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The collisional particle-in-cell method for the Vlasov-Maxwell-Landau equations

Rafael Bailo · José Antonio Carrillo · Jingwei Hu

arXiv: 2401.01689, 2024.

arXiv: 2401.01689, 2024.

@Article{BCH2024
	title={The collisional particle-in-cell method for the {V}lasov-{M}axwell-{L}andau equations},
	author={Bailo, Rafael and Carrillo, José Antonio and Hu, Jingwei},
	journal={Preprint arXiv: 2401.01689},
	year={2024},
	doi={10.48550/arXiv.2401.01689},
	archivePrefix={arXiv},
	arXivId={2401.01689},
	eprint={2401.01689},
}

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 equation, leading to a discretisation of the operator that conserves mass, charge, momentum, and energy, while dissipating the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport-collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability, and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.

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 equation, leading to a discretisation of the operator that conserves mass, charge, momentum, and energy, while dissipating the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport-collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability, and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.