The paper presents a methodology that combines experimental measurements and mathematical-physics analyses to investigate the flow behavior in a nozzle-equipped aperture associated with the solution of its impact on electron beam dispersion in an environmental scanning electron microscope (ESEM). The shape of the nozzle significantly influences the character of the supersonic flow beyond the aperture, especially the shape and type of shock waves, which are highly dense compared to the surrounding gas. These significantly affect the electron scattering, which influences the resulting image. This paper analyzes the effect of aperture and nozzle shaping under specific low-pressure conditions and its impact on the electron dispersion of the primary electron beam.

• Keywords
• Ansys Fluent, CFD, ESEM, critical flow, electron dispersion, nozzle, shock wave,
• Publication type
• Journal Article MeSH

This paper presents mathematical-physics analyses in the field of the influence of inserted sensors on the supersonic flow behind the nozzle. It evaluates differences in the flow in the area of atmospheric pressure and low pressure on the boundary of continuum mechanics. To analyze the formation of detached and conical shock waves and their distinct characteristics in atmospheric pressure and low pressure on the boundary of continuum mechanics, we conduct comparative analyses using two types of inserted sensors: flat end and tip. These analyses were performed in two variants, considering pressure ratios of 10:1 both in front of and behind the nozzle. The first variant involved using atmospheric pressure in the chamber in front of the nozzle. The second type of analysis was conducted with a pressure of 10,000 Pa in front of the nozzle. While this represents a low pressure at the boundary of continuum mechanics, it remains above the critical limit of 113 Pa. This deliberate choice was made as it falls within the team's research focus on low-pressure regions. Although it is situated at the boundary of continuum mechanics, it is intentionally within a pressure range where the viscosity values are not yet dependent on pressure. In these variants, the nature of the flow was investigated concerning the ratio of inertial and viscous flow forces under atmospheric pressure conditions, and it was compared with flow conditions at low pressure. In the low-pressure scenario, the ratio of inertial and viscous flow forces led to a significant reduction in the value of inertial forces. The results showed an altered flow character, characterized by a reduced tendency for the formation of cross-oblique shockwaves within the nozzle itself and the emergence of shockwaves with increased thickness. This increased thickness is attributed to viscous forces inhibiting the thickening of the shockwave itself. This altered flow character may have implications, such as influencing temperature sensing with a tipped sensor. The shockwave area may form in a very confined space in front of the tip, potentially impacting the results. Additionally, due to reduced inertial forces, the cone shock wave's angle is a few degrees larger than theoretical predictions, and there is no tilting due to lower inertial forces. These analyses serve as the basis for upcoming experiments in the experimental chamber designed specifically for investigations in the given region of low pressures at the boundary of continuum mechanics. The objective, in combination with mathematical-physics analyses, is to determine changes within this region of the continuum mechanics boundary where inertial forces are markedly lower than in the atmosphere but remain under the influence of unreduced viscosity.

• Keywords
• Ansys Fluent, ESEM, critical flow, nozzle, one-dimensional flow theory, pressure sensors, sensing techniques for low pressures, temperature sensors,
• Publication type
• Journal Article MeSH

The article describes the combination of experimental measurements with mathematical-physics analyses in flow investigation in the chambers of the scintillator detector, which is a part of the environmental scanning electron microscope. The chambers are divided with apertures by small openings that keep the desirable pressure differences between three chambers: The specimen chamber, the differentially pumped intermediate chamber, and the scintillator chamber. There are conflicting demands on these apertures. On the one hand, the diameter of the apertures must be as big as possible so that they incur minimal losses of the passing secondary electrons. On the other hand, it is possible to magnify the apertures only to a certain extent so the rotary and turbomolecular vacuum pump can maintain the required operating pressures in separate chambers. The article describes the combination of experimental measurement using an absolute pressure sensor and mathematical physics analysis to map all the specifics of the emerging critical supersonic flow in apertures between the chambers. Based on the experiments and their tuned analyses, the most effective variant of combining the sizes of each aperture concerning different operating pressures in the detector is determined. The situation is made more difficult by the described fact that each aperture separates a different pressure gradient, so the gas flow through each aperture has its own characteristics with a different type of critical flow, and they influence each other, thereby influencing the final passage of secondary electrons detected by the scintillator and thus affecting the resulting displayed image.

• Keywords
• Ansys Fluent, ESEM, aperture, critical flow, one-dimensional flow theory, pressure sensor, scintillation detector,
• Publication type
• Journal Article MeSH

This paper describes the combination of experimental measurements with mathematical-physical analysis during the investigation of flow in an aperture at low pressures in a prepared experimental chamber. In the first step, experimental measurements of the pressure in the specimen chamber and at its outlet were taken during the pumping of the chamber. This process converted the atmospheric pressure into the operating pressure typical for the current AQUASEM II environmental electron microscope at the ISI of the CAS in Brno. Based on these results, a mathematical-physical model was tuned in the Ansys Fluent system and subsequently used for mathematical-physical analysis in a slip flow regime on a nozzle wall at low pressure. These analyses will be used to fine-tune the experimental chamber. Once the chamber is operational, it will be possible to compare the results obtained from the experimental measurements of the nozzle wall pressure, static pressure, total pressure and temperature from the nozzle axis region in supersonic flow with the results obtained from the mathematical-physical analyses. Based on the above comparative analyses, we will be able to determine the realistic slip flow at the nozzle wall under different conditions at the continuum mechanics boundary.

• Keywords
• Ansys Fluent, low pressure, nozzle, shear stress, slip flow,
• Publication type
• Journal Article MeSH

Pumping in vacuum chambers is part of the field of environmental electron microscopy. These chambers are separated from each other by a small-diameter aperture that creates a critical flow in the supersonic flow regime. The distribution of pressure and shock waves in the path of the primary electron beam passing through the differentially pumped chamber has a large influence on the quality of the resulting microscope image. As part of this research, an experimental chamber was constructed to map supersonic flow at low pressures. The shape of this chamber was designed using mathematical-physical analyses, which served not only as a basis for the design of its geometry, but especially for the correct choice of absolute and differential pressure sensors with respect to the cryogenic temperature generated in the supersonic flow. The mathematical and physical analyses presented here map the nature of the supersonic flow with large gradients of state variables at low pressures at the continuum mechanics boundary near the region of free molecule motion in which the Environmental Electron Microscope and its differentially pumped chamber operate, which has a significant impact on the resulting sharpness of the final image obtained by the microscope. The results of this work map the flow in and behind the Laval nozzle in the experimental chamber and are the initial basis that enabled the optimization of the design of the chamber based on Prandtl's theory for the possibility of fitting it with pressure probes in such a way that they can map the flow in and behind the Laval nozzle.

• Keywords
• BD sensor, ESEM, Prandtl’s theory, differentially pumped chamber, mach number, static pressure, static probe,
• Publication type
• Journal Article MeSH