Hierarchical agglomerative sub-clustering technique for particles management in PIC simulations

The effectiveness of Particle-In-Cell (PIC) codes lies mainly in the robustness of the methods implemented, under the fundamental assumption that a sufficient number of pseudo-particles is concerned for a correct representation of the system. The consequent drawback is the huge increase of computational time required to run a simulation, to what concerns the particles charge assignment to the grid and the motion of the former through the latter. Moreover the coupling of such methods with Monte-Carlo-Collisional (MCC) modules causes another expensive computational cost to simulate particle multiple collisions with background gas and domain boundaries. Particles management techniques are therefore often introduced in PIC-MCC codes in order to improve the distribution of pseudo-particles in the simulation domain: as a matter of facts, the aim at managing the number of samples according to the importance of the considered region is a main question for codes simulating a local phenomenon in a larger domain or a strongly collisional system (e.g.: a ionizing plasma, where the number of particles increases exponentially). A clustering procedure based on the distribution function sampling applied to the 5D phase space (2D in space, 3D in velocity) is here proposed, representing the leading criterion for particles merging and splitting procedures guaranteeing the second order charge moments conservation. Applied to the study of the electrical breakdown in the early discharge phase of a Plasma Focus device, this technique is shown to increase performances of both PIC kernel and MCC module preserving the solution of the electric field and increasing samples representativeness in stochastic calculations (with respect to more traditional merging and splitting procedures).