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Electrostatic structures have been observed in many regions of space plasmas, including the solar wind, the magnetosphere, the auroral acceleration region. One possible theoretical description of some of these structures is the concept of Bernstein-Greene-Kruskal (BGK) modes, which are exact nonlinear steady-state solutions of the Vlasov-Poisson system of equations in collisionless kinetic theory. We generalize exact solutions of two-dimensional BGK modes in a magnetized plasma with finite magnetic field strength [Ng, Bhattacharjee, and Skiff, Phys. Plasmas {bf13}, 055903 (2006)] to cases with azimuthal magnetic fields so that these structures carry electric current as well as steady electric and magnetic fields. Such nonlinear solutions now satisfy exactly the Vlasov-Poisson-Amp`{e}re system of equations. Explicit examples with either positive or negative electric potential structure are provided.
Inequality width-amplitude relations for three-dimensional Bernstein-Greene-Kruskal solitary waves are derived for magnetized plasmas. Criteria for neglecting effects of nonzero cyclotron radius are obtained. We emphasize that the form of the solitar
In the paper, gridless particle techniques are presented in order to solve problems involving electrostatic, collisionless plasmas. The method makes use of computational particles having the shape of spherical shells or of rings, and can be used to s
We review recent advances in the numerical analysis of the Monge-Amp`ere equation. Various computational techniques are discussed including wide-stencil finite difference schemes, two-scaled methods, finite element methods, and methods based on geome
We study Landau damping in the 1+1D Vlasov-Poisson system using a Fourier-Hermite spectral representation. We describe the propagation of free energy in phase space using forwards and backwards propagating Hermite modes recently developed for gyrokin
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $tto -infty$ to asymptotic dynamics as $tto +infty$. The main novelty is the construction of modified wave operators,