# The Effect of Surface Roughness on Supersonic Nozzle Flow and Electron Dispersion at Low Pressure Conditions

## TL;DR

This study examines how surface roughness affects supersonic nozzle flow and electron beam scattering in low-pressure environments, such as in an ESEM.

## Contribution

The paper introduces a combined experimental and simulation approach to analyze the impact of surface roughness on electron beam scattering in low-pressure ESEM conditions.

## Key findings

- Surface roughness significantly influences electron beam scattering at elevated working pressures in ESEM.
- The influence of roughness on electron beam scattering diminishes at lower pressure values within the ESEM operating regime.
- Ansys Fluent simulations showed strong agreement with experimental results for supersonic flow and shock wave behavior.

## Abstract

This study investigates supersonic flow within a nozzle under low-pressure conditions at the continuum mechanics boundary. This phenomenon is commonly encountered in applications such as the differentially pumped chamber of an Environmental Scanning Electron Microscope (ESEM), which employs an aperture to separate two regions with a great pressure gradient. The nozzle geometry and flow control in this region can significantly influence the scattering and loss of the primary electron beam traversing the differentially pumped chamber and aperture. To this end, an experimental chamber was designed to explore aspects of this low-pressure regime, characterized by a varying ratio of inertial to viscous forces. The initial experimental results obtained using pressure sensors from the fabricated experimental chamber were utilized to refine the Ansys Fluent simulation setup, and in this combined approach, initial analyses of supersonic flow and shock waves in low-pressure environments were conducted. The refined Ansys Fluent system demonstrated a very good correspondence with the experimental findings. Subsequently, an analysis of the influence of surface roughness on the resulting flow behavior in low-pressure conditions was performed on this refined model using the refined CFD model. Based on the obtained results, a comparison of the influence of nozzle roughness on the resulting electron beam scattering was conducted for selected low-pressure variants relevant to the operational conditions of the Environmental Scanning Electron Microscope (ESEM). The influence of roughness at elevated working pressures within the ESEM operating regime on reduced electron beam scattering has been demonstrated. At lower pressure values within the ESEM operating regime, this influence is significantly diminished.