Abstract Details
Abstracts
Author: John M Finn
Requested Type: Poster
Submitted: 2026-03-16 22:10:42
Co-authors: E.G.Evstatiev
Contact Info:
Tibbar Plasma Technologies, LLC
274 DP Road
Los Alamos, NM 87544
US
Abstract Text:
In this poster we present an approach for studying grid instabilities in a 1D electrostatic plasma
with immobile ions, starting with a meshfree approach. We use kernel density estimation to obtain
the electron density, and with this obtain an analogous form for the electric field. The force on
an electron macro-particle integrates the electric field over the same kernel, or particle shape. We
discuss the conservation laws for this system and the equivalence with the Vlasov-Ampere model.
To study stability we describe a linearization process, based on an equilibrium lattice of macro-
particle positions. This leads to a dynamical matrix, which describes the linear equations of motion
for the macro-particles. We then introduce the discretization of these equations to a grid, describing
either momentum conserving particle-in-cell (PIC) or energy conserving PIC (MCP and ECP,
respectively). For the latter discretization, the dynamical matrix is symmetric positive definite
(SPD). We briefly discuss the possibility of instability in MCP, depending on the placement of the
equilibrium lattice relative to the grid. In ECP the dynamical matrix is SPD, guaranteeing stability
for arbitrary lattice placement.
For the ECP discretization, the linearized system conserves both total momentum and energy.
For the MCP discretization, we find that the linearized system only conserves the total momentum
but not the total energy.
We discuss a caveat with the usual Birdsall-Langdon choice of particle width w, comparable to
the grid spacing ∆; because of the w ∼ ∆ assumption, the limit ∆ → 0 does not converge to the
integral form used in the meshfree formulation. This point is deferred to future work.
SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.
Characterization: 4.0
Comments:
Please put in an earlier session than the Poster with first author E. G. Evstatiev