Abstract Details
Abstracts
Author: Dan C Barnes
Requested Type: Poster
Submitted: 2026-03-17 07:52:51
Co-authors:
Contact Info:
TAE Technologies
146 BISHOP LAMY RD
LAMY, New Mexico 87540
US
Abstract Text:
In a new approach to Darwin PIC, an almost-energy-conserving algorithm is obtained by introducing a “pre-potential” Z for the vector potential, so that the usual Coulomb-gauge vector potential A=∇×Z. Then, working with the curl of Ampere’s law (in the Darwin approximation) an almost-energy-conserving differencing is obtained as
∇^2 ∇^2 (Z^(n+1/2)+Z^(n-1/2))/2=μ_0 ∇×∑_p▒〖q_p S_i (x_p^n ) (v_p^(n+1/2)+v_p^(n-1/2))/2〗
This is the three-dimensional extension of the two-dimensional representation of the in-plane vector potential introduced by Sydorenko , et al., and was previously proposed by Barnes .
It is shown that this field equation results in the conservation of the sum of magnetic and kinetic energies, when appropriate spatial differencing is used. As v_p^(n+1/2) depends on the time difference Z^(n+1/2)-Z^(n-1/2) through the inductive electric field -A ̇=∇×Z ̇, this field equation is implicit. Using the method of Lapenta , a mesh-based equation is obtained using Yee centering (Z is face-centered) with Dey-Mittra treatment of cut-cells, from a P/C method in which particles are updated twice, once with the ES field and once with the “MS” (inductive) electric field. A previously applied, semi-implicit ES method is used for that portion of the particle update.
The main computational issue is the large stencil associated with the coupling of various Z field components with the r.h.s of the resulting field corrector equation. A special interpolation method reduces the required accumulation to a minimum.
Results obtained with the QUIK3 (Quasi-Unstructured Implicit Kinetic 3D) code based on this algorithm show excellent energy conservation and dispersion properties as well as computational efficiency using the PETSc package for linear algebra and solver operations.
Characterization: 4.0
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