Validity of 1-D approximation in glow discharge models

Capacitively-Coupled Plasma (CCP) discharges are often modeled using a one-dimensional approximation. Due to commonly used large aspect ratios in the plasma chamber, the center region of the discharge is assumed to be uniform in the radial direction and to exhibit changes only in the axial direction, parallel to the electric field. This approximation allows for faster simulations while capturing the most important physical effects in the discharge.

However, diffusion effects can also be significant under certain operating conditions, especially at low pressures when the mean free path between collisions is higher. Also, charge buildup on the dielectric wall can induce an asymmetric behavior in the plasma.

Thus, we assess the validity and accuracy of assumptions about the dimensionality of the glow discharge models by comparing one- and two-dimensional simulations of an argon CCP. We perform a parametric study to determine at which operating conditions diffusion effects contribute more significantly. Finally, by comparing with the 2-D results, we can quantify and define an additional uncertainty that can be applied to 1-D simulations to account for these effects.