High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Every fusor and fusion system seems to need a vacuum. This area is for detailed discussion of vacuum systems, materials, gauging, etc. related to fusor or fusion research.
Michael Bretti
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High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

INTRODUCTION

PART I - OVERVIEW

For the past several months, I have been working heavily on the design of my high vacuum system. A good deal of my initial research has been going through and reading as many posts as possible from this forum, which has provided an extraordinary amount of knowledge from many years of cumulative experience of many members, slowly transitioning into a more intensive academic study of the subject. I have noticed that there does not appear to be a post yet diving into more rigorous and intensive engineering design, simulation, and calculation for high vacuum systems. This is certainly not needed for the average fusor builder, however I have found this field to be very fascinating and on the rather obscure and lesser practiced areas of engineering in general, and could prove helpful and useful for those looking to take a more rigorous approach to the design process of their system. Since this hobby largely involves long periods of time for waiting on finding the right components, sourcing parts from eBay and other various resources, as well as being a rather expensive hobby, I have decided to spend my free time while waiting for parts to complete all of the major design calculations and simulations that would apply to my system. This has proven to be a tedious and challenging endeavor, but incredibly rewarding in understanding the deeper principles of high vacuum systems and engineering. I have decided to focus purely on the high vacuum system itself for this next year while I await for more funds for my projects. This includes all of the required calculations, simulations, and designs related to the system, as well as building, conditioning, and working with the high vacuum system itself. The main goal for this year will be to establish a well prepared system capable of achieving the desired ultimate vacuum needed, as well as getting all peripheral support systems (power, control, instrumentation, data acquisition) properly running, and generating data on the vacuum system itself, including pump down curves, rate of rise curves, and other data to compare with how close the system actually behaves to my initial calculations. I have decided to share this long term design work here, which I will continue to update and post continuously throughout the year as progress is made. Because there is such a massive amount of information to be presented, I will break each informational post in this walk-through/walk-along in titled sections in the following order:

1.) INITIAL HIGH VACUUM SYSTEM CONCEPT DESIGN, REQUIREMENTS, AND MODELLING

2.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR MOLECULAR FLOW FOR VARIOUS PROCESS GASES

3.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR TRANSITIONAL FLOW FOR VARIOUS PROCESS GASES

4.) TOTAL GAS LOAD DUE TO OUTGASSING AND DETERMINATION OF ULTIMATE PRESSURE DURING PUMPDOWN

5.) PUMPDOWN TIMES FOR ROUGH AND HIGH VACUUM

6.) MAXIMUM GAS LOADS FOR PROCESS GASES FOR VARIOUS EXPERIMENTS

7.) THERMAL MODELLING OF THE HIGH VACUUM SYSTEM

8.) THERMAL MODELLING OF SYSTEM RUNNING A STANDARD FUSOR GRID

9.) ELECTRONICS, CONTROL, AND INSTRUMENTATION

10.) SYSTEM BUILD

11.) SYSTEM CONDITIONING, PUMPDOWN, AND BAKEOUT

12.) PUMPDOWN AND RATE OF RISE CURVES

To supplement the information I will also be providing PDFs of the calculations I have done for the various sections in the process. Due to the fact that the calculations are very long and tedious, I will not post the math here but refer to it from the PDFs. Since I have many calculations repeating the same thing for different gases, I may just only post a single example for each section to reduce document clutter. Pictures, models, and other data will be provided as I go along. While this is not meant to be a substitute in any way for proper research and reading of high vacuum engineering from academic literature, it is my hope that I may be able to provide useful information and help in these areas and add a contribution to this group that has already been such a major help to myself and others. A few additional notes to consider:

- This series of posts is meant as both documentation of my own efforts, as well as a walk-along for more intensive engineering design. I am by no means an expert in this field, and do not claim complete accuracy to data and math present. Inevitably, I will make mistakes along the way, as I am still also in the process of learning, so constructive criticism and correction is always welcome.

- The initial calculations presented are not meant to be hard set actual numbers. Since there are so many variables present in high vacuum systems, these calculations can only provide a very rough guide to what may be expected, and provide a point of initial design comparison and order of magnitude expectations. They are meant as rough estimates and a guide, not exact figures.

- Many material properties and constants used, such as outgassing rates, will vary between sources. Data I have presented here are general values acquired from a variety of sources, and will differ depending on a wide number of factors due to the complex nature of vacuum systems in general.

- This intensive of an approach to high vacuum system design is by no means necessary for any fusioneer to accomplish fusion. The math and modelling can be quite long and tedious, but it certainly do-able - the complexity comes from accounting for such a large amount of variables present in such designs. Most members here are looking to build simple fusors with whatever available resources, and a good, solid working fusor does not require any of these calculations. However, some calculations may be very useful to look at if you want to have a more fundamental grasp of what exactly is happening in the system and understanding how high vacuum systems work. Modelling, whether CAD, thermal, electrostatic, or other, can also provide a very powerful way of understanding your system, and there are so many free resources available now for various types of modelling it is much more accessible now to the determined hobbyist. Since I am not focusing on building a fusor, but various types of experimental setups, these calculations and approach has provided very useful for my own endeavors, as well as any general high vacuum system one may be working on.
Michael Bretti
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

INTRODUCTION

PART II - BASIC FLOW OF CALCULATIONS

The above list, from Sections 2-6, deals with the bulk of calculations and examples from my system. These calculations are presented in the order which I followed in order to figure out the necessary key parameters of my system. I will not go over the basic fundamentals of high vacuum calculation - there are numerous texts and websites on this. However, I will show the progression of steps used to find each number.

Since I am planning to work with a wide range of test setups across a wide range of pressures, various gases need to be accounted for depending on the mode of operation. A quick breakdown includes the following:

1.) Pumpdown from atmosphere: 10^-2 Torr - 10^-7 Torr - molecular and transitional flows with water vapor loading
2.) Standard fusor operation without deuterium: 10^-2 Torr - transitional flow with air and water vapor loads
3.) Standard fusor operation with deuterium: 10^-2 Torr - transitional flow with deuterium
4.) Beam on Target and Beam Injected Fusor Systems for neutron production: <10^-4 Torr - molecular flow with deuterium
5.) Ion Beam systems with argon injection for non-neutron systems: <10^-4 Torr - molecular flow with argon
6.) Electron Gun Systems: <10^-6 Torr - molecular flow with water vapor loading
7.) Micro-thrusters: <10^-6 Torr - molecular flow with water vapor loading and argon
8.) Plasma Sources: <10^-3 Torr - molecular and transitional flows for deuterium, argon, and water vapor loading

As a quick summary, molecular flow governs the flow of gases in high vacuum systems at pressures of around 10^-4 Torr and lower. This is determined due to the fact that mean free path of molecules is large enough that molecules and residual gases interact with the walls of the system more than each other in the space between. Other factors can be used to calculate this region based on the system, which will be presented later. Transitional flow governs the flow of gases in a vacuum system in a region between molecular flow and roughing, usually between 10^-2 Torr and 10^-3 Torr. Due to the wide range of operating parameters, both regimes need to be calculated for my system, using the various gases present in the system. At vacuum levels from low vacuum to about 10^-7 Torr, the dominant gas load due to outgassing is water vapor. Since my systems will not be operating yet in the ultra-high vacuum regime at levels of 10^-8 and lower, which is dominated by the outgassing of hydrogen sorbed in the metals, calculation in this area is not immediate. Since deuterium is already hydrogen, and the molecular masses are almost identical between the two, any calculations used for deuterium would be reasonable for hydrogen in the ultra-high vacuum regime for estimates as well.

The fundamental and most important relationship in high vacuum systems is determined in the equation S=Q/P, where S is the speed in L/s, Q is the gas load in Torr*L/s, and P is the pressure in Torr. By finding the effective speed of the system, ultimate pressure and gas loads for various process can be derived. Speed is determined by a large range of factors, including conductance, which is also a critical factor in high vacuum systems. Conductance itself is dependent on several factors, such as geometry, gas used, and temperature. For all processes calculated in my systems, a temperature of 20C is assumed, which is the standard temperature used in literature for calculations and comparisons, usually using nitrogen or air.

My ultimate goal for these calculations can be boiled down into the following:

a.) Calculate the effective speed of my system for various gases based on processes I will use for molecular flow
b.) Calculate the effective speed of my system for various gases based on processes I will use for transitional flow (derived from molecular flow)
c.) Calculate the gas load due to outgassing (derived from materials and pumping conditions)
d.) Calculate the theoretical ultimate pressure of the system during pumpdown (derived from a and c)
e.) Calculate maximum allowable gas loads for various experiments (derived from a, c, and d)
f.) Calculate pumpdown times from atmosphere to ultimate vacuum (derived from all of the above)

Due to the amount of calculations involved, initially only conductance and pumping speeds were determined for my initial designs. Once a design was selected, the rest of the parameters could be calculated for that final design. Based on all of the above information, I would be able to know roughly how my system should behave for each test setup, assuming the chamber and system is well prepared, sealed, and functioning prior to the experiment. Again these are very rough estimates in ideal scenarios, but should be agreeable with basic expectations for vacuum systems.
Michael Bretti
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

1.) INITIAL HIGH VACUUM SYSTEM CONCEPT DESIGN, REQUIREMENTS, AND MODELLING

The current final version of my system is the result of numerous design iterations, based on a wide variety of parameters, including: costs and available funding, availability of components, experimental goals, CAD modelling, and initial calculations involving system conductances and effective speeds for various gases. When I first decided to tackle this endeavor, I had originally purchased a quite massive chamber. However, over time I realized it would be much more beneficial and safer to start as small as possible, get a solid system running, and then gradually increment up to larger systems. Because of this, I eventually decided upon a topology that is built around 2.75” Conflat hardware, which is ubiquitous and relatively cheap on eBay. Despite its small size, 2.75" CF hardware can be plenty of room for many types of systems - the current 60MeV L-band electron beam LINAC at the research facility that I work travels through 2.75" CF pipeways, so a seemingly small diameter system can go a long way!

My initial goals from my larger system stayed the same however – I wanted to work on a wide variety of systems that interested me. These systems include: electron guns, ion guns, plasma sources, electric space propulsion, beam on target systems, and the fusor. I therefore needed to design a system capable of supporting all of these experiments, while being modular and low cost to build. This requires that I not only be able to operate over a wide range of pressures, but also utilize different gases, and have enough input ports for both adequate instrumentation as well as being able to accommodate the systems I wanted to test.

Prior to obtaining the hardware required for this build, I initially had acquired an excellent diffusion pump which would serve as the backbone to the high vacuum pumping of the system. Based on the above, I came up with an outline of key requirements needed for the system:

1.) Cost
2.) Small size, portable, and manageable to move
3.) Ability to operate from low to high vacuum, in the range of 10^-2 Torr to greater than 10^-7 Torr
4.) Modularity and expandability to support wide range of experiments
5.) Direct pumping line to maximize pump capability in a small system
6.) Input port for high vacuum pumping and roughing
7.) At least 2 input ports for a range of high vacuum gauges capable of reading from 10^-2 torr to greater than 10^-7 Torr
8.) At least 3 input ports for experimental setups
9.) Ability to support electron guns, ion guns, plasma sources, standard fusor, beam on target system, and potentially micro-thrusters, in addition to required feedback such as faraday cups, beam profiling, etc.
10.) At least one viewport for visual feedback
11.) Ability to both isolate and throttle the main chamber from the high vacuum pump

Before I started purchasing parts, I decided to model my system with CAD software. I currently use Fusion360, which I highly recommend to anyone – it is free, and has a massive range of capabilities and is incredibly powerful with a not-too-steep learning curve like some other CAD packages. In addition, it turns out that several online vendor such as Kurt J. Lesker and Ideal Vacuum provide a large selection of free CAD models for vacuum components.

Below is a rendering of V1 of my small-scale multipurpose system:

2.75in Conflat Multipurpose High Vacuum System V1.jpg

Initially, my first design, V1, incorporated a rather odd topology, utilizing a 90 degree manual valve from the diffusion pump to the pipeline. The valve is also useful as a throttle control for the diffusion pump depending on the process I am running. An adapter plate, made of 1" aluminum, would be needed to go from the 5" inlet of the diffusion pump to the 2.75" CF flange on the valve. The pipeline further branches off to a 4-way 2.75” CF cross and KF25 cross to support instrumentation. The valve on the right is for roughing the system. Above the CF cross is the main chamber, consisting of a 2.75” 5-Way CF cross. The initial design was largely dictated by what was available on eBay. 90 degree valves are very cheap and easy to come by, and utilizing a mix of KF25 hardware with CF hardware could reduce the cost considering KF hardware is relatively inexpensive and easy to find. The 5-way cross was chosen due to its ability to support 3 inputs, as well as a viewport, and connection for pumping, and can be found at much lower prices than a 6-way cross, which would be preferable for functionality. The 4-way CF cross allowed me to have connections to both high vacuum and roughing lines, which were initially separated for the system.

Although I could satisfy instrumentation and system input requirements, the setup seemed to be a bit awkward physically, and due to the pipeline and 90 degree bends in it, conductance and pumping speed would suffer. Since 2.75" CF hardware already would have low limits in pumping speed in molecular flow, I did not want to risk scrapping further speed. The lower the speed, the less gas I can support for certain systems that require operation at low vacuum. I scrapped the design in favor of further designs before I got to calculations for the system, as well as the availability of new parts on eBay to improve the design. After many more hours of searching on eBay, I was able to find some inline valves that made me redesign the system and come up with V2. This will be detailed in the next section, along with the associated calculations for V2.
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Dennis P Brown
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Dennis P Brown »

A minor point I'd like to mention. Do not use torr in calculations or for units at all in a technical approach. Use only SI units. One can convert later but all formal work must use SI. If you are writing for just us here, torr is ok but isn't appropriate for a rigorous approach.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Jerry Biehler »

A lot of current papers and books still use torr so you can really use what you want. I just looked through about 10 research papers on my drive and all of them but one uses torr, the other uses Pa.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

Thank you for your concern, however, as Jerry Biehler noted, Torr would be more than acceptable. Every source I have looked at so far for high vacuum engineering, both textbook as well as online, except for a few, refer to Torr for pressure in calculations. Another thing to consider is that most data presented on things like outgassing rates, which become crucial for later calculations, are almost always represented by the units Torr*L/s per cm^2, where a couple I have seen represented using mbar and inches. At this point I would find it very odd to represent any calculations either here or for my own personal work in the SI unit Pascal for vacuum, since most numbers and data are still referred to in Torr in this field. The equations are also independent of any particular unit, so if one wanted to use Pa they still could - however it seems largely inefficient and kind of a moot point when it would probably have to be converted back to Torr for data and comparison to literature anyway. Pressure measurement for high vacuum gauges are also represented and sold usually rated either in Torr or mbar, so when working with vacuum systems, calculating in Torr conceptually would make more sense since it is still the most commonly referred to unit still. All of the calculations I will present here are in Torr, and going forward Torr will be the default measurement for pressure for reference here.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Richard Hull »

I have given my thoughts in the past regarding pressure units solely for use by fusioneers using the fusor. We are not highly technical or the types to write papers for Nature. We are forced into two worlds in our quest for vacuum. One of technical vacuums and the other the scientific vacuum.

For our purposes and for the sake of most reading, we might encounter, the micron and the torr. These are all we need concern ourselves with.

All fusors run solely in a technical vacuum.....Above 1 micron. All fusion pressures can be expressed in microns. Why?.... The cheapest and most used gauges found surplus are TC, (thermocouple gauges). Virtually all of these are in microns. Thus, we work, do fusion and talk mostly in microns in a technical vacuum.

However, most of us strive with diffusion and turbo pumps to achieve some sort of scientific vacuum level in our chambers before introducing the fusion fuel, (deuterium). As this is the case, we might resort to the time honored Torr found in the bulk of classic literature on vacuum. Thus, we might speak of achieving 10e-5 or 10e-6 torr as a base pressure for those advanced enough to speak in scientific notation using torr-speak. This is proper when discussing deeper vacuums than fusor operational pressures.

The beauty of the micron is that when operating a fusor we can use whole numbers. (5, 12, 25 microns). We have an intimate grasp of these pressures due to the base level of most fore-pumps and inexpensive vacuum gauges which we deal with every day. We know that we must be well below 50 microns before starting our diffusion or Turbo pumps and that regardless of where they may take us in the "torr" range, we must add deuterium to at least 5 microns before attempting fusion.

Likewise, there is little sense in using .03 microns. If we are going to use fractional units, use torr as the whole point of using microns was to escape fractional units in fusion operating pressures, preferring whole number units.

Richard Hull
Progress may have been a good thing once, but it just went on too long. - Yogi Berra
Fusion is the energy of the future....and it always will be
The more complex the idea put forward by the poor amateur, the more likely it will never see embodiment
Michael Bretti
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

Thank you for your input. For the sake of consistency in my calculations and notes, everything here that I post will be referred to in terms of Torr, for both low and high vacuum. Conversion to micron from Torr is trivial, and easily convertible between the two.

The goal here again is to describe an example of how one might approach more intensive calculation and design of a high vacuum system in general, and is not meant necessarily solely for fusors. However, all fusors require a good high vacuum system, so it is directly applicable to any fusor. The range for fusors is included in my current scope of requirements, but is not as much of a priority as establishing high vacuum working. For example, one important outcome specifically for fusors that can be gleaned from this could be how one would approach estimating the max gas flow rate of deuterium into the system given the vacuum chamber design and pumping parameters at a given vacuum level. This can be useful in qualifying a design before a lot of time and money is spent, and provides a good understanding of why things work the way they do in terms of vacuum systems.

Again, this is certainly not necessary for anyone working on a fusor, but since I have a lot of time before I build my system, and have an insatiable thirst for understanding the deeper principles of these technologies (not to mention I have found these pursuits not only highly educational and a great way to spend time while waiting for parts, but quite fun as well), I present my information here for those who might find it useful. I also like knowing that I can fully characterize my system and understand what is going on at all levels of operation, and have some idea of what to expect during my experiments.

I am also interested in seeing how close real operation is from theory for the systems I build. I won't be able to afford to run deuterium or other gas injected plasma systems for quite a while, however I will be able to run experiments on the vacuum itself and qualify the system at the vacuum engineering level. I think it could be very interesting to see how the system behaves and focus just on vacuum for now instead of the application used in the vacuum, though I probably would like to at least build an qualify some electron gun designs since they only require high vacuum and no gas input.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Dennis P Brown »

When you say
I am also interested in seeing how close real operation is from theory for the systems I build. ... however I will be able to run experiments on the vacuum itself and qualify the system at the vacuum engineering level.
You do realize the how and whether you clean these used components will affect issues for high vacuum a great deal and needs to be documented - one also must be careful about any contact with ones hands in assembly after cleaning - as such, gloves are critical so as not to cloud your results. Also, issues of bake out/temperature and the time used all matter and these are not easy to do calculations upon since the state of your stating systems (if not new) will be an unknown. Further, you fail to indicate that you will track room humidity so you can include that issue when the system is assembled or ever opened to the atmosphere - I've found that essential for any high vacuum work; even with purged systems.

Strangely, you have said nothing about the fore line system, and whether and how you will deal with back flow from that pump. Again, necessary for others to follow and benefit from your work.

When you say
greater than 10^-7 Torr
relative to its upper limits that will not be attainable unless you have a cooled trap for your DP. That adds further to issues of design and operation of your simple/low cost system relative to your calculations.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

Dennis P Brown,

I appreciate your comments regarding this information. Note however that I have only posted about the introduction and very first stages of the design process I started months ago - everything has evolved since then and been accounted for. Everything that you mentioned will be addressed as I go - preparation, cleaning, and baking of the system will not happen for several months, and will be well documented when the time comes to it. This has already all been weighed in and accounted for.

The foreline system is not mentioned yet because it is not necessary in order to perform the initial calculations at the high vacuum level. The foreline pump has already been properly sized to deal with the system. Although the diffusion pump is rather large, it is severely choked and the gas loads present should not be an issue for the roughing pump. Eventually, I would like to switch to a series diff pumped system, with one diffusion pump backing the main diffusion pump (backed by the foreline pump) to attain higher vacuum levels, among other modifications to allow for operation with Viton o-rings theoretically up to the 10^-9 torr level (yes, viton can be operated to this level with proper implementation). These will be addressed in following sections. Everything I listed out follows a logical progression for the approach I took. Again, this is an example of how one might go about it, and not the only answer. As stated above, these numbers are not hard numbers, but guidelines of what roughly to expect. I am well aware that the amount of variables in real life are far too many to account for accurately, but rough estimates can still be generalized.

The calculations, as already mentioned above in the introduction, also assume that the system is already well prepared, cleaned, baked, etc - they will not be indicative of initial pumpdown efforts, but rather steady state operation when a quality vacuum is achieved. They are calculated for a rather ideal case, but are weighted with correction factors for the worst case scenarios of these ideal cases.

For my upper limits, I do in fact have a cooled baffle. Under a well prepared system in my current configuration given all of the necessary parameters once steady state is achieved, I should in fact be able to achieve in the 10^-7 torr range.

Another reason for data logging the pump down and rate of rise curves will be precisely to identify patterns in pumpdown, including humidity, time pumped, baking, etc. Ultimately, I do have my system set up so that I will be able to seal off the main chamber and continuously bake and pump it with an ion pump, though this will not happen for quite some time.

Thank you again for your comments. I do encourage this to be an open discussion build along, and I know that this community is very scientifically critical in its approach, which is of benefit to everyone.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

2.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR MOLECULAR FLOW FOR VARIOUS PROCESS GASES

PART I – SYSTEM DESIGN V2

SECTION 1 – Design Overview
Based on the prior mentioned availability of a 2.75” CF inline valve, I decided to redesign V1. The design decision to move from V1 to V2 was made primarily due to part availability, and a basic knowledge that a linear path would provide better conductance compared with one of equivalent length with multiple bends. Up until this point no calculations were made influencing design decisions, which were based on limited general knowledge and intuition alone. Subsequent design iterations however were directly influenced by the calculation results from the molecular flow numbers derived from the system. Below is a rendering of the V2 design:

2.75 Conflat Multipurpose High Vacuum System V2.jpg

The new inline valve would allow for a more direct pumping path, and have a vertical topology. The main crosses were kept and just re-oriented to save functionality of the previous system. The third port on the KF25 cross was also decided to be dedicated for gas input and venting the system to atmosphere, and the remaining KF25 inputs stayed the same (thermocouple gauge and high vacuum gauge.) One downside to the valve however was that it was pneumatic – while cheap, it means that I have no control over the flow rate if needed, for example, for a fusor. This required the additional use of some sort of manual valve. After weeks of searching, I came across a 2.75” Conflat manual butterfly valve. This valve also had an additional bonus of being both a sealing and conductance throttle valve, and was found at a very low price. I have found it very difficult to locate similar valves since. The overall cost slightly increased from V1, however it made for a more convenient chamber to mount and work with physically, while allowing for better flow control and potentially better conductance along a more direct path to the chamber. The system was subsequently modelled in CAD to determine the best orientation of parts.

In order to further understand how system topology would affect high vacuum pumping behavior, I decided to start calculations on this design to determine its viability before I started investing in too many parts. Unfortunately I already bought some valves and parts due to the fast nature of things popping up and disappearing on eBay – some of which ended up being recycled to new designs, others are still unused due to further design changes. From V1 to V2 however, this design satisfies more of my initial requirements stated in the introduction and Section 1 of this post. I found though that some things had to be slightly sacrificed. Form factor, functionality, and control was gained, however at slightly higher cost. Conductances and speeds, as illustrated below, did not seem to be as good as I had initially hoped.

SECTION 2 – Calculations for Determining Conductance and Effective Speed in Molecular Flow
Below are the PDFs with the calculations performed on the V2 design to determine conductance and effective pumping speeds in molecular flow for the following gases: air, argon, deuterium, and water vapor:


In order to determine the effective speed of the system, both conductance and maximum pumping speed of the high vacuum pump are needed, given the gas load Q and the ultimate pressure P of the system are unknown. The equations and all of the definitions are in the PDFs for reference. As an important note going forward, effective speed IS NOT THE SAME as the speed of the pump. Effective speed is the total speed of the system accounting for the speed of the pump and the conductances of the pipeline to the chamber. Effective speed is practically always lower than the pump speed, never higher. The KEY LIMITING FACTOR of conductance in a system is dictated by the component with the lowest conductance – that component represents a choke point in the conductance where the total conductance and effective pumping speed WILL ALWAYS BE LOWER. Thus for a system based off of 2.75” CF hardware, you are always limited to the theoretical max limit of conductance for that size pipe, regardless of pump speed. Conductance drastically falls off for length, and for short pipes conductance counter-intuitively can come out lower than for long pipes due to correction factors required when calculating the numbers for such pipes and components.

The max speed of my pump is already known, at 600 L/s for air and 800 L/s for hydrogen, based off the datasheet (the pump is an Edwards EO4 diff pump.) This is represented in Section 1 of the above PDFs.

For calculating the conductance of the pipeline, one approach would be to find the equivalent conductance of a length of pipe for all the parts, assuming the internal diameter stays the same. However, a more accurate approach for finding the worst case conductance under ideal conditions would be to find the conductance of each individual component in the pipeline, and sum all of the conductances – note that series conductances for vacuum systems, when summed, are calculated like resistors in parallel. By finding the total conductance from all the sums, correction factors can be applied for each component, giving a worst-case scenario conductance for the system. In reality, the conductance may probably be higher since I calculated everything in the above PDFs using the largest correction factor numbers for the appropriate calculations as experimentally determined in literature on the subject.

The conductances are calculated in order of the component, from diffusion pump up to the chamber, which is the 5 way cross. Note that each part is calculated in multiple stages. First, the conductance is found using the general formula for a tube. However, since the L/D ratio for the components is less than 5, corrections must be applied. First, the equation for short pipes is calculated using the number for a long pipe. Then, a further error factor correction of about 12% max is factored in to the number, resulting in the final conductance for that part. This 12% is a correction factored applied based on experimental data observed in literature for air @20C, which provides the maximum deviation for the given L/D ratio. Other gases are approximated and estimated to give rough numbers using this correction factor.

Note that the choke point in the system is actually the inline valve, calculated in Section 3. Even though the valve is technically “linear” in fashion, it actually is not a full straight-through gate valve, and hence must be approximated with x2 90 degree bends in series, which cuts the original conductance of the valve in half. This is the limiting factor of the system. Inline valves such as this generally have lower conductance than an equivalent 90 degree valve, despite the fact it looks like the flow is straight through. One should note that motion in molecular flow is random, which plays a large factor in the behavior of gas flow in high vacuum systems, and does not behave as initially expected under non-molecular flows.

In Section 4, the butterfly valve is calculated, and the valve portion must be accounted for in the area of the opening. Even in the fully open position, it still adds impedance. The ratio of the equivalent area was found to be 65.8%, which was applied as an additional correction factor to the valve conductance.

The following sums up the total system conductance and effective pumping speed of the system in molecular flow for each of the gases, calculated in Section 6 of the PDF:

AIR:
Conductance – 8.737 L/s
Effective Speed – 8.612 L/s


ARGON:
Conductance – 7.440 L/s
Effective Speed – 7.349 L/s


DEUTERIUM:
Conductance – 33.137 L/s
Effective Speed – 31.819 L/s

WATER VAPOR:
Conductance – 11.078 L/s
Effective Speed – 10.877 L/s


As can be seen from the above numbers, the conductances and speeds of the system, despite having a very short and direct pipeline, are surprisingly small, except for deuterium. As expected, with all things equal, it can be seen that molecular weight has a direct result on the conductance of a system in molecular flow. The pump, starting with a speed of 600 L/s, has been effectively reduced by more than an order of magnitude, to around 10 L/s for the various process gases (much higher for deuterium). Although these numbers may be ok for deuterium, I wanted extra room for argon, in addition to being able to handle more loading from water vapor. Because of this, a new topology was designed and calculated in the same manner to compare numbers to see if these estimates could be improved. This will be seen in the next section covering design V3 for molecular flow. However, I will not know the actual gas handling load due to effective speed until after ultimate pumpdown pressure is calculated due to water vapor loading, and applying this number for gases involved at all pressures I will be experimenting at.

As a final side note on this section and going forward, I started the calculations on molecular flow since this is the very first step for figuring out the system when gas loads and ultimate pressure are unknown. These will be derived in later sections from these results. Also note that the low vacuum, roughing portion is not covered until later. This is due to the fact that the roughing pump parameters are not needed for the high vacuum calculations, and it is in the high vacuum regime that I will be primarily operating in. For the time being, the only parameter really required for the roughing pump is to make sure that it meets the backing requirements of the diffusion pump. This number is found from the datasheet, and set aside. For 600 L/s operation, a min displacement of 1.83 L/s is required of the two stage pump. However, due to the fact that during high vacuum operation it is clear that I will not see these speeds at the chamber, a smaller pump can be used. I still do want to benefit from the max pumping speed of the diffusion pump, which will have an effect on the effective speed still, and as such, a backing pump has been selected with a displacement of 2.83 L/s, much more than is required for this system with a good safety margin. This should allow me to still attain 600 L/s at the pump inlet, while having additional overhead. Because the actual gas load will be very small for my system, especially at high vacuum, this will be acceptable for handling gas flows during steady state operation for the systems I want to employ, given the limitations of max gas load for my system. Actual details of the roughing calculations however will be detailed in sections 3 and 5.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

2.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR MOLECULAR FLOW FOR VARIOUS PROCESS GASES

PART I/b – COMPARISON OF SYSTEM DESIGN V2 CALCULATIONS WITH ESTIMATES USING DUSHMANS TABLE

I have decided to include this brief Part b of the above section to illustrate the comparison using multiple calculation techniques, to help show the validity of the more intensive method presented. Let us assume that we are to calculate the conductance of System V2 using a very simplified estimate from Dushmans Table. This table is an empirically derived method for approximating conductances of tubes. Using this approach, we would assume the entire pipeline with all its elements are a single element of equivalent length with constant diameter. An example reference to this table can be seen here:

http://www.lesker.com/newweb/technical_ ... e_calc.cfm

This Table is pulled from the above source from the KJL website, and is shown below:

Dushmans Table - KJL.jpg

From System V2 measurements, we know the following parameters:

Total Effective Length = 26.244cm
Average Diameter of 2.75” CF Hardware = 3.556cm

The radius is then 1.778cm. Dividing the length by the radius gives the “L/a” ratio of 14.760, where “L” is length and “a” is radius. Following the table down the “a” column, we end up between rows 1.0 and 2.0. Following this over to the L/a ratio column, we lie somewhere between 12 and 16. This roughly approximates to a conductance value between the lower and upper bounds of 5.013 and 25.210. If we interpolate this data between these major bounds, and generate a table such as the one below,

Extrapolation Example - Dushmans Table, Design V2.jpg

we see that we get a closer approximation of the conductance between the bounds of 1.7 to 1.8 and 14 to 15, of a conductance between 18.571 and 20.784. This conductance is higher than those for air, argon, and water vapor, but less than that of deuterium - in fact, it is almost exactly in the middle of the two extremes between argon and deuterium. This shows that we are well within the expected ballpark for our original intensive calculations. The above method using Dushmans Table however does not account for temperature, molecular mass, or other correction factors for short pipes. Also note that this estimate was found using a straight length of pipe equivalent to length of the actual system, with no bends. If we included the bends in our estimation using the table method, this number would be much lower, and hence much closer to the values similar to air. Thus we can show within reasonable agreement and certainty that breaking down each individual component of a pipeline, applying correction factors, and summing the total for series conductance, is within the expected range, even when compared with very simplified methods of estimation.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Tom McCarthy »

Michael,

This is great, thanks for going to the the time of typing it all up and presenting. I’m learning a lot.

One thing you mention - counter-intuitively, conductance for a short pipe can come out Lowe than a long pipe due to correction factors.

As you’ve said, this is counter-intuitive. Are you sure it’s correct? While I know little about these vacuum calculations, I appreciate that the correction factors used are necessary and presumably well worn. Can a short tube of same diameter have a lower conductance than a longer tube? It seems the maths says one thing, but physics would make you believe another.

Looking forward to seeing the rest of the posts.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

Tom McCarthy,

Thank you for your comment and reply. Your question is a very good one, and I probably should have been more clear in my explanation, so I apologize if there is confusion on this point. The conductance for a short pipe is less when you apply the correction factors and equation for calculating the conductance of a short pipe with an L/D ratio less than 5 for an equivalent pipe. This results in a conductance that is much lower than one would initially expect for a short pipe. So for example, taking the first component in the above PDFs, from the example using AIR, the Diffusion Pump to 2.75" Conflat Plate Adapter, initially when the general equation is used to calculate the conductance, it comes out to 213.992 L/s. However, this equation is only valid for long tubes. When the equation for short tubes are used, this lowers the conductance to 74.649 L/s. Adding further worst case error correction factors, we end up with a final conductance of 65.691 L/s. However, if the tube was originally longer, let's say with a length now of 18cm, now making it with an L/D ratio greater than 5, using only the first equation for long tubes, would lower the conductance to 30.197 L/s, which is about half that of the short tube. No correction factors are needed since the long tube equation describes tubes more accurately that are long. So in reality, a short tube will still have higher conductance than a long tube, but it may be lower than one initially expects. In this example, despite the short pipe being 5 times shorter than the long pipe, the resulting conductance is only about twice as much.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Tom McCarthy »

Ok, that clears things up. Thanks for the thorough explanation.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Richard Hull »

Your efforts are much appreciated.

The emphasis on short pipe plumbing here is related to the fact that folk arrive here with 0.0000 vacuum experience. It seems the first thing they do is purchase a vacuum pump and put 2 or 3 feet of 3/8-inch bore vacuum hose on the pump to their first demo chamber, strangling the pump. Our first advice and response is to have them move the pump inlet inches from the chamber's outlet and use a larger bore tubing in a short run.

A professional vacuum system used in production or advanced research is a "must calculate system". The reason being that inefficiencies in such a system will decrease the net value of a very expensive undertaking, resulting in a slower pump down to the "ready condition". In a production situation, this can result in reduced production and, thereby, increased costs.

Here we are just trying to help newbies get better, very acceptable, but not necessarily perfect results in their first vacuum effort.

Richard Hull
Progress may have been a good thing once, but it just went on too long. - Yogi Berra
Fusion is the energy of the future....and it always will be
The more complex the idea put forward by the poor amateur, the more likely it will never see embodiment
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

Richard Hull,

Thank you for your compliment and reply. If nothing else, hopefully these examples, and walking through this design process and my own mistakes and efforts might show the importance of at least planning a vacuum line/system and how things can affect it, even without rigorous math or analysis (which is still at best only a very rough estimate anyway.) It appears all too easy to completely kill conductance, especially when dealing with high vacuum and molecular flow. Fortunately, fusors do not operate under such strict restrictions around the micron range so, as you stated, it is much less critical for most efforts here.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

2.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR MOLECULAR FLOW FOR VARIOUS PROCESS GASES

SUPPLEMENTAL INFORMATION

For those who are interested in diving into the subject more deeply, below is a scanned photo of the original error curve I have used for reference in my calculations dealing with short tubes (usually 12% for most of my calculations). This was taken from (a rather excellent book on vacuum engineering, one of my favorites that I have read so far):

"Fundamentals of Vacuum Science and Technology"
Gerhard Lewand, Ph.D.
Plasma Physics Laboratory, Princeton University
Copyright 1965 by McGraw-Hill, Inc.

LD Error Curve.jpg
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Jerry Biehler »

The cooled trap I got you is just to reduce backstreaming, it wont do much to help your ultimate vacuum, that will require a LN2 cooled trap which is installed on top of the other trap.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

Jerry Beihler,

Thank you for your comment. However, the baffle should indeed help improve ultimate vacuum despite not having any cryotrapping principles. If we look to solve for the total gas load of a system, we need to account for the load of oil backstreaming, Q(backstreaming). Depending on the mode of operation for a diffusion pump, this could be non-negligible or trivial. For a pump with an optically opaque baffle above it cooled to at least 20C, backstreaming rates are reduced to near negligible levels, and can effectively be removed from the gas loading equation. Effective speed of the system can be easily calculated as shown above, and once the total gas load in known, or roughly estimated, then the ultimate vacuum can be determined. Since the load due to backstreaming is required in finding the total gas load of the system, this does have a direct impact on the ultimate vacuum level attained. I will post actual details of these calculations in coming sections. In my setup, since I am going to be using the water cooled baffle, I can effectively reduce the load due to backstreaming to 0, and this should have a small but noticeable effect on the ultimate vacuum achieved.

The other mode of operation to consider for the diffusion pump in regards to ultimate vacuum achieved is primarily related to the foreline pressure of the diff pump. Assuming a perfectly sealed system, the ultimate pressure that can be attained by the diffusion pump is governed by the medium used for pumping (various types of oils, mercury, etc), and the foreline pressure of the pump. This also greatly plays into backstreaming rates, which again contributes to ultimate vacuum. For diffusion pumps, if the foreline pressure is under 10^-3 - 10^-4 Torr, backstreaming is essentially reduced to negligible amounts. However, since the ultimate vacuum of my foreline will only be around 2x10^-2 Torr, or 20 microns, backstreaming will be noticeable due to the pump operating above the critical pressure which backstreaming rates are reduced to near zero. The ultimate vacuum of a diff pump itself also is largely determined by the backing pressure. A topology utilizing a diff pump backed by a secondary diff pump in series will allow the system to be pumped into the ultra-high vacuum regime, even with only a water cooled baffle, assuming the system has already been well prepared, outgassed, and baked. At least from reading through the forum so far, I do not believe I have seen anyone here utilizing a diff backed diff pump topology, which for fusor efforts is completely overkill and unnecessary. However it should be completely do-able to achieve much higher vacuum without cryo-trapping. This also depends on how I handle the gas loading due to o-rings in my system, which if a differential pumped concentric o-ring topology is used, or the o-rings themselves are chilled (experiments in literature show this to be around at least 6C or lower), then the gas load due to outgassing and permeation can be drastically reduced and allow the system to drop into the 10^-9 Torr regime. For my current system that is backed by a two stage refrigeration pump, I would not be able to reach ultra-high vacuum in the long run with just a water cooled baffle. In the following sections, I can mathematically show that even in an ideal scenario, my current setup should only in theory be able to peak into the upper 10^-7 Torr range. However, by using the proper oil (which I will be using DC705 equivalent), a diff backed diff pumped topology, the water cooled baffle, and differentially pumped concentric o-rings, higher vacuum is attainable without cryotrapping.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

2.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR MOLECULAR FLOW FOR VARIOUS PROCESS GASES

PART 2 – SYSTEM DESIGN V3

SECTION 1 – Design Overview

As mentioned in Part 1 of this category dealing with molecular flow calculations, the conductances found for system V2, while appearing adequate for deuterium, were low for heavier gases. In order to increase the effective speed, the total conductance of the system needed to be increased. As you can see from prior posted models, the pipeline is already incredibly short – a couple of small valves and a four way cross. Reducing the length at this point will not practically help the speeds. Instead, efforts needed to be focused on the choke point of the system. In design V2, this was the inline valve. The best way to effectively combat this is to utilize a valve with the highest possible conductance, which allows for sealing at high vacuum levels. This turns out to be a gate valve. Unfortunately, gate valves, even for 2.75” CF hardware, are either extremely expensive, or very difficult to locate on eBay. Fortunately, by a stroke of luck, I was able to come across one for free from an old vacuum system that was being scrapped at a research facility. On top of this, the gate valve was manual, allowing me to also to eliminate the butterfly valve and have full conductance control using the gate valve instead. From design V2 to design V3, this was the major change – two valves from the prior design were replaced with a single valve for the new design, which not only greatly increased conductance, but allowed for conductance control, isolation, and without increasing the expenses for this system. Below is a CAD rendering of the new V3 design:

2.75in Conflat Multipurpose High Vacuum System V3 - Render 2.jpg

An additional change to note is the placement change of the valve. Instead of having the valve located at the base near the adapter plate, I decided to move this directly under the chamber. This is due to the fact that from the adapter plate to the 2.75” CF hardware, a Viton gasket is needed. Due to the way the bolt holes are set in the gate valve, it would be impossible for me to tighten it to the baseplate, which also utilizes bling tapped holes. Moving it between the 5 way cross chamber and the 4 way cross pipeline was the best compromise. It also serves an additional purpose for pumping at higher vacuums. For long conditioning runs, ideally I would like to use an ion pump so the chamber can be continuously pumped, conditioned, and bake out while drawing next to no power and requiring little maintenance or worry, while it would be problematic to run a diffusion and roughing pump for weeks continuously. The valve would effectively isolate the main chamber from the pipeline to allow for this pumping, in addition to allowing the pipeline to be re-evacuated with the diff pump. Also, ion pumps can be used simultaneously as ion gauges, which allows the upper portion to be monitored. The pipeline will be monitored by other instrumentation on the cross.

Another major change to the design was the decision to remove all KF hardware on the high vacuum side. While KF hardware can still achieve high vacuum levels, I wanted to reduce as many sources of outgassing and permeation as possible near the chamber. The pipeline currently will support two high vacuum gauges mounted to 2.75" conflat flanges.

Finally, design choices and components were selected for the roughing side as well, and modeled as shown above. Since my pump was already selected, I needed a way of connecting it to the roughing inlet of the diff pump. A simple manual 90 degree KF25 isolation valve is connected to the diff pump roughing inlet, followed by a three-way tee that splits to the line and to a thermocouple gauge mounted to a KF25 adapter, which would allow me to measure the pressure as close as possible to the diff pump inlet. A very short bellows section of about 3-4" was selected to allow for a very short connection line, and give some placement flexibility for mounting the two pumps. One concern using oil-sealed roughing pumps, such as refrigeration pumps, can be the backstreaming from the roughing pump to the diff pump, which can contaminate the diff pump oil. In order to mitigate this, I selected to use a molecular sieve filled replaceable foreline trap. The molecular sieve not only helps prevent oil contamination, but has the added benefit of absorbing water vapor pumped from the diff pump which could in turn contaminate the roughing pump oil. In essence, both paths to and from either pump is reasonably well protected. I have found that with a bit of patience and searching on eBay, these traps can be bought for very cheap. Mine arrived used, but in quite excellent condition. Molecular sieve refill, usually of zeolite, alumina, or other adsorbents, can also be purchased relatively cheap - I got a pound of it for about $24.00 from LDS Vacuum.

SECTION 2 – Calculations for Determining Conductance and Effective Speed in Molecular Flow

The calculations for V3 were applied in the same exact manner as for V2, the only major difference was calculating the conductance for the single gate valve as opposed to the inline valve-butterfly valve combo. Below are the PDFs for reference for design V3 calculations:


The resulting conductance of the new gate valve has higher conductance than the butterfly valve fully open, more than double the conductance of the inline valve, and more than double the combined conductance of both the inline and butterfly valve. Because of this, the new chokepoint of the system shifted to the 2.75” CF cross. Since the 2.75” cross is about the shortest I can practically make my pipeline with instrumentation, this represents the limiting conductance for the high vacuum pumping system. All effective speeds are then restricted to lower than this value.

Based on the calculations, I got the following conductances and speeds for the new design for air, argon, deuterium, and water vapor:

AIR:
Conductance – 14.851 L/s
Effective Speed – 14.492 L/s

ARGON:
Conductance – 12.647 L/s
Effective Speed – 12.386 L/s

DEUTERIUM:
Conductance – 56.327 L/s
Effective Speed – 52.622 L/s

WATER VAPOR:
Conductance – 18.831 L/s
Effective Speed – 18.258 L/s

Notice how the difference of a single valve has now almost doubled the total conductance and effective speed of my system. Deuterium rates in particularly are now noticeably higher. However, at this point, for pumpdown, the single most important gas to be concerned with is water vapor (at least until about 10^-8 Torr, which then transitions to hydrogen for the dominant outgassing load), and it is the values for water vapor that I use to further derive the ultimate vacuum of the system. The other gases will factor in after to establish max gas loads for varying vacuum levels, in addition to the load due to water vapor. Because my vacuum line can really not get practically shorter, these are the practical maximum speeds and conductances for this system.

As mentioned in prior posts and exchanges however, I still needed to account for a very large gas load since I will be using a diffusion pump, which is the gas load due to backstreaming. If the backing pressure of the diffusion pump is held to a level of around 10^-4 Torr, backstreaming becomes negligible on its own. However, my 2 stage refrigeration pump will only be able to practically achieve a vacuum at the backing inlet of around 0.015-0.020 Torr, which is not low enough to be below the critical pressure to eliminate backstreaming. Since the pipeline is also as short as possible and direct to the chamber, it could be easier for backstreaming to contaminate the surface, as opposed to having multiple bends or a very long bellows line. As a result, a water cooled baffle is required. Very fortunately, Mr. Jerry Biehler was able to help me locate one that he knew of for sale that would fit my system exactly.

At this point, design tradeoffs need to be considered. With the baffle, backstreaming at the roughing pressures can be eliminated, keeping the system cleaner and allowing a higher ultimate vacuum to be achieved. The cost however is additional money, an additional adapter plate, and two additional large diameter viton o-rings. The baffle and adapter plate will lower the conductance and speed of the system a bit. Adding these viton o-rings could present a problem as they greatly increase both the gas load due to outgassing, as well as set a practical limit on ultimate vacuum due to permeation. This can however be mitigated or eliminated with concentrically placed o-rings with a gap pumped between the main sealing ring and the secondary o-ring to at least 10 Torr, or by cooling the entire o-ring between the flanges to below 6C. However, since the o-rings are located right near the throat of the diffusion pump at areas with large conductances, they will effectively see much higher pumping speeds than if there were viton o-rings placed at the top around the main chamber, like if I were to use KF hardware. This will help in dealing with the extra gas load, however the total gas load due to these o-rings will still need to be calculated to determine the ultimate vacuum. Despite the costs, the benefits seem well worth it based on my initial design criteria and goals.

The next section will outline the new and final design for this chamber, version V4, with the new baffle and adapter plate modeled and calculated.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

2.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR MOLECULAR FLOW FOR VARIOUS PROCESS GASES

PART 3 – SYSTEM DESIGN V4

SECTION 1 – Design Overview
As of the present time, design V4 is the current design of my high vacuum system that I will be implementing. All calculations going forward after this section will refer to the numbers for this design. While I have also calculated other numbers for designs V2 and V3, it would seem largely redundant to repeat them here, since the most important thing to illustrate was key design choices and changes between V2, V3, and now V4 for molecular flow, which all other numbers and calculations are derived from.

As mentioned in the previous Part 2 section, a baffle and additional adapter plate was needed to reduce or eliminate backstreaming from the diffusion pump due to the operating pressure of the backing line and pump. These additions constitute the design change from design V3 to design V4. As also mentioned prior, the high vacuum pipeline has been reduced to the shortest possible path, and as a result, the speeds and conductances found for V3 are the highest practical values attained. Since V4 will be adding the baffle and the adapter plate, these numbers will be reduced – however, you will see that the change is incredibly small, resulting in nearly the same conductance and speed, despite extra components and length being added to the pipeline.

Below is a CAD render of the current V4 design. Due to the top adapter and mounting plate, it is not really possible to see the adapter and baffle very well, so I included two views – one of the complete system, and one of the upper portion removed, exposing the diff pump, baffle, and adapter plate. Note that I did not model the internal baffle fins for the sake of simplicity (the water cooled baffle is the top most component in the second render:

2.75in Conflat Multipurpose High Vacuum System V4 - Final Render.jpg
2.75in Conflat Multipurpose High Vacuum System V4 - Baffle View Final Render.jpg

The baffle and the adapter plate are designed to be clamped between the diffusion pump flange and the top aluminum mounting and adapter plate. As mentioned in a prior post in a different forum topic, the aluminum selected for the adapter plates is ATP-5 tooling and jig plate. The aluminum is machined to an absolute maximum surface roughness of 25 micro-inch. In a paper I found detailing the general design overview of high vacuum chambers for NASA for testing, the maximum recommended surface finish of a flat plate and mating glands for o-rings should be better than 32 micro-inch, whereas rotating feedthrough shafts on o-rings should meet or exceed a surface roughness of 16 micro-inch. ATP-5 exceeds this design criteria for flat mating surfaces, and makes the process much easier since surface preparation and machining would not be required, as opposed to buying standard aluminum plate stock. ATP-5 is also reasonably cost efficient, and the design of the plates makes it simple to fabricate.

SECTION 2 – Calculations for Determining Conductance and Effective Speed in Molecular Flow

The calculations for V4 were applied in the same exact manner as for V3 and V2, the only major difference was calculating the conductance for the new baffle and adapter plate added to the V3 calculations. Below are the PDFs for reference for design V4 calculations for molecular flow:


For the water cooled baffle, the conductance can be approximated by calculating the conductance of the baffle as if it were first just an equivalent diameter short section of an open pipe section. The regular correction factors are then applied. However, for a well-designed optically opaque baffle, the conductance should be reduced to a value of about 50-60% of the speed for use with an appropriately matched pump. Therefore, the number calculated for the equivalent open short section, with correction factors, was further corrected to a value of about 50% of this value.

Based on the calculations, I got the following conductances and speeds for the new design for air, argon, deuterium, and water vapor:

AIR:
Conductance – 13.834 L/s
Effective Speed – 13.522 L/s

ARGON:
Conductance – 11.741 L/s
Effective Speed – 11.516 L/s

DEUTERIUM:
Conductance – 52.471 L/s
Effective Speed – 49.241 L/s

WATER VAPOR:
Conductance – 17.541 L/s
Effective Speed – 17.043 L/s

As you can see from the prior system V3 numbers, the conductances an effective speeds are only slightly less – about 1 L/s for air, argon, and water vapor, and about 3-4 L/s for deuterium. The conductances of the baffle and the adapter plate are still so large compared to the choke point conductance of the system, which adding these in results in only a small change. Therefore, even though slightly more cost and complexity was introduced into the system, the speeds and conductances were successfully kept to almost the same as the practical maximum value. Therefore, the system is much better protected from backstreaming, although the cost will be in high outgassing loads due to the extra o-rings, which will be covered in the following sections.

This concludes Section 2 covering the design iterations from V2 to V4, and illustrating the differences in calculated conductances and speeds for the molecular flow regime for various process gases, as well as engineering design trade-offs, benefits, and costs between each system, based on my initial criteria and parameters. Going forward from here, numbers will be calculated only for the V4 design. The next section to be covered will go into transitional flow calculations. These calculations start to become much more interesting for fusor applications, as the fusor is generally operated in the transitional flow regime. From these calculations, which are initially derived from molecular flow, ultimate vacuum, outgassing rates, and operating gas flows can be calculated. This can be especially important for a fusor if one wanted to estimate the maximum flow rate of deuterium their system can handle at a given pressure in the transitional flow regime.

As a final note, although deuterium is the primary gas of concern for fusors, perhaps greater emphasis should be initially placed on the numbers for water vapor loads, especially if one is initially preparing calculations and estimates for pumped down, since this is the primary gas load of the system up to about 10^-8 Torr. In addition, for figuring out maximum deuterium flow rates, one might want to know first the water vapor load so this can be factored into the final amount of gas flow that can be handled for deuterium, particularly if the system largely uses o-rings for sealing high vacuum joints.
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

3.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR TRANSITIONAL FLOW FOR VARIOUS PROCESS GASES

From the previous Section 2 posts, I covered the calculations for molecular flow for system iterations V2, V3, and V4 for several major gas loads that would be encountered in my experiments. The current design iteration is V4, which all following calculations will be based off of. Now that molecular flow numbers for total pipeline conductance and effective speed of the system have been established, the next phase can be calculated - transitional flow. Where molecular flow deals with the high vacuum regime and and below (generally between 10^-4 Torr and lower), transitional flow deals with the low vacuum area between very rough pumping and the start of molecular flow. This is somewhat of a grey area, but can generally be thought of in the range roughly between 10^-1 Torr and 10^-3 Torr. This area of operation is particularly interesting for a variety of devices, including the fusor, as well as other higher-pressure process operations. Due to the fact that fusors generally operate in the 10^-2 Torr area, the following calculations are made based off of this average pressure, which includes factoring in the mean free path distance for this particular pressure.

As with molecular flow, transitional flow is calculated for each of the major system gases. The PDFs for the calculations are found below as follows:


The first number to establish for the calculations can be seen in Section 1.) Diffusion Pump of the PDFs. Since I already know my diffusion pump model number and have access to the data sheet, I can find the maximum speed of the pump, which is needed for the end calculations. Note that for molecular flow, for air as an example, the maximum speed of the pump is 600 L/s. This however is not the case for the entire pressure range of the diffusion pump. Diffusion pumps follow a certain speed vs. pressure curve, where the speed rises from a low value after the critical backing pressure, up to its maximum at some value in the high vacuum regime, where pump speed remains constant afterwards. Since we are looking to operate at 10^-2 Torr, I must find this point on the curve and approximate the speed of the pump at this pressure. From my datasheet, this value roughly correlates to about 100 L/s. This becomes the maximum speed of my diffusion pump for calculating transitional flow for 10^-2 Torr. You will see that this much lower number will result in a larger discrepancy between the total pipeline conductance and the effective speed, whereas this difference is much smaller in molecular flow due to the much higher maximum speed of the pump.

The following sections from the PDF, Sections 2-7, deals with the calculations for transitional flow for each of the components in the pipeline. Note that molecular flow conductance is needed for these calculations. Also needed is the diameter of the component, as well as the mean free path. For 10^-2 Torr, the mean free path equates to about 0.5 cm. Due to the physics of the flow of gases between transitional and molecular flows, transitional flow conductances and speeds will be higher. This is also a good benefit for allowing for higher gas loads in the system. The total conductances and effective speeds are calculated the same way as in molecular flow. Below are the resulting numbers of conductances and effective speeds for the various gases for the system V4 design:

AIR:
Conductance – 18.621 L/s
Effective Speed – 15.698 L/s

ARGON:
Conductance – 15.881 L/s
Effective Speed – 13.705 L/s

DEUTERIUM:
Conductance – 73.204 L/s
Effective Speed – 42.265 L/s

WATER VAPOR:
Conductance – 23.610 L/s
Effective Speed – 19.100 L/s

If you compare these numbers from the numbers for V4 for molecular flow, you will find that conductance and effective speed are higher for air, argon, and water vapor. The difference between conductance and effective speed is also larger for transitional flow as well, due to the lower maximum pumping speed at this increased pressure. While the conductance is much higher for deuterium between transitional and molecular flow, the effective speed turns out to be lower, based on the following calculation decisions from available data. This is because for molecular flow, the max speed for deuterium is known at 800 L/s as opposed to 600 L/s for air and other similar gases. However, on the speed vs. pressure chart in the datasheet, only data was presented for air. To design for a worse case scenario, I decided to also use the speed of 100 L/s for calculating deuterium at 10^-2 Torr, which is the same as the speed actually given from the datasheet for air. In reality this number will be higher for equivalent pressures between molecular and transitional flows, but since I do not know the exact curve, I am calculating for deuterium based on a worse case basis to establish a lower bound for this number. Therefore, it is very reasonable to expect that the effective speed for deuterium in reality will be much higher than for molecular flow for the given pressure, since the maximum pumping speed for the pump for hydrogen will be higher at 10^-2 Torr than it is for air. In this regard, the total conductance and effective effective speed for water vapor should also be a bit higher than calculated, while the total conductance and effective speed for argon should be lower in reality

While argon remains on the low side, I do not anticipate using argon at vacuum levels in the transitional flow regime – I am really only concerned about deuterium and water vapor. Air is included in all of these calculations because it is a gas that is most often referred to for experimental numbers and measurements in literature, as well as nitrogen, which provides a good comparison baseline. Now that the numbers for transitional flow have been established, I can proceed to calculating the remaining parameters of the system in the following sections, including ultimate pumpdown volume, outgassing loads, pumpdown times, and maximum loads for a given gas at a given pressure.
Michael Bretti
Posts: 175
Joined: Tue Aug 01, 2017 12:58 pm
Real name: Michael Bretti

Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

4.) TOTAL GAS LOAD DUE TO OUTGASSING AND DETERMINATION OF ULTIMATE PRESSURE DURING PUMPDOWN

Introduction
Now that molecular and transitional flows for various process gases have been calculated for the current system, the total outgassing load for the system during pumpdown can be found, ultimately leading to the final estimate for the ultimate vacuum attainable for a variety of pumpdown conditions. This section is perhaps one of the most important and powerful of the sections so far, and can give one a very good idea of what vacuum levels they can expect based on their system design. This is notably most important for pumping down the system, as well as knowing the upper and lower bounds for gas loads supported by the system. The following includes the PDF for the entire process for system V4:


The following sections break down and explain each section of the PDF calculations:

1.) Determination that Selected Pump is Appropriately Sized for System
As a general rule of thumb for designing high vacuum systems, the maximum speed of the pump should be at least two times or greater than the effective speed found for the system. This is calculated for both molecular and transitional flows. For molecular flow, the speed of the pump is 600 L/s for air (800 L/s for hydrogen). The effective speed was calculated to be 17.043 L/s for water vapor (since we are focusing on pumpdown for these calculations), in which case the speed of the pump is significantly higher than the effective speed for molecular flow. Therefore the pump selected is well suited for the system in terms of speed. For transitional flow, based on the pressure vs. speed curve, at the calculated level of 10^-2 Torr, the maximum speed, for air and other equivalent molecular weight gases, is around 100 L/s. The effective speed at this level for water vapor at 10^-2 Torr was found to be 19.100 L/s. Therefore, the pump is also well sized for the system for transitional flows as well.

If we want to double-check for other gases, we can look at the worst case scenario, which would be deuterium. For molecular flow, the effective speed is 49.241 L/s, which falls well below 800 L/s for the pump. The effective speed for transitional flow is 42.265 L/s (assuming a max pumping speed of 100 L/s @ 10^-2 Torr for hydrogen), which is also within the acceptable rule of thumb speed parameter. Therefore the pump should be able to handle any other gas since hydrogen/deuterium is the most demanding for this criteria.

2.) Maximum Theoretical Gas Loads for Ultimate Operating Pressures at Various Flows
A second general rule of thumb design criteria for designing high vacuum systems is that the system should be capable of reaching at least 1/10th the working pressure. That means that the ultimate pressure attainable should be at least 10 times lower than the desired process working pressure. This is very easy to calculate out and is presented in the PDF. For a working pressure of 1x10^-7 Torr for example, the ultimate pressure attainable of the system should be 1x10^-8 Torr. Therefore the ideal minimum ratio is: P(ultimate)=1/P(working).

Since we roughly know the ultimate pressures needed (in the case of this system, the lowest vacuum required would be around 10^-8 Torr), we can calculate the maximum allowable gas load for the system for both molecular and transitional flows. From the equation S=q/P, solving for q, or gas load, we get q=SxP, where S is the effective speed and P is the ultimate pressure. Since I am solving for pumpdown, I need to use an effective speed of 17.043 L/s for molecular flow, and 19.100 L/s for transitional flow average value for transitional flow, (assuming operations at 10^-2 Torr). A table of calculated values is presented in the PDF. For the lower bound ultimate vacuum of 10^-8 Torr, the maximum allowable gas load of the system during pumpdown is 1.704 x 10^-7 Torr-L/S. For the upper bound vacuum level of 10^-2 Torr, now in transitional flow, the maximum allowable gas load is 1.191 x 10^-1 Torr.

3.) Total Gas Load
Now that the bounds have been established, I can calculate the total gas load of the system. The total gas load of the system can be found as the sum of the total gas loads due to the volume of the system, outgassing, diffusion, permeation, backstreaming, and the process gas flow. For pumpdown, volume can essentially be ignored since it will already be mostly pumped out from roughing. Assuming a perfectly sealed system, the gas load due to leaks can be eliminated for simplicity. Diffusion is not an issue for the metals present in the system at high vacuum levels under ultra-high and extreme vacuum levels, so this term can be ignored as well. Since a well-designed, optically opaque water cooled baffle will be employed, backstreaming can be ignored. Because this is pumpdown to high vacuum, no process gases will be introduced, so this gas load is also ignored. This leaves the gas loads due to outgassing and permeation.

To find the total outgassing load due to outgassing and permeation, the system is broken down into each component first, like when molecular and transitional flows are calculated. Then, the load due to outgassing for every material in the component is calculated, based on outgassing rates for the material and the entire surface area exposed to the vacuum. Permeation, which in this case is only due to Viton gaskets, is also calculated by multiplying the permeation constant to the total length of Viton. These numbers are summed together for the total gas load of the part, where all loads from all parts are then summed to find the total gas load of the system during pumping.

As something to note, this is where CAD becomes crucial. By having each part modeled out, it becomes incredibly easy to find the total surface area for each part, and the total lengths for each gasket. For the gaskets, both the length and the surface area must be calculated to find both the gas load due to outgassing as well as permeation. A worst case number was found by using the total surface area of the o-ring as opposed to only the surface exposed to vacuum. Outgassing constants vary between materials, as well as pumpdown times and temperatures. Therefore, the total gas loads were calculated for three different pumpdown scenarios: unbaked and pumped for 1 hour, unbaked and pumped for greater than 24 hours, and baked and pumped for greater than 24 hours. Baking temperature of the system is limited to about 150C due to the Viton gaskets and high vacuum transducers used. This calculation represents possibly the most tedious and exhausting due to an exceptional amount of variables to consider – all materials, all surface areas, as well as different pumpdown scenarios are factored in for the whole system as best as reasonably measurable and for practical purposes. Based on all of these measurements and calculations for the system, the total gas load of the system for pumpdown was found for the following three conditions:

Unbaked, Pumped 1hr
Q(total) = 2.903 x 10^-5 Torr-L/s

Unbaked, Pumped >24hr
Q(total) = 1.428 x 10^-5 Torr-L/s

Baked, Pumped >24hr
Q(total) = 9.589 x 10^-6 Torr-L/s

These relatively high loads are due to the Viton gaskets present in the system. These numbers in reality should be less due to the over-estimation of gas load on the system for the o-rings. From these numbers, the maximum achievable vacuum during pumpdown can finally be calculated.

3.) Maximum Achievable Vacuum During Pumpdown
Applying the equation S=q/P, where S is the effective speed for water vapor at the proper flow regime, q is the total gas load of the system during pumpdown, due to outgassing and permeation, and P is the ultimate pressure. Solving for P, using the effective speed for water vapor in molecular flow of 17.043 L/s, the following numbers are attained:

Unbaked, Pumped 1hr
P = 1.703 x 10^-6 Torr

Unbaked, Pumped >24hr
P = 8.379 x 10^-7 Torr

Baked, Pumped >24hr
P = 5.626 x 10^-7 Torr

Therefore, within reasonable confidence given simplified and worst case estimates, this system should be capable of reaching an ultimate vacuum level in the mid 10^-7 Torr pressure level, assuming the system is properly sealed, baked, outgassed, and pumped.

4.) Critical Factor Determination for Feasibility of Pumping System
A final design rule must be calculated for the system. For a high vacuum system, there is a critical pumping speed at which the system can be reasonably pumped down within a reasonable amount of time and effort, without the need to use cryopumping. This critical pumping speed factor is found by dividing the speed of the system by the total surface area of the high vacuum system. This number should be greater than or equal to 0.01 L/s/cm^2. I calculated this for two different scenarios, assuming water vapor for pumpdown – a simplified surface area model where only the total internal area of all the walls are found, and a over-estimated worst case scenario where the total surface area of all the surface are added to the total surface area of all of the Viton gaskets, even if the gasket face itself is not directly exposed to the high vacuum chamber. As a result:

Critical Pumping Speed for Internal Area Only = 0.020 L/s/cm^2

Critical Pumping Speed for All Possible Exposed Areas = 0.015 L/s/cm^2.

Therefore, the critical pumping speed of the system is valid for pumpdown.

Conclusion
Now that the total gas load during pumpdown as well as the ultimate vacuum has been calculated for a variety of pumpdown conditions, the last steps are to find pumpdown times and the total allowable gas load for each gas over the expected range of vacuum for various processes. This step has been the most exhaustive of the process, employing the use of not only a wide range of constants for various materials and pumping conditions, but meticulous measurements and modeling in CAD, and factoring in all reasonably associated variables to give a good approximation of what to expect for the current system behavior. Based on the general principles and knowledge of high vacuum systems, the ultimate vacuum level approximations for this system are consistent with what one would expect in literature and practice.
Michael Bretti
Posts: 175
Joined: Tue Aug 01, 2017 12:58 pm
Real name: Michael Bretti

Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti »

5.) MAXIMUM GAS LOADS FOR PROCESS GASES FOR VARIOUS EXPERIMENTS

From the previous Section 4 calculations, I was able to show how I calculated the total gas load of my system V4 design during pumpdown, which consists of water vapor due to outgassing and permeation through the viton o-rings of my system. Finally, we reach the last gas-dynamics calculations for this vacuum system, which is determining the maximum gas loads for the system across the entire range of operating pressures for all expected processes and gases, now factoring everything that I have calculated prior. This is probably the most important numbers to generate for this whole system, as it verifies what processes could be supported at various vacuum levels, and if these experiments would be even viable for the current design. (NOTE: Section 5 and Section 6 have been switched due to the fact that pumpdown times are not as dependent on all previous calculations as the final gas loads, and this step would make more sense to follow the previous section as opposed to the original order in my first introduction post, which I do not have access to go back and edit at this point.)

The calculations go back to the simple fundamental equation of S=Q/P. The total gas load can be broken down into the total gas load due to water vapor during pumping added to the total process gas load. Since the total maximum gas load allowable at a given pressure can be calculated for a given effective speed, and the pressure and gas load due to water vapor are already known and calculated, then the total process gas load can be calculated. In addition, the gas load, expressed in Torr-L/s, can be converted to commonly used sccm for ease of comparison of flow rates for standard systems, such as standard fusors or electric space propulsion.

For these calculations, I have calculated the maximum gas loads from the operating pressures of 10^-2 Torr all the way down to 10^-8 Torr, for air, argon, and deuterium. Water vapor is not needed since that was already calculated prior for the pumpdown gas loads. Notice that I have included air in these calculations – I will not be actively admitting air into the system during runs, but instead, the calculations for air provide a basis to determine the leak rate of my system at a given vacuum level, accounting for the pumpdown water vapor load, should I develop a leak in the system when pumping down and conditioning it. This wide range of pressures and molecular weight gases will allow me to also establish the upper and lower bounds of what to expect for all other gases with molecular weights in between deuterium, which is incredibly light, and argon, which will most likely be the heaviest gas I run in the system. The PDFs for the calculations are included below:


Unlike previous entries, I will not summarize the major calculated results. Everything is presented in tables in the PDF, and would be too much data to type out here effectively otherwise. The numbers that are red in the table represent gas flows that are not attainable at a given pressure – in other words, I will not be able to operate the gas at any flow rate at that pressure. All other numbers in the tables are black, which represents all possible operating conditions. For each of the three gases, I calculated all possible flow rates for my effective pressure range in both the molecular flow regions as well as the transitional flow regions. Therefore both low and high vacuum systems are covered, for all processes I anticipate to run in the future. Each scenario is also further broken down and calculated for the three pumping conditions introduced in the previous section as well: unbaked and pumped for 1 hour, unbaked and pumped for greater than 24 hours, and baked and pumped for greater than 24 hours. This will give me a benchmark to compare how the system should behave between various stages of running and conditioning.

Since this is a fusor forum, and most people here would largely only be concerned with numbers for fusor operation, let us take a look specifically at the numbers for deuterium. In the operating range that most fusors are used in, 10^-2 Torr, the calculated maximum allowable process gas flow rate in sccm is found to be 3.381 x 10^1 sccm, or about 33.810 sccm, which is a very reasonable number to expect from this system design given it is optimized for a very short pipeline and high pumping speeds for 2.75” conflat based hardware. In addition, this rate is the same regardless if the system is unbaked and pumped for an hour or baked and pumped for greater than 24 hours – assuming no leaks, the gas load of water vapor due to outgassing and permeation at 10^-2 Torr is several orders of magnitude smaller than the maximum allowable gas load at this pressure for this system, and therefore has little effect on the deuterium gas load flow rates. The differences in unbaked vs. long pumped and baked systems only becomes a factor when processes are operated in the high vacuum, molecular flow region. For example, if I were to run the system at 10^-6 Torr for a deuterium beam-on-target system, the total gas load allowable would be double for a baked and thoroughly pumped system vs. one that has not been baked or pumped for very short times.

This concludes the calculations for finding the ultimate allowable process gas loads for this system. These numbers are one of the major end goals to this entire series of calculations, since I ultimately wanted to determine how much gas my system could handle at various vacuum levels, for various gases, and see how this would change based on the operating criteria for a variety of parameters needed to cover my wide range of future experiments. It also allows me to gauge how to expect my system to operate, and if certain gas loads and vacuum levels are even viable and achievable given this design. The calculations show that the system should be able to support very reasonable flow rates of deuterium in the normal fusor operating range, which is in agreement with observed numbers and flow rates posted elsewhere. Although the current system cannot support process gases at the upper end of the high vacuum region, it can support gas flows at least from low vacuum to processes operating in the 10^-5 to 10^-6 Torr range, which fits with prior calculations that show that the current system can only achieve an ultimate vacuum in the mid-10^-7 Torr range with just the water vapor gas loads due to outgassing and permeation. Further modifications of the system can be implemented as discussed prior to reduce water vapor loads which allow for higher process gas loads. Additional high and ultra-high vacuum pumps can also be employed, such as ion pumps and titanium sublimation pumps with relative ease and low cost to supplement pumping in the upper high vacuum regime (UPDATE: ion pumps and titanium sublimation pumps are not inherently cheap by any stretch purchased new. However, with a good bit of resourcefulness, a suitable ion pump at reasonable cost can potentially be found used on eBay, and a working titanium sublimation pump can be constructed and controlled with few components for low cost as well. Ion pump controllers are more challenging, but can be bought or built reasonably with enough know-how and resourcefulness. Note however these systems require high vacuum lower than 10^-4 to 10^-5 to operate, as well as a relatively clean system with minimized backstreaming if an oil diffusion pump is used.)

The final calculations presented in the next section will determine estimated pumpdown times from atmosphere to rough vacuum, and to high vacuum levels.
Last edited by Michael Bretti on Thu Feb 08, 2018 11:04 am, edited 1 time in total.
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