The drift-kinetic code VENUS-LEVIS was designed to simulate a wide variety of physical phenomena related to fast particles in electromagnetic fields.

The code uses a 4th order Runge-Kutta method to solve the single particle equations of motion, either in the guiding-centre approximation or following the full particle orbits. The formulation is independent of coordinate choice and handles 3D time-varying electromagnetic fields.

The interaction with the background plasma as well as ICRH antennas is emulated via Monte-Carlo collision operators. Particle slowing down, pitch angle scattering, anomalous transport and other physical phenomena are modelled using this numerical technique.

VENUS-LEVIS reproduces realistic neutral beam injection distributions via a dedicated module. Coupled to an equilibrium code such as ANIMEC, it is a perfect tool to investigate the effect of 3D magnetic geometry on fast ion transport, for example in stellerators, tokamak helical cores, resonant magnetic perturbations, magnetic ripple, etc…

### Related publications

Muir, Dean; Pfefferlé, David; Qu, Zhisong; Hole, Matthew; Hegland, Markus: Numerical Integration of Particle Orbits in Discontinuous Fields Using VENUS-LEVIS and SPEC. In: Computer Physics Communications, vol. 271, pp. 108191, 2022, ISSN: 0010-4655. (Type: Journal Article | Abstract | Links | BibTeX)@article{muirNumericalIntegrationParticle2022, The orbit code VENUS-LEVIS is adapted to follow particles in plasma equilibria with discontinuous fields generated by the Stepped Pressure Equilibrium Code (SPEC). The latter is an implementation of the Multi-Region relaxed MHD model, which efficiently computes Taylor states in a series of nested toroidal volumes and supports the formation of magnetic islands and chaotic field regions. To adapt VENUS-LEVIS, an event location procedure is implemented in the existing numerical integrator, which ensures the particle sees the correct field along its trajectory, regardless of the discontinuities present in the Stepped Pressure Equilibrium model. The algorithm is tested in the case where the magnetic field is uniform in the upper and lower half-spaces but has a discontinuity in its direction (shear) on the plane z=0. Particle drifts due to the discontinuity are studied. The convergence properties of the numerical scheme are highlighted by the numerical accuracy, and conservation of the system's invariants, such as energy and momentum. Simulations and convergence studies using the SPEC-LEVIS interface in axisymmetric geometry are then presented. Finally, illustrative particle drifts due to the discontinuity are studied and explained: we examine drifts associated with the change in Larmor radius of passing particles with small excursion from flux surfaces. |

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. In: Plasma Physics and Controlled Fusion, vol. 59, no. 12, pp. 124002, 2017. (Type: Journal Article | Abstract | Links | BibTeX)@article{raghunathan-2017, 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 JET-like 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 VENUS-LEVIS, a guiding-center orbit-following code, to follow heavy impurity particles. In this work, VENUS-LEVIS 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. |

Litaudon, X; al.,: Overview of the JET results in support to ITER. In: Nuclear Fusion, vol. 57, no. 10, pp. 102001, 2017. (Type: Journal Article | Abstract | Links | BibTeX)@article{litaudon-2017, The 2014–2016 JET results are reviewed in the light of their significance for optimising the ITER research plan for the active and non-active operation. More than 60 h of plasma operation with ITER first wall materials successfully took place since its installation in 2011. New multi-machine scaling of the type I-ELM 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 fine-scale 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. H-mode 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. |

Lanthaler, S; Pfefferlé, D; Graves, J P; Cooper, W A: Higher order Larmor radius corrections to guiding-centre equations and application to fast ion equilibrium distributions. In: Plasma Physics and Controlled Fusion, vol. 59, no. 4, pp. 044014, 2017. (Type: Journal Article | Abstract | Links | BibTeX)@article{lanthaler-2017, An improved set of guiding-centre equations, expanded to one order higher in Larmor radius than usually written for guiding-centre codes, are derived for curvilinear flux coordinates and implemented into the orbit following code VENUS-LEVIS. Aside from greatly improving the correspondence between guiding-centre and full particle trajectories, the most important effect of the additional Larmor radius corrections is to modify the definition of the guiding-centre's parallel velocity via the so-called Baños drift. The correct treatment of the guiding-centre push-forward with the Baños term leads to an anisotropic shift in the phase-space distribution of guiding-centres, consistent with the well-known magnetization term. The consequence of these higher order terms are quantified in three cases where energetic ions are usually followed with standard guiding-centre equations: (1) neutral beam injection in a MAST-like low aspect-ratio spherical equilibrium where the fast ion driven current is significantly larger with respect to previous calculations, (2) fast ion losses due to resonant magnetic perturbations where a lower lost fraction and a better confinement is confirmed, (3) alpha particles in the ripple field of the European DEMO where the effect is found to be marginal. |

Wenninger, R; al.,: The DEMO wall load challenge. In: Nuclear Fusion, vol. 57, no. 4, pp. 046002, 2017. (Type: Journal Article | Abstract | Links | BibTeX)@article{wenninger-2017, For several reasons the challenge to keep the loads to the first wall within engineering limits is substantially higher in DEMO compared to ITER. Therefore the pre-conceptual design development for DEMO that is currently ongoing in Europe needs to be based on load estimates that are derived employing the most recent plasma edge physics knowledge. An initial assessment of the static wall heat load limit in DEMO infers that the steady state peak heat flux limit on the majority of the DEMO first wall should not be assumed to be higher than 1.0 MW m−2. This compares to an average wall heat load of 0.29 MW m−2 for the design EU-DEMO1 2015 assuming a perfect homogeneous distribution. The main part of this publication concentrates on the development of first DEMO estimates for charged particle, radiation, fast particle (all static) and disruption heat loads. Employing an initial engineering wall design with clear optimization potential in combination with parameters for the flat-top phase (x-point configuration), loads up to 7 MW m−2 (penalty factor for tolerances etc not applied) have been calculated. Assuming a fraction of power radiated from the x-point region between 1/5 and 1/3, peaks of the total power flux density due to radiation of 0.6–0.8 MW m−2 are found in the outer baffle region. This first review of wall loads, and the associated limits in DEMO clearly underlines a significant challenge that necessitates substantial engineering efforts as well as a considerable consolidation of the associated physics basis. |

Faustin, J M; Cooper, W A; Graves, J P; Pfefferlé, D; Geiger, J: ICRH induced particle losses in Wendelstein 7-X. In: Plasma Physics and Controlled Fusion, vol. 58, no. 7, pp. 074004, 2016. (Type: Journal Article | Abstract | Links | BibTeX)@article{faustin-2016b, Fast ions in W7-X will be produced either by neutral beam injection (NBI) or by ion-cyclotron resonant heating (ICRH). The latter presents the advantage of depositing power locally and does not suffer from core accessibility issues (Drevlak et al 2014 Nucl. Fusion 54 073002). This work assesses the possibility of using ICRH as a fast ion source in W7-X relevant conditions. The SCENIC package is used to resolve the full wave propagation and absorption in a three-dimensional plasma equilibrium. The source of the ion-cyclotron range of frequency (ICRF) wave is modelled in this work by an antenna formulation allowing its localisation in both the poloidal and toroidal directions. The actual antenna dimension and localization is therefore approximated with good agreement. The local wave deposition breaks the five-fold periodicity of W7-X. It appears that generation of fast ions is hindered by high collisionality and significant particle losses. The particle trapping mechanism induced by ICRH is found to enhance drift induced losses caused by the finite orbit width of trapped particles. The inclusion of a neoclassically resolved radial electric field is also investigated and shows a significant reduction of particle losses. |

Faustin, J M; Cooper, W A; Geiger, J; Graves, J P; Pfefferlé, D: Applications of the SCENIC code package to the minority ion-cyclotron heating in Wendelstein 7-X plasmas. In: AIP Conference Proceedings, pp. 060003, 2015. (Type: Inproceedings | Abstract | Links | BibTeX)@inproceedings{faustin-2015, 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 five-fold periodicity of the system. We assess the heat transfer through the toroidal periods via Coulomb collisions. |

Pfefferlé, D: Energetic ion dynamics and confinement in 3D saturated MHD configurations. Swiss Institute of Technology Lausanne (EPFL), 2015. (Type: PhD Thesis | Abstract | Links | BibTeX)@phdthesis{pfefferle-thesis, In the following theoretical and numerically oriented work, a number of findings have been assembled. The newly devised VENUS-LEVIS code, designed to accurately solve the motion of energetic particles in the presence of 3D magnetic fields, relies on a non-canonical general coordinate Lagrangian formulation of the guiding-centre and full-orbit equations of motion. VENUS-LEVIS can switch between guiding-centre and full-orbit equations with minimal discrepancy at first order in Larmor radius by verifying the perpendicular variation of magnetic vector field, not only including gradients and curvature terms but also parallel currents and the shearing of field-lines. By virtue of a Fourier representation of the fields in poloidal and toroidal coordinates and a cubic spline in the radial variable, the order of the Runge-Kutta integrating scheme is preserved and convergence of Hamiltonian properties is obtained. This interpolation scheme is crucial to compute orbits over slowing-down times, as well as to mitigate the singularity of the magnetic axis in toroidal flux coordinate systems. Three-dimensional saturated MHD states are associated with many tokamak phenomena including snakes and LLMs in spherical or more conventional tokamaks, and are inherent to stellarator devices. The VMEC equilibrium code conveniently reproduces such 3D magnetic configurations. Slowing-down simulations of energetic ions from NBI predict off-axis deposition of particles during LLM MHD activity in hybrid-like plasmas of the MAST. Co-passing particles helically align in the opposite side of the plasma deformation, whereas counter-passing and trapped particles are less affected by the presence of a helical core. Qualitative agreement is found against experimental measurements of the neutron emission. Two opposing approaches to include RMPs in fast ion simulations are compared, one where the vacuum field caused by the RMP current coils is added to the axisymmetric MHD equilibrium, the other where the MHD equilibrium includes the plasma response within the 3D deformation of its flux-surfaces. The first model admits large regions of stochastic field-lines that penetrate the plasma without alteration. The second assumes nested flux-surfaces with a single magnetic axis, embedding the RMPs in a 3D saturated ideal MHD state but excluding stochastic field-lines within the last closed flux-surface. Simulations of fast ion populations from NBI are applied to MAST n=3 RMP coil configuration with 4 different activation patterns. At low beam energies, particle losses are dominated by parallel transport due to the stochasticity of the field-lines, whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma as well as drift resonances. |

Pfefferlé, D; Graves, J P; Cooper, W A: Hybrid guiding-centre/full-orbit simulations in non-axisymmetric magnetic geometry exploiting general criterion for guiding-centre accuracy. In: Plasma Physics and Controlled Fusion, vol. 57, no. 5, pp. 054017, 2015. (Type: Journal Article | Abstract | Links | BibTeX)@article{pfefferle-hybrid, To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM). |

Romanelli, F; on behalf of Contributors, JET: Overview of the JET results. In: Nuclear Fusion, vol. 55, no. 10, pp. 104001, 2015. (Type: Journal Article | Abstract | Links | BibTeX)@article{romanelli, Since the installation of an ITER-like 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 day-one tungsten divertor in ITER. Integrated scenarios have been progressed with the re-establishment of long-pulse, high-confinement H-modes 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 ITER-like wall installation have been better characterized towards the development of high fusion yield scenarios in DT. Post-mortem analyses of the plasma-facing 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. |

Pfefferlé, D; Misev, C; Cooper, W A; Graves, J P: Impact of RMP magnetic field simulation models on fast ion losses. In: Nuclear Fusion, vol. 55, no. 1, pp. 012001, 2014. (Type: Journal Article | Abstract | Links | BibTeX)@article{pfefferle-rmp, Two opposing approaches to include resonant magnetic perturbations (RMPs) in fast ion simulations are compared, one where the vacuum field caused by the RMP current coils is added to the axisymmetric MHD equilibrium, the other where the MHD equilibrium includes the plasma response within the 3D deformation of its flux-surfaces. The first model admits large regions of stochastic field-lines that penetrate the plasma without alteration. The second assumes nested flux-surfaces with a single magnetic axis, which excludes stochastic field-lines, and embeds the RMPs within a 3D saturated ideal MHD state. The two descriptions of RMPs have been implemented in the VENUS-LEVIS guiding-centre orbit code. Simulations of fast ion populations resulting from MAST neutral beam injection have been applied to MAST n = 3 RMP coil configuration. At low beam energies, particle losses are dominated by parallel transport due to the stochasticity of the field-lines (vacuum-RMP model), whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma and the resulting drifts (equilibrium-RMP model). |

Faustin, J M; Cooper, W A; Graves, J P; Pfefferlé, D: Modeling of ion-cyclotron resonant heating in Wendelstein 7-X equilibrium. In: Journal of Physics: Conference Series, pp. 012006, 2014. (Type: Inproceedings | Abstract | Links | BibTeX)@inproceedings{faustin-2014, 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 full-wave 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. |

Pfefferlé, D; Cooper, W A; Graves, J P; Misev, C: VENUS-LEVIS and its spline-Fourier interpolation of 3D toroidal magnetic field representation for guiding-centre and full-orbit simulations of charged energetic particles. In: Computer Physics Communications, vol. 185, no. 12, pp. 3127 - 3140, 2014, ISSN: 0010-4655. (Type: Journal Article | Abstract | Links | BibTeX)@article{pfefferle-levis, Curvilinear guiding-centre drift and full-orbit equations of motion are presented as implemented in the VENUS-LEVIS 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 guiding-centre 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 flux-surfaces equilibrium including the RMPs. |

Pfefferlé, D; Graves, J P; Cooper, W A; Misev, C; Chapman, I T; Turnyanskiy, M; Sangaroon, S: NBI fast ion confinement in the helical core of MAST hybrid-like plasmas. In: Nuclear Fusion, vol. 54, no. 6, pp. 064020, 2014. (Type: Journal Article | Abstract | Links | BibTeX)@article{pfefferle-nbi, Energetic ions are found to be transported strongly from the core of MAST hybrid-like plasmas during long-lived mode (LLM) magnetohydrodynamic activity. The resulting impact on the neutral beam ion deposition and concurrent current drive is modelled using the guiding-centre approximation in the internal kinked magnetic topology. General coordinate guiding-centre equations are extended for this purpose. It is found that the kinked core spirals around the position of strongest ionization, which remains geometrically centred, so that a large fraction of the population is deposited in the high shear external region where the plasma is almost axisymmetric. Those particles ionized in the low shear region exhibit exotic drift motion due to the strongly non-axisymmetric equilibrium, periodically passing near the magnetic axis and then reflected by the boundary of the kinked equilibrium, which in this respect acts as a confining pinch. Broad agreement is found against experimental measurement of fast ion particle confinement degradation as the MAST LLM amplitude varies. |

Pfefferlé, D; Graves, J P; Cooper, W A: Exploitation of a general-coordinate guiding centre code for the redistribution of fast ions in deformed hybrid tokamak equilibria. In: Journal of Physics: Conference Series, pp. 012020, 2012. (Type: Inproceedings | Abstract | Links | BibTeX)@inproceedings{pfefferle-first, Self-consistent fast ion distributions are usually obtained using a code that solves the guiding-centre equations, with an appropriate fast ion source (e.g. NBI pinis) and sink (e.g. collision operators). Straight field-line coordinate systems, such as Boozer coordinates, are ordinarily convenient due to the simple separation of longitudinal and cross-field motion, and the simple expression of magnetic differential operators. However, these coordinates are found to be near-singular 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 long-lived 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 Particle-In-Cell (PIC) code VENUS-LEVIS, which has been upgraded with phase-space Lagrangian guiding-centre 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 long-lived 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. |