Mathematical-Physical Analysis of Drag Force of a .223 REM Caliber Projectile

This article deals with the mathematical and physical analysis of the drag force affecting a .223 REM projectile as a basis for further modification of the aerodynamic shape of the projectile by changing the perpendicular shock wave at the projectile tip into a conical one. For the analyses, the Department’s experience from the analysis of the supersonic flow generated during the pumping of the vacuum chambers of the electron microscope was used.

Thermodynamics of Moist Air for Vacuum Technology

The paper is focused on the developing a predictive mathematical model for describing thermodynamic processes connected with the moist air depressurization in vacuum chambers. Equations of the mathematical description are based on principles of the energy and mass conservation, which are complemented by the moist air thermodynamics, the state behavior of water and vapor, including principles of the critical flow. The described problem has been solved using the MATLAB software. In the paper, two cases are applied and discussed: the vacuum drying and the specimen chamber of an environmental scanning electron microscope. The specific requirements are especially important for environmental scanning electron microscopes, where it is possible to observe samples, which contain water, in their natural condition. If the air pressure, temperature and humidity do not have suitable values, observed sample may be dried or damaged.

Mathematical and Physical Analysis of Pressure Gradient in the Experimental Chamber for Subsequent Comparison with Optical Methods

As a part of the research in the field of pumping vacuum chambers in the Environmental Electron Microscope, a research on supersonic flow through the Appertures is being carried out at the Department of Electrical and Electronic Technology of the Brno University of Technology in cooperation with the Institute of Scientific Instruments of the Czech Academy of Science. This paper deals with the possibility of investigating shock waves using the Shlieren optical method, which allows to observe pressure gradients as the first derivation of pressure.

Mathematical and Physical Analysis of the Effect of Conical and Detached Shock Waves at the Tip of a Static Probe in an Experimental Chamber

As part of the research in the field of pumping vacuum chambers in the Environmental Electron Microscope, research on supersonic flow through apertures is being carried out at the Department of Electrical and Electronic Technology of the Brno University of Technology in cooperation with the Institute of Scientific Instruments of the CAS. This paper deals with the influence of the shape of the static probe cone design for static pressure measurements in the supersonic flow regime in the Experimental Chamber. The cone of the probe has an effect on the shape of the shock wave, which significantly influences the detected static pressure value.

Study on the Calculation Method for Pumping Process in as Vacuum System

The calculation methods for vacuum system pumping were usually based on some simple theoretical models, the corresponding results had significant deviations from actual situations. In this study, medium and low vacuum systems (including vacuum chambers, pipes and pumps) were taken as research objects. With a measured vacuum system, and relationship between pump’s suction flowrate and inlet pressure, a new calculation method for vacuum pumping time was proposed, in which laminar or turbulent model was selected according to the pipeline’s flow state. New and traditional laminar method were used to calculate the pumping process of the measured system, which found that in the middle and high pressure stage, the pipeline flow was in turbulent state and the resistance was non-negligible. If the influence of turbulence was ignored, the calculated pressure drop would be faster than actual situation. The calculation result was verified by actual measurement result, indicating that new method is practical for vacuum pumping time calculation.

Application of Prandtl’s Theory in the Design of an Experimental Chamber for Static Pressure Measurements

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.

Development of Low-Magnetic-Permeability Welds of 316L Stainless Steel

Austenitic stainless steel is often used as the construction material for particle accelerator vacuum chambers. It is also a strong candidate construction material for helium vessels of superconducting radiofrequency cavities of highenergy, high-power particle accelerators. One of the major limitations of austenitic stainless steels for their application in particle accelerators is the relatively higher magnetic permeability of its welds. The present paper describes an experimental study to obtain a low-magnetic-permeability gas tungsten arc weld of 316L stainless steel while using ER 316L stainless steel filler metal through controlled addition of nitrogen in the argon shielding gas. It was demonstrated that 316L stainless steel welds, made with the addition of 1.5% nitrogen in the argon shielding gas, were associated with magnetic permeability close to that of the base metal. The welds exhibited good strength and ductility in addition to qualifying the impact test requirement of the American Society of Mechanical Engineers Boiler & Pressure Vessel Code (BPVC) for operation at room temperature and liquid helium temperature (4 K). The technique is important for the fabrication of BPVC-compliant 316L stainless steel vacuum chambers and pressure vessels of particle accelerators, including helium vessels of superconducting radiofrequency cavities.

FCC-ee: the synthesis of a long history of e+e- circular colliders

The design of FCC-ee is relying on the accumulated experience of $$\mathrm {e^{+}e^{-}}$$ e + e - colliders that have been designed, constructed and operated in the past 40 years. FCC-ee will surpass the 26.7 km long Large Electron Positron collider LEP by a factor 4 in size. Like for LEP the large size is justified by the need to control the synchrotron radiation losses that for both machines reach a few percent per turn. To that end LEP had the first large super-conducting (SC) RF system with around 3.8 GV of accelerating voltage. LEP achieved for the first time very large beam-beam parameters of around 0.08, and it relied on transversely polarized beams to determine accurately the beam energy for the experiments. The DA$$\varPhi $$ Φ NE collider, together with PEP II and KEKB split the two beams into separate vacuum chambers to reach much higher Ampere-level beam currents. To overcome beam-beam lifetime and performance issues DA$$\varPhi $$ Φ NE used for the first time the Crab Waist concept for the interaction region (IR) optics. The B-factories, PEP-II and KEKB have verified the double-ring $$\mathrm {e^{+}e^{-}}$$ e + e - collider with multi-ampere stored currents for over 1000 bunches, small $$\beta ^*$$ β ∗ , top-up injection, and achieved then-highest luminosity. KEKB has applied 22-mrad crossing angle at the IP with crab crossing. Both machines inherited accelerator techniques from their predecessors, PEP and TRISTAN, which was a small-scale LEP. Currently the next generation SuperKEKB collider is starting up. It has already achieved some milestones required for FCC-ee such as small $$\beta ^*$$ β ∗ (0.8 mm) and virtual crab-waist scheme with a large Piwinski angle (>10).

Commissioning and operation status of the MAX IV 3 GeV storage ring vacuum system

The 3 GeV electron storage ring of the MAX IV laboratory is the first storage-ring-based synchrotron radiation facility with the inner surface of almost all the vacuum chambers along its circumference coated with non-evaporable getter (NEG) thin film. The coating provides a low dynamic outgassing rate and pumping of active gases. As the NEG coating was applied on an unprecedented scale, there were doubts concerning the storage ring performance. Fast conditioning of the vacuum system and over five years of reliable accelerator operation have demonstrated that the chosen design proved to be good and does not impose limits on the operation. The vacuum system performance is comparable with or better than that of other similar facilities around the world, where conventional designs were implemented. Observed pressure levels are low, and the electron beam lifetime is long and not limited by residual gas density. A summary of the vacuum performance is presented.

MODELING OF PHOSPHORUS PRODUCTION PROCESSES AND DEVELOPING A MANAGEMENT STRUCTURE BASED ON GREY SYSTEMS

The agglomeration process is one of the complex, multidimensional technological processes; it takes place under conditions of a large number of disturbing influences. As a result, the amount of return during sintering reaches 40-50%. The work is devoted to the development of a mathematical model capable of predicting and controlling the sintering point based on real-time data. As the main parameters for the construction of predictive models, data measured in real time were used – the temperature in the vacuum chambers and the gas velocity determined through the measured pressure (rarefaction) in the vacuum chambers. This paper describes the methodology and basic algorithms for modeling agglomeration processes, starting from the ingress of the charge into the sinter machine and ending with the production of a suitable agglomerate. The obtained curves of the developed mathematical model of temperature in vacuum chambers served as the basis for testing the forecast model based on the use of the theory of gray systems and the optimization algorithm of the "swarm of particles". Based on the developed mathematical model, a system for predicting the sintering point is constructed, which is the basis for determining the quality of the agglomerate, which will reduce the return volume during sintering. The general structure of the sinter control system based on a dynamic predictive model is also proposed. The practical significance of the developed predictive model based on the theory of gray systems is as follows: - forecast of the sintering point value of the agglomerate and synthesis of the control action based on the forecast; - the algorithm for constructing a mathematical model of the forecast can be used for any process that has the character of a "gray exponential law".