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This cast doubts on the ability of numerical methods to reproduce accurately experimental results from first principles, especially in light of the important role of the neutrals dynamics underlined in section 2.

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As a baseline for a parametric scan, one can consider that the incoming particle only interacts with the atoms of the wall i. A database for various materials and incident particle masses has been derived using the TRIM code [ ]. Figure 5. See Fubiani et al. In light of the high complexity of particle - wall interaction phenomena and the limited experimental data available to date to support models, it seems presumptuous to expect numerical simulations to predict, or even fully capture, these effects.

Despite these shortcomings, there are important benefits in implementing wall physics models in PIC codes. First, it allows assessing the relative importance of the various processes at play. Second, parametric scans within a range of realistic experimental values can be used to refine the analysis and examine the influence of idealized experimental conditions on plasma parameters. Practically, since the impact of charged particles at the wall can lead to the emission of neutrals and reciprocally, modeling wall physics in PIC codes requires dealing with the interaction creation, removal of macro-particles with different weights.

This situation can be handled similarly to collisions in volume between macro-particles with different weights, as discussed in section 2. In low-pressure plasma PIC modeling, the numerical integration of particle trajectories is typically responsible for most of the computing time. As a result, the implementation of particle-wall models should generally have minimal effects on the overall performances.

In particular, the implementation of wall models is not expected to modify the pros and cons of the different parallelization strategies discussed in section 2. Yet, for configurations where wall effects dominates bulk effects, or configurations with large particle fluxes to the walls, wall effects handling may in principle lead to load unbalance between subdomains with walls and subdomains without walls. One option to alleviate this limitation is to choose a domain decomposition scheme such that the number of boundary cells is, as much as possible, equally distributed over the subdomains. However, the associated benefits might be offset by a greater number of particles crossing from one subdomain to another at each time-step.

Another option for such rare cases might be to use a particle decomposition strategy. However, and besides proper implementation, the ability of PIC-MCC techniques to reproduce and simulate accurately these plasmas hinges upon the description of various phenomena. A particular challenge here lies in the fact that these phenomena cover a wide range of timescales and scale-lengths. In this paper, we discuss more specifically the importance of both neutral dynamics and wall physics. Properties of low-pressure plasmas are often strongly affected by collisions between charged-particles and neutrals.

Accounting for these effects in numerical models requires both a detailed description of the kinematics of charged particle—neutral collisions and a proper description of the neutrals distribution function f n. This is made difficult by the fact that electron—neutral collisions have to be modeled on electron timescales while f n evolves on the much slower neutral particle timescale.

One important feature in charged particle—neutral collision is the anisotropy of these processes, in particular for energetic particles. Failure to account for this property may, under some conditions, affect simulation results and lead to inaccurate or even unphysical results. Many low-pressure laboratory plasmas are also strongly affected by the walls. This makes capturing in numerical models the detailed interaction of electrons, ions and neutrals with the wall a requirement.

Special care must therefore be taken to ensure that all potentially important processes are accounted for.

Dynamics and Kinetics at the Gas−Liquid Interface | The Journal of Physical Chemistry

Unfortunately, while models for particles scattering and wall physics continue to be refined and the experimental database supporting these models grows, it remains ill-fated to assume that implementing these models as is in a PIC-MCC code ensures simulation results accuracy. Until global models describing reliably these complex phenomena become available, the recommended approach to build confidence in simulation results is to start from well established simplified models, and from there to include an additional effect and rely on parametric scans around realistic experimental conditions to quantify the importance of this effect.

Although the detailed scattering physics and wall physics may only be of limited importance in many low-pressure discharges, it should be emphasized that they could play a significant role in some. While, as intended in this paper, some generic guidelines can be put forward to identify conditions where these effects can be important, it most certainly does not cover all cases.

This makes it even more important to assess the importance of these effects in numerical simulations. All three authors RG, GF, and LG have contributed to the bibliographic survey, to the analysis and discussion of the results and to the writing of the manuscript. Part of this work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme — under grant agreement No The views and opinions expressed herein do not necessarily reflect those of the European Commission.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Marc Villemant Onera for constructive discussions. Charles C. Grand challenges in low-temperature plasma physics. Front Phys. The plasma roadmap: low temperature plasma science and technology.

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    Plasma Phys Control Fusion 60 Opportunities for plasma separation techniques in rare earth elements recycling. J Clean Prod. Particle and fluid simulations of low-temperature plasma discharges: benchmarks and kinetic effects.

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    Foundations of modelling of nonequilibrium low-temperature plasmas. Plasma Physics via Computer Simulation. Google Scholar. Computer Simulation Using Particles. Birdsall CK. Conservative numerical schemes for the vlasov equation. J Comput Phys.

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    Asymptotic-preserving particle-in-cell method for the vlasov—poisson system near quasineutrality. Boeuf JP, Chaudhury B.

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    Rotating instability in low-temperature magnetized plasmas. Phys Rev Lett.

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    Modeling of plasma transport and negative ion extraction in a magnetized radio-frequency plasma source. Boeuf JP, Garrigues L. To Appear Phys Plasmas. Exploiting multi-scale parallelism for large scale numerical modelling of laser wakefield accelerators. Plasma Phys Control Fusion 55 Verboncoeur JP.

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    Particle simulation of plasmas: review and advances. Plasma Phys Control Fusion 47 :A Lapenta G. Particle simulations of space weather. Stangeby P, McCracken G. Plasma boundary phenomena in tokamaks. Nucl Fusion 30 — Phys Plasmas 5 — Effects of neutral particles on edge dynamics in Alcator C-Mod plasmas. Phys Plasmas 7 — Neutral pumping in a helicon discharge.

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