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Lectures Year : 2023



Gyrokinetics is a self-consistent kinetic model of magnetised plasmas that applies to dynamical systems characterised by typical frequencies lower than the cyclotron frequency. Any gyrokinetic theory proceeds in two steps. The first one is the derivation of a gyrokinetic Vlasov equation for each charged species. This is done by building a new adiabatic invariant of motion, the magnetic moment, associated with a virtual particle, the gyrocentre, slightly shifted from the particle guiding-centre. It relies on a near-identity change of variables in a 8D extended phase space. This change of variables is not unique. Several options are discussed in this lecture note. The second part is the derivation of particle charge and current densities that enter the Maxwell equations, knowing the gyrocentre distribution functions. It appears that a magnetised plasma behaves as a medium that is both electrically polarised and magnetised. The resulting model encompasses one kinetic equation per species and the Maxwell equations. It can be used to address any self-consistent electromagnetic problem in magnetised plasmas, in particular instabilities and turbulent transport. Sections labelled with a star "*" can be skipped in a first reading. Notations can be found in Appendix A.
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hal-03974985 , version 1 (06-02-2023)
hal-03974985 , version 2 (21-02-2023)


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  • HAL Id : hal-03974985 , version 1


Xavier Garbet, Maxime Lesur. Gyrokinetics. Doctoral. France. 2023. ⟨hal-03974985v1⟩
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