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Gyrokinetic theory is arguably the most important tool for numerical studiesof transport physics in magnetized plasmas. However, exact localenergy-momentum conservation law for the electromagnetic gyrokinetic system hasnot been found despite continuous effort. Without such a local conservationlaw, energy-momentum can be instantaneously transported across spacetime, whichis unphysical and casts doubt on the validity of numerical simulations based onthe gyrokinetic theory. Standard Noether's procedure for deriving conservationlaws from corresponding symmetries does not apply to gyrokinetic systemsbecause the gyrocenters and electromagnetic field reside on differentmanifolds. To overcome this difficulty, we developed a high-order field theoryon heterogeneous manifolds for classical particle-field systems and apply it toderive exact local conservation laws, in particular the energy-momentumconservation law, for the electromagnetic gyrokinetic system. A weakEuler-Lagrange equation is established to replace the standard Euler-Lagrangeequation for the particles. It is discovered that an induced weakEuler-Lagrange current enters the local conservation laws. And it is the newphysics captured by the high-order field theory on heterogeneous manifolds.

plasma science and technology/plasma science and technology

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