https://doi.org/10.1140/epjd/s10053-025-00989-w
Regular Article - Plasma Physics
Numerical simulation of the PIII process considering temperature-dependent thermophysical properties in a viscous sheath
Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran
Received:
6
January
2025
Accepted:
23
March
2025
Published online:
10
May
2025
This paper presents a sheath approximation of the fluid model for plasma and numerically simulates one-dimensional collisional magnetized viscous sheath dynamics in the PIII process. The energy equation has been solved alongside the potential and Navier–Stokes equations (MHD equations) to capture the changes of ion temperature and its effect on ion thermophysical properties. The equations also account for the shear stress from velocity gradients in the transient plasma sheath region, which has temperature-dependent ion viscosities. We have implicitly discretized the MHD equations and used a TDMA algorithm in our in-house code. The influence of magnetic field intensity and angle, voltage pulse amplitude and rise time, and neutral gas pressure on the temporal evolution of sheath dynamics at the target surface has been analyzed. The results show that considering the energy equation and shear stress, increases the perpendicular current flux and decreases the kinetic energy by an average of 
and 
at moderate process parameters, respectively, in comparison with an inviscid isotherm sheath. The parallel current flux has a maximum value at 
The sheath thickness and current fluxes saturate at 
but kinetic energy does not. Increasing the biased voltage rise time firstly decreases current fluxes until dimensionless time 
then subsequently increases it. For perpendicular current flux, an increase in the magnetic field intensity decreases the perpendicular current flux until 
then increases it. The results are highly consistent with a prior study on constant temperature plasma.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
