Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method

We study the two-scale asymptotics for a charged beam under the action of a rapidly oscillating external electric field. After proving the convergence to the correct asymptotic state, we develop a numerical method for solving the limit model involving two time scales and validate its efficiency for the simulation of long time beam evolution

An adaptive numerical method for the Vlasov equation based on a multiresolution analysis.

International audienceIn this paper, we present very first results for the adaptive solution on a grid of the phase space of the Vlasov equation arising in particles accelarator and plasma physics. The numerical algorithm is based on a semi-Lagrangian method while adaptivity is obtained using multiresolution analysis

ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry

This paper presents the current state of the global gyrokinetic code ORB5 as an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177 409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of equations using a PIC scheme and also includes collisions and strong flows. The code assumes multiple gyrokinetic ion species at all wavelengths for the polarization density and drift-kinetic electrons. Variants of the physical model can be selected for electrons such as assuming an adiabatic response or a ``hybrid'' model in which passing electrons are assumed adiabatic and trapped electrons are drift-kinetic. A Fourier filter as well as various control variates and noise reduction techniques enable simulations with good signal-to-noise ratios at a limited numerical cost. They are completed with different momentum and zonal flow-conserving heat sources allowing for temperature-gradient and flux-driven simulations. The code, which runs on both CPUs and GPUs, is well benchmarked against other similar codes and analytical predictions, and shows good scalability up to thousands of nodes

Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model

The influence of the finite number N of particles coupled to a monochromatic wave in a collisionless plasma is investigated. For growth as well as damping of the wave, discrete particle numerical simulations show an N-dependent long time behavior resulting from the dynamics of individual particles. This behavior differs from the one due to the numerical errors incurred by Vlasov approaches. Trapping oscillations are crucial to long time dynamics, as the wave oscillations are controlled by the particle distribution inhomogeneities and the pulsating separatrix crossings drive the relaxation towards thermal equilibrium.Comment: 11 pages incl. 13 figs. Phys. Rev. E, in pres