Moment preserving adaptive particle weighting scheme for pic simulations

Summary form only given. The ratio of computational to physical particles is a key factor in determining the statistical scatter and accuracy in particle-based simulation. This is particularly true for problems characterized by wide ranges of number density such as those found in spacecraft electric propulsion plumes as well as ionizing discharges, where populations of electrons and excited states can grow exponentially. A particle management method must then be devised which balances statistical accuracy requirements with prevention of runaway computational costs. The standard approach of splitting and merging of particles [1], however, cannot guarantee simultaneous conservation of mass, momentum and energy using pair-wise coalescence (2:1 ratio), due to the insufficient degrees of freedom. As a result, various sophisticated models have been designed to minimize or internally store the error resulting from these merges (e.g. [2,3]). Some of these involve the interpolation of particle weights onto a grid, a procedure which can be costly and which may introduce diffusion. Instead, we have devised a simpler method [4] which relies on the generation of two particles, providing the required freedom to conserve all moments up to 2^nd order exactly. Thus, pair-wise reduction is obtained through an equivalent ratio of 4:2, but particle merges of arbitrary ratios (n+2):2 can be obtained with similar conservation properties. Furthermore, the method can be seen to conserve electrostatic energy using the additional available particle position degrees of freedom. The present work extends this exact moment-preserving merge through an octree-based adaptive mesh in velocity space to ensure that merging partners are relatively close in phase space. This mitigates artificial thermalization due to merging of particles with large opposite velocities such as those found in beam-beam interactions. An analogous particle split method is also described for re-populating depleted- VDFs that result from the particle merging. The combined fully-adaptive particle weighting scheme is then applied to several test-problems, e.g. collisionless thermal beams in a potential well, gas breakdown problem by an ionizing beam, etc., which are designed to characterize and test the limits of the method. Results are also compared to fixed particle weight and simple random 4:2 merging solutions. Extension of the method to higher-order moment conservation is also considered.