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

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.

References in corpus (11)

• The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
• Toroidal regularization of the guiding center Lagrangian
• Gauge-free electromagnetic gyrokinetic theory
• Slow manifold reduction for plasma science
• Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics
• Field theory and weak Euler-Lagrange equation for classical particle-field systems
• Covariant Lagrangian Methods of Relativistic Plasma Theory
• Exact conservation laws for gauge-free electromagnetic gyrokinetic equations
• Equivalence of two independent calculations of the higher order guiding center Lagrangian
• A gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories
• General field theory and weak Euler-Lagrange equation for classical particle-field systems in plasma physics

Cited by in corpus (6)

• Exact conservation laws for gauge-free electromagnetic gyrokinetic equations
• Polarization and magnetization in collisional and turbulent transport processes
• The Eulerian variational formulation of the gyrokinetic system in general spatial coordinates
• Higher Order Charge Conserving Electromagnetic Finite Element Particle in Cell Method
• Verification of a hybrid gyrokinetic model using the advanced semi-Lagrange code ssV
• Gauge-invariant variational formulations of electromagnetic gyrokinetic theory