Self-consistent kinetic theory of a plasma sheath

Area of Science:

• Plasma Physics
• Computational Physics
• Chemical Engineering

Background:

• Understanding plasma sheaths is crucial for applications like semiconductor manufacturing and fusion energy.
• Existing models often simplify the kinetic behavior of charged particles within the sheath.
• Accurate modeling requires resolving the spatial and velocity distributions of electrons and ions.

Purpose of the Study:

• To develop and validate a fully kinetic theory model for the sheath of a direct current (dc) glow discharge.
• To numerically solve the Boltzmann equations for electron and Ar+ distribution functions.
• To compare the model's predictions with particle-in-cell Monte Carlo simulations.

Main Methods:

• Direct numerical solution of Boltzmann equations for electron and Ar+ distribution functions.
• Self-consistent electric field calculation using the Poisson equation.
• Collocation method employing Legendre and nonclassical speed quadrature points for spatial and velocity variables.

Main Results:

• The model accurately captures the spatial and velocity dependence of charged particle distribution functions.
• A strong variation in the space- and energy-dependent ion distribution function was observed.
• This variation correlates with a decrease in the ratio of the Debye length to the ion mean free path.

Conclusions:

• The fully kinetic model provides a robust framework for simulating dc glow discharge sheaths.
• The findings highlight the importance of kinetic effects on ion behavior in plasma sheaths.
• The results offer insights for optimizing plasma processes and understanding plasma-sheath interactions.