DSMC methods for simulation of Coulomb collisions in multi-component plasma

The general DSMC method for solving Boltzmann equation for long-range potentials and Landau-Fokker-Planck equation was proposed by Bobylev and Nanbu in 2000 [1] (partly as a development of earlier appoach of Nanbu [2] to Coulomb collisions).  The methods of [1,2] were later applied to various model problems of plasma physics, discussed in detail and further developed by several authors (see, for example, [3,4] and references in [4]). However the general method of [1] was not clearly understood and therefore many authors still use a more complicated original scheme of [2] with reference to [1] just for the formal proof of consistency with the Landau-Fokker-Planck equation. The reason is that the first presentation of the method was done in [1] in too formal and general way. We present in this paper a completely different approach, which leads to basically the same general method, but makes its essence absolutely clear and transparent. The method is explained for the general case of multi-component plasma. We also present some rigorous estimates for accuracy of the method. Finally some numerical results on typical problems of physics of collisional plasma are presented and discussed.      
 
References
 
1. A.V.Bobylev and K.Nanbu, Theory of collision algorithms for gases and plasmas based on the Boltzmann equation and the Landau-Fokker-Planck equation, Phys.Rev.E 61, 4576-4586 (2000).
 
2. K.Nanbu, Theory of cumulative small-angle collisions in plasmas, Phys.Rev. E 55, 4642-4652 (1997).
 
3. A.V.Bobylev, E.Mossberg and I.F.Potapenko, A DSMC method for the Landau-Fokker-Planck equation, in the book Rarefied Gas Dynamics (Proc. of 25th RGD Symposium, St. Petersburg, July 2006), Eds. M.S.Ivanov and A.K.Rebrov, 479-483, Novosibirsk 2007.
 
4. G.Dimarco, R.Caflisch, L.Pareschi, Direct Simulation Monte Carlo schemes for Coulomb interactions in plasmas, Commun. Appl. Indust. Math. 1, 72-91 (2010).