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
Posts: 177
Joined: Tue Aug 01, 2017 4:58 pm
Real name: Michael Bretti

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

Post by Michael Bretti » Sat Feb 03, 2018 4:35 am

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.

Michael Bretti
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Joined: Tue Aug 01, 2017 4:58 pm
Real name: Michael Bretti

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

Post by Michael Bretti » Sun Feb 04, 2018 7:48 pm

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.

Michael Bretti
Posts: 177
Joined: Tue Aug 01, 2017 4:58 pm
Real name: Michael Bretti

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

Post by Michael Bretti » Tue Feb 06, 2018 2:37 am

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: 177
Joined: Tue Aug 01, 2017 4:58 pm
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti » Wed Feb 07, 2018 3:16 am

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: 177
Joined: Tue Aug 01, 2017 4:58 pm
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti » Thu Feb 08, 2018 1:38 am

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 4:04 pm, edited 1 time in total.

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

Post by Dennis P Brown » Thu Feb 08, 2018 1:13 pm

When you say:
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
These are very expensive items new, and not very easy to obtained used; and more often, not in the best condition when used (especially the electronics.) Also, adapters for these components and extra ports can also lead to not insignificant costs. So, might want to modify that part of the post. Newbie's here do not know cost issues very well and I assume you are posting here for all levels of readers.

While your maximum deuterium gas flow for a given system is interesting, you do realize that isn't what most people that build fusors are concerned about at all. Rather, since deuterium gas is difficult to obtain and not inexpensive or if created from heavy water, both time intensive to make and even more expensive, one wants to conserve this gas. Hence, most people are only concerned with using as little as possible. As such, maybe in the future determining minimum flow rates that provide best neutron rates for a fusor would be a more valuable project, I'd think. Your discussions on water vapor issues is a topic that could use a lot more discussion since this is a bane to fusion for fusors. Maybe getting a rough idea of what does adhere for a standard humid atmosphere and typical volume system/chamber with pump down rates (not baked) to get this below an acceptable level would certainly be of use here.

Your calculations and work are rigorous and interesting and frankly, one of the few examples I've seen on this subject. Looking at this subject specifically for fusors usage is relevant (which you do), so focusing on that a bit more would make your articles even more useful. Not that high vacuum is not important since some here do require that for ion accelerator fusion.

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

Post by Michael Bretti » Thu Feb 08, 2018 3:55 pm

Dennis P. Brown,

Thank you very much for your suggestions and insight. It has given me a lot of new ideas to think about that I hadn't originally planned to dive into, but you make very good points.

When I was typing out the last section, I knew I would probably have to specify more about the ion and titanium sublimation pumps. Thank you for bringing that up, I will go back and revise that last statement a bit. They are definitely very expensive pieces of equipment new. I don't even think I have come across titanium sublimation pumps used on eBay. However, in the past couple months of eBay browsing, I have come across a decent number of used ion pumps that appear to be in quite good shape physically. The nice thing is that a lot of pumps sized for 20-25 L/s are fitted with 2.75" Conflat flange hardware, which makes it very convenient to integrate into these smaller systems, and at ultra-high vacuum levels even 20 L/s is a huge pumping boost. These pumps that I have come across so far are in the $100-$250 range, which is quite reasonably priced for ultra-high vacuum pumps. Of course functionality is another matter, but generally ion pumps don't require much maintenance, especially if they are used properly. Old controllers are also not terribly expensive, and if someone can get a standard fusor working with proper instrumentation, then building an ion pump supply should not be too difficult or expensive as well.

I am quite interested in the titanium sublimation pump however because it would be very easy to construct a simple one with little effort and components, and the controller for such would be dirt simple (low voltage high current supply cycled on and off a few minutes a few times an hour). I found this guide that actually shows how to make a simple one based off of 2.75" conflat hardware that I am going to follow and modify myself:

https://www.rbdinstruments.com/blog/hom ... tion-pump/

All it would consist of is a nipple section, an insulated low voltage feedthrough with at least 2 feedthroughs, and some titanium wire. For my own system, I was able to obtain a 2.75" nipple section and an insulated low voltage feedthrough with 4 inputs for free, so all that is needed is the titanium wire and a simple controller. Interestingly, it is very easy to calculate the pumping speeds for both cryopumps and sorbtion pumps, but I have not seen much specifically on titanium sublimation pumping. I am working on a CAD model of the simple design, which I will post about, along with thermal modelling later. I would like to explore and implement a small one for my system to see how well it works.

In regards to the rest of the calculations, all of this work was originally and primarily done for myself for my own system. However, I figured that since I am doing all this work, others might be able to learn and benefit from the process as well, since a lot of people might not have access to a lot of the high vacuum engineering texts that I can obtain very easily, and I have found these texts have vastly more knowledge and insight than what I have found available online. I do try to tie this all back to fusor related operation as best I can, although the fusor is only one operating mode for my system, working at the highest pressures calculated.

It was motivated by two major driving points: 1.) since I will be spending a lot of time and money on this system, I had better make sure that it can do near everything that I want, with room for growth, and I wanted to estimate how reasonable my goals would be for this system, and 2.) how do I know that my system can support the process I aim to achieve? Can it actually support everything at high vacuum with reasonable gas flows? The answer to the second question is currently it can support all my goals except for one. I wanted to experiment with argon-fueled micro electric space propulsion engines at 10^-7 Torr. This was the most stringent limiting factor on my system, which helped push the optimization of speed for my system. Currently, as is it won't be able to support this project, but everything else for now can be run.

Another thing I was interested in, relating to the fusor side, is how much gas flow can my system support? Browsing through prior posts, it appears that the common sccm flow rate for deuterium for fusors operating in the 10^-2 Torr level use anywhere between a few sccm to a couple of tens of sccm of deuterium. How do I really know that my system can support this? I didn't want to spend all of this money and time to build a system to find out it couldn't do what I wanted. Based on all of the above math, I believe I have successfully shown that it is reasonable to support up to several tens of sccm of deuterium in the system at 10^-2 Torr. It also allows me to get a feel for how much gas flow I can support for deuterium beam systems in the high vacuum region, which is even more stringent and challenging. While the system can handle a lot of deuterium flow at low vacuum, it does not mean I will run the system at full flow - the manual gate valve will allow me to change conductance if needed, and I would put much less into the system anyway since it is very expensive. However, it is best to plan for extra room than not enough. Another unseen positive taken from these calculations is with the above calculations for max flow rate for air - if I have a leak that is preventing me from reaching some vacuum level, I at least roughly know how much load from air due to the leak is acting on the system, which could be very useful for troubleshooting and experimental run planning.

I think at this point, it apparent and demonstrated that anyone with a bit of motivation, determination, and some money can build a working fusor capable of fusion, without any rigorous design work or calculation. In comparison with other fusion capable devices, a fusor is incredibly simple, and it has been shown many times that a working system can be slapped together with moderate effort and scrounged components. I am in no way whatsoever downplaying the challenge and accomplishment of getting a running system both operational and proven, which still requires a lot of work and personal investment to achieve. However, there is a major difference between producing neutrons and maximizing neutron production efficiency, as many experienced fusor enthusiasts are well aware of by now. Especially with the new developments and push towards very small fusor systems, we may have reached the point where in order to make that next leap in improvement, more rigorous planning and engineering needs to be taken to maximize its potential, and to better understand the underlying principles of the device. For example, as you mentioned, water vapor is definitely a major bane for fusor operation, and certainly would effect efficiency. Yet a lot of systems presented generally do not appear to go through enough conditioning to fully drive off or reduce the water vapor loads. While running a plasma would certainly help drive off water vapor, and easily burn it out of the grid, for such short runs that the general fusor enthusiast operates at, there is not enough thermal energy acting on the entirety of the system surfaces or long enough pumpdown times at high enough vacuum to effectively drive out all of the water vapor of the whole system. Plasma cleaning definitely helps in bombarding the immediate surfaces, but the process still takes time. Even for systems that are baked to several hundreds of degrees C and pumped at high vacuum levels, it still takes many, many hours of continuous pumping and baking to effectively eliminate or reduce water vapor in the system. Once the system is admitted back to atmosphere, new layers of water vapor will immediately start adsorbing on the surface. Back-filling the chamber with nitrogen or other inert gas would help reduce re-conditioning times.

As you also mentioned, it would be very interesting to start exploring more experiments involving the relationships of water vapor and other contaminants in the system and fusion efficiency. Based on the work I have done so far for my system for example, it should be do-able to estimate for example the total number of water molecules present in the system, and work on minimizing this number. Maybe there is a certain point where decreased water vapor has no more effect on fusion yields. I do not know these answers. And recent developments in small fusor operation does show a higher efficiency for small devices over large devices, operating at higher pressures. Therefore it may be beneficial to see exactly how far a system can be pushed and how much deuterium it can handle at a given operating vacuum level.

There is a lot of info presented here so far, and a lot more that I will be posting and documenting. I apologize for the incredibly long posts, and applaud anyone who has the patience to trudge through them. Hopefully something useful can be gleaned from these efforts for all experience levels. I know when I first started I was eager to try and build this thing as fast as possible and start doing experiments immediately - however, I have come to thoroughly enjoy and savor the design process, slowing it down, and breaking it down to the most fundamental levels, then building on top of it. I do have almost all the parts I need now, and will start to actually assemble the system. I just have a one more post at this point for the main calculations, as well as some thermal modelling work. I hope this weekend to at least assemble the low vacuum roughing side and maybe qualify how well sealed it is and the ultimate vacuum of the roughing pump. I will post more about this as I get to it, as well as other developments such as the titanium sublimation pump build.

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

Post by Richard Hull » Thu Feb 08, 2018 10:15 pm

Just a little note....(Let's make that a long note).... My current fusor, fusor IV, uses a larger 6" sphere and has been around since 2004. It has had a terrible leak ever since I assembled it. I have a very accurate 0.1 torr heated Baratron gauge on the chamber. I use a standard 5 CFM Precision belt drive fore pump that can pump down the foreline, the cold diff pump and the fusor chamber to 10 microns in about 3 minutes. With the Diff pump on, I can hit the high 10e-5 torr level, at best, in the fusor chamber.

If I valve off the chamber at 10e-4 torr it takes only 4 minutes to leak to 2X10-1 torr, (200 microns). This is considered a terrible leak by any standard.

I rarely run the fusor now, save for special events and demos. I have, for years, taken, 2-3 days of 2-3 hour run-ins to condition this leaky fusor to produce 2 million fusions per second. (1 million neutrons/sec). The conditioning time is a lot easier for me to work with than tearing a fully functional fusor apart to locate and seal the leak. Whether this leak, over time, has created a water issue inside the chamber or whether the conditioning has to do with burying D2 into the chamber walls, is unimportant to me. I will say that the leak is in the fusor chamber itself. I have done a halfhearted effort on two occasions to locate the leak with the classic acetone/alcohol spray and have seen no clear sudden increase in pressure. I just gave up.

I realize that a true, dyed-in-the-wool vacuumist and "vacuum-head" demands an absolutely sealed system. Water loads and certain tramp gases are the bane of those demanding 10e-8 torr final vacuums. However, the person doing fusion in a fusor need not worry about water or a little leak, even as bad as mine. As noted before, the average newbie is a vacuum dunce and all his issues revolve around raw beginners failure of technique and failure to read a few basics in good texts or the vacuum forum FAQs here. Another tangle to their feet is in purchasing pumps that are shot or that, by their very nature, are not up to the task even when new. Finally, these same folk seem to never acquire good vacuum metering to even know where they are in a pump down scenario!! In the end, even a fairly rotten sealed fusor will do good fusion if the pumps are great and the operational technique rises to the occasion.

I am in no way condoning sloppy work. One should strive to do the best they can with what they have. There is a point, however, where pushing work to perfection where perfection bears no additional fruit for a specific task at hand.

Believe me... I have been here since 1998, at the very start of all of this, and virtually 100% of all vacuum systems ever assembled here are dismantled and stored or sold off the instant an abject failure to do fusion is at hand and even if there is a fusion win, the systems are doomed to being torn apart and stored or sold off. The folks here are for one thing....Doing fusion! A vacuum system is just a horrible and expensive briar-filled path they must begrudgingly trudge along on their way to the super highway of fusion. Many are at an age where all of this is an entertainment just prior to college or discovering that girls are warm and soft and nice..... fusion and all of its entangling vacuum and high voltage stuff, at this juncture in their lives, will be as dead as yesterday's egg salad.

This post, while not quite as long as others here, does tell the tale of the average vacuum here at fusor.net.

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
Retired now...Doing only what I want and not what I should...every day is a saturday.

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

Post by Michael Bretti » Thu Feb 08, 2018 10:50 pm

Richard Hull,

Thank you very much for sharing your insight and experience. As the first one who has really started and pushed the whole endeavor for amateur fusion, you certainly have some of the most experience and run-time of anyone here. While calculations are good for determining how the system might behave, ultimately it does still come down to practice and running it yourself. I plan on continuing my efforts and optimizing the system, and running new experiments long after I achieve first neutrons (if money allows). Since I have so many other projects lined up that are also non-neutron producing, this will ensure that my system won't be broken down and sold off after all this effort and time (I am also fortunately past college and married now, so I don't have the same distractions as the younger fusioneers will encounter.)

For a small system, maybe bad leaks and water vapor have more detrimental effects on neutron output than a large system like the one you are running, or maybe it will be similar to your experience. It will have to come down to experiment at the end, I couldn't possibly say one way or another. Hopefully if minor effects in the vacuum system itself such as residual water vapor can be proven that they do not interfere with neutron output for small systems, then full efforts can be mounted to maximize and improve its efficiency even more by other means. Chances are your observations are more than valid and applicable for small systems, but it would also be beneficial if someone could experimentally validate this on a small system to remove it from the list of ways to improve efficiency. I suspect that a super clean vacuum would probably give almost non-noticeable improvements, but you never know. My focus will be more on the experiments after, including implementing ion guns and other experiments. Right now I'm just taking it slow, one step at a time and documenting the process as I go and just focusing on the vacuum while I do not have the funds to support neutron experiments yet. By the time I can start doing it, hopefully my system will be well prepared to start pumping out results immediately (no pun intended.)

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

Post by Michael Bretti » Thu Feb 15, 2018 2:10 am

6.) Foreline Parameters and Pumpdown Time from Atmosphere to Rough Vacuum

From the previous five sections and numerous subsections, the major and critical vacuum parameters were explored and calculated for my V4 design. This section will cover the final main calculations for this system. Originally, I was going to include calculation estimates for pumpdown from rough vacuum to high vacuum in addition from atmosphere to rough vacuum. While the roughing times are much simpler, calculating the pumpdown time for high vacuum is much more complex and imprecise, relying on a large amount of simplifications and assumptions that dive into many of the complexities that makes high vacuum engineering a challenge. Because there are several ways of going about these calculations, and due to the assumptions needed and the very rough estimation and wide range of times, I will omit these calculations here for now and focus just on the foreline and roughing parts. Since fusors generally operate in the tens of micron range, which falls into the roughing pumpdown region, this may be of much more use and interest for the majority of people here on the forums.

Below is the PDF for the various foreline parameters and figuring out the pumpdown time from atmosphere to rough vacuum:


A few initial considerations should be noted for the roughing line. For the range explored, from atmosphere to about 10 microns, the load due to outgassing is negligible, and can be omitted. In addition, a well designed foreline should not have any effect on the speed of the foreline pump. Therefore, the effective speed of the system should be equal to the speed at the inlet of the pump. The foreline for this system was kept as short and minimal as possible, incorporating a necessary pressure gauge, isolation valve, and a replaceable molecular sieve foreline trap. While a foreline trap is not required, it can be greatly beneficial from keeping both the diffusion pump oil free of contamination from the roughing pump, and keep the roughing pump oil cleaner by absorbing moisture during initial pumpdown. A used trap on eBay was purchased at more than five times lower than its original cost new, and in excellent condition. Cost needed to be minimized, as well as size to make the system more compact and portable on a single mobile cart.

The first set of calculations in Section 1 of the PDF goes over figuring out some initial key parameters of the roughing line. First, the roughing flow regime is determined. This can fall into one of three categories: purely viscous flow, purely molecular flow, or transitional flow. This is established by the flow factor which is represented by Dp, where D is the diameter of the roughing line, and p is the mean gas pressure. Units here are cm and Torr, respectively. For my system, the diameter of the roughing line is 2.210 cm. The mean pressure is found between the starting and ending pressures – in this case, it is assumed that the starting pressure P1 is 760 Torr (atmosphere), and the ending pressure P2 in the foreline at the backing inlet of the diffusion pump is 2x10^-2 Torr, or 20 microns. Based on the boundary conditions for the Dp factor, it is verified that the roughing flow is indeed purely viscous.

Now that the flow regime is established, the equation for conductance of a pipe in viscous flow can be used to find the conductance of the roughing line. The general equation for viscous flow conductance is given in the PDF – since air at 20C is considered as the gas, this equation can be reduced to a simplified form for this gas input. The line is based off of KF25 hardware, and the diameter is assumed the same for all parts. The line is also treated as a single length line with the total length of all parts, including bends for simplicity. The conductance of the line is found to be 41,487.062 L/s. Note that this number is massively larger than other conductances previously calculated, but again, this is for an entirely different flow regime between atmosphere and very rough vacuum, where gas flow principles are much different than in molecular flows.

Once the conductance is found, then the effective speed can be calculated. First, the maximum speed of the forepump is determined. The flow rate of the selected pump is 6CFM, which can be calculated to 2.830 L/s. The pump speed was determined based off the minimum pumping requirements for maximum throughput of the diffusion pump from the datasheet. From the original diff pump manual, the minimum displacement of the backing pump is 80 L/m, or 1.333 L/s. The manual also specifies that a single stage rotary pump capable of 120 L/m (2 L/s) and an ultimate vacuum of 0.1 Torr is recommended. The backing pump selected is a two-stage pump capable of 0.015 Torr and has about 53% higher throughput than the recommended min displacement, which was also in part selected due to pump availability and cost, and should have plenty of overhead for the gas loads that will be seen in the system or the effects of the foreline trap (in viscous flow). Based on the equation to calculate effective speed with calculated conductance and established max speed, the effective speed was found to be almost exactly 2.830 L/s. Since the foreline conductance is so massive compared to the maximum speed of the pump, there is virtually no change in the calculated effective speed. From this, it can be shown that the conductance of the roughing pipeline in viscous flow has a negligible effect on the maximum pumping speed of the backing pump, and is indeed well planned and designed.

Once the effective speed has been determined, the pumpdown time can be calculated. One of the factors required in the equation is the volume that needs to be pumped. Therefore, the total volume of the system is calculated. Because the roughing pump will pump out the entire volume of the whole system, all parts must be factored. This includes the volume of the foreline, the total internal volume of the diffusion pump, the volume of the high vacuum pipeline, and the volume of the chamber. This was determined from CAD models of the system. The total volume of all above parts was found to be about 5.464 L. Based on this volume, with a effective pump speed of 2.830 L/s, a starting pressure of 760 Torr, a final pressure of 0.020 Torr, and the ultimate pressure attainable by the forepump (from the pump datasheet) of 0.015 Torr, the total pumpdown time is found to be about 23 seconds. Based on the small size of the system, and minimized length of the foreline and high vacuum pipeline, as well as the speed of the pump, this would seem like a very reasonable number to expect.

This section effectively concludes the major engineering design calculations for this system. More advanced calculations may be applied later as the system is tested, or new components are introduced, but at this point all the major required parameters have been well explored and estimated. From here on out, further posts will be dedicated to the actual build and testing of the V4 design as presented and calculated. Other parameters such as thermal modelling of the system and various components, such as the diffusion pump, titanium sublimation pump, and basic fusor grid will also be presented as they are completed as well.

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