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

Fan, Peifeng; Qin, Hong; Xiao, Jianyuan

doi:10.48550/arxiv.2006.11039

Cited by 4 publications

(10 citation statements)

References 66 publications

(115 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Eq. ( 6), L F depends only on first-order derivatives of A. High-order electromagnetic field theories appear in the study of gyrokinetic systems [18][19][20] for magnetized plasmas and radiation reaction for classical charged particles [21,22]. Physics requires that the EL equation ( 4) is gauge symmetric, i.e, invariant under the gauge transformation…”

Section: A Explicitly Gauge-symmetric Euler-lagrange Equationmentioning

confidence: 99%

“…For practical applications, such as in the gyrokinetic theory [18][19][20] for magnetized plasmas, reduced theoretical models are often adopted due to the intrinsic complexity of the systems. The equations of motion for the systems are usually gauge invariant, but the Lagrangian densities are not always specified by manifestly covariant forms.…”

Section: Gauge-symmetric Emts For Electromagnetic Systems Cou-pled Wi...mentioning

confidence: 99%

“…The equation of motion for particles is also derived from the variational principle. However, because particles and field reside on different manifolds, the equation of motion for particles will be the weak EL equation [20,[25][26][27]]…”

Section: A Weak Euler-lagrange Equation and Conservation Lawmentioning

confidence: 99%

“…In this study, we developed a gauge-symmetrization method for the energy and momentum conservation laws in general high-order classical electromagnetic field theories, which appear in the study of gyrokinetic systems [18][19][20] for magnetized plasmas and the Podolsky system [21,22] for the radiation reaction of classical charged particles. The method only removes the electromagnetic gauge dependence from the canonical EMT derived from the spacetime translation symmetry, without necessarily symmetrizing the EMT with respect to the tensor indices.…”

Section: B Gauge-symmetric Energy Conservation Lawmentioning

confidence: 99%

“…But for general electromagnetic field theories with highorder field derivations, symmetry with respect to tensor indices in general does not imply gauge symmetry and vice versa. High-order electromagnetic field theories appear in the study of gyrokinetic systems [18][19][20] for magnetized plasmas and the Podolsky system [21,22] for the radiation reaction of classical charged particles. In the present study, we propose a new method to gauge-symmetrize the canonical EMTs T µν N in general electromagnetic field theories with high-order field derivations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Fan,

Xiao,

Qin

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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 gaugesymmetric (gauge invariant). The Belinfante-Rosenfeld (BR) method is a well-known procedure to symmetrize the EMTs, which also render 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 µν , instead of the 4-potential A µ , to derive a canonical EMT T µν N . We show that the gauge-dependent part of T µν N can be removed using the displacement-potential tensor F σµν ≡ D σµ A ν /4π, where D σµ 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, F σµν reduces to the familiar BR super-potential S σµν , and the method developed can be used as a simpler procedure to calculate S σµν 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.

show abstract

Section: A Explicitly Gauge-symmetric Euler-lagrange Equationmentioning

confidence: 99%

Section: Gauge-symmetric Emts For Electromagnetic Systems Cou-pled Wi...mentioning

confidence: 99%

Section: A Weak Euler-lagrange Equation and Conservation Lawmentioning

confidence: 99%

Section: B Gauge-symmetric Energy Conservation Lawmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Fan,

Xiao,

Qin

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

The Eulerian variational formulation of the gyrokinetic system in general spatial coordinates

et al. 2021

View full text Add to dashboard Cite

The Eulerian variational formulation of the gyrokinetic system with electrostatic turbulence is presented in general spatial coordinates by extending our previous work [H. Sugama et al., Phys. Plasmas 25, 102506 (2018)]. The invariance of the Lagrangian of the system under an arbitrary spatial coordinate transformation is used to derive the local momentum balance equation satisfied by the gyrocenter distribution functions and the turbulent potential, which are given as solutions of the governing equations. In the symmetric background magnetic field, the derived local momentum balance equation gives rise to the local momentum conservation law in the direction of symmetry. This derivation is in contrast to the conventional method using the spatial translation in which the asymmetric canonical pressure tensor generally enters the momentum balance equation. In the present study, the variation of the Lagrangian density with respect to the metric tensor is taken to directly obtain the symmetric pressure tensor, which includes the effect of turbulence on the momentum transport. In addition, it is shown in this work how the momentum balance is modified when the collision and/or external source terms are added to the gyrokinetic equation. The results obtained here are considered useful for global gyrokinetic simulations investigating both neoclassical and turbulent transport processes even in general non-axisymmetric toroidal systems.

show abstract

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

Fan¹,

Chen²,

Xiao³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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 heterogeneousmanifolds 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.

show abstract

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

Cited by 4 publications

References 66 publications

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

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

The Eulerian variational formulation of the gyrokinetic system in general spatial coordinates

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

Contact Info

Product

Resources

About