4 research outputs found
On massless electron limit for a multispecies kinetic system with external magnetic field
We consider a three-dimensional kinetic model for a two species plasma
consisting of electrons and ions confined by an external nonconstant magnetic
field. Then we derive a kinetic-fluid model when the mass ratio tends
to zero. Each species initially obeys a Vlasov-type equation and the
electrostatic coupling follows from a Poisson equation. In our modeling, ions
are assumed non-collisional while a Fokker-Planck collision operator is taken
into account in the electron equation. As the mass ratio tends to zero we show
convergence to a new system where the macroscopic electron density satisfies an
anisotropic drift-diffusion equation. To achieve this task, we overcome some
specific technical issues of our model such as the strong effect of the
magnetic field on electrons and the lack of regularity at the limit. With
methods usually adapted to diffusion limit of collisional kinetic equations and
including renormalized solutions, relative entropy dissipation and velocity
averages, we establish the rigorous derivation of the limit model
Diffusion and guiding center approximation for particle transport in strong magnetic fields
International audienceThe diffusion limit of the linear Boltzmann equation with a strong magnetic field is performed. The giration period of particles around the magnetic field is assumed to be much smaller than the collision relaxation time which is supposed to be much smaller than the macroscopic time. The limiting equation is shown to be a diffusion equation in the parallel direction while in the orthogonal direction, the guiding center motion is obtained. The diffusion constant in the parallel direction is obtained through the study of a new collision operator obtained by averaging the original one. Moreover, a correction to the guiding center motion is derived
The free path in a high velocity random flight process associated to a Lorentz gas in an external field
We investigate the asymptotic behavior of the free path of a variable density
random flight model in an external field as the initial velocity of the
particle goes to infinity. The random flight models we study arise naturally as
the Boltzmann-Grad limit of a random Lorentz gas in the presence of an external
field. By analyzing the time duration of the free path, we obtain exact forms
for the asymptotic mean and variance of the free path in terms of the external
field and the density of scatterers. As a consequence, we obtain a diffusion
approximation for the joint process of the particle observed at reflection
times and the amount of time spent in free flight.Comment: 30 page