21st European Fusion Theory Conference

Sep 23, 2025, 7:45 AM → Sep 26, 2025, 6:00 PM Europe/Zurich

Aix-en-Provence

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Tue, September 23

7:45 AM → 8:15 AM Registration

8:15 AM → 8:30 AM Welcome

8:30 AM → 9:20 AM I.1-Barabaschi: Status of the ITER project

Speaker: Dr Pietro Barabaschi (Iter)

9:20 AM → 10:00 AM I.5-Zarzoso: Energetic particle transport in theory, modelling and experiments in magnetically confined plasmas

Speaker: David Zarzoso (CNRS, Aix-Marseille Université)

10:00 AM → 10:25 AM O.1-Grondin-Exbrayat: Numerical Investigation of Fishbone Phase-space Nonlinear Dynamic : Impact of the MHD Nonlinear Effects

Understanding the dynamics of Energetic Particles (EPs) is essential for optimizing the perfor- mance of fusion devices. EPs serve as the primary energy carriers in fusion plasmas, and their loss due to transport from the core to the edge results in a significant reduction in efficiency of the fusion device. One of the key phenomena driving the EPs transport is the precessional fishbone instability[1].
The precessional fishbone instability is a kinetic instability driven by the destabilization of a magnetohydrodynamic (MHD) mode due to an EP gradient [2].
In this work, we present a numerical study of the precessional fishbone instability using a sim- plified 2D phase-space model [3]. The model couples a reduced MHD framework in cylindrical geometry, which describes the thermal plasma, with a kinetic description of trapped energetic particles. This study builds on the reduced MHD code AMON [4], to which we have added a gyro- and bounce-averaged Vlasov equation for the EPs.
We investigate the resonant interaction between particles and fields, which drives the nonlinear evolution of the EPs gradient, leading to their transport [5]. The question addressed in this study concerns the impact of MHD nonlinearities on the saturation level and the evolution of the mode frequency. While the linear phase of the fishbone instability is relatively well understood [3, 6], our work aims to investigate how MHD nonlinearities influence the level of saturation by preserving the resonant condition thus modifying the frequency chirping behavior [5], which are directly linked to the nature of EPs transport [7].

[1] R.B. White, et al., Physical review letters 62, 539 (1989)
[2] L. Chen, et al., Physics of Plasmas 7, 1519-1522 (1994)
[3] M. Idouakass, et al., Physics of Plasmas 23, 102113 (2016)
[4] A. Poye, et al., Plasmas Physics and Controlled Fusion 56, 125005 (2014) [5] L. Chen, et al., Reviews of Modern Physics 88, 015008 (2016)
[6] A. Fasoli, et al., Nuclear Fusion 47, S264 (2007) [7] F. Zonca, et al., Nuclear Fusion 45, 477 (2005)

Speaker: Alodie Grondin-Exbrayat (Aix-Marseille Université, CNRS, PIIM UMR7345, Marseille, France)

10:25 AM → 10:50 AM Coffee break

10:50 AM → 11:30 AM I.6-Brochard: Transformation of energetic particle distributions into constants of motion coordinates for realistic simulations of EP-driven modes, and application to Alfvén eigenmodes stability in DIII-D plasmas

Speaker: Guillaume Brochard (CEA Cadarache)

11:30 AM → 11:55 AM 0.2-Votta: Runaway electron dynamics in ITER shattered pellet injection mitigated disruptions

Disruptions represent a critical challenge to the safe and reliable operation of future fusion devices like ITER, as they impose severe thermal and mechanical loads on the tokamak structure and generate high-energy runaway electrons (REs). This study expands on the work of [Vallhagen et al, Nucl. Fusion 64 (2024)] and presents a significant upgrade of the DREAM [1] disruption simulation framework to investigate RE dynamics in ITER disruptions mitigated by Shattered Pellet Injection (SPI). The updated simulations account for four new key physical effects. The scraping-off of REs during Vertical Displacement Events is incorporated via a reduced model which reproduces the RE avalanche
gain of higher-fidelity simulations [2]. The plasmoid drift effect, which affects the deposition location of the injected pellet material, is accounted for via an analytical model which has been validated against experimental data on DIII-D [3]. Additionally, a model for suppressing unphysical thin-current channels during the current quench phase is implemented. The Compton seed generation model has been updated with photon spectra reflecting the new ITER tungsten first-wall design. A wide range of realistic disruption scenarios are explored, including cases with low Neon SPI, scans of radial RE transport under varying magnetic perturbations, and trace tritium concentration scans to assess the impact of tritium beta decay RE source. The analysis of these scenarios guides the design of ITER SPI strategies, supporting the development of effective disruption mitigation techniques for ITER and future fusion devices.

[1] M. Hoppe, O. Embreus, and T. Fülöp, “DREAM: A fluid-kinetic framework
for tokamak disruption runaway electron simulations,” Computer Physics
Communications, vol. 268, p. 108098, 2021. doi: 10.1016/j.cpc.2021.108098.

[2] O. Vallhagen, L. Hanebring, T. Fülöp, M. Hoppe, and I. Pusztai, “Re-
duced modeling of scrape-off losses of runaway electrons during tokamak
disruptions,” arXiv preprint arXiv:2410.03512, 2024. Available: https:
//arxiv.org/abs/2410.03512

[3] O. Vallhagen, I. Pusztai, P. Helander, S. L. Newton, and T. Fülöp, “Drift
of ablated material after pellet injection in a tokamak,” Journal of Plasma
Physics, vol. 89, no. 3, 2023. doi: 10.1017/S0022377823000466.

Speaker: Lorenzo Votta (KTH Royal Institute of Technology)

11:55 AM → 12:20 PM O.3-Edes: Resistive Wall Tearing Modes in View of Natural Disruption Dynamics

Plasma disruption is one of the key factors limiting the stable and safe operation of future large tokamaks. It involves a sudden collapse of the plasma confinement and can cause severe heat loads and electromagnetic forces on surrounding structures. Understanding the chain of events leading to unintentional/natural disruptions remaining a critical goal in the pursuit of sustainable fusion energy [1]. The final phase of a disruption is commonly associated with the growth of magnetohydrodynamic (MHD) instabilities, particularly tearing modes. Recent studies indicated that the finite resistivity of the wall can modify the previously predicted stability boundaries of such modes [2], giving rise to what are termed as Resistive Wall Tearing Modes (RWTMs) [2,3]. If this is the main mechanism that triggers the termination of plasma, then predictions on the thermal quench duration must be revised and adjusted to the RWTM growth rates, which need to be studied in detail.
In order to investigate these effects, we developed a linear solver that accounts for wall resistivity, a feature typically omitted in classical tearing mode analysis. This implementation was based on the methodology shown in [4]. The solver was employed to scan for unstable RWTM scenarios, specifically by varying current profile shapes in large-aspect-ratio equilibria, providing a baseline for nonlinear studies. Subsequently, simulations were carried out using the three-dimensional non-linear MHD code JOREK, coupled with STARWALL. Notably, this work marks the first identification of RWTMs in JOREK–STARWALL simulations. Good agreement was found between the linear solver and the JOREK-STARWALL code results in terms of mode growth rates. Further benchmarking are being performed against the CASTOR3D MHD code. The applicability of these findings are also being tested in a more realistic and experimentally relevant setup. Specifically, the effect of wall resistivity on mode growth are being analyzed with JOREK-STARWALL for a JET disruption case previously studied by Hank Strauss using the M3D code [2]. The sensitivity of the mode growth rate to wall resistivity are being examined, and comparison with previous M3D simulations will be discussed.
Our findings offer new insight into the role of RWTMs in disruption dynamics and support the development of improved prediction and mitigation strategies, an essential step toward ensuring the stability and safety of next-generation fusion devices.
References
[1] G. Pucella et al., Nuclear Fusion 61 (2021): 046020
[2] H. Strauss et al., Physics of Plasmas 28 (2021): 032501
[3] H. Strauss et al., Plasma Physics and Controlled Fusion 65 (2023): 084002
[4] J.P. Graves et al., Plasma Physics and Controlled Fusion 64 (2021): 014001

Speaker: Lili Édes (EPFL SPC)

12:20 PM → 1:30 PM Lunch break

1:30 PM → 3:30 PM Poster Session #1

For the Poster list please click on 'Contribution list' down here

1:30 PM Artificial Intelligence surrogate model for accurate long-time plasma turbulence simulations

Turbulent transport represents one of the major topics in plasma physics, especially taking into account its impact on the performance of nuclear fusion devices. However, modelling turbulence requires long-time highly resolved simulations to capture the fine spatial and temporal scales, making it numerically intensive. The use of surrogate models might represent a good compromise between computational cost and physical accuracy. The recent development of Generative Artificial Intelligence (AI) has brought up new perspectives in this regard, with the ability to avoid solving all spatiotemporal scales. We present here the GAIT model [1,2], for Generative Artificial Intelligence Turbulence, based on the combination of two machine learning models, able to efficiently generate long-time turbulent simulations after being trained on a short simulation. A convolutional variational autoencoder (CVAE) serves as a strong dimensionality reduction tool and creates a meaningful and structured representation of turbulence in a reduced dimensionality space called latent space. Then, a recurrent neural network is trained to learn and reproduce the time evolution of the representation of the turbulent state in the latent space. The low dimension of the latent space allows for the generation process to be very efficient, and the parallelization capability of the CVAE allows to reconstruct the real turbulent evolution from the latent space trajectory. As a proof of concept, we apply this new method to a 2D fluid model of drift wave turbulence: the Hasegawa-Wakatani model [3]. A series of quantitative tests, based on both Eulerian and Lagrangian metrics, are applied to the AI generated turbulence to demonstrate the excellent fidelity of the AI surrogate model. We show that our GAIT model successfully reproduces the characteristics of the turbulence, ranging from Fourier spectra comparisons to particle transport analyses, exhibiting an acceleration factor of 400 with respect to standard numerical techniques. The versatility, fidelity and acceleration capability of the GAIT model position our approach as a strong candidate to produce surrogate models in high-dimensional turbulence applications for fusion plasmas.
References:
[1] Clavier, B., Zarzoso, D., del-Castillo-Negrete, D., & Frénod, E. (2025). Generative-machine-learning surrogate model of plasma turbulence. Physical Review E, 111(1), L013202.
[2] Clavier, B., Zarzoso, D., del-Castillo-Negrete, D., & Frénod, E. (under review). A Generative Artificial Intelligence framework for long-time plasma turbulence simulations. Physics of Plasmas.
[3] Hasegawa, A., & Wakatani, M. (1983). Plasma edge turbulence. Physical Review Letters, 50(9), 682.

Speaker: Benoit Clavier (AMU M2P2)

1:30 PM Avalanche source in a 3D hybrid fluid-kinetic model of runaway electrons in tokamaks

Disruptions, i.e. major instabilities in which plasma confinement is lost, are a significant threat to tokamak operation. During a disruption, the resistivity of the plasma increases as the thermal energy is quickly lost, causing the current to decrease. Due to the self-inductance of the plasma this leads to the generation of a strong parallel electric field. As the friction force experienced by fast electrons in a plasma has the peculiarity that it decreases with increasing electron velocity, this electric field can accelerate some fast electrons to relativistic velocities. These so-called runaway electrons (REs) can exponentially multiply due to large-angle collisions with thermal electrons in what is known as the runaway avalanche. Because the avalanche is exponentially sensitive to the pre-disruption plasma current, this can lead to multi-MA RE beams in large future devices such as ITER and may cause severe localized wall damage. Simulations including the RE sources in realistic 3D fields are needed to further the understanding of RE generation and losses and develop viable mitigation scenarios.
The 3D nonlinear MHD code JOREK [1] contains a hybrid fluid-kinetic model that describes the REs with a full-f relativistic particle in cell (PiC) approach using either full-orbit [2] or drift kinetic RE descriptions [3]. We present the status of including the avalanche source in this model. The implementation of the avalanche source consists of a relativistic large-angle collision operator along with a periodic resampling of the markers to limit their number while the number of REs grows exponentially. This implementation was benchmarked [4] against analytical expressions from literature [5] and good agreement was found when applying the same cut-off momentum for the large-angle collisions. Present work concentrates on accurate conservation properties in the resampling, performance optimizations to overcome the large time scale separations of the involved processes, and on first applications to 3D RE beam termination scenarios and possible re-avalanching.

[1] M. Hoelzl, G.T.A. Huijsmans et al. The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas. Nuclear Fusion, 61(6), 2021.

[2] H. Bergström, S-J Liu et al. Introduction of a 3D global non-linear full-f particle-in-cell model for runaway electrons in JOREK. Plasma Physics and Controlled Fusion, 67(3):035004, 2025.

[3] S-J Liu, T Liu, H. Bergström, H-W Zhang, M. Hoelzl, JOREK Team. Hybrid fluid-kinetic simulations of resistive instabilities in runaway electron beams (in preparation)

[4] F. Wouters. Implementation and validation of the avalanche source for a 3D kinetic model of relativistic electrons during disruptions. Master’s thesis, Technical University of Eindhoven, June 2024. Available at https://research.tue.nl/en/studentTheses/implementation-and-validation-of-the-avalanche-source-for-a-3d-ki.

[5] P. Aleynikov and B. N. Breizman. Theory of two threshold fields for relativistic runaway electrons. Physical Review Letters, 114(15):1-5, 2015.

Speaker: Fiona Wouters (Max-Planck-Institute for Plasma Physics, Garching)

1:30 PM Criterion for significant runaway electron generation in activated devices

A disrupting plasma in a high-performance device such as ITER and SPARC may generate
large runaway electron (RE) currents that, upon impact with the tokamak wall, can cause
serious damage to the device. To quickly identify regions of safe operation in parameter
space, it is useful to develop reduced models and analytical criteria that predict when a
significant fraction of the Ohmic current is converted into a current of runaway electrons.
Such models have previously been developed for Dreicer [1,2] and hot-tail [3] seed currents.
In DT experiments however, the contributions to the seed current from tritium decay and
Compton scattering may also be significant or even dominant. In this work, we extend
previous work and develop a semi-analytic criterion that includes seed currents from tritium
decay and Compton scattering. In addition, the avalanche multiplication factor includes
effects of partial screening of injected noble gasses [4]. The result is a semi-analytic model
that can predict significant RE generation in the next generation of activated devices and is
suitable for integrated modeling. The model is validated by fluid simulations using DREAM
[5] and is shown to delineate regions in parameter space of significant runaway generation.
[1] P Helander, L-G Eriksson and F Andersson (2002). Runaway acceleration during magnetic
reconnection in tokamaks. Plasma Phys. Control. Fusion 44, B247–B262
[2] H Smith, P Helander, L-G Eriksson, D Anderson, M Lisak and F Andersson (2006).
Runaway electrons and the evolution of the plasma current in tokamak disruptions. Phys.
Plasmas 13, 102502
[3] T Fülöp, H M Smith and G Pokol (2009). Magnetic field threshold for runaway generation
in tokamak disruptions. Phys. Plasmas 16, 022502
[4] L Hesslow, O Embréus, O Vallhagen and T Fülöp (2019). Influence of massive material
injection on avalanche runaway generation during tokamak disruptions. Nucl. Fusion 59,
084004
[5] M Hoppe, O Embréus and T Fülöp (2021). DREAM: a fluid-kinetic framework for
tokamak disruption runaway electron simulations. Comput. Phys. Commun. 268, 108098

Speaker: Dr Björn Zaar (Chalmers University of Technology)

1:30 PM Effect of Aspect Ratio and Simplified Coil Winding Surfaces on Optimized Quasisymmetric Stellarator Configurations

In stellarators, the absence of axisymmetry poses challenges for confinement, as particle orbits are more prone to drift losses. Quasisymmetry [1] offers a pathway to overcome this limitation by optimizing the magnetic field configuration to approximate the favorable confinement of axisymmetric systems. Nevertheless, traditional stellarator designs often involve high aspect ratios and intricate, three-dimensional coil structures lying on complex Coil Winding Surfaces (CWSs) conformal to the plasma boundary. In this study, the impact of the aspect ratio on ideal MHD equilibrium and stability is examined, aiming to insights into compact, high-field stellarator configurations, which, for instance, could be enabled by High Temperature Superconductors [2]. Equilibrium optimization is performed for quasi-helical or quasi-axial symmetry in vacuum, starting from a variety of aspect ratios and number of field periods, under a combination of constraints. Such constraints include the rotational transform, plasma volume, mirror ratio and vacuum well. In addition, the effect of aspect ratio on ideal interchange and ideal ballooning stability is investigated, up to a normalized pressure β~2%. Finally, the reproduction of such configurations by simplified piecewise cylindrical CWSs is explored. This technique can offer a potential alternative to traditional stellarator coil manufacturing, with the possibility of employing laser engraving to create current paths on simplified surfaces [3].

[1] A. H. Boozer (1983) Phys. Fluids 26, 496–499
[2] V. Prost and F. A. Volpe (2024) Nucl. Fusion 64, 026007
[3] D. Pereira Botelho et al. Phys. Rev. Applied, under review (https://arxiv.org/pdf/2409.20143)

Speaker: Achilleas Evangelias (Renaissance Fusion)

1:30 PM Energetic-particle transport induced by synergy of multiple AEs and MHDs and phase space engineering control techniques in tokamak plasmas

Energetic-particle transport is significantly crucial in magnetic confined fusion. Many factors can enhance the level of energetic-particle transport and even loss, such as synergy of AE and MHD. Thus, control of energetic-particle transport is also imperative. Phase space engineering is a method to analyze, design and optimize complex systems by using phase space theory, which is widely used in many research fields. In magnetic confinement fusion, the gradient of the phase space of energetic particles, that is, the gradient of the distribution function in the three-dimensional phase space composed of the toroidal regular angular momentum, energy and particle ejection angle, is an important free energy driving source for the excitation of energetic particle-related instability, which provides a certain possibility and operability for the phase space regulation of energetic particle-related instability. In this work, we mainly study the phase space modulation of energetic particle-related instability such as Alfven eigenmode and energetic particle mode in the plasma heated by neutral beam injection on HL-2A and HL-3. There are many other factors affecting the instability of energetic particle drive, such as safety factor profile, magnetic shear, minimum safety factor, etc. This work mainly focuses on the phase space distribution function of energetic particles to regulate them, and realizes the regulation of this instability by designing different distribution functions of energetic particles.
There are many experimental phenomena of the interaction between the Alfven eigenmodes and high-energy particle modes on HL-2A and HL-3. These instabilities are located on different rational planes, and there may be a variety of synergies of instabilities, which will greatly improve the transport, redistribution and loss levels of fast particles, and directly affect key physical issues such as the self-heating efficiency of alpha particles in future reactor-graded plasmas. Based on this, the nonlinear MHD dynamic global hybrid simulation program is used to conduct large-scale numerical simulation. On the basis of roughly repeating the above experimental phenomena, the above experimental phenomena are regulated by regulating the distribution function of energetic particles. This work can be used for reference to understand the loss and transport control of energetic particles caused by energetic particle driven instability in future fusion reactors.

Speaker: Xiaolong Zhu

1:30 PM Fluid and Kinetic Modelling of Sheath Transition Region with a Novel Anisotropic Ion Pressure Model and Enhanced Boundary Conditions

Sheath boundary conditions are an unavoidable fact of fluid based Scrape-Off Layer (SOL) modelling. The choice of boundary conditions can dictate the equilibrium that is reached, this choice is usually the Bohm criterion [1]. Recent work by Li et al [2,3,4] proposed a novel boundary condition, in the form of a correction to the Bohm criterion, for modelling based on 1D Particle In Cell (PIC) simulations and an improved plasma transport model which allowed for temperature anisotropy.

While Li et al proposed this correction to the Bohm criterion, the implementation of such a correction was not performed. The work to be presented in this poster has taken the proposals given in [2,3,4] and implemented an anisotropic transport model capable of handling this boundary condition correction within the ReMKiT1D framework [5]. Discussions over the feasibility of this correction to the Bohm criterion, along with the transport model that has been implemented are given. Both of which introduce numerical challenges to a fluid solver, which have required a collection of different numerical methods to overcome.

Alongside this, complimentary PIC simulations with the code BIT1 [6] have sought to provide an additional connection between fluid modelling and first principles kinetic data. Ongoing PIC simulations seek to extend the scope of simulations performed by Li et al. Seeking to explore how anisotropy develops in the pre-sheath, as well as how different sheath entrance criteria affect the application of the Bohm criterion. This will be given alongside a discussion of how this kinetic data is being used to improve the closure of the anisotropic fluid model.

[1] D. Bohm, ‘The Characteristics of Electrical Discharges in Magnetic Fields’, New York: McGraw-Hill, 1949, p. 77. Available: https://doi.org/10.1001/jama.1950.02920020129032

[2] Y. Li, B. Srinivasan, Y. Zhang, and X.-Z. Tang, ‘Bohm Criterion of Plasma Sheaths away from Asymptotic Limits’, Physical Review Letters, vol. 128, no. 8, p. 085002, Feb. 2022, doi:10.1103/PhysRevLett.128.085002.

[3] Y. Li, B. Srinivasan, Y. Zhang, and X.-Z. Tang, ‘Transport physics dependence of Bohm speed in presheath–sheath transition’, Physics of Plasmas, vol. 29, no. 11, p. 113509, Nov. 2022, doi: 10.1063/5.0110379.

[4] Y. Li, B. Srinivasan, Y. Zhang, and X.-Z. Tang, ‘The plasma–sheath transition and Bohm criterion in a high recycling divertor’, Physics of Plasmas, vol. 30, no. 6, p. 063505, Jun. 2023, doi: 10.1063/5.0147580.

[5] S. Mijin, D. Power, R. Holden, W. Hornsby, D. Moulton, and F. Militello, ‘ReMKiT1D - A framework for building reactive multi-fluid models of the tokamak scrape-off layer with coupled electron kinetics in 1D’, Computer Physics Communications, vol. 300, p. 109195, Jul. 2024, doi: 10.1016/j.cpc.2024.109195.

[6] D. Tskhakaya, A. Soba, R. Schneider, M. Borchardt, E. Yurtesen, and J. Westerholm, ‘PIC/MC Code BIT1 for Plasma Simulations on HPC’, in 2010 18th Euromicro Conference on Parallel, Distributed and Network-based Processing, Feb. 2010, pp. 476–481. doi: 10.1109/PDP.2010.47.

This work has been part-funded by the EPSRC Energy Programme [grant number EP/T012250/1] as well as the EPSRC Doctoral Studentship bursary [grant number EP/W524323/1]. This work used the ARCHER2 UK National Supercomputing Service (https://www.archer2.ac.uk).

Speaker: Alfie Adhemar (Imperial College London, UKAEA)

1:30 PM Fully global simulations of electromagnetic turbulence in the stellarator W7-X

Magnetic confinement fusion experiments require high $\beta=\langle p\rangle/(B^2/2\mu_0)$, the ratio of plasma pressure to magnetic pressure, to access high performance. Moderate $\beta$ can be beneficial for ion-temperature-gradient (ITG) driven turbulence. Typically, however, as $\beta$ is increased above a certain threshold, the so-called kinetic-ballooning-mode (KBM) [Tang 1980] can be destabilized. This is a plasma pressure gradient-driven instability which is inherently electromagnetic and can lead to strong outward-directed heat fluxes [Mishchenko_2022], degrading plasma confinement in the process.
While, linearly, KBMs have been successfully studied in the stellarator Wendelstein 7-X with flux-tube simulations [Aleynikova 2022], these local approaches are limited in capturing the full structure of KBMs, which often develop global characteristics on the magnetic surface. In this context, global gyrokinetic simulations - such as those performed with the EUTERPE code [Kleiber 2024] - are a particularly suitable tool, as they allow for the investigation of electromagnetic modes with full radial coupling, offering deeper insight into the onset and development of KBMs in realistic geometries.
To begin exploring such global electromagnetic effects, we focused on the UFM configuration of W7-X, which is Mercier unstable from low $\beta$, making it a convenient initial test case for electromagnetic studies. Linear simulations do not show KBMs, but rather temperature-gradient driven electron modes. Nonlinearly, ion-driven heat fluxes are observed to decrease with $\beta$, showing no signs of the flux enhancement due to KBM-like turbulence that has been seen in some flux-tube studies [Mulholland 2023].
Although KBMs do not appear in the numerical study of the UFM, the configuration provides an opportunity to better understand why confinement improves with increasing $\beta$ in other hill-type stellarators, such as W7-AS and LHD. Further studies in magnetic well configurations will follow, but the current results already indicate that high-$\beta$ operation without KBM turbulence may be possible up to $\left<\beta\right> =4.16\%$.

Speaker: Yann Narbutt (IPP)

1:30 PM Gysela-axi: a flux-driven full-F gyrokinetic code to simulate axisymmetric tokamak plasmas

Gyrokinetic codes are currently the most advanced numerical tools for simulating turbulence in to-kamak plasmas. The code Gysela [1], written in Fortran 90 and developed for more than 20 years, is one of the flux-driven gyrokinetic codes available worldwide. However expanding this code to use more complex mathematical methods such as non-uniform points (vital for handling the different magnitudes of physical quantities in the core and edge regions), and increasingly complex geometries (geometries including both closed and open field lines, and potentially stellarator geometries) has proved to be challenging and sometimes error-prone. The challenges of such extensions are further amplified when trying to organise such a code for use on new GPU architectures, necessary for ex-ascale simulations. This is a challenge shared by other gyrokinetic codes.
For these reasons, the development of a new code was started two years ago, named Gysela-X++, from scratch in modern C++, using MPI and Kokkos [2] to handle parallelism. This choice allows the code to run natively on CPUs and GPUs and thus benefit from the capabilities of exascale supercomputers. Some of the algorithms of this new code are directly taken from the legacy code in Fortran and translated to C++/Kokkos, while other parts of the algorithm are completely refactored to alleviate the restrictions of the Fortran code.
The code is split in two parts: a library of operators "Gyselalib", and a set of independent simulation codes built on top of it. A first version of the code is now available. It simulates axisymmetric toka-mak plasmas and is therefore 4D. This axisymmetric version, named Gysela-axi, is a major milestone as it will serve as the basis for the parallel development of multiple new physics features, most nota-bly tokamaks with X-points, stellarators and neutral physics. In addition, it will permit optimizations efforts and the development of new numerical capacities, including non-uniform grids, in situ diag-nostics and anomaly detection to handle the simulation.
In this contribution, we will present the main features of the Gysela-axi code. Benchmarks against theoretical predictions on the geodesic acoustic mode dynamics and neoclassical physics will be presented. We will also review the numerical capabilities of the code, and discuss the main developments foreseen in the near future for Gysela-X++, the full 5D version of the code.
Biblio:
1. V. Grandgirard et al., « A 5D gyrokinetic full-f global semi-Lagrangian code for flux-driven ion turbulence simulations », Computer Physics Communications 207 (2016) 35–68
2. C. Troot et al., «Kokkos 3: Programming Model Extensions for the Exascale Era», IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 33, NO. 4, APRIL 2022 805

Speaker: Peter Donnel (CEA, IRFM)

1:30 PM Modelling NBI and ICRH synergy in ITER plasmas

Neutral Beam Injection (NBI) and Ion Cyclotron Resonance Heating (ICRH) are two key systems that generate a population of Energetic Particles (EPs) in magnetically confined fusion plasmas. These EPs play a crucial role in plasma performance, providing heat, torque and non-inductive current. Furthermore, beam EPs are excellent candidates for studying wave–particle interaction phenomena involving ion cyclotron waves, enabling the formation of highly energetic plasma particle populations that offer valuable insight into alpha particle physics.
In this contribution, we investigate the interaction between beam EPs and high-frequency waves in an ITER half-field scenario, using modeling tools available within the Integrated Modelling & Analysis Suite (IMAS) framework [1]. Specifically, the ASCOT suite of codes [2] is employed to simulate beam deposition and EP slowing down. Wave propagation and absorption are modeled using the full-wave solver CYRANO [3]. In the considered scenario, the ICRH is applied at the fundamental resonance of hydrogen, targeting minority H heating in a deuterium plasma. The 1D Fokker–Planck solver FOPLA [4] is used to estimate the resulting distribution functions. Synergetic NBI-ICRH effects are explored to assess their impact on plasma performance [5], with the ultimate goal of optimizing combined NBI-ICRH application for future ITER operations. Synergetic effects are also studied in the Constant of Motion phase space through EPCoM workflow [5], capturing the orbit nature of the resulting EPs and proving useful results for transport modeling.
This work validates a multi-code modeling approach within the Heating and Current Drive (H&CD) workflow [6] that can support ITER operation planning. As a next step, we aim to investigate the interaction between beam ICRH-accelerated EPs using the RFOF library implemented in ASCOT, which enables the modelling of wave-particle interaction within the orbit following code. The applicability and potential advantages of using ASCOT-RFOF for synergetic modeling will be evaluated.

Speaker: Chiara De Piccoli (Università degli Studi di Padova, Consorzio RFX)

1:30 PM Modelling of the non-inductive current ramp up scenario on TCV: thermal electron transport in reversed magnetic shear configuration

New plasma current ramp up (RU) scenario has been developed recently on TCV to demonstrate for the first time the possibility to raise the plasma current (Ipl) non-inductively (i.e. with zero flux contribution from the central solenoid) by applying ECCD in the early discharge phase after the break down [1]. Similar strategy has been tested previously in the non-inductive (NI) RU scenario fully based on the bootstrap (BS) current drive mechanism (i.e. with 100% of the bootstrap current fraction) [2]. In the recent scenario a reversed q-profile forms rapidly at the start of the NI current RU and the configuration with negative magnetic shear (sm) is maintained till the end of the Ipl flat-top (FT) phase. The NI current RU operational domain has been explored by changing the plasma density, ECCD power and power deposition, demonstrating the possibility to control the FT plasma current and q-profile. A valuable database for the study of thermal electron transport in reversed shear (RS) configurations has been built.
The transport modelling of plasma evolution in these discharges starting with the early inductive phase and up to the end of the discharge is presented in this work with a purpose to establish the impacts of sm and q-profile on thermal electron transport. This is done by using the Bohm-gyroBohm (BgB) model [3] complemented with the sm-dependent function validated in the advanced scenarios with flat and reversed q-profile performed on JET, DIII-D and TFTR [4]. The interplay between the destabilising effect of q, the stabilising effect of the low/negative sm and the MHD-triggered losses strongly affecting the thermal confinement is analysed. Based on the validated transport models the possibility to optimise the NI current ramp rate in future experiments to avoid a strong MHD activity (double tearing mode) and unreasonably over-driven Ohmic current is investigated. Finally, the capability of the BgB model to reproduce accurately the electron temperature evolution in the on-axis NBI and ICRH heated (JET [5]) and off-axis ECCD RU scenarios is discussed.
The current RU experiments analysed here as well as the validated models reproducing the plasma behaviour in the NI scenarios provide a basis for the development of future fusion reactor designs relying on the NI operation (such as [6, 7]). These experiments and the analysis performed emphasise a strong need in the development of the theory-based integrated modelling tools combining the MHD stability and transport physics – two key phenomena regulating the plasma performance in RS configurations.
[1] S. Coda et al, 30th IAEA FEC, 2025; [2] S. Coda et al, 22nd IAEA FEC, 2008; [3] M. Erba et al, PPCF 39 (1997) 261; [4] I. Voitsekhovitch et al, Phys. Plasmas 6 (1999) 4229; [5] I. Voitsekhovitch et al, PPCF 52 (2010) 105011; [6] B. N. Sorbom et al, FED 100 (2015) 378; [7] K. Kim et al Nucl. Fusion 55 (2015) 053027

See author list of B.P. Duval et al 2024 Nucl. Fusion 64 112023
*See author list of E. Joffrin et al 2024 Nucl. Fusion 64 112019

Speaker: Irina Voitsekhovitch (UKAEA)

1:30 PM Modelling the heating of a pellet-produced plasmoid in the non-linear MHD Code Jorek

Pellet refuelling will be a key technique for sustaining plasma density in future fusion reactors based on the stellarator concept. Although this method is more mature in tokamak experiments, the departure from axisymmetry in stellarators introduces unique challenges and opportunities that remain poorly understood.

Here, the stellarator extension of the 3D nonlinear MHD code JOREK is used to investigate the radial drift of a fully ionised pellet. Since this radial drift depends on the pressure evolution inside the pellet-produced plasmoid, the parallel expansion strongly influences the radial deposition of the new material. Therefore, special care must be taken to accurately model the heating of the plasmoid by hot background plasma particles, which drives the parallel expansion.

The long electron mean free path expected in the core of future reactors means that non-local heating by nearly free-streaming electrons must be considered in our fluid model. Two non-local heating schemes are newly implemented and verified against analytic theory. The new heating scheme is then applied to W7-A-like stellarator configurations, where the radial drift following full pellet ionisation is investigated.

Speaker: Carl Wilhel Rogge (IPP Garching)

1:30 PM Orbit Bifurcations and Drift Frequencies Shifts in Shaped Tokamak Equilibria

Guiding Center (GC) orbits in shaped tokamak equilibria exhibit rich structure, once the magnetic field magnitude develops secondary local minima. Using Negative Triangularity (NT) and small aspect ratio equilibria we show that shaping-induced wells in B introduce additional mirror points and, consequently, multiple families of trapped orbits. Two generic bifurcation scenarios are identified through Hamiltonian phase‑space analysis: (i) a super‑critical pitchfork scenario in which the central trapped‑orbit O-point loses stability while a symmetric pair of stable fixed points emerges, and (ii) a saddle‑node bifurcation that creates stable–unstable pairs of fixed points. These bifurcations reorganize phase space well beyond the domain occupied by the secondary trapped orbits, altering the orbital‑frequency spectrum over a broad range of magnetic moments and energies. Resonance maps reveal multiple simultaneous resonances with n = 0 perturbations, potentially enhancing particle‑orbit stochasticity. Particle tracing simulations indicate enhanced particle and energy transport, due to orbit stochastization, compared to positive triangularity reference cases that do not exhibit bifurcations are verified by particle tracing simulations. The results extend our previous work on bifurcations driven by radial electric field [1], demonstrating that equilibrium shaping can likewise tailor GC dynamics, offering an additional design handle for transport-barrier formation in compact reactors.

References
[1] G. Anastassiou, P. Zestanakis, Y. Antonenas, E. Viezzer and Y. Kominis, J. Plasma Phys. 90, 905900110 (2024)

Speaker: George Tzimopoulos (National Technical University of Athens)

1:30 PM Self-consistent Fluid-kinetic Implementation of Flux Expansion in a 1D Hybrid Fluid-kinetic Code

Understanding plasma behaviour in the scrape-off layer (SOL) is critical for predicting particle and energy exhaust in magnetically confined fusion devices. A key feature in the SOL is magnetic flux expansion, which reduces peak heat loads on divertor targets by spreading exhaust across a larger surface area. This phenomenon is typically modelled using fluid codes, which incorporate flux expansion geometrically through area factors in the governing equations [1,2]. However, fluid models often rely on well-behaved time and length scales, such as those in the Braginskii closure, which break down in the plasma edge [3]. In particular, detached conditions and transient events like edge-localised modes (ELMs) can lead to strongly non-equilibrium behaviour, requiring kinetic treatment to accurately capture the non-local and non-equilibrium physics [4,5,6].
The work to be presented in this poster consists of a novel finite volume discretisation for a kinetic model that includes magnetic flux expansion, suitable for implementation in a reduced one-dimensional Vlasov-Fokker-Planck (VFP) code. Unlike in 2D or 3D kinetic models – where expansion and mirroring arise naturally from the coordinate geometry – such effects must be explicitly reconstructed in 1D through the formulation of the governing terms and their spatial discretisation. The kinetic equation is decomposed using Legendre polynomials in the pitch-angle coordinate in velocity space, and the resulting terms are volume-integrated over an expanding grid cell. To ensure consistency with flux-expanding fluid models, the Legendre-decomposed advection and mirror force terms are constructed in such a way as to preserve the expected discretised equations for the fluid moments in the appropriate limit. This introduces specific constraints on the decomposed terms.
Implementation of this discretisation within ReMKiT1D, a 1D framework for SOL modelling, will be discussed, along with an outline of the planned steps for further development [7].

---

References
[1] Dudson, B. D. et al. Plasma Phys. Control. Fusion, 61(6) (2019)
[2] Derks, G. L. et al. Plasma Phys. Control. Fusion 64 (2022)
[3] Braginskii, S. I. Reviews of Plasma Physics 1, 205 (1965)
[4] Tskhakaya, D. et al. Contrib. Plasma Phys., 48(1–3), 89–93 (2008)
[5] Chankin, A. V. et al. Plasma Phys. Control. Fusion, 60 (2018)
[6] Mijin, S. et al. Plasma Phys. Control. Fusion, 62(9) (2020)
[7] Mijin, S. et al. Comput. Phys. Commun., 300 (2024)

This work has been part-funded by the EPSRC Energy Programme [grant number EP/W006839/1].

Speaker: Vera Oberhauser (Imperial College London)

1:30 PM Toward a nonlinear Schroedinger equation for the description of geodesic-acoustic-modes in tokamaks: Analytic gyrokinetic studies of the nonlinear self-interaction

The geodesic-acoustic-mode (GAM) is a plasma oscillation observed in fusion reactors with toroidal geometry and is recognized to be the nonstationary branch of the zonal flows. Prior studies have established that as a direct consequence of nonlinear gyrokinetic theory, the GAM dynamics is well described by an equation of Schroedinger type - i. e. an equation whose linear contribution is exactly of the same form as the linear Schroedinger equation, while the nonlinear dynamics necessitates an integro-differential expression.

The presented work takes a closer look into the nonlinear contributions by deriving approximate, but well-defined analytic expressions from the (exact) integro-differential operators. At the lowest order of accuracy, prior numerical studies anticipate the retrieval of a cubic nonlinear Schroedinger equation. This may come unexpected since nonlinear interactions usually have a quadratic structure, such as e. g. the $\vec{E}\!\times\!\vec{B}$-nonlinearity. The third power is found to stem from an interaction of quadratic structures generated by the GAMs (with oscillation frequencies that are either zero or twice the GAM frequency) with the GAM itself. Analytic results are compared to gyrokinetic simulations.

Speaker: David Korger

1:30 PM Toward understanding the impact of ion species in the plasma response to magnetic perturbations

High confinement mode operation of tokamaks is inevitably linked to edge localized mode (ELM) instabilities. Larger tokamaks like ITER will be severely threatened by their occurrence as they are associated with large transient heat loads that exceed material limits. Applying 3D resonant magnetic perturbations (RMP) is a possible means to suppress ELMs. However, so far RMP ELM suppression was only reliably achieved in plasmas with deuterium as the main ion species. Experiments in ASDEX Upgrade showed the loss of ELM suppression if the main ion mix contains a significant fraction of helium [1] or hydrogen [2]. This observation begs the question if RMP ELM suppression is reliably achievable in deuterium-tritium plasmas of future tokamak reactors. Therefore, we aim to improve our understanding of the plasma response to the field perturbations.
The plasma response to RMPs encompasses an electron-dominated parallel current density narrowly localized at perturbation-mode-specific resonant surfaces while the "outer" solution is supposed to be well described by ideal MHD. However, a toroidal MHD-kinetic hybrid model [3], shows that there is an interface layer between the resonant, electron-dominated layer and the outer ideal MHD region. The interface layer is governed by ion effects and impacts RMP-plasma interaction, in particular, via quasilinear effects. Thus, this layer is a contender for explaining ion-related effects on the plasma response. To fully resolve the ion-governed layer, the respective Larmor radius effects have to be resolved appropriately which is not yet the case for the current kinetic part of the model [3] that is based on a finite Larmor radius expansion. Consequently, we report on the development of the linear non-local kinetic plasma response code KIM [4]. Properly accounting for the finite Larmor radius, this code aims at resolving the plasma response in the ion-dominated layer and the respective effects.

References
[1] W. Suttrop et al 2023, 49th EPS Conference on Plasma Physics, P4.062
[2] N. Leuthold et al 2024, Nucl. Fusion 64 026017
[3] P. Lainer et al 2025, in preparation
[4] M. Markl et al 2024, 50th EPS Conference on Plasma Physics, P2.066

Speaker: Markus Markl (Graz University of Technology)

3:30 PM → 4:00 PM Coffee break

4:00 PM → 4:40 PM I.7-Vallhagen: Semi-analytical model for the pellet rocket effect in magnetic confinement fusion plasmas

Speaker: Oskar Vallhagen (Chalmers University of Technology)

4:40 PM → 5:05 PM 0.4-Ciraolo: Transport and turbulence in edge tokamak plasma: Hierarchy of models in SOLEDGE3X code and comparison with experiments

Accurate numerical modelling of turbulent transport in edge tokamak plasma remains a significant challenge. Many key experimental features, such as the formation of edge transport barriers, are still difficult to simulate, especially for ITER-sized tokamaks. Predicting the scrape-off layer (SOL) width or the power load imbalance between the inner and outer divertor legs remain an open issue, their characterization being essential to determine the plasma regimes to be developed in future fusion power plants. First-principle modelling of edge plasma turbulence is therefore a key area of research in the fusion community, as it allows to extrapolate from present day experiments to future tokamaks.
Inspired by the hierarchy of models used to simulate turbulence in the neutral fluid community, the SOLEDGE3X fluid code incorporates a broad range of models with varying fidelity [1], which allows a stage approach analysis to the problem of edge turbulence. These range from empirical diffusivities, which are used to perform so-called "transport" simulations, to full-scale 3D first-principle turbulence modelling, where turbulent structures are self-consistently simulated. In between, a reduced approach inspired by the k-epsilon model [2], widely used in the computational fluid dynamics community, is proposed to capture key features of edge plasma turbulence and incorporate them into transport simulations [3]. Specifically, the growth of the turbulent energy "k" is governed by the primary interchange and drift wave instabilities, while turbulence saturation is achieved through a semi-empirical closure based on scaling laws [4]. Such approach allows for a quick assessment of the main turbulent characteristics of the plasma edge.
In this contribution, we present a direct comparison of the various approaches to model TCV and WEST edge plasma transport and turbulence, ranging from empirical transport modelling, transport modelling with k-epsilon prediction, and first-principle modelling. The fluctuation levels and cross-field transport predicted by the k-epsilon model is directly compared with first-principle simulations and experimental measurements. Interestingly, the k-epsilon model is able to recover not only the ballooned feature of radial transport at the outer midplane but also an increased radial transport along the divertor leg. A special focus will be put on comparing the behaviour of divertor localized filaments observed experimentally in TCV with fast cameras and recovered by 3D turbulence modelling [5].
[1] H. Bufferand et al., Nucl. Fusion 61 (2021), 116052
[2] W.P. Jones, B.E. Launder, Int. J. Heat Mass Transfer 15, (1972), 301
[3] S. Baschetti et al., Nucl. Fusion 61 (2021), 106020
[4] R.J. Goldston et al Nucl. Fusion 52 (2012), 013009
[5] H. Bufferand et al., Nucl. Mat. Energy 41 (2024), 101824

Speaker: Guido Ciraolo (CEA)

5:05 PM → 5:30 PM O.5-Hallatschek: Non-gyrokinetic high-frequency mode instability for tokamak edge like gradients

The stability analysis of gyrokinetic slab ITG modes is well-established and results in temperature and density gradient stability thresholds that depend on the parallel and perpendicular wavenumbers.

In a recent PRL [1], using 6D turbulence simulations with a specially optimized code that resolves the Larmor orbits, we found potentially significant non-gyrokinetic instabilities for steep, but not unrealistic, gradients in the tokamak edge with simplified slab geometry. These instabilities may be classified as unstable ion-Bernstein waves (IBW). To understand these phenomena, we extended the ITG analysis to high-frequency non-gyrokinetic modes. This extension requires modifying the zero-frequency gyrokinetic polarization using the Gordeyev function, as well as providing rigorous estimates of the magnitudes of the infinite sums appearing in the dispersion relation.

Similar to the ITG modes, we derive a threshold criterion for the instability. However, unlike gyrokinetic ITGs, the non-gyrokinetic modes require only the presence of a temperature gradient and not a particularly high ratio of temperature to density gradients. In contrast, gyrokinetic ITGs are suppressed when the density gradient is too large relative to the temperature gradient (the $\eta_i$ criterion). Interestingly, the IBW growth rate tends to increase with the density gradient.

It is likely that including additional physics (e.g., magnetic curvature or interactions with kinetic electrons) will significantly amplify the drive of similar non-gyrokinetic instabilities, potentially leading to an expansion of the field of strongly magnetized plasma turbulence.

[1] M. Raeth, K. Hallatschek, "High-Frequency Nongyrokinetic Turbulence at Tokamak Edge Parameters", Phys. Rev. Lett 133, 195101

Speaker: Dr Klaus Hallatschek (Max-Planck-Institute for Plasma Physics)

Wed, September 24

8:30 AM → 9:20 AM I.2-Alonso: Fundamental physics and technology considerations of stellarator reactor design

Speaker: Arturo Alonso (CIEMAT)

9:20 AM → 10:00 AM I.8-Goodman: Searching for SQuIDs: Developments in the optimisation of Stable Quasi-Isodynamic Designs

Speaker: Alan Goodman (Max Planck Institute for Plasma Physics)

10:00 AM → 10:25 AM O.6-Calvo: A new class of optimized stellarators with zero bootstrap current

Typically, stellarator optimization relies on the notion of omnigenity [1, 2], which guarantees small radial neoclassical transport at the low collisionalities that are characteristic of fusion-grade plasmas. In omnigenous magnetic fields, collisionless particles do not move radially on average and, in the course of their motion along flux surfaces, they never undergo transitions between different types of orbits. Quasi-isodynamic fields are a subset of omnigenous fields that give zero bootstrap current at low collisionality [3], a property that makes them compatible with an island divertor, an advanced exhaust solution for stellarators. Quasi-isodynamicity is the approach Wendelstein 7-X is based on [4], and probably the most mature concept for stellarator reactors.

The recent introduction of the notion of piecewise omnigenity [5] represents a major theoretical breakthrough. In piecewise omnigenous fields, the average radial displacement of collisionless particles is zero, but in their motion over magnetic surfaces, particles experience transitions between different types of trapped orbits. The discovery of piecewise omnigenous fields radically expands the space of known configurations that are optimized with respect to radial neoclassical transport. In particular, piecewise omnigenous fields are free from certain topological constraints obeyed by magnetic field strength contours in omnigenous configurations that often lead to complex coils.

In this conference contribution, we will show that the potential of piecewise omnigenity goes far beyond the optimization of radial neoclassical transport by proving that there exist piecewise omnigenous fields that give zero bootstrap current at low collisionality [6]. We will analytically derive the mathematical condition for zero bootstrap current and will confirm the accuracy of this condition by means of neoclassical simulations. Our results imply that two fundamental properties of plasmas confined in quasi-isodynamic fields (small radial neoclassical transport and vanishing bootstrap current) can also be attained by piecewise omnigenous fields, providing a pathway to new, possibly simpler stellarator reactor designs.

[1] J. R. Cary and S. G. Shasharina, Phys. Rev. Lett. 78, 674 (1997).
[2] F. I. Parra, I. Calvo, P. Helander et al., Nucl. Fusion 55, 033005 (2015).
[3] P. Helander and J. Nührenberg, Plasma Phys. Control. Fusion 51, 055004 (2009).
[4] H. Wobig, Plasma Phys. Control. Fusion 35, 903 (1993).
[5] J. L. Velasco, I. Calvo, F. J. Escoto et al., Phys. Rev. Lett. 133, 185101 (2024).
[6] I. Calvo, J. L. Velasco, P. Helander et al., arXiv:2505.02546. Submitted to Phys. Rev. Lett.

Speaker: Ivan Calvo (Laboratorio Nacional de Fusion, CIEMAT, Madrid, Spain)

10:25 AM → 10:50 AM Coffee break

10:50 AM → 11:30 AM I.9-Kazakov: Alpha-Particle Physics Studies in D-3He Plasmas at JET and JT-60SA in Support of the ITER Rebaseline

Speaker: Dr Yevgen O. Kazakov (LPP/ERM, Bruxelles, Belgium)

11:30 AM → 11:55 AM O.7- De Gianni: Effect of the magnetic geometry on Trapped Electron Modes instability: linear and non linear analysis

Good plasma confinement is crucial to harness fusion energy. Experiments on the TCV [1] and DIII-D [2] tokamaks have shown that negative triangularity (NT) reduces the turbulent transport, hence improving confinement. Trapped Electron Modes (TEM) are thought to play an important role in this process. A full understanding of the underlying physics is necessary for assuring NT plasmas to be reactor relevant, but is still missing. To identify the key physical mechanisms driving the improvement of confinement in TEMs dominated NT plasmas, a reduced analytical model has been recently derived, focusing on TEMs linear stability [3]. In this contribution, the model of [3] is extended by including a simplified model for ions without accounting for their resonant response - thus excluding ITGs. This extension enables a qualitative agreement of the model with gyrokinetic (GK) simulations performed with GYSELA [4] and GENE [5] in the linear regime, and an evaluation of the impact of Finite Larmor Radius effects on stability.
The model highlights the key role of "Finite Mode Width" (FMW) effects, which is the poloidal localization of the linear modes – ballooning character. A key quantity for understanding the importance of FMW effects is the precession frequency, the growth rate in the fluid limit scaling like its square root. The ballooning of the instability gives more weight to deeply trapped electrons, whose precession frequency is lower for NT than for positive triangularity (PT). On the other hand, the benchmark with GENE highlights the key role played by the trapped electrons parallel dynamic (related to their bouncing frequency) and by passing electrons in the shear dependence of the different linear stability of TEMs in negative and positive triangularity.
Although it provides precious insights into the underlying physics, a linear analysis is not sufficient to explain the experimental results [1][2]. Therefore, a nonlinear analysis has been carried out using the gyrokinetic code GYSELA. In particular, the electric and diamagnetic components of the Reynolds stress, which drive the zonal flows, will be shown to exhibit significant differences in NT and PT configurations.
References
[1] Y. Camenen et al., Nucl. Fusion 47 (2007)
[2] M. Austin et al., Phys. Rev. Lett. 122 (2019)
[3] X. Garbet et al., Nucl. Fusion 64 (2024) [4] V. Grandgirard et al., Comput. Phys. Comm. 207 (2016)
[5] G. Merlo et F. Jenko, Journ. Plasma Phys. 89 (2023)

Speaker: Ludovica De Gianni (CEA Cadarache)

11:55 AM → 12:20 PM O.8-Zestanakis: Geometric Identification of Mode-Particle Resonances and Transport Barriers in Realistic Tokamak Equilibria

Symmetry‑breaking perturbations in fusion plasmas—whether produced by intrinsically excited magnetohydrodynamic modes such as Alfvénic Eigenmodes and Geodesic Acoustic Modes, or by externally applied fields such as Resonant Magnetic Perturbations and Toroidal‑Field ripples—interact with charged particles through resonances that govern the transport of particles, energy, and momentum. Building on our earlier analysis for large‑aspect‑ratio equilibria [1–5], we generalize Orbital Spectrum Analysis (OSA) to numerically reconstructed, realistic tokamak equilibria. A computationally efficient semi-analytical geometrical method yields Guiding Center orbital frequencies and the kinetic safety factor for any given unperturbed axisymmetric equilibrium. The resulting resonance diagrams pinpoint all mode-particle resonances and locate transport barriers at the extrema of the kinetic safety factor. Systematic comparisons with numerical particle tracing validate the predicted resonance and transport barrier positions with excellent agreement for thermal and energetic particles alike. The methodology therefore furnishes a computationally efficient tool for assessing the response of all particle species to multi‑scale symmetry‑breaking perturbations in realistic equilibria.

References
[1] P.A. Zestanakis, Y. Kominis, G. Anastassiou and K. Hizanidis, Phys. Plasmas 23, 032507 (2016)
[2] Y. Antonenas, G. Anastassiou and Y. Kominis, J. Plasma Phys. 87, 855870101 (2021)
[3] H.T. Moges, Y. Antonenas, G. Anastassiou, Ch. Skokos and Y. Kominis, Phys. Plasmas 31, 012302 (2024)
[4] G. Anastassiou, P. Zestanakis, Y. Antonenas, E. Viezzer and Y. Kominis, J. Plasma Phys. 90, 905900110 (2024)
[5] Y. Antonenas, G. Anastassiou and Y. Kominis, Phys. Plasmas 31, 102302 (2024)

Speaker: Panagiotis Zestanakis (National Technical University of Athens)

12:20 PM → 1:30 PM Lunch break

1:30 PM → 3:30 PM Poster Session #2

For the Poster list please click on 'Contribution list' down here

1:30 PM A new multigrid solver for stellarator neoclassical transport

Solution of the drift kinetic equation [1] is a required step in analyzing and optimizing neoclassical transport in stellarators. A variety of codes [2-6] have been developed to handle the complex geometry and wide range of collisionality regimes present in stellarators. Existing codes are generally either high fidelity codes that are accurate in a wide range of regimes, but are too expensive to be efficiently used in optimization loops or predictive transport frameworks, or lower fidelity codes that are faster are limited in their regimes of validity or miss important physical phenomena such as the bootstrap current or ambipolar electric field. We have developed a new neoclassical code that attempts to bridge this gap, offering high fidelity solutions capturing as much of the physics as possible, while being significantly faster and more memory efficient than existing high fidelity codes. We do this by making use of novel stable finite difference discretizations combined with a multigrid method to solve the resulting linear system. Automatic differentiation is used to obtain derivatives for use in optimization. Applications are discussed including self consistent optimization of the bootstrap current and optimization of “electron root” plasmas [7].

References
[1] R. D. Hazeltine, “Recursive derivation of drift-kinetic equation,” Plasma Physics, 1973
[2] S. Hirshman, et. al. “Plasma transport co-efficients for nonsymmetric toroidal confinement systems,” The Physics of fluids, 1986.
[3] W. Kernbichler, et. al. “Recent progress in neo-2; a code for neoclassical transport computations based on field line tracing,” Plasma and Fusion Research, 2008
[4 ]M. Landreman, et. al. “Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas,” Physics of Plasmas, 2014
[5] J. L. Velasco, et. al. “Knosos: A fast orbit-averaging neo- classical code for stellarator geometry,” Journal of Computational Physics, 2020
[6] Escoto, F. J., et al. "MONKES: a fast neoclassical code for the evaluation of monoenergetic transport coefficients in stellarator plasmas." Nuclear Fusion, 2024
[7] Neto, E. Lascas, et al. "Electron root optimisation for stellarator reactor designs." Journal of Plasma Physics, 2025

Speaker: Rory Conlin (University of Maryland)

1:30 PM Circular-orbit correction to electron fluxes through the magnetised plasma sheath

The magnetised plasma sheath is a region that forms in front of a solid target and is composed of a magnetic presheath, where the electrostatic potential varies on the scale of the ion Larmor radius, and a Debye sheath, where the potential varies on the scale of the Debye length. The transmission of electrons and of their energy through the magnetised sheath must be calculated to find the wall boundary conditions for magnetised plasmas. Assuming a negligible electron Larmor radius, the transmitted electron particle and heat fluxes depend on a constant velocity cutoff which is related to the combined potential drop across the magnetised sheath. Near the target, the thermal electron Larmor radius is typically smaller than the Debye length, but not negligible, such that the electron parallel velocity cutoff has a correction which depends on the actual size of the electron orbit, i.e., on its magnetic moment. By exploiting the grazing incidence of the magnetic field at the target, we propose an analytical model for this cutoff function. The model is based on a circular-orbit approximation of the electron trajectory, and only depends on the potential drop across the Debye sheath and on an approximate calculation of the wall electric field. We verify the accuracy of the electron particle and heat fluxes thus computed by comparing with results obtained by solving for the self-consistent Debye sheath potential profile.

Speaker: Alessandro Geraldini

1:30 PM Computationally efficient calculation of bootstrap current for nearly omnigeneous devices

Evaluation of the bootstrap current is an important part of stellarator optimization procedures aiming at self-consistent equilibria or configurations with strongly reduced bootstrap current. The later is especially relevant for an accurate control of the $\iota$ profile, enabling the operation of an island divertor. For such optimization workflows, a fast method of evaluating the bootstrap current is highly desired. Such an evaluation is straightforward for perfectly omnigeneous stellarators (which include quasi-helical configurations as a particular case). For such devices magnetic field maxima along a field line are aligned and the trapped-passing boundary layer width is the same for all magnetic wells on this line (ripples are equivalent). In these configurations, the bootstrap effect is tokamak-like [1] and can be well represented by the Shaing-Callen formula [2] in the long mean free path regime. However, in realistic configurations omnigeneity is always at least slightly violated, because it cannot be realized exactly and because of the compromise with other optimization criteria. As shown recently [3], slight violations of the alignment of local maxima and of the ripple equivalence lead to the deviation of the bootstrap current from its Shaing-Callen limit. These deviations scale with the mean free path as $l_c$ and $l_c^{1/2}$, respectively. Here, we extend the formula describing this deviation "offset" in devices with predominant poloidal closure of magnetic field strength contours~\cite{bootstrap} to general quasi-symmetry. This formula only requires the computation of double integrals on the magnetic surface, leading to computation times not exceeding the evaluation of the Shaing-Callen expression. We apply its numerical implementation to devices close to omnigeneity and check the results against direct evaluation by the neoclassical solver NEO-2 [4].

[1] P. Helander, J. Geiger, H. Maassberg, Phys. Plasmas 18(9): 092505 (2011)
[2] K. C. Shaing and J. D. Callen, Phys. Fluids, 26(11):3315-3326 (1983)
[3] C. G. Albert et al., Journal of Plasma Physics, 91(3):E77 (2025)
[4] W. Kernbichler et al., Plasma Phys. Control. Fusion, 58(10):104001 (2016)

Speaker: Sergei Kasilov (Graz University of Technology)

1:30 PM Effects of equilibrium pressure on plasma response to RMPs in a spherical tokamak

This study presents a comprehensive analysis of the equilibrium pressure on the plasma response to resonant magnetic perturbations (RMPs) in the spherical tokamak (ST) MAST-U, employing both single-fluid and MHD-kinetic hybrid models (implemented via the MARS-F/K codes). As a key finding, the study identifies two different pressure-driven eigenmodes, exhibiting Sturmian property, that affect the Troyon no-wall limits for the onset of the $n=1$ and $n=2$ ($n$ is the toroidal mode number) ideal external kink instabilities as well as the corresponding plasma response to the applied RMP. With increasing equilibrium pressure, the plasma response to RMPs is significantly enhanced in the ST plasma, particularly in the high-pressure regime where kinetic effects strongly stabilize the external kink instability. The Troyon no-wall limit divides the plasma response into two regions: well below the limit, the response amplitudes and trends (versus pressure) are similar between the fluid and kinetic models; as the equilibrium pressure approaches the Troyon limit, the kinetic model predicts significant amplification of the RMP field, up to 30 times for cases considered. A relatively weak dependence of the optimal coil phasing on the equilibrium pressure is computed in this ST plasma, similar to the trend obtained for the conventional aspect ratio devices. These findings underscore the importance of incorporating kinetic effects in accurate prediction of the plasma response to RMPs in high-pressure ST tokamak plasmas and provide a theoretical basis for optimizing RMP-based control of the edge-localized modes in future ST devices.

Speaker: Guanqi Dong

1:30 PM Energetic Particle Transport in burning plasmas

Burning plasmas in fusion reactors are complex systems where energetic particles (EP) play a fundamental role in cross-scale interactions [1]. This study reviews phase space zonal structures (PSZS) [2-5] and their significance in transport analyses. Using synthetic diagnostics from the HMGC and ORB5 codes [6,7], we illustrate the role of PSZS in capturing transport dynamics in burning plasmas Gyrokinetic simulations accurately. While transport studies assume Maxwellian equilibria, for EPs and burning plasmas in general, a more comprehensive description is needed to capture self-organization processes. By deriving governing equations for PSZS using multi-scale perturbation theory, we can model modifications of the equilibrium caused by resonant interactions. This approach allows us to recover standard transport equations in the proper limit.

A new phase space transport workflow called ATEP [8] is proposed to accurately describe PSZS dynamics. This workflow enables us to restart Global Gyrokinetic codes from PSZS distributions, extending simulations over long time scales without assuming a model distribution function. By comparing global gyrokinetic simulation results, e.g, from ORB5, and ATEP we effectively construct a hierarchical approach for PSZS evolution. Additionally, we introduce the Dyson-Schrödinger model (DSM) [9]in the hierarchy of transport models, filling the gap between ORB5 and ATEP. A numerical workflow [10] based on the PEANUTS suite of codes is presented to solve DSM.

Speaker: Matteo Valerio Falessi (ENEA)

1:30 PM Energy balance for unstable ion Bernstein waves in 6D kinetic Vlasov simulations

We present a novel method for calculating particle and energy flows in the 6D kinetic Vlasov equation with adiabatic
electrons. This approach enables the determination of energy and particle fluxes from lower-order moments of
the distribution function, such as the kinetic energy density and the momentum transfer tensor. In addition to this
decomposition, we derive the residual Poynting flux in the electrostatic limit and evaluate its contribution to the
total energy flux.
The results indicate that energy fluxes are primarily dominated by the 𝑬 × 𝑩 heat flux, with additional contributions
from the momentum transfer tensor and the Poynting flux. Our analysis reveals an additional contribution that
is negligible for low-frequency gyrokinetic modes but may become significant for high-frequency modes, such as
ion Bernstein waves (IBWs). This technique offers two major advantages. First, it allows for the identification
of individual contributions to the energy flux, including the 𝑬 × 𝑩 heat flux known from gyrokinetics, thereby
establishing a direct connection to established theory. Second, it reduces inherent gyro-oscillations in both energy
and particle fluxes by decomposing the expressions into components with fewer gyrooscillations, allowing for more
reliable diagnostics. [2].
The resulting expressions for the energy and particle fluxes are compared with simulation results of ion temperature
gradient (ITG) turbulence, using both local and nonlinear treatments of the temperature gradient. By comparing
the analytical expressions with the simulated fluxes and the decay of the initial temperature profile, we demonstrate
good agreement with the sum of the individual contributions, thereby confirming the validity of the proposed
method.
Previous research [1, 3] has shown that the fully kinetic system exhibits behaviors beyond the scope of gyrokinetics
in scenarios with large density and temperature gradients, such as those found at the edge of a tokamak during tran-
sition phases. A comprehensive understanding of all energy transport channels is therefore essential—particularly
when the model is extended to incorporate more detailed electron physics.
References
[1] M. Raeth and K. Hallatschek. High-frequency nongyrokinetic turbulence at tokamak edge parameters. Phys. Rev. Lett., 133:195101, Nov
2024.
[2] M. Raeth and K. Hallatschek. Energy balance for 6d kinetic ions with adiabatic electrons. Physics of Plasmas, 32(5), 2025.
[3] Mario Raeth. Beyond gyrokinetic theory: Excitation of high-frequency turbulence in 6d vlasov simulations of magnetized plasmas with
steep temperature and density gradients. PhD Thesis - University Library: Technical University of Munich, 2023.

Speaker: Mario Raeth (Max Planck Institute for Plasma Physics)

1:30 PM Exploring 3D turbulent transport in linear plasma devices using SOLEDGE3X

The study presents global 3D simulations of a linear plasma device using the first-principles drift-reduced fluid code SOLEDGE3X. The effects of parallel currents on shaping the turbulent regime are investigated, focusing on the interplay between drift-wave and sheath-driven instabilities. In open field-line regions of a tokamak, sheath losses have traditionally been regarded as the sole driver of parallel instabilities. However, in high-density regimes - where elevated resistivity amplifies bulk parallel losses — drift-wave instabilities can also emerge, especially when collisionality is high and connection lengths are long. The scenario is even more complex if one considers the possibility that different dominant instability mechanisms are simultaneously present in distinct regions of the domain, so that only 3D models can capture the global picture.\
In this light, the present study aims to identify the plasma parameters range in which drift-wave turbulence overtakes sheath-losses in a linear plasma device. The device is modeled by a slab geometry with uniform, straight magnetic field-lines which orthogonally intersect a wall at both ends of the domain. Sheath (Bohm) boundary conditions are applied along the parallel direction at the end walls, whereas periodic boundary conditions are assumed in cross-field directions. A centrally located particle and energy source with a Gaussian cross-section is added, making turbulence essentially flux-driven. \
The onset of drift-wave turbulence is evaluated both analytically and numerically for several values of plasma resistivity and connection length, attempting to detect the critical values of the control parameters leading to a partial disconnection of the plasma column from the sheath. As expected, the results show multiple turbulent behaviors for long and resistive plasma columns: parallel modes are excited in the region far from the sheath, indicating that the underlying physics goes beyond simple flute-like dynamics. The distinction of "sheath-connected" and "resistive" cross-field planes along the domain enables a comparison with reduced 2D models, where an ad-hoc parallel closure must be chosen. Similarities and differences between the models are shown, thus highlighting the role of the true three-dimensional geometry even when the dominant parallel losses are established and the 2D model should reproduce the turbulent behavior. In this context, particular attention is given to the role of the third dimension - along the direction of the magnetic field - on drift wave dynamics, as in 2D models it is usually studied by imposing a prescribed parallel wave vector while 3D simulations can self-consistently capture the superposition of stable and unstable parallel modes.\
In high-density regimes, another key mechanism that becomes increasingly relevant is the interaction between plasma and impurities. The second part of this study extends the analysis to multi-species fluid simulations using the SOLEDGE3X code, applied to a linear configuration inspired by Magnum-PSI — a large linear plasma device designed to reproduce fusion-relevant edge plasma conditions. Overall, the goal is to advance the understanding of turbulent impurity transport in magnetized, collisional plasmas with open magnetic field-lines, where a comprehensive understanding is still missing.\
The analysis of flux-driven turbulence allows for the investigation of multi-species interactions without resorting to ad-hoc anomalous transport models. In this framework, the impact of the Zhdanov closure is investigated through the comparison with trace impurity simulations, where impurities are passively advected by the main plasma. The role of impurity charge, mass and concentration is addressed to identify regimes where significant changes in turbulent transport arise, thus offering clearer insight into the mutual interaction between main plasma components and impurities.

Speaker: Michele Lambresa (Aix-Marseille Université)

1:30 PM Geometry effects on gyrokinetic instabilities and turbulence in W7-X

The stellarator Wendelstein 7-X (W7-X) demonstrated the effectiveness of reducing neoclassical transport through magnetic field optimization [1]. Its confinement is primarily governed by turbulence arising from instabilities at scales comparable to the gyroradius [2,3]. For small plasma beta (the ratio of kinetic to magnetic pressure), these instabilities are predominantly electrostatic and often driven by ion temperature gradients (ITG). ITG-driven turbulence is sensitive to magnetic field properties—a dependence that needs to be considered in the design of the next-generation optimized stellarators. However, the experimental characterization and theoretical modeling of turbulence in W7-X remain incomplete, particularly regarding its geometrical properties.
In this contribution, we numerically investigate gyrokinetic plasma turbulence in W7-X, with a focus on potential performance improvements through the modification of geometrical properties. Specifically, we compare density fluctuation measurements from the Phase Contrast Imaging (PCI) diagnostic [4,5] with both linear and nonlinear simulations performed using the gyrokinetic code stella [6]. As part of this comparison, we examine the impact of the mirror ratio and the global value of the rotational transform on plasma performance [7]. Our simulations show good agreement with analytical expectations, although some experimental observations still remain puzzling. Finally, we propose a method for locally modifying ITG turbulence through tailored adjustments of the rotational transform profile [8]. This approach builds on the influence of electron cyclotron current drive in plasmas heated via electron cyclotron resonance [9].

[1] Beidler, C. D. et al., Nature 596, 7871 (2021): 221-226
[2] Bozhenkov, S. A. et al., Nuclear Fusion 60.6 (2020): 066011
[3] Navarro, A. Banón et al., Nuclear Fusion 63.5 (2023): 054003
[4] Edlund, Eric M. et al., Review of Scientific Instruments 89.10 (2018)
[5] Huang, Z. et al., Journal of Instrumentation 16.01 (2021): P01014
[6] Barnes, M. et al., Journal of Computational Physics 391 (2019): 365-380
[7] Bähner, J.-P. et al., submitted to Nuclear Fusion (2025)
[8] Podavini, L. et al., Journal of Plasma Physics 90.4 (2024): 905900414
[9] Zanini, M. et al., Nuclear Fusion 61.11 (2021): 116053

Speaker: Linda Podavini (Max Planck Institute for Plasma Physics, Greifswald)

1:30 PM Heat flux decay length scaling based on first principle turbulence codes

This abstract outlines the motivations behind my PhD project and introduces preliminary work whose results will be presented in a poster format. The content consists of a set of turbulence simulations exploring the parameter space.

Speaker: Hugo Corvoysier (IRFM/CEA)

1:30 PM Integrating Core and Edge models for highly radiative scenario development

Accurate prediction of core turbulent transport, along with its coupling to edge transport models or physics-informed edge boundary conditions, is essential for developing operational scenarios for future fusion devices. Nonlinear gyrokinetic models for core transport, though highly accurate, are computationally expensive to use in this type of integrated modeling. Instead, quasilinear models offer a practical alternative, providing a balance between accuracy and computational cost, thus allowing the development of coupled core-edge frameworks. This work uses the recent developments in METIS [1] (an integrated modeling platform), specifically the implementation of quasilinear turbulent transport computations using TGLF [2], to deliver accurate core transport modeling for the coupled edge transport model SOLEDGE3X-EIRENE.
The neural network version of the quasilinear gyrokinetic model QuaLiKiz [3] is coupled to METIS and is employed in simulations of WEST plasmas, but has exhibited limitations in reproducing edge transport inside the separatrix, e.g, capturing the dependence of energy confinement time on plasma current. On the other hand, the quasilinear gyrofluid model TGLF has demonstrated improved predictive capabilities in ASDEX Upgrade (AUG) plasma simulations [4], addressing some limitations of QuaLiKiz. Motivated by the improved predictive performance of TGLF, it has been implemented in METIS to enhance the predictive accuracy of integrated modeling. The impact on core turbulence of nitrogen seeding in a WEST plasma featuring the formation of an X-point radiator regime is examined, showing a reduction in ion heat diffusivity and thereby improving confinement properties. The METIS-TGLF integrated model is further applied to simulate steady-state temperature profiles for an ITER-like baseline scenario (Ip = 15 MA) with successful iterative convergence, and compared against the QuaLiKiz 10D neural network surrogate.
Based on these results, the METIS-TGLF core integration is being coupled to the SOLEDGE3X-EIRENE to develop a framework for simulating the behavior of both core and edge plasma. This will allow the investigation of the impact of core-edge interactions, such as the edge boundary conditions (separatrix densities, temperatures, impurity content) on core turbulent transport and the following impact of the change of core conditions on the edge plasma, e.g., the power crossing the separatrix and levels of transport at the edge. It also opens the possibility to study highly radiative plasma scenarios, such as the XPR, where the interactions between the core and edge are instrumental [5] for plasma scenario predictions and could be used to prepare JT-60SA operations in such regimes, after being validated on experimental WEST data.

References:
[1] J.F. Artaud et al 2018 Nucl. Fusion 58 105001
[2] Staebler G., Kinsey J. and Waltz R. 2005 Phys. Plasmas 12 102508
[3] Phys. Plasmas 27, 022310 (2020)
[4] C. Angioni et al 2022 Nucl. Fusion 62 066015
[5] X. Yang et al 2020 Nucl. Fusion 60 086012

Speaker: Rajbir Kaur (IRFM, CEA, Cadarache)

1:30 PM ITER 15 MA-reference case - Electromagnetic effects in the core with integrated modelling and local gyro-kinetic simulations

The turbulence in the core of future devices will be very different from current devices [1]. Fast ions and electromagnetic (EM) effects have a complex impact on the turbulence both through linear effects, such as linear EM stabilization of electrostatic (ES) modes, and nonlinear effects, such as enhanced coupling to zonal flows. As an initial step towards better understanding this regime we focus on the local electromagnetic effects for the ITER 15MAreference case. We have used the JETTO case published in [1] as a starting point for heating, equilibrium, pedestal etc. We have performed predictive integrated modelling simulations with JETTO with and without EM effects with the gyro-fluid model TGLF [2] to see the impact on the predicted profiles. We evolve densities, temperatures and the current as well as reevaluate the equilibrium continuously with an internal boundary at ρ=0.9. For the EM simulation at the magnetic axis the normalized plasma pressures, ꞵe, is 5.1% and the result of the predicted profiles is displayed in Figure 1. Interestingly, the ES and EM predictive simulations give almost the same results up to ρ=0.5 and diverge in the core. I.e. they differentiate where ꞵe, is larger. Based on these simulations, we plan to perform stand alone linear analysis with TGLF and the gyro-kinetic code GKW [3] to study the unstable modes at several radial positions. Preliminary results suggest the emergence of Kinetic Ballooning Modes in the core which could explain the difference in the predictive simulations. Additionally, this study is being used to verify TGLF and its settings against GKW. Understanding the new transport regime in upcoming devices will enable the development of improved reduced transport models critical to future device design and operation.
References
[1] P. Mantica et al., Plasma Phys. Control. Fusion 62, 014021 (2020)
[2] G. M. Staebler et al., Physics of Plasmas 12, 102508 (2005)
[3] A. Peeters et al., Physics Communications 180, 2650–2672 (2009)

Speaker: Emil Fransson (Aix-Marseille Université)

1:30 PM SELFCONSISTENCY BETWEEN RAY-TRACING/FOKKER-PLANCK AND MHD EQUILIBRIUM FOR THE LOWER HYBRID CUTTNE DRIVE SIMULATION.

In the last decades, the modelling of RF-driven toroidal current advanced importantly at the Lower Hybrid (LH) frequency in tokamaks, especially in non-inductive regimes [1]. Of particular importance is the understanding of spectral broadening in the scrape-off layer (SOL), enabling single-pass wave absorption [2], notably in in high-density, low-temperature plasmas with small aspect ratios. Introduced heuristically [3], this mechanism is now mainly justified through density filamentation at the plasma edge [4].
However, LH-driven current modelling coherent with the electric field remains a complex challenge due to their interdependent nature [5], as the electric field strongly influence the MHD equilibrium affecting the wave propagation and the current drive. To address this, a fully self-consistent simulation approach has been developed. It couples multiple computational tools: the C3PO/LUKE solver [6] for ray-tracing and 3D Fokker-Planck calculations, METIS for integrated plasma modelling [7], and FEEQS for solving the MHD equilibrium [8], integrated within the SLUKE framework, facilitating scripting and distributed computing. A key advantage of this approach is its ability to overcome inconsistencies arising from simplified LH models used in early-stage MHD equilibrium estimates, as the initial simulations often produce a current density profile that diverges significantly from the one required by the equilibrium model. The self-consistent loop corrects this by iteratively updating the LH current and electric field profiles until convergence is achieved, typically within ten iterations.
The method has been validated using well-diagnosed Tore Supra plasmas The example here highlighted, discharge #45525 (Fig.1), is characterized in flat top regime at time interval 27-28s, with a fairly hot hydrogen plasma (Te0 = 5.6 keV) reaching peak density ne0=1.9x10+19m-3. Simulations demonstrate convergence of the current density and electric field profiles after several iterations.
This modeling framework will be applied to other tokamaks like WEST to assess its applicability across different magnetic configurations and eventually with adapted to other RF waves, such as Electron Bernstein Waves [9]. Overall, this approach represents a significant step forward in the predictive modeling of RF-driven current in fusion plasmas.
[1] Y. Peysson et al., EPJ Web of Conferences, 157, 02007 (2017)
[2] Y. Peysson et al., Journal of Fusion Energy, 39, 270 (2020)
[3] J. Decker et al., Phys. Plasmas, 21, 092504 (2014)
[4] B. Biswas et al., Nucl. Fusion, 63, 016029 (2023)
[5] N. Fisch, Rev. Mod. Phys., 59, 1, 175 (1987)
[6] Y. Peysson and J. Decker, Fusion Science and Technology, 65, 22 (2014)
[7] J.F. Artaud et al., Nucl. Fusion, 58, 105001 (2018)
[8] H. Heumann et al., Journal of Plasma Physics, 81, 905810301 (2015)
[9] T. Wilson et al., EPJ Web of Conferences, 277, 01011 (2023)

Speaker: Riccardo Saura (CEA-IRFM)

1:30 PM Simulating Parametric Recombination Processes Between Injected and Trapped Microwaves

Evidence from magnetically confined fusion experiments over the past decades shows that X-mode waves used for ECRH (X2) are prone to nonlinear wave interactions. These interactions are known as parametric decay instabilities, and they typically occur in localized regions of the plasma edge. The instabilities originate from thermal upper-hybrid (UH) waves that are trapped by non-monotonic plasma structures. When the injected X2 wave frequency is approximately twice the UH frequency, it can decay into two of the trapped UH waves. The coupling and trapping allow the two UH waves to grow exponentially in time if the power threshold is exceeded. Such instabilities can reduce ECRH efficiency through anomalous absorption of the X2 wave, but recent studies suggest that these processes may also serve as novel diagnostic tools for plasma edge turbulence.
However, the overall absorption of the X2 wave is highly dynamical, and it strongly depends on the saturation mechanisms of the instability, each governed by specific plasma conditions.

We develop analytical models within the WKB approximation to study the spatiotemporal evolution of the two trapped UH waves. The waves are described by a nonlinear envelope equation derived from geometric optics, which is solved on a spatial grid and integrated forward in time to obtain the initial exponential growth. We focus on a less-explored saturation mechanism that involves a parametric recombination of the injected X2 wave and either of the two UH waves, resulting in up-shifted X-mode waves above the R-cutoff. The model is extended to include the recombination process, and we quantify the energy transfer from the injected X2 wave to the up-shifted X-mode waves. Finally, the results are benchmarked against 1D3V kinetic Particle-in-Cell simulations using the code EPOCH.

Speaker: Johan Kølsen de Wit (Technical University of Denmark)

1:30 PM Towards 3D drift-kinetic transport modeling of the electric field in stellarators

We present an iterative algorithm for the self-consistent computation of the electrostatic potential in 3D magnetic fields using the guiding-center tracing code GORILLA. Due to the piecewise linear interpolation of electromagnetic field quantities leading to linear equations of motion within small volume elements, GORILLA has favourable computational costs while still retaining symplectic properties. Its application to transport problems especially in the transition from core to edge plasma therefore seems promising. For the self-consistent electric field computation, we do not address the full Laplace equation but rather solve for the charge neutrality condition in an iterative manner. This is a completely local ansatz avoiding any potentially complicated fitting with smooth functions. The results will be compared to a procedure which has already been demonstrated to work in 1D tests modelling parallel motion or modelling neoclassical perpendicular transport in 1D. Both cases have been shown to lead to ambipolar electric fields.

Speaker: Jonatan Schatzlmayr

1:30 PM Turbulent transport in the pedestal of small-ELMs regimes at JET

Recent experiments at the JET tokamak with the Be/W wall have led to the development of new H-mode regimes featuring high energy confinement and small edge-localized modes (ELMs). These regimes, achieved with low or no gas injection, reproduce key plasma parameters relevant to the ITER baseline scenario, such as $q_{95} = 3.2$, $\beta_{\text{p}} < 1$, $\beta_{\text{N}} = 1.8$–$2$, $H_{98} = 1$–$1.4$, and low pedestal collisionality ($\nu_{e,\text{ped}}^* = 0.1$–$0.4$) are referred to as baseline-small-ELMs (BSE) regimes, and represent ideal scenarios for investigating transport processes of reactor-relevant plasmas.

In this work, turbulent transport processes in the pedestal region of a selected BSE regime are investigated through a comparative analysis with a standard H-mode with type-I ELMs. Previous analyses using local gyrokinetic simulations with the GENE code are here extended with global, gradient-driven simulations retaining the full pedestal region ($0.86 < \rho_\text{tor}< 0.98$), representing a more comprehensive model for studying pedestal turbulence.

Local linear stability analyses at the pedestal top show that, at ion-scales, the type-I ELM regime is dominated by hybrid ITG-KBM and KBM modes, while the BSE regime is dominated by hybrid ITG-TEM modes, due to the lower $\beta_e$ from reduced density. At electron-scales, multiple ETG branches are destabilized in both regimes. Nonlinear ion-scale turbulence simulations for the BSE regime focused on the impact of key edge transport saturation mechanisms - the interplay between electromagnetic effects and equilibrium $E \times B$ shear. A strong electromagnetic stabilization mechanism, accompanied by enhanced large-scale zonal flow activity, is found to be crucial in achieving transport levels compatible with experimental observations.

The first global simulations of the instability spectrum for the BSE regime are consistent with local results, with ITG-TEM modes being the most unstable. A systematic sensitivity analysis, involving variations in density and temperature profiles as well as impurity content, will be presented to quantify their effects.

These results contribute to advancing the understanding of turbulent transport mechanisms in the pedestal region of new H-mode BSE regimes. Future work will focus on assessing the role of global effects in turbulence saturation.

Speaker: Mattia Dicorato (Max Planck Institute for Plasma Physics, Garching, Germany)

1:30 PM Variational moments solution of the anisotropic axisymmetric equilbrium problem

Pressure anisotropy due to auxiliary heated fast ions or runaway electrons can significantly
impact the macroscopic magnetic equilibrium. Moreover, since the plasma toroidal
diamagnetism is predominantly impacted by the perpendicular pressure, measurements of the
outside poloidal magnetic field combined with measurements of the toroidal flux allow to
distinguish between both components, as shown in [1]. In scenarios of predominantly parallel
anisotropy, inverse aspect ratio asymptotic expansions of the equations predict a weak impact
on the overall geometry. Moreover, standard derivations of force balance in the presence of
energetic particles assume a prescribed shape for their distribution function such as the
modified bi-Maxwellian [2], and employ the trace limit to neglect them in the quasineutrality.
It is thus necessary to assess whether the latter effects are indeed negligible with respect to the parallel anisotropy.

Speaker: Guillaume Van Parys (Swiss Plasma Center - EPFL)

1:30 PM Who would bet on micro-tearing modes driving a large heavy impurity flux?

In tokamak plasmas, micro-tearing modes (MTMs) are destabilised at high plasma beta and large electron temperature gradient. They are electro-magnetic instabilities particularly prone to be excited in spherical tokamaks, where beta is large, and in improved confinement regimes or in the pedestal for conventional tokamaks.
For MTMs, the transport arising from magnetic flutter scales as the thermal velocity (Rechester-Rosenbluth estimate). It can be very large for the electron channel but is negligible for heavy impurities. This is probably why impurity transport by MTMs has not received much attention until now.
However, MTMs not only lead to radial magnetic field fluctuations, but also to electric potential fluctuations. It is found that these electric potential fluctuations drives a convective flux of heavy impurities. This pinch is directed outward and can reach very large values, with Cp=V/D up to 40. It is due to perpendicular compression from the magnetic and Coriolis drifts in the tail of the electrostatic mode structure. The resulting pinch is particularly large for heavy impurities, when the mode structure is extended along the field lines and strongly increases with toroidal rotation.
The main mechanism of the MTM impurity pinch will be presented together with its main parametric dependencies and quasi-linear estimates for realistic cases.

Speaker: Yann Camenen (CNRS, Aix-Marseille Univ., PIIM UMR7345)

3:30 PM → 4:00 PM Coffee break

4:00 PM → 4:40 PM I.10-Duarte: Shifting and Splitting of Resonance Lines due to Dynamical Friction in Plasmas

Speaker: Vinicius Duarte (Princeton Plasma Physics Laboratory)

4:40 PM → 5:05 PM O.9-Sanchez: CIEMAT-QI4X: a reactor-relevant stellarator configuration compatible with an island divertor

The stellarator concept offers advantages for a fusion reactor compared to the tokamak, but stellarator magnetic fields require careful optimization to achieve a confinement quality comparable to that of tokamaks. The numerical optimization for reduced neoclassical transport has already been experimentally validated in W7-X [1] and HSX [2], and great improvements have been made in the last few years including fast-ion confinement and turbulent transport in the set of optimization criteria [3,4,5]. However, insufficient attention is usually paid to the rotational transform profile during the optimization process. In the optimization of quasi-symmetric configurations, few restrictions are commonly set to the rotational transform profile. In the optimization of quasi-isodynamic (QI) configurations, if an island divertor is pursued, the rotational transform is usually constrained only to avoid the lowest-order rational values in the plasma column and to approach a low-order rational value at the edge [3,4]. However, if the rotational transform profile is not optimized more carefully than this, several issues, such as the formation of low-order islands, the overlapping of neighboring islands, and the insufficient quality of the edge island for a divertor, can appear, which can be worsened by finite b effects [6]. Furthermore, these issues can be very sensitive to coil design details and construction errors.
In this work, we show how including a strict control of the rotational transform profile and the magnetic shear in the optimization process can improve the flux surface quality and the structure of the divertor island, and propose new metrics to be included in the optimization with this purpose. Using this strategy we have obtained a new reactor-relevant QI configuration, named CIEMAT-QI4X, which keeps the physics properties of the QI configuration presented in [3] (reduced neoclassical and turbulent transport, low bootstrap current, and good fast ion confinement), while at the same time improves the flux surface quality and shows a prominent low-order island at the edge suited to design an island divertor. Furthermore, its optimized rotational transform profile makes it more robust to coil construction errors. A set of optimized magnetic coils for this configuration is also presented.

Speaker: Edilberto Sanchez

5:05 PM → 5:30 PM O.10-Jamann: Insights into the ExB staircase via synthetic reflectometry and gyrokinetic modeling

Tokamak plasmas are complex non-equilibrium systems where turbulence plays a critical role in the transport of heat and particles. These turbulent processes span a wide range of spatial and temporal scales, making their observation particularly challenging. Ultra-fast sweeping reflectometry is a diagnostic technique capable of measuring electron density fluctuations with very high spatial and temporal resolution, capturing phenomena driven by both MHD activity and microturbulence. This technique has been used to observe meso-scale structures, such as the ExB staircase — a successive radial pattern of poloidal flows and avalanches [1]. This tertiary structure emerges from the self-organization of turbulence and regulates turbulent transport by alternating spatially between phases of free energy accumulation (zonal mean flows) and bursts of outward transport. Such organization is believed to enhance plasma confinement and could be of significant importance for future fusion devices.
In this work, we propose to probe turbulence maps generated by the gyrokinetic code GYSELA using the synthetic reflectometry diagnostic FeDoT [2]. FeDoT is based on a two-dimensional (2D) Finite Difference Time Domain (FDTD) full-wave numerical scheme with absorbing boundary conditions. It supports arbitrary antenna configurations, and can simulate both O-mode and X-mode polarizations at any probing incidence angle. This flexibility enables the extraction of key turbulence characteristics, including frequency spectra, fluctuation levels and radial correlation lengths.
The turbulence data analyzed in this study originates from flux-driven simulations with kinetic electrons. The external source can be modulated to vary the distance to “marginality” (see G. Dif-Pradalier et al., this conference), allowing us to investigate its influence on the formation of the ExB staircase. This approach enables a direct comparison of synthetic diagnostic results obtained in scenarios both with and without staircase formation. The simulated reflectometry signals are then compared to experimental measurements to identify and validate ExB staircase signatures. Additionally, we propose new diagnostic signatures that may further enhance the detection and characterization of these meso-scale structures.
This integrated approach, coupling synthetic diagnostics and flux-driven gyrokinetic simulations, advances the interpretation of experimental measurements and paves the way toward a deeper understanding of turbulent self-organization mechanisms in tokamak plasmas.

References
[1] G. Dif-Pradalier et al. Phys. Rev. Lett. 114, 085004 (2015) ; G. Hornung et al. Nuclear Fusion: 57.1 (2016).
[2] A. Glasser et al. Plasma Phys. Control. Fusion 67 035022 (2025).

Speaker: Antoine Jamann (CEA, IRFM, F-13108 Saint Paul-lez-Durance, France)

Thu, September 25

8:30 AM → 9:20 AM I.3-Hizanidis: A quantum computing approach to electromagnetic wave propagation in fusion plasmas

Speaker: Kyriakos Hizanidis (National Technical University of Athens (NTUA), Greece)

9:20 AM → 10:00 AM I.11-Ewart: Rapid thermalisation, and non-thermal equilibria in near-collisionless plasmas

Speaker: Robert Ewart (Princeton University)

10:00 AM → 10:25 AM O.11-Dif-Pradalier: Weakly driven machines of the future: a challenge for plasma turbulence modelling

Self-organised turbulent processes are common in many non-equilibrium physical and biological systems and lead to pattern formation. Well-known examples in magnetic fusion include zonal flows or magnetic islands. Other processes can occur, often less emphasised, such as turbulence self-advection (spreading), front propagation or blob emission and many other structures, such as staircases, can also arise and affect transport. In regimes of "marginal stability", such nonlinear structures play a prominent role and slow, large-scale patterns resulting from the long-term evolution of turbulence profoundly affect transport processes. Such regimes are likely to be highly relevant regimes for future machines, where a tenfold decrease in power density is expected, and require a flux-driven description. Precise comparisons with state-of-the-art gradient-driven or quasilinear approaches yield significantly different transport levels, mean gradients and flow patterns, both in the core [1] and at the plasma edge [2].

We propose to review what flux-driven models and near marginal regimes entail and why they are particularly relevant for future machines. We have shown that proximity to marginal stability leads to significant discrepancies with local or quasilinear approaches. We extend this investigation of near marginal regime through a comprehensive series of flux-driven gyrokinetic calculations with a kinetic electron response, using the GYSELA code, scanning distance to marginality. We discuss the physical processes specific to marginal regimes, the implications for fundamental theory and practical modelling of future machines, and current avenues for addressing these important issues.

Speaker: Guilhem Dif-Pradalier (CEA, IRFM)

10:25 AM → 10:50 AM Coffee break

10:50 AM → 11:30 AM I.12-Foster: Alpha-particle orbits near rational flux surfaces in stellarators

11:30 AM → 11:55 AM O.12-Rofman: Finite beta effects in global, electromagnetic, gyrokinetic, linear and nonlinear simulations of Alfvén eigenmodes and microturbulence

Future nuclear fusion reactors will have to magnetically confine burning plasmas. In such scenarios, even a small fraction of fusion-born energetic particles (EP), which are 100 times hotter than the electrons, will contribute greatly to the kinetic pressure and therefore to the shaping of the MHD equilibrium, mainly via the Shafranov Shift. Nonetheless, many numerical works still prefer to use simplified magnetic geometries (e.g. ad-hoc or concentric circular MHD) to draw operational conclusions.
In this work we perform first-principles numerical simulations using the gyrokinetic, electromagnetic, global code ORB5 to study the effect of a self consistent high $\beta$ equilibrium on the arising Alfv\'en Eigenmodes (destabilized by EPs) and (electromagnetic) Ion Temperature Gradient (ITG) microturbulence.
Exploring the parameter space of both bulk plasma profiles and EP fraction, we show the linear (mainly stabilizing) effects of accounting for the bulk plasma and EP kinetic pressure in the MHD equilibrium, on the unstable TAE and ITG modes in our system. Focusing on the early nonlinear phase of a single toroidal mode TAE and ITG (separately), we study the impact of self-generated zonal flows on the shearing rates, kinetic profiles and fluxes, in both consistent and not consistent MHD equilibrium.

Overall, we show that a burning plasma with a self-consistent MHD equilibrium behaves significantly differently than if the bulk or EP pressure is not considered.

Speaker: Baruch Rofman (Ecole Polytechnique F\'ed\'erale de Lausanne, Swiss Plasma Center, CH-1015 Lausanne, Switzerland)

11:55 AM → 12:20 PM O.13- De Lucca: Electromagnetic suppression of drift-wave turbulence and the LH transition

Leveraging the results of a series of $3$D flux-driven $2$-fluid simulations in a diverted equilibrium with GBS, it is shown how a regime of high confinement can develop as the power crossing the separatrix exceeds a critical value. As the edge temperature increases, the resistive-ballooning turbulence characteristic of L-mode conditions becomes subdominant, and turbulence is mostly driven by the electron drift-wave instability. Electromagnetic effects then act to suppress drift-wave turbulence by enhancing the electron adiabatic response. For the resistive branch of the drift-wave instability in particular, the strength of suppression is proportional to the background gradients driving the instability. Under a set of specified conditions, the plasma can therefore become unstable to the spontaneous formation of an edge transport barrier. In this regime, a steepening of the edge profiles in $n, T_e$ leads to a further decrease of turbulent flux and a feedback loop develops, driving the transport barrier formation. Furthermore, the transition to a high-confinement regime is impeded when the toroidal magnetic field points in the unfavourable direction for H-mode access. The power required to access this regime $P_{\text{th}}$ is analytically derived in a simplified geometry, via a local quasi-linear estimate for the $E \times B$ turbulent transport rate in the electromagnetic drift-wave regime. The resulting scaling law for $P_{\text{th}}$ is compared with the ITPA experimental database for the threshold power $P_{\text{LH}}$ to access H-mode in tokamaks, yielding good overall agreement $R^2 \simeq 0.7$.

Speakers: Brenno Jason Sanzio Peter De Lucca, Louis Stenger (EPFL), Paolo Ricci (EPFL), Zeno Tecchiolli (EPFL)

12:20 PM → 1:30 PM Lunch break

1:30 PM → 2:10 PM I.13-Garcia: Resilient Stellarator Divertor Characteristics in the Helically Symmetric eXperiment

2:10 PM → 6:10 PM ITER visit

Fri, September 26

8:30 AM → 9:20 AM I.4-Belli: Multiscale analysis of improved confinement regimes in D-T plasmas

Speaker: Emily Belli

9:20 AM → 10:00 AM I.14-Mishchenko: Global electromagnetic turbulence and waves in stellarator plasmas

Speaker: Alexey Mishchenko

10:00 AM → 10:25 AM O.15-Mariani: Predicting the transport of a DTT negative triangularity scenario

Experiments at TCV [1–3], DIII-D [4–6] and AUG [7,8] indicate that Negative Triangularity (NT) plasmas [9] can achieve H-mode-like performance with negligible ELM activity. Therefore, NT is investigated as a possible scenario for fusion reactors [10, 11]. However, the physics of NT is still to be fully understood. An experimental and theoretical effort is ongoing to fill this gap.

A NT scenario is being designed for the Divertor Tokamak Test (DTT) facility [13], under construction in Italy, which aims to test alternative designs and materials for the EU DEMO divertor. Its transport properties are being studied by performing integrated modelling (ASTRA [14]/TGLF [15]), gyrokinetic simulations (GENE [16]) and experiments with DTT-like shapes on actual tokamaks. The first results of DTT predictions [17], as well as of experiments performed at TCV [3] and AUG [8], indicated that with the first proposed DTT NT shape with relatively small average triangularity, a beneficial effect of NT was found in the edge/scrape-off layer [18]. The NT confinement levels were found intermediate between positive delta H-mode and L-mode and NT core pressure values which are similar to the ones predicted for the Positive Triangularity (PT) H-mode scenario, in absence of ELMs, making the NT option an attractive alternative.

Then, a new DTT shape with larger upper NT and reduced volume was proposed, to further optimize the scenario. A newly developed ASTRA/TGLF interface that provides a realistic plasma shape was also adopted, since the standard ASTRA/TGLF Miller geometry was found a too strong approximation for the DTT ‘teardrop’-like NT shapes. In this way, the formation of a proto-pedestal in the edge pressure was observed in the simulations, further improving the NT performance almost reaching the PT H-mode. These ASTRA simulations provided input for more complex GENE-TANGO simulations, which are ongoing.

References
[1] Y. Camenen, et al., 2005 Plasma Phys. Control. Fusion 47, 1971.
[2] S. Coda, et al., 2022 Plasma Phys. Control. Fusion 64, 014004.
[3] A. Balestri, et al., 2024 Plasma Phys. Control. Fusion 66, 065031.
[4] M.E. Austin, et al., 2019 Phys. Rev. Lett. 122, 115001.
[5] A. Marinoni, et al., 2019 Phys. Plasmas 26, 042515.
[6] A. Marinoni, et al., 2021 Nucl. Fusion 61, 116010.
[7] T. Happel, et al., 2023 Nucl. Fusion 63, 016002.
[8] L. Aucone, et al., 2024 Plasma Phys. Control. Fusion 66, 075013.
[9] A. Marinoni, et al., 2021 Rev. Mod Plasma Phys. 5, 6.
[10] S.Yu. Medvedev, et al., 2015 Nucl. Fusion 55, 063013.
[11] M. Kikuchi, et al., 2019 Nucl. Fus. 59(5), 056017.
[12] J. Ball on behalf of the TSVV 2 team, AAPPS-DPP 2023.
[13] R. Ambrosino, et al., 2021 Fusion Eng. Des. 167, 112330.
[14] G.V. Pereverzev and P.N. Yushmanov 2002 IPP Report 5/98.
[15] G.M. Staebler, et al., 2016 Phys. Plasmas 23 062518.
[16] F. Jenko, et al., 2000 Phys. Plasmas 7 1904.
[17] A. Mariani, et al., 2024 Nucl. Fusion 64, 046018.
[18] A. Mariani, et al., 2024 Nucl. Fusion 64, 106024.

Speaker: Alberto Mariani (ISTP-CNR Milano)

10:25 AM → 10:50 AM Coffee break

10:50 AM → 11:30 AM I.15-Qiu: Nonlinear saturation of toroidal Alfvén eigenmode wia ion induced scattering in nonuniform plasmas

Speaker: Dr Zhiyong Qiu (Zhejiang University, Hangzhou, China)

11:30 AM → 11:55 AM O.16-Singh: JOREK modelling of Runaway Electron beam benign termination in JET

The runaway electron (RE) beam benign termination observed in JET pulse 95135 has been modelled in [1] using the nonlinear MHD code JOREK [2]. The study demonstrated the role of magnetic stochasticity in causing RE loss. This demonstration was based on particular assumptions regarding the properties of the background plasma, such as resistivity, that might not be accurate due to the recombination following massive deuterium injection. The transport of REs was modelled through an ad-hoc diffusion due to the high computational demands of fully advective simulation. Moreover, an ideal wall boundary condition was used which tends to have a stabilizing effect on the MHD activity.
In this work, the same RE beam termination event was modelled using RE advection at the speed of light. Different resistivity values were also considered to assess the influence of this uncertain parameter. In particular, the influence of the plasma resistivity on the RE footprint on the wall was studied. It was found that higher resistivity results in MHD modes growing faster and up to larger amplitudes. The intense magnetic stochasticity observed with high resistivities results in a larger wetted area on the wall, contributing to a more benign termination of RE. Similar results were found for ITER in [3].
In addition, the comparison between the RE transport modelled with diffusion and advection showed a slower RE termination event with the advection model with respect to the diffusion due to a slower MHD modes growth rate, consistent with what is shown in [4]. At the same time, a resistive wall boundary condition [5, 6] leads to a faster RE termination due to the absence of the stabilizing effects caused by an ideal wall. As a result, with a background plasma resistivity corresponding to an electron temperature of 10 eV, the RE current loss occurs in 50 µs, which is comparable to the experimentally observed value of 20 µs [1]. With a higher resistivity, the loss time gets even closer to the experimental value.
Finally, in order to better understand the physics of RE beam termination, we also studied the evolution toward a highly MHD-unstable regime. In contrast to the above results, where the simulations were started from an already unstable state, this approach involves ramping up the plasma current from a stable equilibrium. This method provides a more self-consistent view of how benign terminations can arise.
[1] V Bandaru et al 2021 Plasma Phys. Control. Fusion 63 035024
[2] M Hölzl et al 2021 Nucl. Fusion 61 065001
[3] V. Bandaru et al 2024 Nucl. Fusion 64 076053
[4] H. Bergström et al 2025 Plasma Phys. Control. Fusion 67 035004
[5] P. Merkel et al. arXiv:1508.04911 (2015)
[6] M Hölzl et al 2012 J. Phys.: Conf. Ser. 401 012010

Speakers: Cristian Sommariva (Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland), Eric Nardon (CEA, IRFM), Hannes Bergström (Max Planck Institute for Plasma Physics, Garching, Germany), Lovepreet Singh (CEA IRFM), Matthias Hoelzl (Max Planck Institute for Plasma Physics, Garching, Germany), Vinodh Bandaru (Indian Institute of Technology Guwahati, Guwahati, Assam, India)

11:55 AM → 12:20 PM O.17-Lanzarone: Comparison of Neural Network and XGBoost Decision Trees as Reduced Linear Gyrokinetic Model Surrogates for Growth Rate and Stability Prediction

Integrated modelling of tokamaks combines a host of different codes to self-consistently model plasma discharges with key applications in modelling plasma scenarios and reactor designs as well as analysing experimental discharges. Fast and accurate integrated modeling is crucial to enable rapid iteration and efficient use of limited computational resources. Currently, a major bottleneck in integrated modelling is the running of gyro-kinetic simulations to calculate transport fluxes for each time-step, with even the fastest reduced models using the quasi-linear approximation still being orders of magnitude too slow for routine use. To address this challenge, machine learning surrogate models have been explored as a means of significantly accelerating transport predictions. Previous work has demonstrated the use of real time capable Neural Network (NN) surrogate models trained on QuaLiKiz [1] simulations to predict core tokamak transport quasi-linear heat and particle fluxes [2,3] as well as local linear stability and mode eigenvalues [4].
We investigate the viability of another machine learning algorithm: Gradient Boosted Decision Trees (XGBoost [5]) which have been shown to have superior performance to neural networks in tasks involving tabular data such as that from simulations, and for predicting functions with sharp transitions [6] such as the threshold for the onset of mode instability in plasmas. We compare NNs and XGBoost models trained on linear QuaLiKiz simulations spanning a 22D JET experimental space [3] to predict the stability of a local simulation as well as the growth rates of unstable modes. The performance of both algorithms is examined in a focused comparison study using 100,000 training points and across a broader range of training set sizes, to capture scaling trends, ranging from 100 to 3 million training points.
Both models achieve comparable accuracy using 100,000 data points, however XGBoost has a significant edge in inference speed by a factor of approximately 50 while maintaining smaller model variance due to random initialisation, as well as greatly reduced training and hyperparameter optimisation times. These last two aspects are particularly important when considering active learning within the training pipeline in which models are frequently retrained as new data is acquired. Early scaling results shown in Figure 1 suggest advantages of XGBoost in low-data regimes showing increased robustness to hyperparameter variation.

References:
1] QuaLiKiz homepage: http://qualikiz.com
[2] K.L van de Plassche, J. Citrin, C. Bourdelle, Y. Camenen et al., Phys. Plasmas, 27 (2020)
022310
[3] A. Ho, J. Citrin, C. Bourdelle, Y. Camenen, F. J. Casson, K. L. van de Plassche, H. Weisen, JET Contributors; Neural network surrogate of QuaLiKiz using JET experimental data to populate training space. Phys. Plasmas 1 March 2021; 28 (3): 032305. https://doi.org/10.1063/5.0038290
[4] E. Fransson, A. Gillgren, A. Ho, J. Borsander, O. Lindberg, W. Rieck, M. Åqvist, P. Strand; A fast neural network surrogate model for the eigenvalues of QuaLiKiz. Phys. Plasmas 1 December 2023; 30 (12): 123904. https://doi.org/10.1063/5.0174643
[5] Chen, T., & Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 785–794). New York, NY, USA: ACM. https://doi.org/10.1145/2939672.2939785
[6] Léo Grinsztajn, Edouard Oyallon, Gaël Varoquaux. Why do tree-based models still outperform deep learning on typical tabular data?. 36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks, Nov 2022, New Orleans, United States. hal-03723551v3

Speaker: Matisse Lanzarone (Universite Aix-Marseille)

12:20 PM → 1:30 PM Lunch break

1:30 PM → 2:10 PM I.16-Ferraro: Extended-MHD Stellarator Modeling with M3D-C1

Speaker: Dr Nathaniel Ferraro (Princeton Plasma Physics Laboratory, Princeton University, Princeton, USA)

2:10 PM → 2:50 PM I.17-Garcia-Regana: The role of impurities on electrostatic stellarator turbulence

Speaker: Jose Manuel Garcia-Regana (CIEMAT)

2:50 PM → 3:15 PM O.14-Varadarajan: Integrated Modelling of Tungsten Erosion, Transport, and Radiation in WEST Geometry

Core contamination is a key issue for full Tungsten devices and will be a major concern for the operation of ITER. Today’s experiments on medium size tokamaks such as WEST or AUG are vital to further characterize the mechanisms at play that regulate Tungsten concentration. WEST for instance, is characterized by a near-constant radiated fraction, regardless of input power. To better understand experimental observations and predict core contamination, the computational domain of the edge plasma code SOLEDGE-3X is now extended to describe the plasma from the first wall to the core including Tungsten. It self-consistently models the main ion species (usually a Hydrogen isotope), as well as light and heavy impurities in the core and in the edge, performing integrated simulations of plasma scenarios. On the wall, the gross erosion is estimated using the Eckstein formula, supplemented by prompt redeposition from both an analytical formula [1] and a neural network [2]. In the core, a new 1D model is used that solves particle and energy balance for all species, and is time-evolved along with the 2D edge-SOL. Core turbulence is taken into account using QLKNN-10D [3], a neural network trained on a database of QuaLiKiz simulations [4]. In addition, Neoclassical transport of heavy impurities is accounted for in the core using a reduced model benchmarked against NEO, that takes rotational effects into account [5]. Using this framework, tungsten sources, transport and radiation are investigated. A special focus is put on understanding self-regulation mechanisms, in particular the feedback between Tungsten sources and core radiation, which impacts the power entering the scrape-off layer.

REFERENCES:
D. Tskhakaya and M. Groth, Journal of Nuclear Materials 463 (2015): 624–628
L. Cappelli et al., PPCF 65, no. 9 (2023): 095001
K. L. Van De Plassche et al., PoP 27, no. 2 (2020): 022310
Stephens, C.D., X. Garbet, J. Citrin, C. Bourdelle, K.L. van de Plassche, and F. Jenko., Journal of Plasma Physics 87, no. 4 (2021): 905870409.
P. Maget et al, PPCF 62, 105001 (2020); D. Fajardo et al, PPCF 64, 055017 (2022)

Speaker: Naren Varadarajan (IRFM)

3:15 PM → 3:35 PM Closing session