Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas

Bobylev, A. V.; Potapenko, I. F.

doi:10.1016/j.jcp.2013.03.024

Cited by 41 publications

(43 citation statements)

References 21 publications

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“…In particular, we introduce a quasi-Maxwellian approximation for the Landau equation with general cross-section and show that its solution can be (at least formally) approximated by the Wild sum. This property can be used in both theoretical study and the Monte Carlo methods for the Landau equation [16,17]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

On Some Properties of the Landau Kinetic Equation

2015

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We discuss some general properties of the Landau kinetic equation. In particular, the difference between the "true" Landau equation, which formally follows from classical mechanics, and the "generalized" Landau equation, which is just an interesting mathematical object, is stressed. We show how to approximate solutions to the Landau equation by the Wild sums. It is the so-called quasi-Maxwellian approximation related to Monte Carlo methods. This approximation can be also useful for mathematical problems. A model equation which can be reduced to a local nonlinear parabolic equation is also constructed in connection with existence of the strong solution to the initial value problem. A self-similar asymptotic solution to the Landau equation for large v and t is discussed in detail. The solution, earlier confirmed by numerical experiments, describes a formation of Maxwellian tails for a wide class of initial data concentrated in the thermal domain. It is shown that the corresponding rate of relaxation (fractional exponential function) is in exact agreement with recent mathematically rigorous estimates.

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Section: Introductionmentioning

confidence: 99%

On Some Properties of the Landau Kinetic Equation

2015

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“…The macroparticles undergo ion-ion Coulomb collisions. These collisions have been considered with the help of DSMC-like method developed in [14]. Processes of deuterium ionisation and DD fusion have been considered with the help of direct simulation Monte Carlo (DSMC) method.…”

Section: Model Descriptionmentioning

confidence: 99%

Hybrid MHD/PIC simulation of a deuterium gas puff z pinch

Shmelev

Oreshkin

Chaikovsky

2017

J. Phys.: Conf. Ser.

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“…These include those by Takizuka and Abe (TA) [30], Nanbu [31], and Sherlock [32]. They share a similar approach [33], being based on small-angle approximations of the Boltzmann equation. The Boltzmann equation for interaction of species i is…”

Section: Plasma Simulations With Small-angle Collisions Onlymentioning

confidence: 99%

“…Note that P L = P L (v ij ), in contrast with the multiple-scattering methods based on the Vlasov-Fokker-Planck equation [33], in which particles are always collided at every time step but with a scattering angle dependent upon v ij . Large-angle collisions are carried out for a pair if u ∈ U(0, 1) < P L , otherwise no collision takes place.…”

Section: Small-angle and Large-angle Collision Algorithmmentioning

confidence: 99%