Abstract Details
Abstracts
Author: Evstati G Evstatiev
Requested Type: Poster
Submitted: 2026-03-12 18:41:56
Co-authors: J.M.Finn
Contact Info:
Sandia National Laboratories
1515 Eubank Blvd SE
Albuquerque, New Mexico 87123
USA
Abstract Text:
We use the methods developed in Part I to determine the stability properties of
the momentum conserving particle-in-cell (PIC) and the energy conserving PIC methods (MCP
and ECP), emphasizing a small number of particles per cell
(Nppc), as opposed to previous analyses with infinite Nppc.
The stability properties of a system with a total of Np number of particles are encapsulated in a
finite size (Np × Np) dynamical matrix. It is shown that in the MCP method, a uniform stationary
cold plasma is generally unstable when the lattice of particles is arbitrarily placed relative to the
grid. We term this new instability the shift instability. Scaling of the growth rates with Ng and
Nppc are found. The dynamical matrix for the ECP method is symmetric, positive definite
(SPD), so that the ECP method is stable regardless of the relative placement
of the particle lattice and the grid.
For Nppc > 1, the dynamical matrix is block circulant, with
blocks of dimension Nppc × Nppc. A generalization of the discrete Fourier trransform (DFT) approach for circulant matrices is
possible but a related (and generally smaller) Ng × Ng matrix can be found, and
this matrix is circulant, allowing DFT analysis.
It is shown that the sums in MCP and ECP are the trapezoidal approximations to
the meshfree integrals. These sums equal the m = 0 DFT coefficients and the trapezoidal rule
error is the aliasing error. As the lattice is displaced relative to the grid, the DFT analysis applied
to the MCP method indicates an instability for the cold stationary plasma, due to aliasing.
Alternately, the shift ε of the lattice can
be understood as the instantaneous position of a cold drifting plasma of velocity v0, i.e., ε → v0 t,
allowing for parametric instabilities for both the MCP and ECP cases. The
possibility of applying this cold beam analysis to a warm plasma is discussed. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.
Characterization: 4.0
Comments:
Please place this poster after the poster with first author J. M. Finn