Coulomb Collision Algorithms for Particle Codes

This paper surveys some of the particle code algorithms used to model Coulomb collisions in fully ionized plasmas, e.g., pair-wise operators such as the Takizuka-Abe$^{1}$ scheme and extensions$^{2}$, Langevin equation collision operators$^{3,4}$, and partially linearized gyrokinetic collisions operators for strongly magnetized plasmas.$^{5,6,7}$ Some recent experience is reported.$^{8 }$ Issues such as physics completeness, accuracy, and comparative algorithm performance are highlighted. 1. T. Takizuka and H. Abe, J. Comput. Phys. \textbf{25}, 205 (1977). 2. K. Nanbu, Phys. Rev. E \textbf{55}, 4642 (1997). 3. M.E. Jones, et al., J. Comp. Phys. \textbf{123}, 169 (1996). 4. W.M. Manheimer, M. Lampe, and G. Joyce, et al., J. Comp. Phys. \textbf{138}, 565 (1997). 5. X.Q. Xu and M.N. Rosenbluth, Phys. Fluids B \textbf{3}, 627 (1991). 6. A.M. Dimits and B.I. Cohen, Phys. Rev. E \textbf{49}, 709 (1994). 7. Z. Lin, W. M. Tang, and W. W. Lee, \textit{Phys.Plasmas }\textbf{2}, 2975 (August 1995). 8. B.I. Cohen, et al., ``Effects of ion-ion collisions and inhomogeneity in two-dimensional kinetic ion simulations of stimulated Brillouin backscattering,'' accepted for publication in Phys. Plasmas (2006).