The kinetic codes used to model the coupled dynamics of electromagnetic fields and charged particle transport have requirements for spatial, temporal, and charge resolution. These requirements may vary by the solution technique and scope of the problem. In this report, we investigate the resolution limits in the energy-conserving implicit particle-in-cell code CHICAGO. This report has the narrow aim of determining the maximum acceptable grid spacing for the dense plasmas generated in models of z-pinch target gases and power-flow electrode plasmas. In the 2D sample problem, the plasma drifts without external forces with velocity of 10 cm/µs. Simulations are scaled by plasma density to maintain uniform strides across the plasma and from the plasma to the boundaries. Additionally, the cloud-in-cell technique is used with 400 particles per cell and Δt = 0.85× the Courant limit. For the linear cloud distribution, the criterion for conserving energy is ΔE/Etot < 0.01 for 50,000 time steps. The grid resolution is determined to crudely be Δx ≲ 3ls, where ls is the electron collisionless skin depth. For the second-order cloud distribution the criterion is ΔE/Etot < 0.005 yielding Δx ≤ 15ls. These scalings are functions of the chosen vd, Δt, particles-per-cell, and number of steps.
A six-month research effort has advanced the hybrid kinetic-fluid modeling capability required for developing non-thermal warm x-ray sources on Z. The three particle treatments of quasi-neutral, multi-fluid, and kinetic are demonstrated in 1D simulations of an Ar gas puff. The simulations determine required resolutions for the advanced implicit solution techniques and debug hybrid particle treatments with equation-of-state and radiation transport. The kinetic treatment is used in preliminary analysis of the non-Maxwellian nature of a gas target. It is also demonstrates the sensitivity of the cyclotron and collision frequencies in determining the transition from thermal to non-thermal particle populations. Finally, a 2D Ar gas puff simulation of a Z shot demonstrates the readiness to proceed with realistic target configurations. The results put us on a very firm footing to proceed to a full LDRD which includes continued development transition criteria and x-ray yield calculation.
This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.