The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving deterministic particle method arXiv:1910.03080 has been developed for the single species spatially homogeneous Landau equation. This method relies on a regularization of the Landau collision operator so that an approximate solution, which is a linear combination of Dirac delta distributions, is well-defined. Based on a weak form of the regularized Landau equation, the time dependent locations of the Dirac delta functions satisfy a system of ordinary differential equations. In this work, we extend this particle method to the multispecies case, and examine its conservation of mass, momentum, and energy, and decay of entropy properties. We show that the equilibrium distribution of the regularized multispecies Landau equation is a Maxwellian distribution, and state a critical condition on the regularization parameters that guarantees a species independent equilibrium temperature. A convergence study comparing an exact multispecies BKW solution to the particle solution shows approximately 2nd order accuracy. Important physical properties such as conservation, decay of entropy, and equilibrium distribution of the particle method are demonstrated with several numerical examples.

翻译：多物种Landau碰撞算子描述了由不同种类粒子（如电子和离子）组成的等离子体中的双粒子、小散射角或擦边碰撞。近期，一种保持结构的确定性粒子方法（arXiv:1910.03080）被提出用于单物种空间均匀Landau方程。该方法依赖于对Landau碰撞算子的正则化，使得以狄拉克δ分布线性组合形式表示的近似解具有良定义性。基于正则化Landau方程的弱形式，狄拉克δ函数随时间变化的位置满足常微分方程组。本研究将此粒子方法推广至多物种情形，并考察其质量、动量、能量守恒性质及熵衰减特性。我们证明了正则化多物种Landau方程的平衡分布为麦克斯韦分布，并给出了确保物种无关平衡温度的正则化参数临界条件。将精确多物种BKW解与粒子解进行对比的收敛性研究表明该方法具有近似二阶精度。通过多个数值算例验证了粒子方法的重要物理特性，如守恒性、熵衰减以及平衡分布。