arXiv subjects

Jianyuan Xiao

Publications and source records attributed to Jianyuan Xiao.

At least 19 recordsLinked to original sources

arXiv2026

TokaGLINT: A Scalable GPU-Tailored Implicit Solver for Full 3D Tokamak Electromagnetic Simulations

We introduce TokaGLINT, a GPU-accelerated implicit solver for electromagnetic field computations in full 3D tokamak simulations, aimed at efficient large-scale parallel GPU computing. Its central innovation lies in the co-design of hierarchical domain decomposition and a fast exact local solver, where hierarchical partitioning is tailored to match fine-grained intra-card subdomains and exploit the tensor-based solver dedicated to curvilinear-coordinate symplectic CN-FDTD-discretized 3D Maxwell equations. Backed by automated operator fusion and batching customized for the intra-card multi-subdomain structure, the solver decouples unknowns through discrete transformations and leverages tensor-structured computations to achieve high hardware utilization, while preserving the long-time stability characteristic of symplectic discretizations. TokaGLINT scales the electromagnetic field solve beyond 10,000 GPUs, achieving 90.1% weak and 53.9% strong scaling efficiency, while delivering a 2.67X single-node speedup over an unpreconditioned BiCGStab baseline (HIP-enabled HYPRE). It is validated in EAST tokamak simulations within the SymPIC plasma simulation code, enabling high-fidelity long-duration modeling.

cs.DC↗

arXiv2025

Verification of Electromagnetic Fully-kinetic Symplectic Particle-in-cell Method in Microinstabilities Simulation of

We present a symplectic electromagnetic fully-kinetic particle-in-cell simulation of microinstabilities in plasma, using parameters from the Cyclone Base Case [Dimits, et al., Physics of Plasmas 7, 969 (2000)]. The results show that the growth rates of unstable modes, including ion temperature gradient (ITG), trapped electron mode (TEM), and kinetic ballooning mode (KBM), are consistent with those obtained from previous gyrokinetic models. Additionally, the \b{eta}-stabilization of the ITG is reproduced. The analysis also reveals that the impact of the ion-electron mass ratio and the numerical speed of light on the growth rate of the most unstable modes is minimal. This suggests that the fully kinetic method offers a potential for reduced computational cost when investigating the physics of drift wave instabilities at relevant space-time scales.

physics.plasm-ph↗

arXiv2024

A conservative, implicit solver for 0D-2V multi-species nonlinear Fokker-Planck collision equations

In this study, we present an optimal implicit algorithm specifically designed to accurately solve the multi-species nonlinear 0D-2V axisymmetric Fokker-Planck-Rosenbluth (FPR) collision equation while preserving mass, momentum, and energy. Our approach relies on the utilization of nonlinear Shkarofsky's formula of FPR (FPRS) collision operator in the spherical-polar coordinate. The key innovation lies in the introduction of a new function named King, with the adoption of the Legendre polynomial expansion for the angular coordinate and King function expansion for the speed coordinate. The Legendre polynomial expansion will converge exponentially and the King method, a moment convergence algorithm, could ensure the conservation with high precision in discrete form. Additionally, post-step projection onto manifolds is employed to exactly enforce symmetries of the collision operators. Through solving several typical problems across various nonequilibrium configurations, we demonstrate the high accuracy and superior performance of the presented algorithm for weakly anisotropic plasmas.

math.NA↗

arXiv2024

Relaxation model for a homogeneous plasma with spherically symmetric velocity space

We derive the transport equations from the Vlasov-Fokker-Planck equation when the velocity space is spherically symmetric. The Shkarofsky's form of Fokker-Planck-Rosenbluth collision operator is employed in the Vlasov-Fokker-Planck equation. A closed-form relaxation model for homogeneous plasmas could be presented in terms of Gauss hypergeometric2F1 functions. This has been accomplished based on the Maxwellian mixture model. Furthermore, we demonstrate that classic models such as two-temperature thermal equilibrium model and thermodynamic equilibrium model are special cases of our relaxation model and the zeroth-order Braginskii heat transfer model can also be derived. The present relaxation model is a nonequilibrium model based on the hypothesis that the plasmas system possesses finitely distinguishable independent features, without relying on the conventional near-equilibrium assumption.

physics.plasm-ph↗

arXiv2024

Bohm-like Neoclassical Transport in Highly Collisional Toroidal Plasmas with High Density Gradients

Conventional neoclassical theory in the Pfirsch-Schlüter regime fails to accurately model collision-induced transport in toroidal plasmas with high density gradients. In this scenario, we find that collision suppresses the return flow, leading to the dominance of the transport flux by the vacuum toroidal field drift with a reduced Bohm-like scaling. The new regime is also confirmed by full-orbit particle simulations, and can be employed to improve the accurate modeling of impurity transport in toroidal magnetized plasmas.

physics.plasm-ph↗

arXiv2022

Explicit high-order symplectic integrators of coupled Schrodinger equations for pump-probe systems

Two-beam coupling within the field of nonlinear optics, which transfers energy from one light beam to the other under certain conditions, has received considerable attention in inertial confinement fusion (ICF) and plasma optics. To evaluate the coupling dynamics precisely, we modeled this process with full-wave coupled Schrodinger equations (CSEs) and a nonlinear refractive index. We found that the CSEs constituted a Hamiltonian system and proposed an arbitrary higher-order explicit symplectic algorithm to solve the CSEs numerically. The numerical results given by the developed BEAM code showed a good agreement with those from particle-in-cell simulations, which demonstrated the validity of the model and algorithm. The model and numerical algorithm presented in this work can be extended to more nonlinear optical interactions described by coupled-wave equations.

physics.comp-ph↗

arXiv2021

Hybrid simulation of energetic particles interacting with magnetohydrodynamics using a slow manifold algorithm and GPU acceleration

The hybrid method combining particle-in-cell and magnetohydrodynamics can be used to study the interaction between energetic particles and global plasma modes. In this paper we introduce the M3D-C1-K code, which is developed based on the M3D-C1 finite element code solving the magnetohydrodynamics equations, with a newly developed kinetic module simulating energetic particles. The particle pushing is done using a new algorithm by applying the Boris pusher to the classical Pauli particles to simulate the slow-manifold of particle orbits, with long-term accuracy and fidelity. The particle pushing can be accelerated using GPUs with a significant speedup. The moments of the particles are calculated using the $δf$ method, and are coupled into the magnetohydrodynamics simulation through pressure or current coupling schemes. Several linear simulations of magnetohydrodynamics modes driven by energetic particles have been conducted using M3D-C1-K, including fishbone, toroidal Alfvén eigenmodes and reversed shear Alfvén eigenmodes. Good agreement with previous results from other eigenvalue, kinetic and hybrid codes has been achieved.

physics.plasm-ph↗

arXiv2021

Discovering exact, gauge-invariant, local energy-momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas. However, exact local energy-momentum conservation law for the electromagnetic gyrokinetic system has not been found despite continuous effort. Without such a local conservation law, energy-momentum can be instantaneously transported across spacetime, which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory. Standard Noether's procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds. To overcome this difficulty, we developed a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact local conservation laws, in particular the energy-momentum conservation law, for the electromagnetic gyrokinetic system. A weak Euler-Lagrange equation is established to replace the standard Euler-Lagrange equation for the particles. It is discovered that an induced weak Euler-Lagrange current enters the local conservation laws. And it is the new physics captured by the high-order field theory on heterogeneous manifolds.

physics.plasm-ph↗

arXiv2021

Unified perspective on single cyclotron electron with radiation-reaction from classical to quantum

We show a unified physical picture of single cyclotron electron with radiation-reaction, which bridges the classical electron models and quantum mechanical self-consistent field theory. On a classical level, we suggest an improved electrodynamical action, which build the classical electron models into a first-principle framework. The link between dynamical defections and non-physical action configurations emerges naturally. On a quantum level, a self-consistent description for electron gyro-motion with self-force is constructed in the Schrödinger-Maxwell theory. We derive a class of asymptotic equations. The leading and next-to-leading orders give a good analogue of a classical cyclotron electron, and the limit field theory avoids classical electron induced defections gracefully. Beyond the Hamiltonian perturbation theory, we use state-of-the-art geometric simulator to observe single electron gyro-motions at quantum region. The non-linear and non-perturbative features captured by simulations provide a complete physical picture in a very wide range. We show an optimal complementary relation between classical and quantum cyclotron electrons, and find a strange and inexplicable electron chimera state existing at strong non-linear regions, which may be observed in astrophysical environments and strong magnetic experiments.

physics.gen-ph↗

arXiv2021

High-order Field Theory and Weak Euler-Lagrange-Barut Equation for Classical Relativistic Particle-Field Systems

It is widely accepted that conservation laws, especially energy-momentum conservation, have fundamental importance for both classical and quantum systems in physics. A widely used method to derive the conservation laws is based on Noether's theorem. However, for classical relativistic particle-field systems, this process is still impeded. Different from the quantum situation, the obstruction emerged when we regard the particle's field as a classical world line. The difficulties come from two aspects. One is the mass-shell constraint and the other comes from the heterogeneous-manifolds that particles and fields reside on. This study develops a general geometric (manifestly covariant) field theory for classical relativistic particle-field systems. In considering the mass-shell constraint, the Euler-Lagrange-Barut (ELB) equation as a geometric version of the Euler-Lagrange (EL) equation is applied to determine the world lines of the relativistic particles. As a differential equation in the standard field theory, the infinitesimal criterion of the symmetry condition is converted into an integro-differential equation. To overcome the second difficulty, we develop a weak ELB equation on the 4D space-time. The weak version of the ELB equation will play an essential role in establishing the connections between symmetries and local conservation laws. Using field theory together with the weak ELB equation developed here, the conservation laws can be systematically derived from the symmetries that the systems admit.

physics.plasm-ph↗

arXiv2021

A gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

For electromagnetic field theories, canonical energy-momentum conservation laws can be derived from the underpinning spacetime translation symmetry according to the Noether procedure. However, the canonical Energy-Momentum Tensors (EMTs) are neither symmetric nor gauge-symmetric (gauge invariant). The Belinfante-Rosenfeld (BR) method is a well-known procedure to symmetrize the EMTs, which also renders them gauge symmetric for first-order field theories. High-order electromagnetic field theories appear in the study of gyrokinetic systems for magnetized plasmas and the Podolsky system for the radiation reaction of classical charged particles. For these high-order field theories, gauge-symmetric EMTs are not necessarily symmetric and vice versa. In the present study, we develop a new gauge-symmetrization method for EMTs in high-order electromagnetic field theories. The Noether procedure is carried out using the Faraday tensor F, instead of the 4-potential A, to derive a canonical EMT T_N. We show that the gauge-dependent part of T_N can be removed using the displacement-potential tensor \mathcal{F}=\mathcal{D}*A/4π, where \mathcal{D} is the anti-symmetric electric displacement tensor. This method gauge-symmetrize the EMT without necessarily making it symmetric, which is adequate for applications not involving general relativity. For first-order electromagnetic field theories, such as the standard Maxwell system, \mathcal{F} reduces to the familiar BR super-potential \mathcal{S}, and the method developed can be used as a simpler procedure to calculate \mathcal{S} without employing the angular momentum tensor in 4D spacetime. When the electromagnetic system is coupled to classical charged particles, the gauge-symmetrization method for EMTs is shown to be effective as well.

physics.class-ph↗

arXiv2021

Explicit Structure-Preserving Geometric Particle-in-Cell Algorithm in Curvilinear Orthogonal Coordinate Systems and Its Applications to Whole-Device 6D Kinetic Simulations of Tokamak Physics

Explicit structure-preserving geometric Particle-in-Cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm [1-12], achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the SymPIC code, which is designed for high-efficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state sub-sonic ion flow in the range of 10 km/s, agreeing with experimental observations [13, 14] and analytical calculations [15, 16]. Kinetic ballooning instability in the self-consistent kinetic steady state is simulated. It shows that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times ...

physics.plasm-ph↗

arXiv2021

Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic quantum plasmas (RQP) phenomena. The Lagrangian density of an interacting bispinor-gauge fields theory is constructed in a conjugate real fields form. The canonical symplectic form and canonical equations of this field theory are obtained by the general Hamilton's principle on cotangent bundle. Based on discrete exterior calculus, the gauge field components are discreted to form a cochain complex, and the bispinor components are naturally discreted on a staggered dual lattice as combinations of differential forms. With pull-back and push-forward gauge covariant derivatives, the discrete action is gauge invariant. A well-defined discrete canonical Poisson bracket generates a semi-discrete lattice canonical field theory (LCFT), which admits the canonical symplectic form, unitary property, gauge symmetry and discrete Poincaré subgroup. The Hamiltonian splitting method, Cayley transformation and symmetric composition technique are introduced to construct a class of high-order numerical schemes. These schemes involve two degenerate fermion flavors and are locally unconditional stable, which also preserve the geometric structures. Equipped with statistically quantization-equivalent ensemble models of the Dirac vacuum and non-trivial plasma backgrounds, the schemes are expected to have excellent performance in secular simulations of relativistic quantum effects. The algorithms are verified in detail by numerical energy spectra. Real-time LCFT simulations are successfully implemented for the nonlinear Schwinger mechanism induced $e$-$e^+$ pairs creation and vacuum Kerr effect, which open a new door toward high-quality simulations in SFQED and RQP.

quant-ph↗

arXiv2020

Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics

Since variational symplectic integrators for the guiding center was proposed [1,2], structure-preserving geometric algorithms have become an active research field in plasma physics. We found that the slow manifolds of the classical Pauli particle enable a family of structure-preserving geometric algorithms for guiding center dynamics with long-term stability and accuracy. This discovery overcomes the difficulty associated with the unstable parasitic modes for variational symplectic integrators when applied to the degenerate guiding center Lagrangian. It is a pleasant surprise that Pauli's Hamiltonian for electrons, which predated the Dirac equation and marks the beginning of particle physics, reappears in classical physics as an effective algorithm for solving an important plasma physics problem. This technique is applicable to other degenerate Lagrangians reduced from regular Lagrangians.

physics.plasm-ph↗

arXiv2019

General field theory and weak Euler-Lagrange equation for classical particle-field systems in plasma physics

A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-time, whereas each particle's trajectory is defined on the 1D time-axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange equation for particles is developed on the 4D space-time, which plays a pivotal role in establishing the connections between symmetries and local conservation laws in space-time. Especially, the non-vanishing Euler derivative in the weak Euler-Lagrangian equation generates a new current in the conservation laws. Several examples from plasma physics are studied as special cases of the general field theory. In particular, the relations between the rotational symmetry and angular momentum conservation for the Klimontovich-Poisson system and the Klimontovich-Darwin system are established.

physics.plasm-ph↗

arXiv2019

Structure-preserving geometric particle-in-cell algorithm suppresses finite-grid instability -- Comment on "Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm'' by Huang et al

A recent paper by Huang et al. [Computer Physics Communications 207, 123 (2016)] thoroughly analyzed the Finite Grid Instability(FGI) and spectral fidelity of standard Particle-In-Cell (PIC) methods. Numerical experiments were carried out to demonstrate the FGIs for two PIC methods, the energy-conserving algorithm and the momentum-conserving algorithm. The paper also suggested that similar numerical experiments should be performed to test the newly developed Structure-Preserving Geometric (SPG)-PIC algorithm. In this comment, we supply the results of the suggested numerical experiments, which show that the SPG-PIC algorithm is able to suppress the FGI.

physics.plasm-ph↗

arXiv2019

PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability

We prove that in finite dimensions, a Parity-Time (PT)-symmetric Hamiltonian is necessarily pseudo-Hermitian regardless of whether it is diagonalizable or not. This result is different from Mostafazadeh's, which requires the Hamiltonian to be diagonalizable. PT-symmetry breaking often occurs at exceptional points where the Hamiltonian is not diagonalizable. Our result implies that PT-symmetry breaking is equivalent to the onset of instabilities of pseudo-Hermitian systems, which was systematically studied by Krein et al. in 1950s. In particular, we show that the mechanism of PT-symmetry breaking is the resonance between eigenmodes with different Krein signatures.

quant-ph↗

arXiv2019

Field theory and structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence

A field theory and the associated structure-preserving geometric Particle-In-Cell (PIC) algorithm are developed to study low frequency electrostatic perturbations with fully kinetic ions and adiabatic electrons in magnetized plasmas. The algorithm is constructed by geometrically discretizing the field theory using discrete exterior calculus, high-order Whitney interpolation forms, and non-canonical Hamiltonian splitting method. The discretization preserves the non-canonical symplectic structure of the particle-field system, as well as the electromagnetic gauge symmetry. As a result, the algorithm is charge-conserving and possesses long-term conservation properties. Because drift wave turbulence and anomalous transport intrinsically involve multi time-scales, simulation studies using fully kinetic particle demand algorithms with long-term accuracy and fidelity. The structure-preserving geometric PIC algorithm developed adequately servers this purpose. The algorithm has been implemented in the \textsl{SymPIC} code, tested and benchmarked using the examples of ion Bernstein waves and drift waves. We apply the algorithm to study the Ion Temperature Gradient (ITG) instability and turbulence in a 2D slab geometry. Simulation results show that at the early stage of the turbulence, the energy diffusion is between the Bohm scaling and gyro-Bohm scaling. At later time, the observed diffusion is closer to the gyro-Bohm scaling, and density blobs generated by the rupture of unstable modes are the prominent structures of the fully developed ITG turbulence.

physics.plasm-ph↗