Assessment of the Effects of Coulomb Collision Algorithms on High-Density Plasma Evolution in PIC Codes

Transport of relatively high-density fully ionized plasma can depend significantly on effects of Coulomb collisions. We assess the behavior and accuracy of Coulomb collision algorithms in electrostatic PIC codes. Coulomb collisions are included using the method of Nanbu
¹
with the binary pairing of particles per element using the strategy of Takizuka and Abe
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. We also have examined the particle-field method
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using a hybrid method in which field particles are cast from a fit to the local distribution. The PIC codes evolve the plasma using energy-conserving, semi-implicit time integration that relaxes the grid spacing requirement that the Debye length be resolved
⁴
allowing the use of much coarser grid spacing in the mesh. Both collision algorithms require the logarithm of the ratio of Debye length to minimum impact parameter, the so-called Coulomb log. While its value is not expected to vary greatly within a given plasma, its value can have a first-order effect on collision frequency and therefore, plasma transport. Several formulations for computing the Coulomb log are assessed.