  Coulomb collisions in particle simulations for weakly coupled plasmas are
modeled by the Landau-Fokker-Planck equation, which is typically solved by
Monte-Carlo (MC) methods. One of the main disadvantages of MC is the timestep
accuracy constraint {\nu}{\Delta}t << 1 to resolve the collision frequency
{\nu}. The constraint becomes extremely stringent for self-collisions in the
presence of high charge state species and for inter-species collisions with
large mass disparities (such as present in Inertial Confinement Fusion
hohlraums), rendering long-time-scale simulations prohibitively expensive or
impractical. To overcome these difficulties, we explore a hybrid Maxwellian-MC
(HMMC) model for particle simulations. Specifically, we devise a collisional
algorithm that describes weakly collisional species with particles, and highly
collisional species and fluid components with Maxwellians. We employ the Lemons
method for particle-Maxwellian collisions, enhanced with a more careful
treatment of low-relative-speed particles, and a five-moment model for
Maxwellian-Maxwellian collisions. Particle-particle binary collisions are dealt
with classic Takizuka-Abe MC, which we extend to accommodate arbitrary particle
weights to deal with large density disparities without compromising
conservation properties. HMMC is strictly conservative and significantly
outperforms standard MC methods in situations with large mass disparities among
species or large charge states, demonstrating orders of magnitude improvement
in computational efficiency. We will substantiate the accuracy and performance
of the proposed method with several examples of varying complexity, including
both zero-dimensional relaxation and one-dimensional transport problems, the
latter using a hybrid kinetic-ion/fluid-electron model.
