COUPLED 2025

Extending PIC using Scovel-Weinstein theory

  • Burby, Joshua (University of Texas at Austin)
  • Quashie, Mandela (Michigan State University)
  • Tang, Qi (George Tech)

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Particle-in-cell (PIC) methods comprise the backbone of kinetic plasma simulations. In its simplest form, PIC entails replacing the smooth single-particle distribution function with a sum of delta functions concentrated on a large collection of marker particles. In this sense each PIC marker particle carries no information about distribution function gradients. In the early '90s, Scovel-Weinstein developed an alternative method for discretizing kinetic plasma models that resembles PIC, but with marker particles that explicitly carry gradient information of any desired order. They presented the theoretical underpinnings of their method in an elegant paper steeped in Lie theory. A follow-up paper examining practical implementation of the method was apparently planned, but never came to fruition. Perhaps owing to the considerable mathematical prerequisites needed to understand the theory paper, Scovel-Weinstein PIC remains largely untested to this day. After sketching the underlying mathematics that enable incorporating shape degrees of freedom without introducing artificial dissipation, I will describe our recent investigations into practical implementation of Scovel-Weinstein theory. In particular I will discuss our assessment of Scovel-Weinstein PIC's potential for data-compression by way of replacing mesoscopic collections of ordinary PIC particles with many fewer complex particles carrying shape degrees of freedom.