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

Xiao, Jun; Qin, Hong

doi:10.1088/1741-4326/ab38dc

Cited by 17 publications

(39 citation statements)

References 113 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Similar and subsequent studies (Xiao et al. 2013, 2015 a , 2017; Xiao & Qin 2019, 2021; Zheng et al. 2020) have also illustrated that discrete variational principles and Whitney forms are useful tools in designing structure-preserving geometric PIC algorithms (Squire et al.…”

Section: Introductionmentioning

confidence: 69%

See 1 more Smart Citation

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

et al. 2021

Self Cite

View full text Add to dashboard Cite

We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

show abstract

Section: Introductionmentioning

confidence: 69%

“…It is desirable to apply structure-preserving geometric algorithms to these models as well. A structure-preserving geometric PIC algorithm on a cubic mesh for this system was developed recently (Xiao & Qin 2019). The construction of the algorithm starts from a field theory, i.e.…”

Section: Introductionmentioning

confidence: 99%

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…The DEL equation is employed to solve for the discrete field ψ on the spacetime lattice when a discrete Lagrangian density L d is prescribed. This has been the only usage of the DEL equation in the literature that I am aware of so far 48,49,[51][52][53]55,57,58,61,64,68,[70][71][72][73][74][75] . I will come back to this shortly.…”

Section: Machine Learning and Serving Of Discrete Field Theoriesmentioning

confidence: 99%

“…The advantages of variational integrators over standard integration schemes based on discretization of differential equations have been demonstrated. For example, variational integrators in general are symplectic or multi-symplectic 48,49,[51][52][53]55,57,58,61,64,68,[70][71][72][73][74][75] , and as such are able to bound globally errors on energy and other invariants of the system for all simulation time-steps. More sophisticated discrete field theories have been designed to preserve other geometric structures of physical systems, such as the gauge symmetry 52,75 and Poincaré symmetry 72,80,81,83 .…”

Section: (3)mentioning

confidence: 99%

Machine learning and serving of discrete field theories

Qin

2020

Sci Rep

Self Cite

View full text Add to dashboard Cite

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach of learning discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton’s laws of motion and universal gravitation. The proposed algorithms are expected to be applicable when the effects of special relativity and general relativity are important.

show abstract

“…It was Squire, Qin & Tang (2012) that first derived an exactly charge-conserving variational PIC scheme by imposing gauge symmetry on a discrete action. Several gauge-symmetric algorithms have since followed, especially in the form of Hamiltonian PIC schemes (He et al 2015(He et al , 2016Xiao et al 2015;Qin et al 2016;Kraus et al 2017;Xiao, Qin & Liu 2018;Xiao & Qin 2019).…”

mentioning

confidence: 99%

The geometric theory of charge conservation in particle-in-cell simulations

Glasser

Qin

2020

J. Plasma Phys.

Self Cite

View full text Add to dashboard Cite

In recent years, several gauge-symmetric particle-in-cell (PIC) methods have been developed whose simulations of particles and electromagnetic fields exactly conserve charge. While it is rightly observed that these methods’ gauge symmetry gives rise to their charge conservation, this causal relationship has generally been asserted via ad hoc derivations of the associated conservation laws. In this work, we develop a comprehensive theoretical grounding for charge conservation in gauge-symmetric Lagrangian and Hamiltonian PIC algorithms. For Lagrangian variational PIC methods, we apply Noether’s second theorem to demonstrate that gauge symmetry gives rise to a local charge conservation law as an off-shell identity. For Hamiltonian splitting methods, we show that the momentum map establishes their charge conservation laws. We define a new class of algorithms – gauge-compatible splitting methods – that exactly preserve the momentum map associated with a Hamiltonian system’s gauge symmetry – even after time discretization. This class of algorithms affords splitting schemes a decided advantage over alternative Hamiltonian integrators. We apply this general technique to design a novel, explicit, symplectic, gauge-compatible splitting PIC method, whose momentum map yields an exact local charge conservation law. Our study clarifies the appropriate initial conditions for such schemes and examines their symplectic reduction.

show abstract

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

Cited by 17 publications

References 113 publications

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

Machine learning and serving of discrete field theories

The geometric theory of charge conservation in particle-in-cell simulations

Contact Info

Product

Resources

About