Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solutions

A finite Larmor radius approximation is derived from the classical Vlasov equation, in the limit of large (and uniform) external magnetic field. We also provide an heuristic derivation of the electroneutrality equation in the finite Larmor radius setting. Existence and uniqueness of a solution is proven in the stationary frame for solutions depending only on the direction parallel to the magnetic field and factorizing in the velocity variables

The Finite Larmor Radius Approximation

International audienceThe presence of a large external magnetic field in a plasma introduces an additional time-scale which is very constraining for the numerical simulation. Hence it is very useful to introduce averaged models which remove this time-scale. However, depending on other parameters of the plasma different starting models for the asymptotic analysis may be considered- . We introduce here a generic framework for our analysis which fits many of the possible regimes and apply it in particular to justify the Finite Larmor Radius approximation both in the linear case and in the non linear case in the plane transverse to the magnetic field

Effect of Finite Larmor Radius on the Cosmic Ray Penetration into an Interplanetary Magnetic Flux Rope

We discuss a mechanism for cosmic ray penetration into an interplanetary magnetic flux rope, particularly the effect of the finite Larmor radius and magnetic field irregularities. First, we derive analytical solutions for cosmic ray behavior inside a magnetic flux rope, on the basis of the Newton-Lorentz equation of a particle, to investigate how cosmic rays penetrate magnetic flux ropes under an assumption of there being no scattering by small-scale magnetic field irregularities. Next, we perform a numerical simulation of a cosmic ray penetration into an interplanetary magnetic flux rope by adding small-scale magnetic field irregularities. This simulation shows that a cosmic ray density distribution is greatly different from that deduced from a guiding center approximation because of the effect of the finite Larmor radius and magnetic field irregularities for the case of a moderate to large Larmor radius compared to the flux rope radius.Comment: 17 pages, 14 figures, accepted for publication in The Astrophysical Journa

Finite Larmor radius approximation for the Fokker-Planck-Landau equation

The subject matter of this paper concerns the derivation of the finite Larmor radius approximation, when collisions are taken into account. Several studies are performed, corresponding to different collision kernels. The main motivation consists in computing the gyroaverage of the Fokker-Planck-Landau operator, which plays a major role in plasma physics. We show that the new collision operator enjoys the usual physical properties; the averaged kernel balances the mass, momentum, kinetic energy and dissipates the entropy.Comment: 62 page

Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates

In this paper, we present some new results about the approximation of the Vlasov-Poisson system with a strong external magnetic field by the 2D finite Larmor radius model. The proofs within the present work are built by using two-scale convergence tools, and can be viewed as a new slant on previous works of Fr\'enod and Sonnendr\"ucker and Bostan on the 2D finite Larmor Radius model. In a first part, we recall the physical and mathematical contexts. We also recall two main results from previous papers of Fr\'enod and Sonnendr\"ucker and Bostan. Then, we introduce a set of variables which are so-called canonical gyrokinetic coordinates, and we write the Vlasov equation in these new variables. Then, we establish some two-scale convergence and weak-* convergence results

Gyroaverage operator for a polar mesh

International audienceIn this work, we are concerned with numerical approximation of the gyroaverage operators arising in plasma physics to take into account the effects of the finite Larmor radius corrections. The work initiated in [5] is extended here to polar geometries. A direct method is proposed in the space configuration which consists in integrating on the gyrocircles using interpolation operator (Hermite or cubic splines). Numerical comparisons with a standard method based on a Padé approximation are performed: (i) with analytical solutions, (ii) considering the 4D drift-kinetic model with one Larmor radius and (iii) on the classical linear DIII-D benchmark case [6]. In particular, we show that in the context of a drift-kinetic simulation, the proposed method has similar computational cost as the standard method and its precision is independent of the radius. PACS. PACS-key discribing text of that key – PACS-key discribing text of that ke

Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow

Finite Larmor radius (FLR) effects on non-diffusive transport in a prototypical zonal flow with drift waves are studied in the context of a simplified chaotic transport model. The model consists of a superposition of drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. High frequency FLR effects are incorporated by gyroaveraging the ExB velocity. Transport in the direction of the density gradient is negligible and we therefore focus on transport parallel to the zonal flows. A prescribed asymmetry produces strongly asymmetric non- Gaussian PDFs of particle displacements, with L\'evy flights in one direction but not the other. For zero Larmor radius, a transition is observed in the scaling of the second moment of particle displacements. However, FLR effects seem to eliminate this transition. The PDFs of trapping and flight events show clear evidence of algebraic scaling with decay exponents depending on the value of the Larmor radii. The shape and spatio-temporal self-similar anomalous scaling of the PDFs of particle displacements are reproduced accurately with a neutral, asymmetric effective fractional diffusion model.Comment: 14 pages, 13 figures, submitted to Physics of Plasma