Recent Publications

Fluid dynamics simulations of gas retention systems for shattered pellet injectors

Á. Gyenge, B. Farkas

Parameter optimization of the reduced-order scrape-off-layer model DIV1D using Markov-Chain Monte Carlo sampling

Roel Rik Maria Hazelhof, Gijs Lukas Derks, Clemens Verhoosel, Stefan Dasbach, David vander Mijnsbrugge, Sven Wiesen

Accurate and efficient modeling of scrape-off layer (SOL) dynamics is essential for controlling divertor detachment in future fusion reactors. The reduced-order SOL model DIV1D provides a fast alternative to high-fidelity codes such as SOLPS-ITER, but it contains fitting parameters that are traditionally tuned manually and with limited knowledge about their posterior distribution. This paper introduces a Bayesian framework employing Markov Chain Monte Carlo (MCMC) sampling to fit DIV1D to mapped SOLPS-ITER solutions. The framework quantifies parameter uncertainties through posterior likelihood distributions, revealing parameter correlations and multi-modal behavior. A Sobol sensitivity analysis, extended with a novel adaptive formulation, provides additional insight into parameter influence and interactions. Application to SOLPS-ITER simulations of TCV shows improved fits compared to the benchmark parameter set, while results across a SOLPS-ITER density ramp on TCV highlight systematic trends and parameter correlations, suggesting the potential of density-dependent adaptive fitting. Extension of the method to SOLPS-ITER simulations of AUG demonstrates its robustness and adaptability. Overall, the Bayesian MCMC framework reduces manual workload and enables reproducible and interpretable parameter estimation, leading to improved reduced-order SOL modeling capabilities.

Beam optics and stripping losses in a full-scale ITER negative ion source: multibeamlet analysis by beam emission spectroscopy

Riccardo Agnello, Marco Barbisan, Roberto Pasqualotto, Antonio Pimazzoni, Emanuele Sartori, Barbara Zaniol, Edgard Zuin

Consorzio RFX (CNR ENEA INFN University of Padova Acciaierie Venete SpA), École Polytechnique Fédérale de Lausanne Swiss Plasma Center, Consiglio Nazionale delle Ricerche, Università degli Studi di Padova

In this work, Beam Emission Spectroscopy (BES) is applied to the investigation of beam divergence and stripping losses in the full-scale ITER negative ion source prototype SPIDER, operating in multibeamlet configuration. A semi-analytical model is developed to simulate the emission spectra produced by overlapping beamlets, accounting for realistic beamlet divergence, aiming, and beam composition along the accelerator and drift regions. The comparison between synthetic and experimental spectra shows that the Doppler broadening measured in multibeamlet operation cannot be interpreted solely in terms of single-beamlet divergence, but results from the combined effects of beamlet overlap, residual magnetic deflections, electrostatic repulsion, and halo contributions. Using beamlet parameters independently obtained from calorimetric diagnostics, the model reproduces a significant fraction of the experimentally measured divergence. Moreover, the possibility of displacing a line-of-sight allows the detection of variations in the populations of particles with different divergences, namely the core and halo components, across the beam. As a phenomenological characterization, stripping losses are systematically quantified over a wide range of operational parameters, showing an approximately linear increase with source pressure and values consistent with previous single-beamlet studies. These results demonstrate the capability of BES, combined with multibeamlet modelling, to support beam optimization and performance assessment in ITER-relevant negative ion sources.

Deep learning tearing mode evolution prediction for instability control

Runyu Luo, Wei Zheng, Fengming Xue, Chengshuo Shen, Zhengkang Ren, Yu Zhong, Ruomu Wang, Yong Hua Ding, Zhongyong Chen, Nengchao Wang

Huazhong University of Science and Technology, Institution of Fusion and Plasmas

To address the general need for control oriented prediction of deleterious m/n=2/1 tearing mode evolution in tokamak plasmas, this work develops a data-driven framework and is validated on J-TEXT experimental database. Based on multi-diagnostic histories and future control reference trajectories, including resonant magnetic perturbation (RMP) and electron cyclotron resonance heating (ECRH) references, the framework forecasts the rotating 2/1 tearing mode evolution trajectory over the energy confinement time scale by jointly forecasting the occurrence probability, rotation frequency, and mode amplitude, while locked phases are treated as the termination of the rotating state in the present framework. A sequence based learning model is adopted to capture correlations among diagnostic signals and control references, enabling direct multistep generation of full evolution trajectories for multiple prediction targets in a single forward pass. To help the model form latent representations of the rotating 2/1 tearing mode state, a curriculum learning strategy is employed to guide the model from simpler present window, 2/1 mode identification tasks, to long horizon evolution prediction, which is informative for predicting control relevant transitions. To further evaluate the prediction performance critical for tearing mode suppression involving the appearance and termination of rotating tearing mode states, this research constructed targeted subsets. Finally, the model achieves an AUC of 98.4% on the full test dataset. On targeted subsets, it attains an onset prediction accuracy of 82.87%, and achieves an 11.4% relative improvement in similarity of predicted amplitude evolution trends. Finally, to examine the physical consistency of the model’s response to changes in control references, counterfactual analyses are performed under modified control conditions. The results indicate that the framework is capable of reproducing the corresponding evolution of key parameters of the rotating 2/1 tearing mode state, supporting its potential as a data driven surrogate for future control-oriented studies.

On the feasibility of model-based feedback control of vertical instability growth rate using out-vessel coils in ARC-like scenarios

Arunav Kumar, Cesar Clauser, Theodore Golfinopoulos, Jon C. Hillesheim

In this work, we propose a model-based feedback controller that regulates the vertical instability growth rate ($γ_{gr}$) of a high-elongation, double-null tokamak directly, using only out-vessel poloidal field (PF) coils. High elongation raises the achievable plasma current and fusion performance but makes the plasma vertically unstable, and in a fusion power plant the in-vessel coils that present devices rely on for stabilization may be absent, leaving only distant out-vessel circuits. The controller couples a machine learning surrogate of non-rigid, profile agnostic vertical instability metric to a constrained quadratic program: the surrogate supplies real-time $γ_{gr}$ estimates and, via automatic differentiation, the actuator sensitivities, while the program allocates coil voltages to track a target growth rate, maintain double-null divertor balance, and respect electromechanical limits. We tested this method on the ARC~V3A power plant design configuration across 24 closed-loop simulations spanning equilibrium variations, actuator degradations, and transient disturbances. We achieved full or marginal success in 83\% of these cases (full in 50\%, marginal in a further 33\%) and lose control in the remaining 17\%; the failures map the boundary of out-vessel controllability (occurring at the highest growth rates) and under actuator limits. The controller does not regulate boundary shape explicitly: separatrix geometry follows indirectly from growth rate and flux balance control and would require a separate shape control layer for sustained scenario evolution.

Areal-time disruption prediction and mitigation system for the EXL-50U spherical torus

J. P. Zhou, S. F. Liu, J. Q. Cai, H. Y. Zhao, J. Li, Y. P. Zhang, D. Guo, C. Wu, A. Wang, H. Y. Li, et al.

This work presents a real-time disruption prediction and mitigation system developed for high-current operations in the EXL-50U Spherical Torus. By leveraging Reflective Memory (RFM) technology, the system establishes a low-latency real-time data path, creating a fully integrated pipeline that synchronizes multi-channel diagnostic acquisition, online preprocessing, real-time inference, and Massive Gas Injection (MGI) triggering. At its core, a lightweight prediction model based on a Temporal Convolutional Network (TCN) with a channel attention mechanism extracts disruption precursor features while adaptively weighting the importance of different diagnostic channels. {Tested across discharges \#14036--\#14790, the system achieves a true positive rate of 82.4\% and a false positive rate of 16.5\%, with end-to-end latency below $1~\mathrm{ms}$ in online operation.} Mitigation experiments further show that the MGI system can supply the required gas inventory and trigger a rapid post-injection plasma response, supporting the operational requirements of EXL-50U and providing engineering guidance for future devices such as EHL-2. These results confirm the engineering feasibility of integrated real-time disruption control on EXL-50U, offering a robust basis for future research in higher-parameter fusion devices.

Efficient Quantum Simulation of Linearized Vlasov--Poisson Dynamics Using Trotter and THRIFT Hamiltonian Simulation Methods

Kartick Paul, Rahul V, S. Aravinda, Reetesh K. Gangwar

The Vlasov--Poisson system provides the fundamental kinetic description of plasma and plays a central role in understanding collective phenomena such as Landau damping and wave--particle interactions. Efficient numerical simulation of these dynamics remains challenging because of the high dimensionality of phase space. In this work, we studied magnetized and non-magnetized plasma using a quantum simulation framework for the linearized Vlasov-Poisson equation by reformulating the discretized system as a Hermitian Hamiltonian suitable for gate-based quantum computation. The time evolution is implemented using first, second and fourth-order Trotter--Suzuki product formulas and the recently proposed Time-Resolved Interaction Framework (THRIFT). The performance of the different simulation methods is systematically evaluated through electric field evolution, state fidelity, convergence behavior, energy conservation, entanglement entropy and quantum resource requirements, including circuit depth and two-qubit gate complexity, for both magnetized and non-magnetized plasma models. To further reduce finite time step errors without increasing circuit depth, Richardson extrapolation is incorporated as a error-mitigation technique. The results provide a comprehensive comparison of Trotter and THRIFT approaches and establish practical guidelines for accurate and resource-efficient quantum simulation of plasma dynamics on gate-based quantum computers.

AI Surrogate Modeling for Real-Time Tokamak Equilibrium Prediction: Benchmarking Neural Architectures and Validation on EXL-50U

Guoyang Shi, Zitong Zhang, Siqi Ding, Jianguo Chen, Yapeng Zhang, Jiayi Zhi, Hanyue Zhao, Tianyuan Liu

Fast and reliable plasma equilibrium prediction is essential for real-time tokamak operation and control, but conventional Grad-Shafranov (GS) solvers are often too costly for real-time deployment. We develop an AI surrogate framework and benchmark five architectures (MLP, CNN, FNO, Transformer, and KAN) on a numerical GS database with 100,000 IID and 10,000 OOD samples. Under a unified protocol, we evaluate accuracy, inference efficiency, model scaling, and robustness. We also establish device-level validation on the EXL-50U tokamak by linking numerical GS solutions, surrogate predictions, and the standard Shape Editor reference to assess simulation-to-device consistency. The surrogates achieve errors of $10^{-3}$-$10^{-2}$ relative to GS solutions, while the GS-to-device discrepancy remains at $10^{-3}$. Transformer gives the best IID accuracy, whereas CNN offers the best balance of accuracy, robustness, and speed, reaching 0.7 ms TensorRT latency. On unseen plasma geometries and parameter regimes, CNN and FNO show the strongest extrapolation stability, with 4%-5% relative $L_2$ error, while models with weaker inductive biases degrade more substantially. Scaling data and model capacity improves interpolation but not necessarily extrapolation, revealing a trade-off between capacity and OOD generalization. Overall, this work provides a systematic, device-consistent benchmark for AI-based GS prediction and practical guidance for selecting reliable surrogates for real-time plasma control and fusion applications.

Helical jets driven by a ring of laser irradiation

Kian Orr, Brandon K. Russell, Kirill Lezhnin, Yang Zhang, Geoffrey Pomraning, Petros Tzeferacos, Hantao Ji, Lan Gao

Plasma jets are formed in various astrophysical systems as plasma is rapidly ejected from a source, with a subset of these jets being magnetized and having a helical structure. Here, we demonstrate that helical jets may be formed using a ring of laser pulses that arrive on planar foils sequentially with increasing energy. The formation of the jets and their properties, including kinetic helicity, are studied through a set of three-dimensional magneto-hydrodynamics simulations with conditions informed by the parameters of the OMEGA laser facility. We find that jets with a higher degree of helicity may be generated under realistic experimental conditions when compared to a uniform jet. Synthetic x-ray and Thomson scattering diagnostics computed from simulated data demonstrate that the helical jet provides a unique fingerprint in both its morphology and plasma parameters. This laboratory helical jet platform may allow for controlled experimental study of the dynamics of helical plasma structures and, through interaction with other jets or targets, can allow for studies of shear-driven turbulence and mixing relevant to interactions between astrophysical jets and ambient clouds or crosswind.

Tuning of generalized k-omega turbulence model for prediction of heat transfer and pressure drop for helium cooled demo FW

Christine Klein, Frederik Arbeiter

INR KIT

Interpretable statistical feature engineering for early disruption prediction in the short pulse ADITYA tokamak

Jyoti Agarwal, Kavit Patel, Bhaskar Chaudhury, Abhishek Sharma, Shrichand Jakhar, Manika Sharma

Reliable early disruption prediction is critical for the safe operation and real-time control of tokamaks. However, machine learning based prediction frameworks have predominantly targeted medium and long pulse devices, with comparatively limited attention given to short pulse tokamaks where available warning time is inherently constrained. In this work, an interpretable machine learning framework is developed for feature engineering and early prediction of disruptions in the ADITYA using the initial plasma evolution information, prior to the activation of the negative converter of the ohmic transformer power supply. Statistical descriptors comprising the mean, variance, skewness, kurtosis and wavelet energy entropy are extracted from routinely available plasma diagnostics over different operation time windows. Decision tree based feature selection is employed to identify physically meaningful disruption precursors and to reduce feature dimensionality. These selected features are used to train a random forest classifier. The proposed framework achieves stable predictive performance across different analysis windows, with a maximum ROC-AUC of 0.87 for 0-35 ms and 0-40 ms windows. Comparable and in some cases improved, performance is obtained using the reduced feature set, demonstrating that the selected statistical descriptors retain the essential information required for disruption prediction. The proposed methodology provides an interpretable and computationally efficient framework for real time disruption prediction in short pulse tokamaks and establishes that carefully engineered statistical descriptors can effectively replace raw time series inputs for early disruption prediction, thereby offering a practical pathway toward real time plasma control in short pulse tokamaks similar to ADITYA and ADITYA-U.

Wasserstein Moment Nudging for Vlasov-Poisson Data Assimilation

Liyao Lyu, Xinyue Yu, David Schneidinger, Hayden Schaeffer

We introduce a continuous data assimilation method for particle-in-cell simulations of the Vlasov-Poisson equation when only hydrodynamic moments are observed. The forecast state is an empirical measure on phase space, whereas the observed fields (density, bulk velocity, and temperature) constrain only a few velocity moments and leave the velocity-space shape of the distribution undetermined. We construct the moment feedback as a Wasserstein gradient flow of a moment-mismatch functional over phase-space measures. The resulting drift acts directly on particle positions and velocities, couples the density, momentum, and energy residuals through a single variational structure, and vanishes on the entire moment-compatible set. Under the standard Wasserstein metric, the energy residual produces a position correction that grows quadratically with the particle speed, and the particle system falls outside standard well-posedness theory. Our primary formulation pairs the quadratic moment mismatch with a velocity-weighted Wasserstein metric that penalizes spatial transport at large peculiar velocity relative to the observed bulk flow, which removes this growth. A direction-split variant retains the plain metric instead. Under the same weighted metric, an alternative moment-relative-entropy functional yields an affine, shape-preserving velocity correction and explicit global moment balances for the space-inhomogeneous system. We prove that the finite-particle scheme with linear Lenard-Bernstein collisions is globally well posed. In 1D1V and 2D2V experiments with several collision models, the nudged formulations reduce bulk-velocity and temperature errors by up to two orders of magnitude relative to an unassimilated run.

State-Space Model-Enabled Reinforcement Learning for Magnetic Configuration Controlon EXL-50U

Pei Guo, Zhengyuan Chen, Jianguo Chen, Xuanhe Wang, Guoyang Shi, Siqi Ding, Yapeng Zhang, Lei Xing, Yong Liu, Xiang Gu, et al.

Accurate feedback control of the plasma current ($I_p$) and centroid position $(R_c,Z_c)$ is essential for the stable operation of spherical torus (ST) plasmas. Conventional proportional-integral-derivative (PID) controllers require extensive manual tuning and struggle with the fast, strongly coupled dynamics that arise as plasma performance improves. Reinforcement learning (RL) has recently emerged as a promising alternative to such complex magnetic control problems, yet its practical deployment on ST devices remains challenging. This paper presents a practical RL controller for the EXL-50U ST, trained within a rigid RZIP state-space model (SSM) that enables efficient offline policy learning. A lightweight plasma position reconstructor is developed to estimate $(R_c,Z_c)$ from magnetic probe signals within the real-time control cycle. The trained policy is seamlessly deployed on the EXL-50U plasma control system, achieving stable regulation of $I_p$ and $(R_c,Z_c)$ and sustaining discharges up to 650 ms under RL control. These results demonstrate the feasibility and practical potential of model-informed RL for magnetic configuration control in ST devices, offering a promising direction beyond conventional PID-based schemes.

Modified Kalman Filtering Derived from Non-Maxwellian Distribution Functions in Open Systems

Olivier Izacard

Kalman filtering is exact for linear dynamics with Gaussian state and observation statistics, but a mean-covariance representation cannot retain finite non-Gaussian structure generated by source-driven kinetic evolution. We formulate a modified filtering theory for open plasma systems in which the additional state structure is derived from a non-Maxwellian velocity-space distribution (NMDF) rather than introduced as an empirical residual family. A kinetic manifold defines $f_s(\mathbf X_s,\mathbf v)$, while a fixed diagnostic map $H_D$ generates the measurement PDF $p_{D,s}$; the projected kinetic equation determines the state-prediction dynamics. The posterior evolves continuously and is corrected by Bayes' rule, with positivity-constrained relative-entropy projection when required. The Gaussian posterior with affine dynamics and a linear Gaussian observation model recovers the Kalman-Bucy and discrete Kalman limits. The first explicit non-Gaussian closure is a five-coordinate INMDF from exact five-moment inversion, with Kappa retained as a broad-tail alternative. Using seven Alcator C-Mod Langmuir-probe ion-saturation-current PDFs, six kinetic manifolds are propagated through the same source statistics, noise model, normalization, and probe response. Because the published histograms lack time ordering, recursive tracking is not tested. In universal leave-one-condition-out prediction, double-INMDF ranks first in all four held-out divertor conditions, with mean error 0.0989 versus 0.1089 for MDF. Within-region calibration gives nearly identical divertor errors for first- and double-INMDF, 0.0936 and 0.0937, while two-Maxwellian gives the smallest midplane error, 0.0718. Predictions remain conditional on published source and noise controls, but show that a frozen source-to-kinetic response generalizes to an unseen current PDF and that the preferred response is region dependent.

Unstructured mesh-based global variance reduction method for deep-penetration fusion neutronics calculations in RMC

Jie Li, Pengfei Shen, Kok Yue Chan, Yongpeng Kong, Qing Li, Kan Wang

Tsinghua University, Nuclear Power Institute of China, National University of Defense Technology

Machine-agnostic Gaussian process-based surrogate model for electron cyclotron heating and current drive

Andrew M. Irvin, Livia Casali, Sebastian De Pascuale, Ehab Hassan

University of Tennessee-Knoxville, Oak Ridge National Laboratory, Ain Shams University

A Memory-Efficient Adjoint State Optimization Method Based on Time-Reversible Dynamical Low-Rank Approximation

Lukas Einkemmer, Julian Mangott

The primary challenge of conducting PDE-constrained optimization for high-dimensional problems, such as kinetic equations, is the often prohibitive memory cost. Computing gradients using the adjoint state method would require the storage of the entire time history of the forward solution. For such problems, where the memory cost for storing a single instance of the forward solution can already be a limiting factor, this is clearly not feasible. In this paper, we propose a memory-efficient adjoint state method that compresses the forward and adjoint solution with a dynamical low-rank approximation (a model order reduction technique) and bypasses the need to store the entire forward solution by employing a time-reversible low-rank integrator. The dynamical low-rank approach introduces a number of challenges: reversibility can fail in the rank-deficient case and the low-rank trajectories can show chaotic behavior. In particular, the latter has a number of important consequences for the optimization problem. We address those challenges and show that our method can drastically reduce the memory requirement for gradient-based optimization of kinetic equations. In particular, we consider two examples from kinetic plasma physics: optimizing beam profiles to suppress a bump-on-tail instability and shaping a particle beam using external electric fields.

AXUV synthetic diagnostic for ASDEX Upgrade and its application for SPI simulations

Ferenc Lengyel, Weikang Tang, Matthias Hölzl, Matthias Bernert, Matěj Tomeš, Peter Halldestam, Paul Heinrich, Gergely Papp, Stefan Jachmich, Umar Sheikh, et al.

We introduce an Absolute eXtended UltraViolet (AXUV) diode-based camera forward-modelling tool to support the validation of mitigated disruption simulations and the interpretation of experimental phenomena, with applications to the ASDEX Upgrade (AUG) tokamak. AXUV diodes measure electromagnetic radiation across a wide spectral range with a significantly higher time resolution (~microseconds) than foil bolometers (~milliseconds), albeit with a non-uniform spectral responsivity. AXUV is suitable for examining fast phenomena, such as shattered pellet injection (SPI), where the radiation localisation and radiated power provide information on the deposition of pellet material. Due to the characteristics and degradation of AXUV diodes, absolute power measurements are subject to large systematic uncertainties, especially when the spectra are time-varying, as in e.g. mixed Ne/D2 SPI experiments. These challenges motivated the development of a synthetic diagnostic within the Cherab-Raysect optical modelling framework, which is applied here to four AXUV cameras in two poloidal cross-sections of AUG. The synthetic diagnostic provides a means to understand how the diodes measure radiation under SPI conditions and to connect first-principles plasma simulations with experimental measurements. The details of the synthetic diagnostic are presented, and the capabilities are illustrated with applications to AUG SPI simulations performed in JOREK. The synthetic signals generated from these simulations are compared with experimental measurements from the 2022 SPI campaign and show qualitatively similar features in many respects. Particularly good agreement was found in the time evolution of the studied high Ne-content (10%) pellet, whereas a different, low Ne-content (0.17%) case exhibited more pronounced differences, likely due to the absence of background impurities in the underlying SPI simulations.

Zero-dimensional multi-physics-constrained parameter design and optimization for advanced quasi-isodynamic stellarators

Ziyuan Sun, Zixuan Guo, Xianglin Hao, Longjun Qin, Qian Liu, Xiang Teng

A zero-dimensional (0D) multi-physics-constrained framework for parameter design and optimization of Stable Quasi-Isodynamic Designs (SQuIDs) is presented. Single- and multi-objective optimizations for three staged devices are carried out using an in-house stellarator 0D systems code: YF-1 for discharge demonstration, YF-2 for scientific break even, and YF-3 for a commercial demonstration plant. Pareto searches map the main design trade-offs across the three generations. The equal weight optima for YF-2 and YF-3 both lie in the electron-root favorable regime of the adopted root proxy: YF-2 recovers $Q_{phys} \sim 1$, while YF-3 reaches an ignited point at reactor scale. Future work will couple engineering feasibility and economic assessment modules for integrated plant evaluation.

Power-law-anchored residual learning for H-mode energy confinement time in tokamaks: interpolation and parameter-defined extrapolation

Zhaokun Wang, Tianyuan Liu, Jianguo Chen, Guoyang Shi, Siqi Ding, Yuejiang Shi, Xianmei Zhang

Reliable prediction of the energy confinement time is essential for magnetic-confinement fusion. Conventional power-law scalings provide constrained extrapolation trends but cannot represent complex nonlinearities, whereas neural networks interpolate accurately but may behave unpredictably outside the training distribution. We propose a unified power-law-anchored residual-learning framework in which a frozen empirical power-law scaling supplies the global trend and a nonlinear model learns only the systematic residual in logarithmic space. PLR-KAN is developed as the primary implementation, while a parameter-matched PLR-MLP serves as a controlled architecture replacement. Using the ITPA DB5.2.3 H-mode confinement database, we evaluate interpolation and parameter-defined held-out cohorts over ten complete training pipelines. PLR-KAN retains near-best interpolation accuracy, achieving R2=0.9671+/-0.0027, while substantially improving the stability of direct KAN under parameter-defined distribution shifts. It outperforms direct KAN across all five non-epsilon single-parameter-defined cohorts and the core-five joint cohort, reaching R2=0.9263+/-0.0157 in the latter. Results from PLR-MLP further demonstrate that the benefit of power-law anchoring is not specific to KAN, although the effectiveness of residual transfer remains architecture and direction dependent. As an exploratory extension, a Mahalanobis-distance-based prediction-time gate improves stability in selected shifted regions but is not universally beneficial and cannot compensate for missing device or physics-regime coverage. Overall, power-law-anchored residual learning provides a practical balance between nonlinear interpolation capability and empirically constrained extrapolation behavior.