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

TL;DR

This paper develops a high-order field theory on heterogeneous manifolds to derive exact, gauge-invariant local energy-momentum conservation laws for electromagnetic gyrokinetic systems, addressing a longstanding challenge in plasma physics.

Contribution

It introduces a novel high-order field theory framework on heterogeneous manifolds to derive conservation laws for gyrokinetics, overcoming limitations of standard Noether's procedure.

Findings

Derived exact local energy-momentum conservation laws for gyrokinetics.

Identified the role of weak Euler-Lagrange currents in conservation laws.

Established a new theoretical foundation for plasma transport simulations.

Abstract

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.