Lagrangian averaged gyrokinetic-waterbag continuum

Nicolas Besse
2016 Communications in Mathematical Sciences  
In this paper, we first present the derivation of the anisotropic Lagrangian averaged gyrowaterbag continuum (LAGWBC-α) equations. The gyrowaterbag (short for gyrokinetic-waterbag) continuum can be viewed as a special class of exact weak solution of the gyrokinetic-Vlasov equation, allowing us to reduce the latter into an infinite-dimensional set of hydrodynamic equations while keeping its kinetic features, such as Landau damping. In order to obtain the LAGWBC-α equations from the gyrowaterbag
more » ... m the gyrowaterbag continuum we use an Eulerian variational principle and Lagrangian averaging techniques introduced by Holm, Marsden, and Ratiu [27, 28] , Marsden and Shkoller [32, 33] for the mean motion of ideal incompressible flows, extended to barotropic compressible flows by Bhat et al. [13] and some supplementary approximations for the electrical potential fluctuations. Regarding the original gyrowaterbag continuum, the LAGWBC-α equations show some additional properties and several advantages from the mathematical and physical viewpoints, which make this model a good candidate for accurately describing gyrokinetic turbulence in magnetically confined plasma. In the second part of this paper, we prove local-in-time well-posedness of an approximate version of the anisotropic LAGWBC-α equations, which we call the isotropic LAGWBC-α equations, by using quasilinear PDE type methods and elliptic regularity estimates for several operators. Key words. Gyrokinetic-waterbag model, gyrowaterbag model, well-posed problem, gyrokinetic turbulence, Lagrangian averaged models, Eulerian and Lagrangian variational principles, gyrokinetic-Vlasov equations, multi-fluids systems, infinite-dimensional hyperbolic system of conservation laws in several space dimension, magnetically confined fusion plasmas.
doi:10.4310/cms.2016.v14.n3.a1 fatcat:gabo726objezzffz63dnmezm7e