arXiv subjects

Zhixin Lu

Publications and source records attributed to Zhixin Lu.

At least 19 recordsLinked to original sources

arXiv2026

Minute-Scale High-Fidelity Gyrokinetic Simulations with Portability from Laptop to Supercomputer

Global gyrokinetic particle simulations remain computationally expensive, as they demand both adequate marker statistics and three-dimensional field solvers. In this work, we present a hybrid spectral method within the particle-in-Fourier (PIF) framework and implement it in the electrostatic model of GTC. Charge scatter and field gather are performed between particles and fields on a two-dimensional poloidal mesh, while the corresponding Poisson solver is discretized using radial finite differences and poloidal $m$-harmonics. Truncated spectral transforms are employed to connect multiple representations for fields, avoiding costly particle-grid operations for each individual $m$-harmonic within the particle loop. Benchmarks against conventional particle-in-cell (PIC) simulations successfully reproduce single-$n$ ion temperature gradient (ITG) mode structures and dispersion relations, as well as multi-$n$ nonlinear ITG transport and its regulation by zonal flows. Compared to conventional PIC, the proposed method reduces the effective problem size by more than a factor of 48 and achieves a speedup of over two orders of magnitude for single-$n$ cases. A 2000-step single-$n$ simulation with approximately 2 million markers completes in 78.2 seconds on a laptop GPU, while multi-$n$ turbulence simulation also completes within minutes. Furthermore, the elimination of toroidal particle-shift communication yields promising preliminary scaling performance on multiple NVIDIA A100 GPUs. The numerical scheme is broadly applicable for accelerating particle simulations on platforms ranging from laptops to supercomputers.

physics.plasm-ph↗

arXiv2026

OpenMP GPU Acceleration and Portability of TRIMEG-C1 for Electromagnetic Gyrokinetic Simulations in Tokamak Plasmas

The Triangular mesh-based gyrokinetic code TRIMEG-C1 solves the gyrokinetic equations using the particle-in-cell scheme to simulate electromagnetic instabilities in tokamak plasmas. TRIMEG-C1 utilizes a high-order C1 finite element method, which captures the accurate physics with lower grid resolution than the C0 method. In this work, we focus on achieving a portable implementation on multiple graphics processing unit (GPU) architectures to accelerate the TRIMEG-C1 code for future physics studies. The OpenMP framework is chosen as the acceleration framework for GPU offloading on different hardware platforms, specifically, NVIDIA and AMD GPUs. The particle pushing procedure, as well as particle-to-grid operations have been adapted for GPU execution. A speedup of $\approx9$ for the particle pusher kernel is achieved on 2 AMD MI300A APUs (Accelerated Processing Unit) compared with 2 AMD 9754 CPUs. In addition, the efficiency of hybrid MPI-OpenMP offloading parallelization was assessed by oversubscribing GPU resources. The Ion Temperature Gradient (ITG) mode was simulated using the GPU implementation, and its correctness was verified by comparing the physics results in terms of the energy growth rate and the two-dimensional mode structures.

physics.plasm-ph↗

arXiv2026

Suppressed Stiffness of energetic particle transport due to thermal plasma nonlinearity in tokamak plasmas

Energetic particle (EP) transport stiffness plays a crucial role in determining EP confinement in tokamak plasmas. This work investigates the impact of nonlinear thermal plasma dynamics on EP transport using global gyrokinetic simulations with the TRIMEG code. Simulations are performed for the ITPA toroidal Alfv'en eigenmode (TAE) benchmark, and extended to beta-induced (BAE) and reversed shear Alfven eigenmodes (RSAE). Two models are compared: a fully nonlinear treatment of all species and a reduced model with only nonlinear EP. For TAE simulations, while linear properties of the instability are identical in both cases, significant differences arise in the nonlinear regime. Including thermal plasma nonlinearity reduces the saturation level following an overshoot phase and modifies the radial mode structure, including mode broadening and poloidal harmonic splitting. These changes significantly affect EP transport. Specifically, the dependence of EP flux on the EP drive becomes weaker when nonlinear thermal plasma dynamics are included. The saturation level changes from an approximately quadratic scaling to a weaker, nearly linear dependence, reducing the scaling of EP flux with the EP gradient from quartic to quadratic. Zonal flow generation is observed but plays a minor role in regulating the instability. Without accounting for thermal nonlinearity, the EP flux can be overestimated by an order of magnitude. Simulations of BAEs and RSAEs demonstrate similar effects of thermal plasma nonlinearity on mitigating the saturation level. These results demonstrate that nonlinear thermal plasma effects provide an important feedback mechanism that reduces EP transport stiffness and regulates Alfvenic mode saturation, which is essential for predictive modeling of EP confinement in burning plasmas such as ITER.

physics.plasm-ph↗

arXiv2026

Gyrokinetic global simulation of Alfvenic ion temperature gradient mode in reversed magnetic shear

In this work, a systematic study of electromagnetic instabilities driven by the temperature gradient in magnetically confined fusion plasmas with reversed magnetic shear is conducted using gyrokinetic particle-in-cell simulations. An electromagnetic instability arising in the low-beta regime is investigated, where beta=8*pi*nT/B^2 denotes the ratio of plasma pressure to magnetic pressure. Within a reversed shear safety factor (q) profile, when a mode rational surface coincides with the position of zero shear, an instability dominated by only one poloidal harmonic emerges, rather than the conventional ion-temperature-gradient (ITG) mode. Simulation results demonstrate that the instability exhibits pronounced electromagnetic polarization even in the low-beta regime, with a real frequency significantly higher than that of ITG modes, and show that it is destabilized by the temperature gradient and not by the density gradient. This instability can be observed even for a monotonic q profile with weak magnetic shear. Based on a systematic comparison with other typical electrostatic and electromagnetic instabilities, this instability is identified as a weak shear Alfvenic-ion-temperature-gradient (WSAITG) mode, which may provide an explanation for the low-frequency Alfven modes (LFAM) observed in experiments. Wave-particle resonance analysis in phase space reveals that, in contrast to the ITG mode, well-passing particles provide an additional resonant population that drives the WSAITG mode.

physics.plasm-ph↗

arXiv2026

On nonlinear saturation of toroidal Alfvén eigenmode due to thermal plasma nonlinearities

The nonlinear saturation of toroidal Alfven eigenmode (TAE) due to thermal plasma nonlinearities is investigated using gyrokinetic particle-in-cell simulations and theoretical analysis. In the single toroidal mode number simulations with zonal fields filtered out, we find that the saturation level of TAE is governed by thermal plasma nonlinearities for gamma_L/omega_n > 0.47%, which has weak dependence on the linear drive gamma_L, i.e., "stiffness" in saturation level. We find that the frequency of TAE decreases as the amplitude of it increases, which is induced by the phase-space zonal structure (PSZS) of thermal plasmas universally existed in particle-in-cell simulations. The saturation of TAE can be finally reached when the mode merges into the continuum. Following this process, the separation of neighboring poloidal harmonics and mode transition to energetic particle modes can be observed. In simulations with zonal fields, zonal fields can essentially counteract the effects of PSZS of thermal plasmas, leading to roughly a factor of 2 enhancement of the TAE saturation level compared to the single toroidal mode number simulation, implying the necessity of including zonal modes in evaluating the saturation level of TAE.

physics.plasm-ph↗

arXiv2026

A High-order piecewise field-aligned triangular finite element method for electromagnetic gyrokinetic particle simulations of tokamak plasmas with open field lines

A high-order piecewise field-aligned triangular finite element method is developed and implemented for global electromagnetic gyrokinetic particle-in-cell simulations of tokamak plasmas with open field lines. The approach combines locally field-aligned finite element basis functions with unstructured $C^{1}$ triangular meshes in cylindrical coordinates, enabling whole-volume simulations with substantially reduced computational effort, while avoiding the grid distortion associated with globally field-aligned coordinates and the associated singularity at the separatrix of diverted plasmas. The formulation is compatible with both $δf$ and full-$f$ models and employs mixed-variable representations, along with a generalized pullback scheme, to control numerical cancellation in electromagnetic simulations. The method is implemented in the TRIMEG-C1 code and demonstrated using linear and nonlinear electromagnetic simulations of the TCV-X21 configuration. The results indicate that the approach accurately captures the key features of electromagnetic ion-temperature-gradient and kinetic ballooning mode physics, including the separatrix regions in the simulation, thereby providing a robust framework for whole-volume electromagnetic gyrokinetic simulations in realistic tokamak geometries.

physics.plasm-ph↗

arXiv2026

Smooth Polar B-Splines with High-Order Regularity at the Origin

We introduce a smooth B-spline discretization in polar coordinates on the unit disc that corrects the loss of regularity present at the origin caused by the coordinate singularity in standard tensor-product B-spline formulations. The method constructs "smooth polar splines" via a Galerkin projection of harmonic polar functions $S_l^{-m}(r,θ) := r^l \sin(mθ)$ and $S_l^{m}(r,θ) := r^l \cos(mθ)$, derived from the polar representation of Cartesian monomials, onto the central tensor-product B-spline basis in the innermost radial region. The radial component reproduces $r^l$ exactly for $0 \le l \leq p$, where $p$ is the B-spline degree, satisfying the near-origin regularity condition. However, exact compatibility with $C^\infty$-regularity at the origin is recovered only in the limit $Δθ\to 0$, when the angular component resolves all angular harmonics accurately. The smooth polar splines are linear combinations of standard tensor-product B-splines and lie in the same function space, enabling mapping between the $C^\infty$-regular subspace and the original discretization space via an exact prolongation operator and a corresponding restriction operator acting on the discrete variables. They match standard tensor-product B-splines away from the origin, preserve orthogonality among the newly constructed origin-centered basis functions, and maintain local support and sparse matrices. This smoothness and locality improve the conditioning of mass and stiffness matrices, conserve charge, and reduce statistical errors in particle-in-cell simulations near the origin, while eliminating spurious eigenvalues in eigenvalue problems. The approach provides a robust, high-order, and efficient adaptation of tensor-product B-splines for polar coordinates in physics simulations.

physics.comp-ph↗

arXiv2025

Identifying Stochastic Dynamics from Non-Sequential Data (DyNoSeD)

Inferring stochastic dynamics from data is central across the sciences, yet in many applications only unordered, non-sequential measurements are available-often restricted to limited regions of state space-so standard time-series methods do not apply. We introduce DyNoSeD, a first-principles framework that identifies unknown dynamical parameters from such non-sequential data by minimizing Fokker-Planck residuals. We develop two complementary routes: a local route that handles region-restricted data via locally estimated scores, and a global route that fits dynamics from globally sampled data using a kernel Stein discrepancy without explicit density or score estimation. When the dynamics are affine in the unknown parameters, we prove a necessary-and-sufficient condition for the existence and uniqueness of the inferred parameters and derive a sensitivity analysis that identifies which parameters are tightly constrained by the data and which remain effectively free under over-parameterization. For general non-affine case, both routes define differentiable losses amenable to gradient-based optimization. As demonstrations, we recover (i) the three parameters of a stochastic Lorenz system from non-sequential data (region-restricted data for the local route and full steady-state data for the global route) and (ii) a 3x7interaction matrix of a nonlinear gene-regulatory network derived from a published B-cell differentiation model, using only unordered steady-state samples and applying the global route. Finally, we show that the same Fokker-Planck residual viewpoint supports a "dynamics-to-density" complement that trains a normalized density estimator directly from known dynamics without any observations. Overall, IDyNSD provides two first-principles routes for system-identification from non-sequential data, grounded in the Fokker-Planck equation, that link data, density, and stochastic dynamics.

nlin.CD↗

arXiv2025

Generalized mixed variable-pullback scheme with non-ideal Ohm's law for electromagnetic gyrokinetic simulations

In this work, the non-ideal Ohm's law is integrated in the mixed variable-pullback scheme for the gyrokinetic particle simulations. This scheme captures the evolution of the symplectic solution of the gyrokinetic model accurately not only in the MHD limit but also in the electrostatic limit. This scheme also provides a pure symplectic ($v_\shortparallel $) scheme for electromagnetic gyrokinetic particle simulations without causing the traditional cancellation problem in the pure Hamiltonian scheme. Various mixed variable schemes have been comprehensively analyzed for the 1D shear Alfvèn wave problem with kinetic electrons, with the connection to the traditional pure Hamiltonian scheme and the symplectic scheme. It is demonstrated that the pure $v_\shortparallel $ form with the non-ideal Ohm's law has comparable performance to the widely used mixed variable-pullback scheme with the ideal Ohm's law. The mixed variable-pullback scheme without Ohm's law is also proposed as a feasible improvement of the traditional pure Hamiltonian scheme with minimum modification and considerable performance improvement in terms of a marker number reduction.

physics.plasm-ph↗

arXiv2025

TRIMEG-GKX: an electromagnetic gyrokinetic particle code with a Piecewise Field-Aligned Finite Element Method for Micro- and Macro-Instability Studies in Tokamak Core Plasmas

The features of the TRIMEG-GKX code are described with emphasis on the exploration using novel/different schemes compared to other gyrokinetic codes, particularly the use of object-oriented programming, filter/buffer-free treatment, and a high-order piecewise field-aligned finite element method. The TRIMEG-GKX code solves the electromagnetic gyrokinetic equation using the particle-in-cell scheme, taking into account multi-species effects and shear Alfvén physics. The mixed-variable/pullback scheme has been implemented to enable electromagnetic studies. This code is parallelized using particle decomposition and domain cloning among computing nodes, replacing traditional domain decomposition techniques. The applications to study the micro- and macro-instabilities are demonstrated, including the energetic-particle-driven Alfvén eigenmode, ion temperature gradient mode, and kinetic ballooning mode. Good performance is achieved in both ad hoc and experimentally reconstructed equilibria, such as those of the ASDEX Upgrade (AUG), Tokamak à configuration variable (TCV), and the Joint European Torus (JET). Future studies of edge physics using the high-order $C^1$ finite element method for triangular meshes in the TRIMEG-C1 code will be built upon the same numerical methods.

physics.plasm-ph↗

arXiv2025

Hierarchy of chaotic dynamics in random modular networks

We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic phases, separated by a crossover region characterized by low values of the maximal Lyapunov exponent and participation ratio dimension, but with high values of the Lyapunov dimension that change significantly across the region. Counterintuitively, chaos can be attenuated by either adding noise to strongly modular connectivity or by introducing modularity into random connectivity. Extending the model to include a multilevel, hierarchical connectivity reveals that a loose balance between activities across levels drives the system towards the edge of chaos.

physics.bio-ph↗

arXiv2024

Piecewise Field-Aligned Finite Element Method for Multi-Mode Nonlinear Particle Simulations in tokamak plasmas

This paper presents a novel approach for simulating plasma instabilities in tokamak plasmas using the piecewise field-aligned finite element method in combination with the particle-in-cell method. Our method traditionally aligns the computational grid but defines the basis functions in piecewise field-aligned coordinates to avoid grid deformation while naturally representing the field-aligned mode structures. This scheme is formulated and implemented numerically. It also applied to the unstructured triangular meshes in principle. We have conducted linear benchmark tests, which agree well with previous results and traditional schemes. Furthermore, multiple-$n$ simulations are also carried out as a proof of principle, demonstrating the efficiency of this scheme in nonlinear turbulence simulations within the framework of the finite element method.

physics.plasm-ph↗

arXiv2024

Gyrokinetic Electromagnetic Particle Simulations in Triangular Meshes with C1 Finite Elements

The triangular mesh-based gyrokinetic scheme enables comprehensive axis-to-edge studies across the entire plasma volume. Our approach employs triangular finite elements with first-derivative continuity (C1), building on previous work to facilitate gyrokinetic simulations. Additionally, we have adopted the mixed variable/pullback scheme for gyrokinetic electromagnetic particle simulations. The filter-free treatment in the poloidal cross-section with triangular meshes introduces unique features and challenges compared to previous treatments using structured meshes. Our implementation has been validated through benchmarks using ITPA-TAE (Toroidicity-induced Alfvén Eigenmode) parameters, showing its capability in moderate to small electron skin depth regimes. Additional examinations using experimental parameters confirm its applicability to realistic plasma conditions.

physics.plasm-ph↗

arXiv2024

A Novel Pseudo Nearest Neighbor Classification Method Using Local Harmonic Mean Distance

In the realm of machine learning, the KNN classification algorithm is widely recognized for its simplicity and efficiency. However, its sensitivity to the K value poses challenges, especially with small sample sizes or outliers, impacting classification performance. This article introduces a novel KNN-based classifier called LMPHNN (Novel Pseudo Nearest Neighbor Classification Method Using Local Harmonic Mean Distance). LMPHNN leverages harmonic mean distance (HMD) to improve classification performance based on LMPNN rules and HMD. The classifier begins by identifying k nearest neighbors for each class and generates distinct local vectors as prototypes. Pseudo nearest neighbors (PNNs) are then created based on the local mean for each class, determined by comparing the HMD of the sample with the initial k group. Classification is determined by calculating the Euclidean distance between the query sample and PNNs, based on the local mean of these categories. Extensive experiments on various real UCI datasets and combined datasets compare LMPHNN with seven KNN-based classifiers, using precision, recall, accuracy, and F1 as evaluation metrics. LMPHNN achieves an average precision of 97%, surpassing other methods by 14%. The average recall improves by 12%, with an average accuracy enhancement of 5%. Additionally, LMPHNN demonstrates a 13% higher average F1 value compared to other methods. In summary, LMPHNN outperforms other classifiers, showcasing lower sensitivity with small sample sizes.

cs.LG↗

arXiv2024

Energetic particles transport in constants of motion space due to collisions in tokamak plasmas

The spatio-temporal evolution of the energetic particles in the transport time scale in tokamak plasmas is a key issue of the plasmas confinement, especially in burning plasmas. In order to include sources and sinks and collisional slowing down processes, a new solver, ATEP-3D was implemented to simulate the evolution of the EP distribution in the three-dimensional constants of motion (CoM) space. The Fokker-Planck collision operator represented in the CoM space is derived and numerically calculated. The collision coefficients are averaged over the unperturbed orbits to capture the fundamental properties of EPs. ATEP-3D is fully embedded in ITER IMAS framework and combined with the LIGKA/HAGIS codes. The finite volume method and the implicit Crank-Nicholson scheme are adopted due to their optimal numerical properties for transport time scale studies. ATEP-3D allows the analysis of the particle and power balance with the source and sink during the transport process to evaluate the EP confinement properties.

physics.plasm-ph↗

arXiv2024

High-order stochastic integration schemes for the Rosenbluth-Trubnikov collision operator in particle simulations

In this study, we consider a numerical implementation of the nonlinear Rosenbluth-Trubnikov collision operator for particle simulations in plasma physics in the framework of the finite element method (FEM). The relevant particle evolution equations are formulated as stochastic differential equations, both in the Stratonovich and Itô forms, and are then solved with advanced high-order stochastic numerical schemes. Due to its formulation as a stochastic differential equation, both the drift and diffusion components of the collision operator are treated on an equal footing. Our investigation focuses on assessing the accuracy of these schemes. Previous studies on this subject have used the Euler-Maruyama scheme, which, although popular, is of low order, and requires small time steps to achieve satisfactory accuracy. In this work, we compare the performance of the Euler-Maruyama method to other high-order stochastic methods known in the stochastic differential equations literature. Our study reveals advantageous features of these high-order schemes, such as better accuracy and improved conservation properties of the numerical solution. The main test case used in the numerical experiments is the thermalization of isotropic and anisotropic particle distributions.

physics.plasm-ph↗

arXiv2023

Gyrokinetic simulations of neoclassical electron transport and bootstrap current generation in tokamak plasmas in the TRIMEG code

For magnetic confinement fusion in tokamak plasmas, some of the limitations to the particle and energy confinement times are caused by turbulence and collisions between particles in toroidal geometry, which determine the "anomalous" and the neoclassical transport, respectively. In this work, we focus on the implementation of neoclassical physics in the gyrokinetic code TRIMEG, which is a TRIangular MEsh-based Gyrokinetic code that can handle both the closed and open field line geometries of a divertor tokamak. We report on the implementation of a simplified Lorentz collision operator in TRIMEG. Since the code uses an unstructured mesh, a procedure for calculating the flux surface averages of particle and energy fluxes and the bootstrap current is derived without relying on the poloidal coordinate, which is useful also for other simulations in unstructured meshes. With the newly implemented collision operator, we study electron transport and bootstrap current generation for various simplified and realistic geometries. In comparison to neoclassical theory, good agreement is obtained for the large aspect ratio case regarding the particle and energy fluxes as well as the bootstrap current. However, some discrepancies are observed at moderate aspect ratio and for a case with the realistic geometry of the ASDEX Upgrade tokamak. These deviations can be explained by different treatments and approximations in theory and simulation. In this paper, we demonstrate the capability to calculate the electron transport and bootstrap current generation in TRIMEG, which will allow for the self-consistent inclusion of neoclassical effects in gyrokinetic simulations in the future.

physics.plasm-ph↗

arXiv2022

Full $f$ and $δf$ gyrokinetic particle simulations of Alfvén waves and energetic particle physics

In this work, we focus on the development of the particle-in-cell scheme and the application to the studies of Alfvén waves and energetic particle physics in tokamak plasmas. The $δf$ and full $f$ schemes are formulated on the same footing adopting mixed variables and the pullback scheme for electromagnetic problems. The TRIMEG-GKX code [Lu et al. J. Comput. Phys. 440 (2021) 110384] has been upgraded using cubic spline finite elements and full $f$ and $δf$ schemes. The EP-driven TAE has been simulated for the ITPA-TAE case featured by a small electron skin depth $\sim 1.18\times10^{-3}\;{\rm m}$, which is a challenging parameter regime of electromagnetic simulations, especially for the full $f$ model. The simulation results using the $δf$ scheme are in good agreement with previous work. Excellent performance of the mixed variable/pullback scheme has been observed for both full $f$ and $δf$ schemes. Simulations with mixed full $f$ EPs and $δf$ electrons and thermal ions demonstrate the good features of this novel scheme in mitigating the noise level. The full $f$ scheme is a natural choice for EP physics studies which allows a large variation of EP profiles and distributions in velocity space, providing a powerful tool for kinetic studies using realistic experimental distributions related to intermittent and transient plasma activities.

physics.plasm-ph↗