A Set of Benchmark Tests for Validation of 3-D Particle in Cell Methods

O'Connor, Scott; Crawford, Zane D.; Verboncoeur, John P.; Luginsland, J.W.; Shanker, B.

doi:10.1109/tps.2021.3072353

Cited by 19 publications

(7 citation statements)

References 18 publications

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“…Likewise, the code can be verified by comparing the results with different model simulations or codes to provide some indication of applicability to different models [23][24][25][26]. In addition, many studies have given benchmark cases based on numerical simulations or analytical solutions [27][28][29] in order to help fill the void of benchmark and validation problems to develop new PIC codes.…”

Section: Implications Of Particle Balance In Steady Statementioning

confidence: 99%

Note on particle balance in particle-in-cell/Monte Carlo model and its implications on the steady-state simulation

Chen

et al. 2023

Plasma Sources Sci. Technol.

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The steady-state criterion for plasma numerical simulations can be determined by the particle balance relation. In this study, we utilized a one-dimensional (1D) particle-in-cell/Monte Carlo (PIC/MC) model to investigate particle transport in a capacitively coupled plasma (CCP) discharge, including particle density change, flow, generation, and loss. Our analysis revealed that the generation rate and loss rate are equivalent in both time and space, indicating a fine balance in the steady state of the discharge system. Additionally, we presented the spatio-temporal distribution and time-averaged particle transport term for electrons and ions to demonstrate how particles attain equilibrium at varying pressures. This validation method can be particularly useful in numerical simulations where determining steady state can be challenging. Our findings establish the correctness and reliability of the method.

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Section: Implications Of Particle Balance In Steady Statementioning

confidence: 99%

Note on particle balance in particle-in-cell/Monte Carlo model and its implications on the steady-state simulation

Chen

et al. 2023

Plasma Sources Sci. Technol.

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“…The particle element method combined with the Monte Carlo collision process (PIC/MC) is widely used to simulate plasma characteristics [59,60]. The PIC method divides the preset space into small grids, and calculates the macroscopic parameters on each grid point by tracking the position and momentum of the particles.…”

Section: Methodsmentioning

confidence: 99%

Influence of pulse width on the breakdown process of nanosecond pulse discharge at low pressure

Wang

et al. 2023

J. Phys. D: Appl. Phys.

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The pulse plasma discharge breakdown is a longstanding research topic in plasma physics, yet the formation process remains elusive. In this study, we investigate the breakdown process under nanosecond pulses with different pulse widths (1 ns, 10 ns, and 100 ns), utilizing the 1D implicit Particle-in-Cell/Monte Carlo collision (PIC/MCC) method. Our simulation results indicate that pulse width plays a crucial role in the evolution of plasma breakdown. Specifically, under 1 ns pulses, the breakdown occurs after the pulse voltage ceases, demonstrating that increasing pulse width accelerates the changes in plasma parameters but does not affect the breakdown time. Under 10 ns pulses, the removal of voltage leads to a significant increase in anode sheath thickness. Under 100 ns pulse, the ions collide in the cathode sheath after the pulse ends, resulting in ion energy loss. Finally, by scanning the parameter space, we give the Paschen curve and observe higher breakdown voltage in the pulse case and the impact of ion secondary electrons.

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“…We have chosen to illustrate these using DH-MFEM-PIC as results for EB-MFEM-PIC are available 23,24,40 . First, we consider a particle beam in a 0.1 m PEC cylindrical cavity with a radius of 0.02 m. The particle beam has a voltage of 7.107 kV and current of 0.25A, simulated by inserting ten particles per time step.…”

Section: Violation Of Conditionmentioning

confidence: 99%

“…A combination of Sr + ions at 1K and electrons at 100K are placed at a density of 5 × 10 8 particles per cubic meter such that the system is initially charge neutral. Further details on the experiment setup can be found in 40 and derivations of the analytic results in 41 .…”

Section: Violation Of Conditionmentioning

confidence: 99%

Rubrics for Charge Conserving Current Mapping in Finite Element Particle in Cell Methods

Crawford,

O'Connor,

Luginsland

et al. 2021

Preprint

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Modeling of kinetic plasmas using electromagnetic particle in cell methods (EM-PIC) is a problem that is well worn, in that methods developed have been used extensively both understanding physics and exploiting them for device design. EM-PIC tools have largely relied on finite difference methods coupled with particle representations of the distribution function. Refinements to ensure consistency and charge conservation have largely been an ad-hoc efforts specific to finite difference methods. Meanwhile, solution methods for field solver have grown by leaps and bounds with significant performance metrics compared to finite difference methods. Developing new EM-PIC computational schemes that leverage modern field solver technology means re-examining analysis framework necessary for self-consistent EM-PIC solution. In this paper, we prescribe general rubrics for charge conservation, demonstrate how these are satisfied in conventional finite difference PIC as well as finite element PIC, and prescribe a novel charge conserving finite element PIC. Our effort leverages proper mappings on to de-Rham sequences and lays a groundwork for understanding conditions that must be satisfied for consistency. Several numerical results demonstrate the applicability of these rubrics.

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A Set of Benchmark Tests for Validation of 3-D Particle in Cell Methods

Cited by 19 publications

References 18 publications

Note on particle balance in particle-in-cell/Monte Carlo model and its implications on the steady-state simulation

Note on particle balance in particle-in-cell/Monte Carlo model and its implications on the steady-state simulation

Influence of pulse width on the breakdown process of nanosecond pulse discharge at low pressure

Rubrics for Charge Conserving Current Mapping in Finite Element Particle in Cell Methods

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