Gyrokinetics from variational averaging: Existence and error bounds
| Autor: | Stefan Possanner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Physics
Mathematical analysis Vlasov equation FOS: Physical sciences 34C29 35Q75 70H09 78A35 82D10 Motion (geometry) Statistical and Nonlinear Physics Mathematical Physics (math-ph) Gauge (firearms) 01 natural sciences Physics - Plasma Physics Charged particle 010305 fluids & plasmas Magnetic field Plasma Physics (physics.plasm-ph) 010101 applied mathematics Third order Phase space 0103 physical sciences Gyrokinetics 0101 mathematics Mathematical Physics |
| Zdroj: | Journal of Mathematical Physics |
| Popis: | The gyrokinetic paradigm in the long wavelength regime is reviewed from the perspective of variational averaging (VA). The VA-method represents a third pillar for averaging kinetic equations with highly-oscillatory characteristics, besides classical averaging or Chapman-Enskog expansions. VA operates on the level of the Lagrangian function and preserves the Hamiltonian structure of the characteristics at all orders. We discuss the methodology of VA in detail by means of charged-particle motion in a strong magnetic field. The application of VA to a broader class of highly-oscillatory problems can be envisioned. For the charged particle, we prove the existence of a coordinate map in phase space that leads to a gyrokinetic Lagrangian at any order of the expansion, for general external fields. We compute this map up to third order, independent of the electromagnetic gauge. Moreover, an error bound for the solution of the derived gyrokinetic equation with respect to the solution of the Vlasov equation is provided, allowing to estimate the quality of the VA-approximation in this particular case. Keywords: averaging methods, Vlasov equation, Lagrangian mechanics, motion of charged particles, magnetized plasmas |
| Databáze: | OpenAIRE |
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