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In multi-layer insulation (MLI) for space or terrestrial cryogenic applications, large densities of gas molecules (particles) between individual layers reduce the thermal performance of the insulation because particle collisions transfer heat. This poses an incentive to provide pathways for particles to escape the system quickly, such as perforation.
This paper uses two quality metrics for an MLI-setup: the perforation escape ratio (PER), defined as the ratio of the number of particles escaping through the layers (broadside pumping) to the total number of outgassed particles, and the pressure distribution across the layers.
The present stationary Monte Carlo simulations investigate the outgassing behaviour of MLI-setups at the end of pumping, where an equilibrium state is approached and molecular flow is assumed. Some of the findings of the “Lockheed report” (Keller et al., 1974) [1] are reproduced, and the two aforementioned quality metrics are analysed for different cases. We find that the residual pressure decreases and the parameter PER increases as (a) the perforated area increases, (b) the perforation size decreases, and (c) the number of layers decreases. Both the pressure and the parameter PER increase as (a) the layer size increases, (b) the distance between layers decreases, and (c) the porosity of the edges decreases.

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Multilayer insulation (MLI), using alternate layers of shield and spacer in high vacuum, is the most effective cryogenic insulation developed to date. Due to unpredictable changes in parameters such as winding pressure, uniform contact pressure and interstitial pressure, accurate theoretical prediction of MLI performance is very difficult. Thus, an experimental investigation has been carried out on a few indigenous MLI materials. The investigations are centred on the influence of the number of layers and layer density, with the cold boundary at the same temperature as liquid nitrogen. The experiments have been carried out using a cylindrical vessel with guard vessels on the top and bottom flat surfaces. The interstitial pressure, which depends on conditions pertaining to specific parameters, such as outgassing rate of materials, cryopumping speed and time for evacuation, has also been measured. The results are compared with those obtained from a theoretical analysis carried out for the same combination of shield and spacer materials.

This book aims to help vacuum scientists and engineers in the gas dynamics modelling of accelerator vacuum systems. It brings together the main considerations which have to be discussed and investigated during modelling and optimisation in a design of particle accelerator vacuum system, as well as to give some analytical solutions that could be useful in vacuum system design optimisation. This includes, first of all, an analysis of experimental data that should be used as inputs to analytical models; secondly, an understanding of what physical and chemical processes are happening in the vacuum chamber with and without a beam; and thirdly, choosing and applying a model (or available software) and interpreting the results. It is expected that readers have theoretical knowledge and practical experience in vacuum science and technology, thermodynamics and gas dynamics, as well as have some basic knowledge in particle accelerators.
The structure of the book corresponds to a workflow in design of accelerator vacuum chamber:
(1) Chapter 1 describes first considerations at the beginning of work on a new machine such as what type of machine and what vacuum specifications, rough vacuum estimations, etc.
(2) Chapters 2 to 5 provide an input data for gas dynamics models:
- Synchrotron radiation (SR) is one of the main characteristics that required in modelling of vacuum systems of many particle accelerators. Chapter 2 describes photon flux, critical energy, power and angular distribution from dipoles, quadrupoles, wigglers and undulators. The authors were writing the formulas in the format that could be useful for the vacuum designers.
- Chapter 3 is focused on two important effects in the interaction between SR and vacuum chamber walls: photon reflectivity and photoelectron production.
- Chapter 4 describes main materials used in for accelerator vacuum chambers, their cleaning procedure, thermal outgassing, electron, photon and ion stimulated desorption.
- Chapter 5 is devoted to a very special vacuum technology – non-evaporable getter coating.
3) Chapters 6 to 10 describe the gas dynamics models:
- Chapter 6 describes vacuum system modelling using two main approached: a one-dimensional diffusion model and a three-dimensional Test Particle Monte-Carlo Method.
- Chapter 7 describes specific problems of particle accelerators at cryogenic temperature.
- Chapter 8 demonstrates how vacuum chamber design of positively charged machines can be affected by mitigation of beam induced electron multipacting and e-cloud.
- Chapter 9 describes the ion induced pressure instability, another potential problem of positively charged machines, gas dynamics model, a number of analytical solutions and stability criteria.
- Chapter 10 is fully devoted to the heavy ion machine vacuum problems and solutions.

The ESTEC calorimeter was designed for heat transfer measurements on blankets of multi layered insulation (MLI). This work comprises a Finite Element thermal model based on the computer code ANSYS which is used for an interpretation of the experimental data gained during the 35 years of measurement. A parameter study of various test setup parameters was performed to find possible improvements for future calorimeter designs. Similar blanket lay-ups were used to test the influence of number of layers and material parameters on the analysis results. The influence of residual gas conduction in the MLI blankets was further studied and included in the numerical model. The results of the study form the basis of a further improvement of the measurement accuracy and of possible design improvements.

A new kind of calorimeter has been developed at Austrian Aerospace to measure specific material parameters needed for the analysis of thermal vacuum insulation. A detailed description of the measuring device and the measurement results will be given in this paper. This calorimeter facility allows to measure the heat flow through the insulation under vacuum conditions in a wide temperature range from liquid nitrogen to ambient. Both boundary temperatures can be chosen within this range. Furthermore the insulation can be characterized at high vacuum or under degraded vacuum, the latter is simulated by using helium or nitrogen gas. The mechanisms of heat transfer have been investigated, namely infrared radiation between the reflective layers of the insulation and conduction through the interleaving spacer material. A mathematical description of the heat flow through the insulation has been derived. Based on this, the heat flow for a typical insulation material has been calculated by finite element analysis by use of the sotware tool Ansys®. Such a transient calculation is needed to determine the time to reach thermal equilibrium, which is mandatory for a proper interpretation and evaluation of the measurement. The new insulation measurement results combined with the proposed type of analysis can be applied to better understand the thermal behavior of any kind of cryogenic system.

About 40 papers treating multilayer insulations were studied and
compared. Most of these papers present heat transfer measurements in
addition to thermal analysis. Here the equations are given which are
required for an evaluation of the measurements and in particular for
comparisons. Equations are presented which are required to predict the
influences of the packing density, temperatures, fraction of perforation
area and interstitial pressure. The equation giving gas conductivity
versus pressure is modified according to measurements. In space the
interstitial pressure is usually below 0.01 Pa and the heat transfer can
be expressed as the sum of a conductive and radiative term. The equation
finally proposed for spacecraft permits to consider the influence of
temperature, number of layers, blanket size and perforation area.

Heat flux and optical property measurement for multilayer insulation

Standard guide for evacuated reflective insulation in cryogenic service

"Standard guide for evacuated reflective insulation in cryogenic service," tech. rep., ASTM International, West Conshohocken, PA, 2019.

Monte Carlo simulations of ultra high vacuum and synchrotron radiation for particle accelerators

- M Ady

M. Ady, "Monte Carlo simulations of ultra high vacuum and synchrotron radiation for particle
accelerators," May 2016. Presented 03 May 2016.