arXiv subjects

Xian-Zhu Tang

Publications and source records attributed to Xian-Zhu Tang.

At least 19 recordsLinked to original sources

arXiv2026

An Efficient Solver for Finite Element-based Constrained Transport in 3D Magnetohydrodynamics Applied to Magnetic Confinement Fusion

We present an efficient solver framework for the stiff magnetic wave coupling arising in resistive magnetohydrodynamics (MHD) on realistic tokamak geometries. The approach builds on an implicit-implicit (IMIM) time-splitting that separates fast magnetic waves and anisotropic heat transport from slower acoustic dynamics while retaining full coupling (Krzysik et al. 2026). Within this formulation, the magnetic wave subsystem appears as an anisotropic curl-curl operator, enabling the use of scalable auxiliary-space Maxwell (AMS) multigrid solvers. To exploit this structure at the discrete level, we employ curl-conforming finite element spaces for the magnetic field and design the velocity space to preserve the curl-curl structure induced by the Lorentz-force coupling. The resulting compatible discretization preserves the discrete magnetic divergence constraint while producing linear systems directly amenable to efficient AMS-based solvers. We demonstrate solver efficiency as well as the accuracy and stability of the resulting structure-preserving discretization on fully nonlinear three-dimensional tokamak test cases.

math.NA↗

arXiv2026

A Physics-Informed Neural Network for Solving the Quasi-static Magnetohydrodynamic Equations

A physics-informed neural network (PINN) is developed, for the first time, to learn the time-dependent quasi-static magnetohydrodynamic (MHD) equations in axisymmetric tokamak geometry, without any experimental or synthetic data. The initial study considered an ITER-like tokamak and found that a PINN, after careful treatment, was capable of learning the solution to the MHD system and predict a vertically displacing plasma, where general agreement with ground truth simulation was observed. The proof-of-principle demonstration highlights the potential of physics-constrained deep learning to learn complex plasma behavior.

physics.plasm-ph↗

arXiv2026

Self-mediation of runaway electrons via self-excited wave-wave and wave-particle interactions

Nonlinear dynamics of runaway electron induced wave instabilities can significantly modify the runaway distribution critical to tokamak operations. Here we present the first-ever fully kinetic simulations of runaway-driven instabilities towards nonlinear saturation in a warm plasma where collisional damping is subdominant. It is found that the slow-X modes grow an order of magnitude faster than the whistler modes, and they parametrically decay to produce whistlers much faster than those directly driven by runaways. These parent-daughter waves, as well as secondary and tertiary wave instabilities, initiate a chain of wave-particle resonances that strongly diffuse runaways to the backward direction. This reduces almost half of the current carried by high-energy runaways, over a time scale orders of magnitude faster than experimental shot duration. These results beyond quasilinear analysis may impact anisotropic energetic electrons broadly in laboratory, space and astrophysics.

physics.plasm-ph↗

arXiv2026

Collisional-radiative data for tokamak disruption mitigation modeling

Effective tokamak disruption mitigation is crucial for ensuring the safety and integrity of fusion power reactors. Accurate collisional-radiative (CR) modeling of a radiative plasma is a critical component in predictive disruption mitigation design. In this paper, we focus on quasi-steady-state CR modeling applicable to the current quench phase of a tokamak disruption. We employ the ATOMIC collisional-radiative code from the Los Alamos suite and the newly developed Fusion Collisional-Radiative (FCR) code to model the atomic processes, providing high-fidelity data for radiative power loss, as well as average and effective charge states for hydrogen, helium, neon, and argon plasma species over a wide range of tokamak-relevant electron temperatures and electron densities. Fine-structure-resolved CR models are used for hydrogen and helium plasma species, while configuration-average CR models are implemented for neon and argon plasma species. The calculated values are compared with the superconfiguration CR model (FLYCHK) and the commonly used coronal equilibrium approximation to demonstrate the advantages and limitations of each model. To facilitate coupling of high-fidelity CR data to plasma simulation models, we represent the ATOMIC/FCR results over the relevant plasma parameter range using a smooth tensor product B-spline surface in electron temperature and electron density. This approach yields compact coefficient tables that can be evaluated efficiently while preserving spline smoothness across the domain. These data were previously used to examine ways to minimize runaway electrons in a tokamak current quench, and they are now made available in easy-to-use forms for community use and benchmarking.

physics.plasm-ph↗

arXiv2026

Hybrid collisional-radiative modeling for high-fidelity atomic kinetics

The fidelity of collisional-radiative (CR) models is critical for advancing our understanding of radiative properties and ionization balance in fusion plasmas. In this work, we present and evaluate hybrid CR schemes that combine fine-structure resolution with superconfiguration averaging, offering a practical compromise between accuracy and computational efficiency. Two hybrid CR models are developed for helium, lithium, and beryllium, retaining detailed fine-structure states up to selected principal quantum numbers, while higher-lying states are statistically averaged to form superconfigurations. These models are applied to compute radiative power loss, as well as average and effective charge states, across a wide range of electron temperatures and densities. The results are benchmarked against a fully fine-structure-resolved CR model to assess the accuracy of the hybrid approach. The findings demonstrate the versatility of hybrid CR schemes and their suitability for detailed plasma simulations where predictive fidelity must be balanced with computational cost.

physics.plasm-ph↗

arXiv2025

Excitation of whistler and slow-X waves by runaway electrons in a collisional plasma

Runaway electrons are known to provide robust ideal or collisionless kinetic drive for plasma wave instabilities in both the whistler and slow-X branches, via the anomalous Doppler-shifted cyclotron resonances. In a cold and dense post-thermal-quench plasma, collisional damping of the plasma waves can be competitive with the collisionless drive. Previous studies have found that for its higher wavelength and frequency, slow-X waves suffer stronger collisional damping than the whistlers, while the ideal growth rate of slow-X modes is higher. Here we study runaway avalanche distributions that maintain the same eigen distribution and increase only in magnitude over time. The distributions are computed from the relativistic Fokker-Planck-Boltzmann solver, upon which a linear dispersion analysis is performed to search for the most unstable or least damped slow-X and whistler modes. Taking into account the effect of plasma density, plasma temperature, and effective charge number, we find that the slow-X modes tend to be excited before the whistlers in a runaway current ramp-up. Furthermore, even when the runaway current density is sufficiently high that both branches are excited, the most unstable slow-X mode has much higher growth rate than the most unstable whistler mode. The qualitative and quantitative trends uncovered in current study indicate that even though past experiments and modeling efforts have concentrated on whistler modes, there's a compelling case that slow-X modes should also be a key area of focus.

physics.plasm-ph↗

arXiv2025

An adaptive Newton-based free-boundary Grad-Shafranov solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad--Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad--Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad--Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two non-trivial constraints, which correspond to the nonlinear finite element discretization of the Grad--Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. It is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

math.NA↗

arXiv2025

Collisionless ablative plasma shocks

An ablative plasma shock can emanate from the interface between a cold/dense plasma and a hot/dilute ambient plasma, where the plasma mean-free-path is much longer than the temperature gradient length. The shock is driven by thermal flux from the hot plasma into the cold plasma, primarily through tail electrons mediated by an ambipolar electric field, and it propagates into the ambient hot/dilute plasma. Since the collisional mean-free-path is usually much longer than the Debye length, the ablative plasma shock is mostly collisionless, with the shock front width set by the upstream hot plasma Debye length and the shock speed by the downstream cold plasma sound speed. The shock heating of ions is extremely efficient via collisionless mixing of upstream hot ions and downstream cold ions, both of which have been converted into shock-front-bound flows accelerated by the ambipolar electric field that has a deep potential well anchored inside the shock front.

physics.plasm-ph↗

arXiv2025

A Runaway Electron Avalanche Surrogate for Partially Ionized Plasmas

A physics-constrained deep learning surrogate that predicts the exponential ``avalanche'' growth rate of runaway electrons (REs) for a plasma containing partially ionized impurities is developed. Specifically, a physics-informed neural network (PINN) that learns the adjoint of the relativistic Fokker-Planck equation in steady-state is derived, enabling a rapid surrogate of the RE avalanche for a broad range of plasma parameters, motivating a path towards an ML-accelerated integrated description of a tokamak disruption. A steady-state power balance equation together with atomic physics data is embedded directly into the PINN, thus limiting the PINN to train across physically consistent temperatures and charge state distributions. This restricted training domain enables accurate predictions of the PINN while drastically reducing the computational cost of training the model. In addition, a novel closure for the relativistic electron population used when evaluating the secondary source of REs is developed that enables improved accuracy compared to a Rosenbluth-Putvinski source. The avalanche surrogate is verified against Monte Carlo simulations, where it is shown to accurately predict the RE avalanche growth rate across a broad range of plasma parameters encompassing distinct tokamak disruption scenarios.

physics.plasm-ph↗

arXiv2025

Distinct parallel electrostatic collisionless shocks in hot-cold ablative mixing plasmas

Hot-cold ablative mixing plasmas are ubiquitous in astrophysical and laboratory systems, where a cold/dense plasma is roughly in pressure balance with a hot/dilute plasma. Examples include the plasma thermal quench during major disruptions in tokamaks, interaction between a central hot-spot and the solid liner in an inertial confinement fusion (ICF) capsule, and the formation of large-scale structures in galaxy clusters. In such systems, a parallel electrostatic collisionless shock forms and plays a critical role in both the thermal collapse of the hot plasma and the ablative mixing of cold ions. The formation and dynamics of such shocks are investigated by employing one-dimensional VPIC simulations and theoretical analyses, revealing key differences from the well-studied collisionless shocks where an over-pressured, high-density plasma expands into a rarefied background. Notably, the shock formation has a weak dependence on the plasma pressure, provided that the density ratio between the cold and hot plasmas is large. Instead, the shock is primarily governed by the plasma temperatures on both sides. The collisionless electron thermal conduction flux in both upstream and downstream regions follows the free-streaming limit itself, but its spatial gradient exhibits convective scaling, ensuring the same characteristic length scale of the electron temperature and density evolution.

physics.plasm-ph↗

arXiv2025

Similarity for downscaled kinetic simulations of electrostatic plasmas: reconciling the large system size with small Debye length

A simple similarity has been proposed for kinetic (e.g., particle-in-cell) simulations of plasma transport that can effectively address the longstanding challenge of reconciling the tiny Debye length with the vast system size. This applies to both transport in unmagnetized plasma and parallel transport in magnetized plasmas, where the characteristics length scales are given by the Debye length, collisional mean free paths, and the system or gradient lengths. The controlled scaled variables are the configuration space, $\mathbf{x}/\mathscr{L},$ and artificial collisional rates, $\mathscr{L}μ$, which is realized through scaling the Coulomb Logarithm in the simulations, $\mathscr{L}\ln Λ.$ Whereas, the scaled time, $t/\mathscr{L}$, and electric field, $\mathscr{L}\mathbf{E}$, are automatic outcomes. The similarity properties are examined, demonstrating that the macroscopic transport physics is preserved through a similarity transformation while keeping the microscopic physics at its original scale of Debye length. To showcase the utility of this approach, two examples of 1D plasma transport problems were simulated using the VPIC code: the plasma thermal quench in tokamaks [J. Li, et al., Nuclear Fusion \textbf{63}, 066030 (2023)] and the plasma sheath in the high-recycling regime [Y. Li, et al., Physics of Plasmas \textbf{30}, 063505 (2023)].

physics.plasm-ph↗

arXiv2024

A Physics-Constrained Deep Learning Treatment of Runaway Electron Dynamics

An adjoint formulation leveraging a physics-informed neural network (PINN) is employed to advance the density moment of a runaway electron (RE) distribution forward in time. A distinguishing feature of this approach is that once the adjoint problem is solved, its solution can be used to project the RE density forward in time for an arbitrary initial momentum space distribution of REs. Furthermore, by employing a PINN, a parametric solution to the adjoint problem can be learned. Thus, once trained, this adjoint-deep learning framework is able to efficiently project the RE density forward in time across various plasma conditions while still including a fully kinetic description of RE dynamics. As an example application, the temporal evolution of the density of primary electrons is studied, with particular emphasis on evaluating the decay of a RE population when below threshold. Predictions from the adjoint-deep learning framework are found to be in good agreement with a traditional relativistic electron Fokker-Planck solver, for several distinct initial conditions, and across an array of physics parameters. Once trained the PINN thus provides a means of generating RE density time histories with exceptionally low online execution time.

physics.plasm-ph↗

arXiv2024

An Efficient Surrogate Model of Secondary Electron Formation and Evolution

This work extends the adjoint-deep learning framework for runaway electron (RE) evolution developed in Ref. [C. McDevitt et al., A physics-constrained deep learning treatment of runaway electron dynamics, Submitted to Physics of Plasmas (2024)] to account for large-angle collisions. By incorporating large-angle collisions the framework allows the avalanche of REs to be captured, an essential component to RE dynamics. This extension is accomplished by using a Rosenbluth-Putvinski approximation to estimate the distribution of secondary electrons generated by large-angle collisions. By evolving both the primary and multiple generations of secondary electrons, the present formulation is able to capture both the detailed temporal evolution of a RE population beginning from an arbitrary initial momentum space distribution, along with providing approximations to the saturated growth and decay rates of the RE population. Predictions of the adjoint-deep learning framework are verified against a traditional RE solver, with good agreement present across a broad range of parameters.

physics.plasm-ph↗

arXiv2024

An accurate SUPG-stabilized continuous Galerkin discretization for anisotropic heat flux in magnetic confinement fusion

We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for example, for magnetic confinement fusion. The new discretization is based on a mixed formulation, introducing a form of the directional derivative along the magnetic field as an auxiliary variable and discretizing both the temperature and auxiliary fields in a continuous Galerkin (CG) space. Both the temperature and auxiliary variable equations are stabilized using the streamline upwind Petrov-Galerkin (SUPG) method, ensuring a better representation of the directional derivatives and therefore an overall more accurate solution. This approach can be seen as the CG-based version of our previous work (Wimmer, Southworth, Gregory, Tang, 2024), where we considered a mixed discontinuous Galerkin (DG) spatial discretization including DG-upwind stabilization. We prove consistency of the novel discretization, and demonstrate its improved accuracy over existing CG-based methods in test cases relevant to magnetic confinement fusion. This includes a long-run tokamak equilibrium sustainment scenario, demonstrating a 35% and 32% spurious heat loss for existing primal and mixed CG-based formulations versus 4% for our novel SUPG-stabilized discretization.

math.NA↗

arXiv2024

Large radiation back-flux from Monte Carlo simulations of fusion neutron-material interactions

Radiation back-fluxes, generated from neutron-material interactions in fusion power reactors, can dramatically impact the plasma dynamics, e.g., by seeding runaway electrons during disruptions via Compton scattering of background electrons by wall-emitted gamma radiation. Here, we quantify these back-fluxes, including neutrons, gamma rays, and electrons, using Monte Carlo calculations for a range of structural material candidates and first wall thicknesses. The radiation back-flux magnitudes are remarkably large, with neutron and gamma radiation back-fluxes on the same order of magnitude as the incident fusion neutron flux. Electron back-fluxes are two orders of magnitudes lower, but are emitted at sufficiently high energies to provide a relatively large back-current through the sheath which may cause sheath reversal. Material configuration plays a key role in determining back-flux magnitudes. The structural material chiefly determines the neutron back-flux magnitude, while the first wall thickness principally attenuates the gamma ray and electron back-fluxes. In addition to prompt back-fluxes, which are emitted immediately after fusion neutrons impact the surface, significant delayed gamma ray and electron back-fluxes arise from nuclear decay processes in the activated materials. These delayed back-flux magnitudes range from 2%--7% of the prompt back-fluxes, and remain present during transients when fusion no longer occurs. During disruptions, build-up of delayed gamma radiation back-flux represents potential runaway electron seeding mechanisms, posing additional challenges for disruption mitigation in a power reactor compared with non-nuclear plasma operations. This work highlights the impact of these radiation back-fluxes plasma performance and demonstrates the importance of considering back-flux generation in materials selection for fusion power reactors.

physics.plasm-ph↗

arXiv2024

Scalable Implicit Solvers with Dynamic Mesh Adaptation for a Relativistic Drift-Kinetic Fokker-Planck-Boltzmann Model

In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker-Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. We develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations.

math.NA↗

arXiv2024

A Physics-Informed Deep Learning Description of Knudsen Layer Reactivity Reduction

A physics-informed neural network (PINN) is used to evaluate the fast ion distribution in the hot spot of an inertial confinement fusion target. The use of tailored input and output layers to the neural network is shown to enable a PINN to learn the parametric solution to the Vlasov-Fokker-Planck equation in the absence of any synthetic or experimental data. As an explicit demonstration of the approach, the specific problem of Knudsen layer fusion yield reduction is treated. Here, predictions from the Vlasov-Fokker-Planck PINN are used to provide a non-perturbative solution of the fast ion tail in the vicinity of the hot spot thus allowing the spatial profile of the fusion reactivity to be evaluated for a range of collisionalities and hot spot conditions. Excellent agreement is found between the predictions of the Vlasov-Fokker-Planck PINN and results from traditional numerical solvers with respect to both the energy and spatial distribution of fast ions and the fusion reactivity profile demonstrating that the Vlasov-Fokker-Planck PINN provides an accurate and efficient means of determining the impact of Knudsen layer yield reduction across a broad range of plasma conditions.

physics.plasm-ph↗

arXiv2024

A fast algebraic multigrid solver and accurate discretization for highly anisotropic heat flux I: open field lines

We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii) efficient implicit linear solvers. We simultaneously address each of these challenges by constructing a new finite element discretization with excellent accuracy properties, tailored to a novel solver approach based on algebraic multigrid (AMG) methods designed for advective operators. We pose the problem in a mixed formulation, introducing the directional temperature gradient as an auxiliary variable. The temperature and auxiliary fields are discretized in a scalar discontinuous Galerkin space with upwinding principles used for discretizations of advection. We demonstrate the proposed discretization's superior accuracy over other discretizations of anisotropic heat flux, achieving error $1000\times$ smaller for anisotropy ratio of $10^9$, for $closed$ $field$ $lines$. The block matrix system is reordered and solved in an approach where the two advection operators are inverted using AMG solvers based on approximate ideal restriction (AIR), which is particularly efficient for upwind discontinuous Galerkin discretizations of advection. To ensure that the advection operators are non-singular, in this paper we restrict ourselves to considering open (acyclic) magnetic field lines for the linear solvers. We demonstrate fast convergence of the proposed iterative solver in highly anisotropic regimes where other diffusion-based AMG methods fail.

math.NA↗