/article/10.1088/13616587/aa896f}, doi = {10.1088/13616587/aa896f}, year = {2017}, date = {20171009}, 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 JETlike 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 VENUSLEVIS, a guidingcenter orbitfollowing code, to follow heavy impurity particles. In this work, VENUSLEVIS 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, VENUSLEVIS}, 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 JETlike 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 VENUSLEVIS, a guidingcenter orbitfollowing code, to follow heavy impurity particles. In this work, VENUSLEVIS 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. 
25.  Kazakov, Ye O; al., Efficient generation of energetic ions in multiion plasmas by radiofrequency heating Journal Article Nature Physics, 13 , 2017. Abstract  Links  BibTeX  Tags: fast particles, heating, ion cyclotron resonance @article{kazakov2017, title = {Efficient generation of energetic ions in multiion plasmas by radiofrequency heating}, author = {Ye O Kazakov and al.}, url = {http://dx.doi.org/10.1038/nphys4167}, doi = {10.1038/nphys4167}, year = {2017}, date = {20170619}, journal = {Nature Physics}, volume = {13}, abstract = {We describe a new technique for the efficient generation of highenergy ions with electromagnetic ion cyclotron waves in multiion plasmas. The discussed ‘threeion’ scenarios are especially suited for strong wave absorption by a very low number of resonant ions. To observe this effect, the plasma composition has to be properly adjusted, as prescribed by theory. We demonstrate the potential of the method on the worldlargest plasma magnetic confinement device, JET (Joint European Torus, Culham, UK), and the highmagneticfield tokamak Alcator CMod (Cambridge, USA). The obtained results demonstrate efficient acceleration of 3He ions to high energies in dedicated hydrogen–deuterium mixtures. Simultaneously, effective plasma heating is observed, as a result of the slowingdown of the fast 3He ions. The developed technique is not only limited to laboratory plasmas, but can also be applied to explain observations of energetic ions in spaceplasma environments, in particular, 3Herich solar flares.}, keywords = {fast particles, heating, ion cyclotron resonance}, pubstate = {published}, tppubtype = {article} } We describe a new technique for the efficient generation of highenergy ions with electromagnetic ion cyclotron waves in multiion plasmas. The discussed ‘threeion’ scenarios are especially suited for strong wave absorption by a very low number of resonant ions. To observe this effect, the plasma composition has to be properly adjusted, as prescribed by theory. We demonstrate the potential of the method on the worldlargest plasma magnetic confinement device, JET (Joint European Torus, Culham, UK), and the highmagneticfield tokamak Alcator CMod (Cambridge, USA). The obtained results demonstrate efficient acceleration of 3He ions to high energies in dedicated hydrogen–deuterium mixtures. Simultaneously, effective plasma heating is observed, as a result of the slowingdown of the fast 3He ions. The developed technique is not only limited to laboratory plasmas, but can also be applied to explain observations of energetic ions in spaceplasma environments, in particular, 3Herich solar flares. 
24.  Litaudon, X; al., Overview of the JET results in support to ITER Journal Article Nuclear Fusion, 57 (10), pp. 102001, 2017. Abstract  Links  BibTeX  Tags: fast particles, heating, VENUSLEVIS @article{litaudon2017, title = {Overview of the JET results in support to ITER}, author = {X Litaudon and al.}, url = {https://iopscience.iop.org/article/10.1088/17414326/aa5e28}, doi = {10.1088/17414326/aa5e28}, year = {2017}, date = {20170615}, journal = {Nuclear Fusion}, volume = {57}, number = {10}, pages = {102001}, abstract = {The 2014–2016 JET results are reviewed in the light of their significance for optimising the ITER research plan for the active and nonactive operation. More than 60 h of plasma operation with ITER first wall materials successfully took place since its installation in 2011. New multimachine scaling of the type IELM divertor energy flux density to ITER is supported by first principle modelling. ITER relevant disruption experiments and first principle modelling are reported with a set of three disruption mitigation valves mimicking the ITER setup. Insights of the L–H power threshold in Deuterium and Hydrogen are given, stressing the importance of the magnetic configurations and the recent measurements of finescale structures in the edge radial electric. Dimensionless scans of the core and pedestal confinement provide new information to elucidate the importance of the first wall material on the fusion performance. Hmode plasmas at ITER triangularity (H = 1 at β N ~ 1.8 and n/n GW ~ 0.6) have been sustained at 2 MA during 5 s. The ITER neutronics codes have been validated on high performance experiments. Prospects for the coming D–T campaign and 14 MeV neutron calibration strategy are reviewed.}, keywords = {fast particles, heating, VENUSLEVIS}, pubstate = {published}, tppubtype = {article} } The 2014–2016 JET results are reviewed in the light of their significance for optimising the ITER research plan for the active and nonactive operation. More than 60 h of plasma operation with ITER first wall materials successfully took place since its installation in 2011. New multimachine scaling of the type IELM divertor energy flux density to ITER is supported by first principle modelling. ITER relevant disruption experiments and first principle modelling are reported with a set of three disruption mitigation valves mimicking the ITER setup. Insights of the L–H power threshold in Deuterium and Hydrogen are given, stressing the importance of the magnetic configurations and the recent measurements of finescale structures in the edge radial electric. Dimensionless scans of the core and pedestal confinement provide new information to elucidate the importance of the first wall material on the fusion performance. Hmode plasmas at ITER triangularity (H = 1 at β N ~ 1.8 and n/n GW ~ 0.6) have been sustained at 2 MA during 5 s. The ITER neutronics codes have been validated on high performance experiments. Prospects for the coming D–T campaign and 14 MeV neutron calibration strategy are reviewed. 
23.  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 threeion ICRF heating and fast ion generation scheme for tokamaks and stellarators Journal Article Plasma Physics and Controlled Fusion, 59 (8), pp. 084001, 2017. Abstract  Links  BibTeX  Tags: fast particles, heating, ion cyclotron resonance, neoclassical transport, stellarator @article{faustin2017, title = {Modelling of advanced threeion 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 Pfefferlé and J Geiger and Ye O Kazakov and Van D Eester}, doi = {10.1088/13616587/aa72a4}, year = {2017}, date = {20170613}, journal = {Plasma Physics and Controlled Fusion}, volume = {59}, number = {8}, pages = {084001}, abstract = {Absorption of ioncyclotron 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 7X stellarator. The work presented here assesses the possibility of using the newly developed threeion 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 JETlike plasmas. The RFinduced particle pinch is seen to strongly impact the fast ion pressure profile in particular. Our results show that in typical highdensity W7X plasmas, the threeion species scheme generates more energetic ions than the more traditional minority heating scheme, which makes threeion scenario promising for fastion confinement studies in W7X.}, keywords = {fast particles, heating, ion cyclotron resonance, neoclassical transport, stellarator}, pubstate = {published}, tppubtype = {article} } Absorption of ioncyclotron 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 7X stellarator. The work presented here assesses the possibility of using the newly developed threeion 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 JETlike plasmas. The RFinduced particle pinch is seen to strongly impact the fast ion pressure profile in particular. Our results show that in typical highdensity W7X plasmas, the threeion species scheme generates more energetic ions than the more traditional minority heating scheme, which makes threeion scenario promising for fastion confinement studies in W7X. 
22.  Pfefferlé, D; Hirvijoki, E; Lingam, M Exact collisional moments for plasma fluid theories Journal Article Physics of Plasmas, 24 (4), pp. 042118, 2017. Abstract  Links  BibTeX  Tags: chapmanenskog, collisional moments, collisions, fluid theory, hermite polynomials, nonlinear resistivity @article{pfefferleexact, title = {Exact collisional moments for plasma fluid theories}, author = {D Pfefferlé and E Hirvijoki and M Lingam}, doi = {10.1063/1.4979992}, year = {2017}, date = {20170420}, journal = {Physics of Plasmas}, volume = {24}, number = {4}, pages = {042118}, abstract = {The velocityspace moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multiindex Hermitepolynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two wellknown functions, namely, the RosenbluthMacDonaldJuddTrubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the rootmeansquare of the corresponding thermal velocities and a bilinear dependency on densities and higherorder velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the ChapmanEnskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional tenmoment equations with exact conservation laws for momentum and energytransfer rates.}, keywords = {chapmanenskog, collisional moments, collisions, fluid theory, hermite polynomials, nonlinear resistivity}, pubstate = {published}, tppubtype = {article} } The velocityspace moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multiindex Hermitepolynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two wellknown functions, namely, the RosenbluthMacDonaldJuddTrubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the rootmeansquare of the corresponding thermal velocities and a bilinear dependency on densities and higherorder velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the ChapmanEnskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional tenmoment equations with exact conservation laws for momentum and energytransfer rates. 
21.  Lingam, M; Hirvijoki, E; Pfefferlé, D; Comisso, L; Bhattacharjee, A Nonlinear resistivity for magnetohydrodynamical models Journal Article Physics of Plasmas, 24 (4), pp. 042120, 2017. Abstract  Links  BibTeX  Tags: collisional moments, collisions, fluid theory, hermite polynomials, nonlinear resistivity @article{lingamnonlinear, title = {Nonlinear resistivity for magnetohydrodynamical models}, author = {M Lingam and E Hirvijoki and D Pfefferlé and L Comisso and A Bhattacharjee}, doi = {10.1063/1.4980838}, year = {2017}, date = {20170420}, journal = {Physics of Plasmas}, volume = {24}, number = {4}, pages = {042120}, abstract = {A new formulation of the plasma resistivity that stems from the collisional momentumtransfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocityspace moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentumtransfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the wellestablished electron inertia and Hall terms is also examined. The subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.}, keywords = {collisional moments, collisions, fluid theory, hermite polynomials, nonlinear resistivity}, pubstate = {published}, tppubtype = {article} } A new formulation of the plasma resistivity that stems from the collisional momentumtransfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocityspace moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentumtransfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the wellestablished electron inertia and Hall terms is also examined. The subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection. 
20.  Lanthaler, S; Pfefferlé, D; Graves, J P; Cooper, W A Higher order Larmor radius corrections to guidingcentre equations and application to fast ion equilibrium distributions Journal Article Plasma Physics and Controlled Fusion, 59 (4), pp. 044014, 2017. Abstract  Links  BibTeX  Tags: driftkinetic, guidingcentre, MHD equilibrium, perturbation theory, VENUSLEVIS @article{lanthaler2017, title = {Higher order Larmor radius corrections to guidingcentre equations and application to fast ion equilibrium distributions}, author = {S Lanthaler and D Pfefferlé and J P Graves and W A Cooper}, url = {https://iopscience.iop.org/article/10.1088/13616587/aa5e70}, doi = {10.1088/13616587/aa5e70}, year = {2017}, date = {20170315}, journal = {Plasma Physics and Controlled Fusion}, volume = {59}, number = {4}, pages = {044014}, abstract = {An improved set of guidingcentre equations, expanded to one order higher in Larmor radius than usually written for guidingcentre codes, are derived for curvilinear flux coordinates and implemented into the orbit following code VENUSLEVIS. Aside from greatly improving the correspondence between guidingcentre and full particle trajectories, the most important effect of the additional Larmor radius corrections is to modify the definition of the guidingcentre's parallel velocity via the socalled Baños drift. The correct treatment of the guidingcentre pushforward with the Baños term leads to an anisotropic shift in the phasespace distribution of guidingcentres, consistent with the wellknown magnetization term. The consequence of these higher order terms are quantified in three cases where energetic ions are usually followed with standard guidingcentre equations: (1) neutral beam injection in a MASTlike low aspectratio 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 = {driftkinetic, guidingcentre, MHD equilibrium, perturbation theory, VENUSLEVIS}, pubstate = {published}, tppubtype = {article} } An improved set of guidingcentre equations, expanded to one order higher in Larmor radius than usually written for guidingcentre codes, are derived for curvilinear flux coordinates and implemented into the orbit following code VENUSLEVIS. Aside from greatly improving the correspondence between guidingcentre and full particle trajectories, the most important effect of the additional Larmor radius corrections is to modify the definition of the guidingcentre's parallel velocity via the socalled Baños drift. The correct treatment of the guidingcentre pushforward with the Baños term leads to an anisotropic shift in the phasespace distribution of guidingcentres, consistent with the wellknown magnetization term. The consequence of these higher order terms are quantified in three cases where energetic ions are usually followed with standard guidingcentre equations: (1) neutral beam injection in a MASTlike low aspectratio 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. 
19.  Wenninger, R; al., The DEMO wall load challenge Journal Article Nuclear Fusion, 57 (4), pp. 046002, 2017. Abstract  Links  BibTeX  Tags: confinement, DEMO, fast particles, magnetic ripple, MHD equilibrium, neoclassical transport, perturbation theory, VENUSLEVIS, wall load @article{wenninger2017, title = {The DEMO wall load challenge}, author = {R Wenninger and al.}, url = {https://iopscience.iop.org/article/10.1088/17414326/aa4fb4}, doi = {10.1088/17414326/aa4fb4}, year = {2017}, date = {20170209}, 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 preconceptual 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 EUDEMO1 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 flattop phase (xpoint 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 xpoint 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.}, keywords = {confinement, DEMO, fast particles, magnetic ripple, MHD equilibrium, neoclassical transport, perturbation theory, VENUSLEVIS, 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 preconceptual 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 EUDEMO1 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 flattop phase (xpoint 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 xpoint 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. 
18.  Hirvijoki, E; Brizard, A J; Pfefferlé, D Differential formulation of the gyrokinetic Landau operator Journal Article Journal of Plasma Physics, 83 (1), 2017. Abstract  Links  BibTeX  Tags: collisions, gyrokinetics, rosenbluth potential @article{hirvijoki2017, title = {Differential formulation of the gyrokinetic Landau operator}, author = {E Hirvijoki and A J Brizard and D Pfefferlé}, editor = { }, doi = {10.1017/S0022377816001203}, year = {2017}, date = {20170105}, journal = {Journal of Plasma Physics}, volume = {83}, number = {1}, publisher = {Cambridge University Press}, address = {Cambridge, UK}, abstract = {Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the socalled Landau representation, this paper investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.}, keywords = {collisions, gyrokinetics, rosenbluth potential}, pubstate = {published}, tppubtype = {article} } Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the socalled Landau representation, this paper investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent. 
2016 

17.  Hirvijoki, E; Lingam, M; Pfefferlé, D Fluid moments of the nonlinear Landau collision operator Journal Article Physics of Plasmas, 23 (8), pp. 080701, 2016. Abstract  Links  BibTeX  Tags: collisional moments, collisions, fluid theory, hermite polynomials @article{hirvijoki2016, title = {Fluid moments of the nonlinear Landau collision operator}, author = {E Hirvijoki and M Lingam and D Pfefferlé}, url = {http://dx.doi.org/10.1063/1.4960669}, doi = {10.1063/1.4960669}, year = {2016}, date = {20160809}, journal = {Physics of Plasmas}, volume = {23}, number = {8}, pages = {080701}, abstract = {An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inversesquare force particle dynamics to arbitrary collisionality and flow.}, keywords = {collisional moments, collisions, fluid theory, hermite polynomials}, pubstate = {published}, tppubtype = {article} } An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inversesquare force particle dynamics to arbitrary collisionality and flow. 
16.  Faustin, J M; Cooper, W A; Graves, J P; Pfefferlé, D; Geiger, J Fast particle loss channels in Wendelstein 7X Journal Article Nuclear Fusion, 56 (9), pp. 092006, 2016. Abstract  Links  BibTeX  Tags: fast particles, heating, ion cyclotron resonance, MHD equilibrium, neoclassical transport, neutral beam injection, stellarator @article{faustin2016a, title = {Fast particle loss channels in Wendelstein 7X}, author = {J M Faustin and W A Cooper and J P Graves and D Pfefferlé and J Geiger}, url = {https://iopscience.iop.org/article/10.1088/00295515/56/9/092006}, doi = {10.1088/00295515/56/9/092006}, year = {2016}, date = {20160729}, journal = {Nuclear Fusion}, volume = {56}, number = {9}, pages = {092006}, abstract = {One of the main goals of Wendelstein 7X (W7X) is to demonstrate the fast particle confinement properties of the quasiisodynamic 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 W7X design. Confinement properties of NBI particles in W7X 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 highmirror 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 7X (W7X) is to demonstrate the fast particle confinement properties of the quasiisodynamic 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 W7X design. Confinement properties of NBI particles in W7X 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 highmirror 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. 
15.  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 Nuclear Fusion, 56 (11), pp. 112002, 2016. Abstract  Links  BibTeX  Tags: confinement, DEMO, fast particles, magnetic ripple, MHD equilibrium, neoclassical transport, perturbation theory @article{pfefferledemo, title = {Effects of magnetic ripple on 3D equilibrium and alpha particle confinement in the European DEMO}, author = {D Pfefferlé and W A Cooper and A Fasoli and J P Graves}, url = {https://iopscience.iop.org/article/10.1088/00295515/56/11/112002}, doi = {10.1088/00295515/56/11/112002}, year = {2016}, date = {20160722}, 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 fluxsurfaces and single magnetic axis are obtained with the VMEC freeboundary 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 slowingdown with the VENUSLEVIS orbit code in the guidingcentre approximation. Fast ion losses through the lastclosed fluxsurface are numerically evaluated with two ripple models: (1) using the 3D equilibrium and (2) algebraically adding the nonaxisymmetric ripple perturbation to the 2D equilibrium. By virtue of the small ripple field and its nonresonant nature, both models quantitatively agree. Differences are however noted in the toroidal location of particles losses on the lastclosed fluxsurface, which in the first case is 3D and in the second not. Superbanana transport, i.e. ripplewell 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.}, 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 fluxsurfaces and single magnetic axis are obtained with the VMEC freeboundary 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 slowingdown with the VENUSLEVIS orbit code in the guidingcentre approximation. Fast ion losses through the lastclosed fluxsurface are numerically evaluated with two ripple models: (1) using the 3D equilibrium and (2) algebraically adding the nonaxisymmetric ripple perturbation to the 2D equilibrium. By virtue of the small ripple field and its nonresonant nature, both models quantitatively agree. Differences are however noted in the toroidal location of particles losses on the lastclosed fluxsurface, which in the first case is 3D and in the second not. Superbanana transport, i.e. ripplewell 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. 
14.  Faustin, J M; Cooper, W A; Graves, J P; Pfefferlé, D; Geiger, J ICRH induced particle losses in Wendelstein 7X Journal Article Plasma Physics and Controlled Fusion, 58 (7), pp. 074004, 2016. Abstract  Links  BibTeX  Tags: fast particles, ion cyclotron resonance, MHD equilibrium, neutral beam injection, stellarator, VENUSLEVIS @article{faustin2016b, title = {ICRH induced particle losses in Wendelstein 7X}, author = {J M Faustin and W A Cooper and J P Graves and D Pfefferlé and J Geiger}, url = {https://iopscience.iop.org/article/10.1088/07413335/58/7/074004}, doi = {10.1088/07413335/58/7/074004}, year = {2016}, date = {20160531}, journal = {Plasma Physics and Controlled Fusion}, volume = {58}, number = {7}, pages = {074004}, abstract = {Fast ions in W7X will be produced either by neutral beam injection (NBI) or by ioncyclotron 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 W7X relevant conditions. The SCENIC package is used to resolve the full wave propagation and absorption in a threedimensional plasma equilibrium. The source of the ioncyclotron 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 fivefold periodicity of W7X. 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, VENUSLEVIS}, pubstate = {published}, tppubtype = {article} } Fast ions in W7X will be produced either by neutral beam injection (NBI) or by ioncyclotron 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 W7X relevant conditions. The SCENIC package is used to resolve the full wave propagation and absorption in a threedimensional plasma equilibrium. The source of the ioncyclotron 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 fivefold periodicity of W7X. 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. 
13.  Cooper, W A; Brunetti, D; Duval, B P; Faustin, J M; Graves, J P; Kleiner, A; Patten, H; Pfefferlé, D; Porte, L; Raghunathan, M; Reimerdes, H; Sauter, O; Tran, T M Saturated ideal kink/peeling formations described as threedimensional magnetohydrodynamic tokamak equilibrium states Journal Article Physics of Plasmas, 23 (4), pp. 040701, 2016. Abstract  Links  BibTeX  Tags: internal kink, MHD equilibrium @article{cooper2016, title = {Saturated ideal kink/peeling formations described as threedimensional 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 Pfefferlé and L Porte and M Raghunathan and H Reimerdes and O Sauter and T M Tran}, doi = {10.1063/1.4945743}, year = {2016}, date = {20160406}, journal = {Physics of Plasmas}, volume = {23}, number = {4}, pages = {040701}, abstract = {Free boundary magnetohydrodynamic equilibrium states with spontaneous three dimensional deformations of the plasmavacuum 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 PfirschSchlüter current driving a fieldaligned 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 Hmode operation in shaped tokamak plasmas.}, keywords = {internal kink, MHD equilibrium}, pubstate = {published}, tppubtype = {article} } Free boundary magnetohydrodynamic equilibrium states with spontaneous three dimensional deformations of the plasmavacuum 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 PfirschSchlüter current driving a fieldaligned 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 Hmode operation in shaped tokamak plasmas. 
2015 

12.  Faustin, J M; Cooper, W A; Geiger, J; Graves, J P; Pfefferlé, D Applications of the SCENIC code package to the minority ioncyclotron heating in Wendelstein 7X plasmas Inproceedings AIP Conference Proceedings, pp. 060003, 2015. Abstract  Links  BibTeX  Tags: fast particles, ion cyclotron resonance, stellarator, VENUSLEVIS @inproceedings{faustin2015, title = {Applications of the SCENIC code package to the minority ioncyclotron heating in Wendelstein 7X plasmas}, author = {J M Faustin and W A Cooper and J Geiger and J P Graves and D Pfefferlé}, doi = {10.1063/1.4936501}, year = {2015}, date = {20151210}, booktitle = {AIP Conference Proceedings}, journal = {AIP Conference Proceedings}, volume = {1689}, number = {1}, pages = {060003}, abstract = {We present SCENIC simulations of a W7X 4He plasma with 1% H minority and with an antenna model close to the design foreseen for the W7X ICRF antenna [1, 2]. A high mirror and a standard equilibrium are considered. The injected wave frequency is fixed at 33.8 MHz and 39.6MHz respectively and only fundamental minority heating is considered. Included in this calculation is a new realistic model of the antenna, where it is found that the localization of the antenna geometry tends to break the fivefold periodicity of the system. We assess the heat transfer through the toroidal periods via Coulomb collisions.}, keywords = {fast particles, ion cyclotron resonance, stellarator, VENUSLEVIS}, pubstate = {published}, tppubtype = {inproceedings} } We present SCENIC simulations of a W7X 4He plasma with 1% H minority and with an antenna model close to the design foreseen for the W7X ICRF antenna [1, 2]. A high mirror and a standard equilibrium are considered. The injected wave frequency is fixed at 33.8 MHz and 39.6MHz respectively and only fundamental minority heating is considered. Included in this calculation is a new realistic model of the antenna, where it is found that the localization of the antenna geometry tends to break the fivefold periodicity of the system. We assess the heat transfer through the toroidal periods via Coulomb collisions. 
11.  Cooper, W A; Brunetti, D; Faustin, J M; Graves, J P; Pfefferlé, D; Raghunathan, M; Sauter, O; Tran, T M; Chapman, I T; Ham, C J; Aiba, N; team, The MAST; contributors, JET Free boundary equilibrium in 3D tokamaks with toroidal rotation Journal Article Nuclear Fusion, 55 (6), pp. 063032, 2015. Abstract  Links  BibTeX  Tags: internal kink, MHD equilibrium, plasma flow @article{cooper2015, 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 Pfefferlé 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/00295515/55/i=6/a=063032}, doi = {10.1088/00295515/55/6/063032}, year = {2015}, date = {20150522}, journal = {Nuclear Fusion}, volume = {55}, number = {6}, pages = {063032}, abstract = {The threedimensional 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 longlived modes under free boundary conditions. Helical core solutions are triggered when 〈β〉 exceeds a threshold value, typically 2.7% in JETlike 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 JETlike 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} } The threedimensional 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 longlived modes under free boundary conditions. Helical core solutions are triggered when 〈β〉 exceeds a threshold value, typically 2.7% in JETlike 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 JETlike 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. 
10.  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: driftkinetic, fast particles, guidingcentre, Hamiltonian, internal kink, magnetic ripple, MHD equilibrium, neoclassical transport, neutral beam injection, stellarator, VENUSLEVIS @phdthesis{pfefferlethesis, title = {Energetic ion dynamics and confinement in 3D saturated MHD configurations}, author = {D Pfefferlé}, url = {https://infoscience.epfl.ch/record/207958}, doi = {10.5075/epflthesis6561}, year = {2015}, date = {20150504}, 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 VENUSLEVIS code, designed to accurately solve the motion of energetic particles in the presence of 3D magnetic fields, relies on a noncanonical general coordinate Lagrangian formulation of the guidingcentre and fullorbit equations of motion. VENUSLEVIS can switch between guidingcentre and fullorbit 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 fieldlines. 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 RungeKutta integrating scheme is preserved and convergence of Hamiltonian properties is obtained. This interpolation scheme is crucial to compute orbits over slowingdown times, as well as to mitigate the singularity of the magnetic axis in toroidal flux coordinate systems. Threedimensional 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. Slowingdown simulations of energetic ions from NBI predict offaxis deposition of particles during LLM MHD activity in hybridlike plasmas of the MAST. Copassing particles helically align in the opposite side of the plasma deformation, whereas counterpassing 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 fluxsurfaces. The first model admits large regions of stochastic fieldlines that penetrate the plasma without alteration. The second assumes nested fluxsurfaces with a single magnetic axis, embedding the RMPs in a 3D saturated ideal MHD state but excluding stochastic fieldlines within the last closed fluxsurface. 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 fieldlines, whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma as well as drift resonances.}, keywords = {driftkinetic, fast particles, guidingcentre, Hamiltonian, internal kink, magnetic ripple, MHD equilibrium, neoclassical transport, neutral beam injection, stellarator, VENUSLEVIS}, pubstate = {published}, tppubtype = {phdthesis} } In the following theoretical and numerically oriented work, a number of findings have been assembled. The newly devised VENUSLEVIS code, designed to accurately solve the motion of energetic particles in the presence of 3D magnetic fields, relies on a noncanonical general coordinate Lagrangian formulation of the guidingcentre and fullorbit equations of motion. VENUSLEVIS can switch between guidingcentre and fullorbit 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 fieldlines. 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 RungeKutta integrating scheme is preserved and convergence of Hamiltonian properties is obtained. This interpolation scheme is crucial to compute orbits over slowingdown times, as well as to mitigate the singularity of the magnetic axis in toroidal flux coordinate systems. Threedimensional 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. Slowingdown simulations of energetic ions from NBI predict offaxis deposition of particles during LLM MHD activity in hybridlike plasmas of the MAST. Copassing particles helically align in the opposite side of the plasma deformation, whereas counterpassing 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 fluxsurfaces. The first model admits large regions of stochastic fieldlines that penetrate the plasma without alteration. The second assumes nested fluxsurfaces with a single magnetic axis, embedding the RMPs in a 3D saturated ideal MHD state but excluding stochastic fieldlines within the last closed fluxsurface. 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 fieldlines, whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma as well as drift resonances. 
9.  Pfefferlé, D; Graves, J P; Cooper, W A Hybrid guidingcentre/fullorbit simulations in nonaxisymmetric magnetic geometry exploiting general criterion for guidingcentre accuracy Journal Article Plasma Physics and Controlled Fusion, 57 (5), pp. 054017, 2015. Abstract  Links  BibTeX  Tags: fast particles, fullorbit, guidingcentre, neoclassical transport, neutral beam injection, VENUSLEVIS @article{pfefferlehybrid, title = {Hybrid guidingcentre/fullorbit simulations in nonaxisymmetric magnetic geometry exploiting general criterion for guidingcentre accuracy}, author = {D Pfefferlé and J P Graves and W A Cooper}, url = {http://stacks.iop.org/07413335/57/i=5/a=054017}, doi = {10.1088/07413335/57/5/054017}, year = {2015}, date = {20150415}, journal = {Plasma Physics and Controlled Fusion}, volume = {57}, number = {5}, pages = {054017}, abstract = {To identify under what conditions guidingcentre or fullorbit 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 fieldlines. The criterion is derived for general threedimensional 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 guidingcentre and fullorbit 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 fluxsurfaces 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 offaxis redistribution of neutral beam injection fast particles in the presence of MAST longlived modes (LLM).}, keywords = {fast particles, fullorbit, guidingcentre, neoclassical transport, neutral beam injection, VENUSLEVIS}, pubstate = {published}, tppubtype = {article} } To identify under what conditions guidingcentre or fullorbit 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 fieldlines. The criterion is derived for general threedimensional 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 guidingcentre and fullorbit 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 fluxsurfaces 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 offaxis redistribution of neutral beam injection fast particles in the presence of MAST longlived modes (LLM). 
8.  Romanelli, F; on behalf of Contributors, JET Overview of the JET results Journal Article Nuclear Fusion, 55 (10), pp. 104001, 2015. Abstract  Links  BibTeX  Tags: VENUSLEVIS @article{romanelli, title = {Overview of the JET results}, author = {F Romanelli and JET on behalf of Contributors}, url = {http://stacks.iop.org/00295515/55/i=10/a=104001}, doi = {10.1088/00295515/55/10/104001}, year = {2015}, date = {20150322}, journal = {Nuclear Fusion}, volume = {55}, number = {10}, pages = {104001}, abstract = {Since the installation of an ITERlike wall, the JET programme has focused on the consolidation of ITER design choices and the preparation for ITER operation, with a specific emphasis given to the bulk tungsten melt experiment, which has been crucial for the final decision on the material choice for the dayone tungsten divertor in ITER. Integrated scenarios have been progressed with the reestablishment of longpulse, highconfinement Hmodes by optimizing the magnetic configuration and the use of ICRH to avoid tungsten impurity accumulation. Stationary discharges with detached divertor conditions and small edge localized modes have been demonstrated by nitrogen seeding. The differences in confinement and pedestal behaviour before and after the ITERlike wall installation have been better characterized towards the development of high fusion yield scenarios in DT. Postmortem analyses of the plasmafacing components have confirmed the previously reported low fuel retention obtained by gas balance and shown that the pattern of deposition within the divertor has changed significantly with respect to the JET carbon wall campaigns due to the absence of thermally activated chemical erosion of beryllium in contrast to carbon. Transport to remote areas is almost absent and two orders of magnitude less material is found in the divertor.}, keywords = {VENUSLEVIS}, pubstate = {published}, tppubtype = {article} } Since the installation of an ITERlike wall, the JET programme has focused on the consolidation of ITER design choices and the preparation for ITER operation, with a specific emphasis given to the bulk tungsten melt experiment, which has been crucial for the final decision on the material choice for the dayone tungsten divertor in ITER. Integrated scenarios have been progressed with the reestablishment of longpulse, highconfinement Hmodes by optimizing the magnetic configuration and the use of ICRH to avoid tungsten impurity accumulation. Stationary discharges with detached divertor conditions and small edge localized modes have been demonstrated by nitrogen seeding. The differences in confinement and pedestal behaviour before and after the ITERlike wall installation have been better characterized towards the development of high fusion yield scenarios in DT. Postmortem analyses of the plasmafacing components have confirmed the previously reported low fuel retention obtained by gas balance and shown that the pattern of deposition within the divertor has changed significantly with respect to the JET carbon wall campaigns due to the absence of thermally activated chemical erosion of beryllium in contrast to carbon. Transport to remote areas is almost absent and two orders of magnitude less material is found in the divertor. 
2014 

7.  Pfefferlé, D; Misev, C; Cooper, W A; Graves, J P Impact of RMP magnetic field simulation models on fast ion losses Journal Article Nuclear Fusion, 55 (1), pp. 012001, 2014. Abstract  Links  BibTeX  Tags: fast particles, neutral beam injection, resonant magnetic perturbations, VENUSLEVIS @article{pfefferlermp, title = {Impact of RMP magnetic field simulation models on fast ion losses}, author = {D Pfefferlé and C Misev and W A Cooper and J P Graves}, url = {https://iopscience.iop.org/article/10.1088/00295515/55/1/012001}, doi = {10.1088/00295515/55/1/012001}, year = {2014}, date = {20141219}, 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 fluxsurfaces. The first model admits large regions of stochastic fieldlines that penetrate the plasma without alteration. The second assumes nested fluxsurfaces with a single magnetic axis, which excludes stochastic fieldlines, and embeds the RMPs within a 3D saturated ideal MHD state. The two descriptions of RMPs have been implemented in the VENUSLEVIS guidingcentre 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 fieldlines (vacuumRMP model), whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma and the resulting drifts (equilibriumRMP model).}, keywords = {fast particles, neutral beam injection, resonant magnetic perturbations, VENUSLEVIS}, 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 fluxsurfaces. The first model admits large regions of stochastic fieldlines that penetrate the plasma without alteration. The second assumes nested fluxsurfaces with a single magnetic axis, which excludes stochastic fieldlines, and embeds the RMPs within a 3D saturated ideal MHD state. The two descriptions of RMPs have been implemented in the VENUSLEVIS guidingcentre 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 fieldlines (vacuumRMP model), whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma and the resulting drifts (equilibriumRMP model). 
6.  Faustin, J M; Cooper, W A; Graves, J P; Pfefferlé, D Modeling of ioncyclotron resonant heating in Wendelstein 7X equilibrium Inproceedings Journal of Physics: Conference Series, pp. 012006, 2014. Abstract  Links  BibTeX  Tags: confinement, fast particles, ion cyclotron resonance, neoclassical transport, stellarator, VENUSLEVIS @inproceedings{faustin2014, title = {Modeling of ioncyclotron resonant heating in Wendelstein 7X equilibrium}, author = {J M Faustin and W A Cooper and J P Graves and D Pfefferlé}, url = {http://stacks.iop.org/17426596/561/i=1/a=012006}, doi = {10.1088/17426596/561/1/012006}, year = {2014}, date = {20141127}, 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 fullwave 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, VENUSLEVIS}, 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 fullwave 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. 
5.  Pfefferlé, D; Cooper, W A; Graves, J P; Misev, C Computer Physics Communications, 185 (12), pp. 3127  3140, 2014, ISSN: 00104655. Abstract  Links  BibTeX  Tags: cubic spline, curvilinear coordinates, fast particles, numerical method, VENUSLEVIS @article{pfefferlelevis, title = {VENUSLEVIS and its splineFourier interpolation of 3D toroidal magnetic field representation for guidingcentre and fullorbit simulations of charged energetic particles}, author = {D Pfefferlé and W A Cooper and J P Graves and C Misev}, doi = {10.1016/j.cpc.2014.08.007}, issn = {00104655}, year = {2014}, date = {20140816}, journal = {Computer Physics Communications}, volume = {185}, number = {12}, pages = {3127  3140}, abstract = {Curvilinear guidingcentre drift and fullorbit equations of motion are presented as implemented in the VENUSLEVIS code. A dedicated interpolation scheme based on Fourier reconstruction in the toroidal and poloidal directions and cubic spline in the radial direction of flux coordinate systems is detailed. This interpolation method exactly preserves the order of the RK4 integrating scheme which is crucial for the investigation of fast particle trajectories in 3D magnetic structures such as helical saturated tokamak plasma states, stellarator geometry and resonant magnetic perturbations (RMP). The initialisation of particles with respect to the guidingcentre is discussed. Two approaches to implement RMPs in orbit simulations are presented, one where the vacuum field is added to the 2D equilibrium, creating islands and stochastic regions, the other considering 3D nested fluxsurfaces equilibrium including the RMPs.}, keywords = {cubic spline, curvilinear coordinates, fast particles, numerical method, VENUSLEVIS}, pubstate = {published}, tppubtype = {article} } Curvilinear guidingcentre drift and fullorbit equations of motion are presented as implemented in the VENUSLEVIS code. A dedicated interpolation scheme based on Fourier reconstruction in the toroidal and poloidal directions and cubic spline in the radial direction of flux coordinate systems is detailed. This interpolation method exactly preserves the order of the RK4 integrating scheme which is crucial for the investigation of fast particle trajectories in 3D magnetic structures such as helical saturated tokamak plasma states, stellarator geometry and resonant magnetic perturbations (RMP). The initialisation of particles with respect to the guidingcentre is discussed. Two approaches to implement RMPs in orbit simulations are presented, one where the vacuum field is added to the 2D equilibrium, creating islands and stochastic regions, the other considering 3D nested fluxsurfaces equilibrium including the RMPs. 
4.  Cooper, W A; Hirshman, S P; Chapman, I T; Brunetti, D; Faustin, J M; Graves, J P; Pfefferlé, D; Raghunathan, M; Sauter, O; Tran, T M; Aiba, N An approximate single fluid 3dimensional magnetohydrodynamic equilibrium model with toroidal flow Journal Article Plasma Physics and Controlled Fusion, 56 (9), pp. 094004, 2014. Abstract  Links  BibTeX  Tags: internal kink, MHD equilibrium, plasma flow @article{cooper2014, title = {An approximate single fluid 3dimensional 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 Pfefferlé and M Raghunathan and O Sauter and T M Tran and N Aiba}, url = {http://stacks.iop.org/07413335/56/i=9/a=094004}, doi = {10.1088/07413335/56/9/094004}, year = {2014}, date = {20140813}, journal = {Plasma Physics and Controlled Fusion}, volume = {56}, number = {9}, pages = {094004}, abstract = {An approximate model for a single fluid threedimensional (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 longlived 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} } An approximate model for a single fluid threedimensional (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 longlived 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. 
3.  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 hybridlike plasmas Journal Article Nuclear Fusion, 54 (6), pp. 064020, 2014. Abstract  Links  BibTeX  Tags: confinement, fast particles, guidingcentre, internal kink, MHD equilibrium, neoclassical transport, neutral beam injection, VENUSLEVIS @article{pfefferlenbi, title = {NBI fast ion confinement in the helical core of MAST hybridlike plasmas}, author = {D Pfefferlé 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/10.1088/00295515/54/6/064020}, doi = {10.1088/00295515/54/6/064020}, year = {2014}, date = {20140523}, journal = {Nuclear Fusion}, volume = {54}, number = {6}, pages = {064020}, abstract = {Energetic ions are found to be transported strongly from the core of MAST hybridlike plasmas during longlived mode (LLM) magnetohydrodynamic activity. The resulting impact on the neutral beam ion deposition and concurrent current drive is modelled using the guidingcentre approximation in the internal kinked magnetic topology. General coordinate guidingcentre 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 nonaxisymmetric 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, guidingcentre, internal kink, MHD equilibrium, neoclassical transport, neutral beam injection, VENUSLEVIS}, pubstate = {published}, tppubtype = {article} } Energetic ions are found to be transported strongly from the core of MAST hybridlike plasmas during longlived mode (LLM) magnetohydrodynamic activity. The resulting impact on the neutral beam ion deposition and concurrent current drive is modelled using the guidingcentre approximation in the internal kinked magnetic topology. General coordinate guidingcentre 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 nonaxisymmetric 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. 
2013 

2.  Cooper, W A; Chapman, I T; Schmitz, O; Turnbull, A D; Tobias, B J; Lazarus, E A; Turco, F; Lanctot, M J; Evans, T E; Graves, J P; Brunetti, D; Pfefferlé, D; Reimerdes, H; Sauter, O; Halpern, F D; Tran, T M; Coda, S; Duval, B P; B, Labit; Pochelon, A; Turnyanskiy, M R; Lao, L; Luce, T C; Buttery, R; Ferron, J R; Hollmann, E M; Petty, C C; van Zeeland, M; Fenstermacher, M E; Hanson, J M; Lütjens, H Bifurcated helical core equilibrium states in tokamaks Journal Article Nuclear Fusion, 53 (7), pp. 073021, 2013. Abstract  Links  BibTeX  Tags: helical core, internal kink, MHD equilibrium @article{cooper2013, 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 Pfefferlé 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 Lütjens}, url = {http://stacks.iop.org/00295515/53/i=7/a=073021}, doi = {10.1088/00295515/53/7/073021}, year = {2013}, date = {20130611}, 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 à configuration variable (TCV), DIIID and mega amp spherical torus (MAST) tokamaks. The internal helical deformations only weakly modulate the plasma–vacuum 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 threedimensional 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} } 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 à configuration variable (TCV), DIIID and mega amp spherical torus (MAST) tokamaks. The internal helical deformations only weakly modulate the plasma–vacuum 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 threedimensional bifurcated solutions constitute a paradigm shift that motivates the applications of tools developed for stellarator research in tokamak physics investigations. 
2012 

1.  Pfefferlé, D; Graves, J P; Cooper, W A Journal of Physics: Conference Series, pp. 012020, 2012. Abstract  Links  BibTeX  Tags: fast particles, helical core, internal kink, MHD equilibrium, VENUSLEVIS @inproceedings{pfefferlefirst, title = {Exploitation of a generalcoordinate guiding centre code for the redistribution of fast ions in deformed hybrid tokamak equilibria}, author = {D Pfefferlé and J P Graves and W A Cooper}, url = {http://stacks.iop.org/17426596/401/i=1/a=012020}, doi = {10.1088/17426596/401/1/012020}, year = {2012}, date = {20121203}, booktitle = {Journal of Physics: Conference Series}, journal = {Journal of Physics: Conference Series}, volume = {401}, number = {1}, pages = {012020}, abstract = {Selfconsistent fast ion distributions are usually obtained using a code that solves the guidingcentre equations, with an appropriate fast ion source (e.g. NBI pinis) and sink (e.g. collision operators). Straight fieldline coordinate systems, such as Boozer coordinates, are ordinarily convenient due to the simple separation of longitudinal and crossfield motion, and the simple expression of magnetic differential operators. However, these coordinates are found to be nearsingular at the boundary of the internal helical region associated with an n = m = 1 infernal mode. These important configurations are associated with many tokamak phenomena, including snakes and longlived modes [1] in spherical or more conventional devices. Such internal helical states occur when there is a radially extended region where the safety factor is close to unity. Recent calculations predict the possibility of helical equilibria in ITER hybrid scenarios [2]. The ANIMEC code [3] conveniently produces an equilibrium helical state despite choosing for example an axisymmetric fixed boundary. The corresponding magnetic field in these coordinates can now be fed to the newly devised ParticleInCell (PIC) code VENUSLEVIS, which has been upgraded with phasespace Lagrangian guidingcentre orbit equations [4], embodying full 3D anisotropic electromagnetic fields and a formulation that is independent of coordinate choice, despite retaining intrinsic Hamiltonian properties. The simulations are applied to MAST experiments where the presence of a longlived mode can effect confinement of neutral beam ions, potentially affecting NBI heating and current drive [1]. Neighbouring equilibria from ANIMEC, one helical in the core and the other axisymmetic, permits a precise means of identifying the effect of 3D geometry on the simulated confinement properties of MAST's neutral beam fast ion population. In agreement with the compared experimental data from MAST neutron camera, a significant fraction of particles are pushed out of the helical core region affecting both the measured radial neutron distribution and the heating and current drive properties of the neutral beam population.}, keywords = {fast particles, helical core, internal kink, MHD equilibrium, VENUSLEVIS}, pubstate = {published}, tppubtype = {inproceedings} } Selfconsistent fast ion distributions are usually obtained using a code that solves the guidingcentre equations, with an appropriate fast ion source (e.g. NBI pinis) and sink (e.g. collision operators). Straight fieldline coordinate systems, such as Boozer coordinates, are ordinarily convenient due to the simple separation of longitudinal and crossfield motion, and the simple expression of magnetic differential operators. However, these coordinates are found to be nearsingular at the boundary of the internal helical region associated with an n = m = 1 infernal mode. These important configurations are associated with many tokamak phenomena, including snakes and longlived modes [1] in spherical or more conventional devices. Such internal helical states occur when there is a radially extended region where the safety factor is close to unity. Recent calculations predict the possibility of helical equilibria in ITER hybrid scenarios [2]. The ANIMEC code [3] conveniently produces an equilibrium helical state despite choosing for example an axisymmetric fixed boundary. The corresponding magnetic field in these coordinates can now be fed to the newly devised ParticleInCell (PIC) code VENUSLEVIS, which has been upgraded with phasespace Lagrangian guidingcentre orbit equations [4], embodying full 3D anisotropic electromagnetic fields and a formulation that is independent of coordinate choice, despite retaining intrinsic Hamiltonian properties. The simulations are applied to MAST experiments where the presence of a longlived mode can effect confinement of neutral beam ions, potentially affecting NBI heating and current drive [1]. Neighbouring equilibria from ANIMEC, one helical in the core and the other axisymmetic, permits a precise means of identifying the effect of 3D geometry on the simulated confinement properties of MAST's neutral beam fast ion population. In agreement with the compared experimental data from MAST neutron camera, a significant fraction of particles are pushed out of the helical core region affecting both the measured radial neutron distribution and the heating and current drive properties of the neutral beam population. 