Related papers: A particle method for the homogeneous Landau equat…
We propose a novel score-based particle method for solving the Landau equation in plasmas, that seamlessly integrates learning with structure-preserving particle methods [arXiv:1910.03080]. Building upon the Lagrangian viewpoint of the…
We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation in plasma physics. The methods are stochastic variations of the particle methods proposed by Carrillo et al. [J. Comput. Phys.:…
The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving…
Inspired by the gradient flow viewpoint of the Landau equation and the corresponding dynamic formulation of the Landau metric in [arXiv:2007.08591], we develop a novel implicit particle method for the Landau equation in the framework of the…
In this paper we present a spectral collocation method for the fast evaluation of the Landau collision operator for plasma physics, which allows us to obtain spectrally accurate numerical solutions. The method is inspired by the seminal…
The Landau collision integral is often considered the gold standard in the context of kinetic plasma simulation due to its conservative properties, despite challenges involved in its discretization. The primary challenge when implementing…
In this paper, we propose and implement a structure-preserving stochastic particle method for the Landau equation. The method is based on a particle system for the Landau equation, where pairwise grazing collisions are modeled as diffusion…
We introduce an extension of the particle-in-cell (PIC) method that captures the Landau collisional effects in the Vlasov-Maxwell-Landau equations. The method arises from a regularisation of the variational formulation of the Landau…
We propose a collision-oriented particle system to approximate a class of Landau-type equations. This particle system is formally derived from a particle system with random collisions in the grazing regime, and happens to be a special…
This paper proposes a novel numerical integrator for modeling multispecies Coulomb collisions in kinetic plasmas. The proposed scheme provides an energy-, momentum-, and positivity-preserving particle discretization of the nonlinear Landau…
We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient…
We propose a particle method for numerically solving the Landau equation, inspired by the score-based transport modeling (SBTM) method for the Fokker-Planck equation. This method can preserve some important physical properties of the Landau…
We derive the spatially homogeneous Landau equation for Maxwellian molecules from a natural stochastic interacting particle system. More precisely, we control the relative entropy between the joint law of the particle system and the…
We present a numerical framework for the simulation of collisional plasma dynamics, based on a coupling between Direct Simulation Monte Carlo (DSMC) and Particle-in-Cell (PIC) methods for the Vlasov-Maxwell-Landau system. The approach…
We study a regularized version of the Landau equation, which was recently introduced in~\cite{CHWW20} to numerically approximate the Landau equation with good accuracy at reasonable computational cost. We develop the existence and…
This paper contributes new insights into discretizing Coulomb collisions in kinetic plasma models. Building on the previous works [Carrillo et al. J. Comp. Phys. X 7:100066 (2020), Hirvijoki and Burby Phys. Plasmas 27(8):082307 (2020)], I…
We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and energy and facilitates the integration over the…
In this paper, we present a new framework for addressing the nonlinear Landau collision operator in terms of particle-in-cell methods. We employ the underlying metriplectic structure of the collision operator and, using a macro particle…
The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational costs and limits simulations to short physical run-times and often to setups in less than three spatial…
We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is…