arXiv subjects

Peifeng Fan

Publications and source records attributed to Peifeng Fan.

10 recordsLinked to original sources

arXiv2026

Central Equations and Band Structures of Linear Magnetohydrodynamic Waves in a Magneto-Lattice

We investigate the band structures and propagation properties of linear ideal magnetohydrodynamic (MHD) waves in a plasma with a spatially periodic background magnetic field (a magneto-lattice ). We develop a plane-wave expansion approach in two equivalent forms: one written using the usual linearized MHD perturbation variables and another written in terms of the fluid displacement. We validate both formulations with numerical tests, including an empty-lattice limit that recovers the uniform-plasma dispersion. The method enables efficient computation of dispersion relations and reveals intrinsic frequency band gaps and cutoff behavior caused by magnetic periodicity. We show that the band gap width increases with the amplitude of the periodic magnetic-field modulation (relative to the uniform background field), leading to suppression of selected wave modes. In addition, the magnetic periodicity splits the Alfv\'en continuum into multiple branches, a feature absent in uniform plasmas. These results provide a framework for tailoring MHD wave propagation in structured plasmas and may be useful for future studies of plasma metamaterials and topological plasma waves.

physics.plasm-ph↗

arXiv2024

Hall Transport of Charged Particles in Magnetic Disk Array

The concept of periodic structures has driven the development of advanced materials like photonic and phononic crystals. These metamaterials typically rely on complex repeating units or meta-atoms, limiting their adaptability after fabrication. To overcome this limitation, we introduce the concept of metafields, which are repeating patterns of local magnetic fields instead of material structures. Unlike metamaterials, which consist of atoms arranged in structured patterns, metafields focus on the patterns of fields alone, allowing for dynamic property adjustments through external electric currents. This study explores a specific metafield where the repeating pattern is the magnetic disk (MD), defined by a uniform magnetic field perpendicular to its surface. By arranging multiple MDs, we form a magnetic disk array (MDA) and theoretically investigate the charged particle dynamics within this array. Our analysis highlights Hall transport phenomena, such as Hall diffusivity, conductivity, and thermal Hall effects. Using complex variables, we derive the collision integral and Boltzmann equation for particle distribution, applying perturbation methods and Fourier analysis to calculate transport coefficients. Simulations reveal a one-way preferential diffusion at the interface between MDAs with opposing field directions, where diffusion intensity varies with the particle movement direction. This highlights metafields' potential for dynamic particle control applications.

physics.app-ph↗

arXiv2024

General relaxation model for a homogeneous plasma with spherically symmetric velocity space

A kinetic moment-closed model (KMCM), derived from the Vlasov-Fokker-Planck (VFP) equation with spherically symmetric velocity space, is introduced as a general relaxation model for homogeneous plasmas. The closed form of this model is presented by introducing a set new functions called $R$ function and $R$ integration. This nonlinear model, based on the finitely distinguishable independent features (FDIF) hypothesis, enables the capture of the nature of the equilibrium state. From this relaxation model, a general temperature relaxation model is derived when velocity space exhibits spherical symmetry, and the general characteristic frequency of temperature relaxation is presented.

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

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↗

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↗

arXiv2017

Geometric field theory and weak Euler-Lagrange equation for classical relativistic particle-field systems

A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically without splitting the space and time coordinates, i.e., space-time is treated as one identity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that particles and field reside on different manifold. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of electromagnetic fields and also a functional of particles' world-lines. The other difficulty associated with the geometric setting is due to the mass-shell condition. The standard Euler-Lagrange (EL) equation for a particle is generalized into the geometric EL equation when the mass-shell condition is imposed. For the particle-field system, the geometric EL equation is further generalized into a weak geometric EL equation for particles. With the EL equation for field and the geometric weak EL equation for particles, symmetries and conservation laws can be established geometrically. A geometric expression for the energy-momentum tensor for particles is derived for the first time, which recovers the non-geometric form in the existing literature for a chosen coordinate system.

physics.plasm-ph↗