A new method to dispatch split particles in Particle-In-Cell codes

Smets, Roch; Aunai, N.; Ciardi, A.; Drouin, Matthieu; Pinto, Martin Campos; Deegan, Philip

doi:10.1016/j.cpc.2020.107666

Cited by 5 publications

(5 citation statements)

References 26 publications

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“…Currently, PRO++ OMG utilizes a second-order interpolation scheme and implementing a third order scheme could help reduce noise [63]. In addition, a particle splitting scheme can be applied in the exhaust region to improve statistics and thus the noise levels on the electric field calculation [64,65].…”

Section: Self-consistent Ambipolar Electric Fieldmentioning

confidence: 99%

Kinetic simulations of collision-less plasmas in open magnetic geometries ^*

Kumar¹,

Caneses²

2022

Plasma Phys. Control. Fusion

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Laboratory plasmas in open magnetic geometries can be found in many diﬀerent applications such as (1) Scrape-Of-Layer (SOL) and divertor regions in toroidal conﬁnement fusion devices , (2) linear divertor simulators, (3) plasma-based thrusters and (4) magnetic mirrors. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along ﬂux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic Particle-In-Cell (PIC) simulations can be applied but at the expense of large computational eﬀort. A common way to resolve this is to use a hybrid approach: kinetic ions and ﬂuid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (1) the eﬀect of non-uniform magnetic ﬁelds, (2) ﬁnite fully-absorbing boundaries for the particles and (3) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. Results show that the eﬀect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric ﬁeld is calculated and is shown to modify the ion velocity distribution function in manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, inclusion of a Monte-Carlo based Fokker-Planck collision operator is discussed in the context of future work.

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Section: Self-consistent Ambipolar Electric Fieldmentioning

confidence: 99%

Kinetic simulations of collision-less plasmas in open magnetic geometries ^*

Kumar¹,

Caneses²

2022

Plasma Phys. Control. Fusion

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“…Whether it is at the start time of the simulation or when a new level at the finest resolution is being created during the simulation, a refined level is initialized by refining data existing on the next coarser level. Fields are refined using linear spatial interpolation while macroparticles are refined using the splitting procedure described in Smets et al [36]. This splitting procedure ensures that the combination of the refined macroparticle b-splines is either exactly or optimally close to the b-spline of the original coarse macroparticle, and thus preserves the contribution of macroparticles to the mesh.…”

Section: Initialization Of a New Refined Levelmentioning

confidence: 99%

“…This splitting procedure ensures that the combination of the refined macroparticle b-splines is either exactly or optimally close to the b-spline of the original coarse macroparticle, and thus preserves the contribution of macroparticles to the mesh. Unlike other methods (see [36] and references therein), it ensures that no or minimal spurious noise is added to the refined grid. The method uses pre-computed and tabulated values for the relative position and weights of the refined macroparticles.…”

Section: Initialization Of a New Refined Levelmentioning

confidence: 99%

“…Thus the contribution of the refined particles to the fine mesh will differ in some uncontrolled way from what would be that of the coarse population. This typically adds a significant amount of noise on the refined mesh [36]. If macroparticles only interact with the finest mesh at their location, and splitting is used not to decrease their number per cell, the opposite operation, i.e.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hybrid Particle-In-Cell model with Adaptive Mesh Refinement

Aunai¹,

Smets²,

Deegan³

et al. 2022

Preprint

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Collisionless magentized plasmas a priori need to be evolved using Vlasov-Maxwell kinetic formalism. However the tremendous number of spatial and temporal scales involved in phenomena of interest makes it prohibitive, from a computational standpoint. Fully kinetic particle in cell and single fluid MHD codes are commonly used at very small or very large scales. The hybrid formalism, treating ions kinetically and electrons as a fluid, is in principle advantageous to fill the gap between these two extremities. However, a correct treatment of critical regions such as reconnection X-lines require a good resolution of sub-ion dissipative scales, which still constitute a major challenge if aiming at simulating meso/macro scale systems. This work presents a new code, named PHARE, which successfully implements the adaptive mesh refinement mechanism in a hybrid particle-in-cell code. Such a code is able to dynamically focus the resolution in critical regions while others not only have a coarser spatial resolution, but are also evolved much less often thanks to a recursive time stepping procedure. Adopting a patch based AMR mechanism, the code architecture is made so that the specific solver/physical model that is solved at a given refined level is abstracted, thus giving the opportunity to handling multi-formalisms AMR patch hierarchies, where, for instance, coarsest levels are solved in MHD while dynamicall created refined levels are solved within the Hybrid framework.

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“…Currently, PRO++ OMG utilizes a secondorder interpolation scheme and implementing a third order scheme could help reduce noise. 52 In addition, a particle splitting scheme can be applied in the exhaust region to improve statistics and thus the noise levels on the electric field calculation ( 53,54 ) It is worth noting that resolving the parallel electric field in a self-consistent manner is required to correctly describe the parallel transport of ions along the magnetic flux. This becomes increasingly important in devices like WHAM 5 and MPEX 1 where radiofrequency plasma heating can produce mirror-trapped fast particles.…”

Section: Self-consistent Ambipolar Electric Fieldmentioning

confidence: 99%

Kinetic simulations of collision-less plasmas in open magnetic geometries

Kumar,

Marin

2021

Preprint

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Laboratory plasmas in open magnetic geometries can be found in many different applications such as (1) Scrape-Of-Layer (SOL) and divertor regions in toroidal confinement fusion devices (≈ 1 − 10 2 eV), (2) linear divertor simulators (≈ 1 − 10 eV), (3) plasma-based thrusters (≈ 10 eV) and (4) magnetic mirrors (≈ 10 2 − 10 3 eV). A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic Particle-In-Cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (1) the effect of non-uniform magnetic fields, (2) finite fully-absorbing boundaries for the particles and (3) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. Results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, inclusion of a Monte-Carlo based Fokker-Planck collision operator is discussed in the context of future work. † This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doepublic-access-plan).

show abstract

A new method to dispatch split particles in Particle-In-Cell codes

Cited by 5 publications

References 26 publications

Kinetic simulations of collision-less plasmas in open magnetic geometries ^*

Kinetic simulations of collision-less plasmas in open magnetic geometries ^*

Hybrid Particle-In-Cell model with Adaptive Mesh Refinement

Kinetic simulations of collision-less plasmas in open magnetic geometries

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A new method to dispatch split particles in Particle-In-Cell codes

Cited by 5 publications

References 26 publications

Kinetic simulations of collision-less plasmas in open magnetic geometries *

Kinetic simulations of collision-less plasmas in open magnetic geometries *

Hybrid Particle-In-Cell model with Adaptive Mesh Refinement

Kinetic simulations of collision-less plasmas in open magnetic geometries

Contact Info

Product

Resources

About

Kinetic simulations of collision-less plasmas in open magnetic geometries ^*

Kinetic simulations of collision-less plasmas in open magnetic geometries ^*