Electron gun with DIY Einzel lens

[Luca_Cappelletti]

Hello, I'm going to spend some words about my recent work in trying to build an electron gun, the aim of this setup is to bombard samples with electrons and be able to do so over a narrow target also varying the energy of the incoming electron.
For this reason, I chose to build a simple electron source (a tungsten filament) that creates the electrons, and then I used an Einzel electrostatic lens, that is because this kind of lens should maintain a fixed focal spot, even if the voltage applied to the focusing anode is varied proportionally to the accelerating voltage.
At this time I have already made the first prototype tested it, and found some problems, now I'm almost ready to test the second prototype that has had some big changes.
1° prototype:
At the start of this, I didn't know a lot about electrostatic lenses, so I made some mistakes, this is the first prototype:

to decide the dimensions I just eyeballed them a little bit and used simulation software to verify if the system would (theoretically work)
at the time I didn't know that on this forum there is a dedicated section for ion gun =(
To detect the electron I just coated a microscope glass with the phosphor that is found inside fluorescent light bulbs, it works really well and also reflects some of the light coming from the filament that would otherwise make it difficult to see the phosphor glow from electron bombardment.
The vacuum system consists of a T KF50 connected in the middle to a turbo via a metal flexible hose of dimension KF40, which also has a Pirani gauge, on the other two sides of the T there is my gun and at the opposite side a manifold that converts the KF50 to a conflat 2.7inch, (the only glass window I could find is that):

the filament I have been using (not the one in the first photo that came from an x-ray tube but now I have swapped for a less powerful filament) comes all from halogen light bulb, at the beginning I used the bare light bulb with just the top part cut of, but that produced unfocused beam, after enclosing the filament in a metal cage with a smaller hole for electron to come out I got some better result:

the later version of the filament
and the following photo shows the difference between the electron beam before and after the filament source was enclosed in the aluminum foil cage:

The biggest problem with this design, that I discovered after building and testing it, is that as you can see the electrons are spread in one direction, so they are not well-focused, this problem is due to the construction itself because while traveling down the path, the electron is moving really close to the two brass rod that is at 0V that connect the final anode, and I think this causes them to spread in that direction.
Another problem is overheating, the filament is a 35w lightbulb, which is only wasting heat, it consumes 35w and can produce way more electrons by thermionic effect than I could ever need, so I searched for less powerful and smaller light bulbs and found some that are used inside car light that can operate at 1-2W.
SECOND prototype:
This time I learned to use CST Particle Studio better, and tried to take into account every aspect.
To solve the problem of the ground electrode on the side it was essential to reduce as little as possible the time the electron are subject to the electrostatic field of the connecting rod to the last electrode, and to do so it is required to get the electrode as close as possible.
First of all, I increased the diameter of the electrostatic lens, by doing so it is easier to fix them from the inside, using insulating material, it is also now possible to use the same potential as the filament voltage (the negative HV in the range of 5-10kV), because the new diameter (18mm inside) is larger compared to the previous (10mm) inside the cylinder lens, and so the electric field in the center is smaller (if we apply the same potential to the two electrodes), and so if this potential was applied to the smaller electrode, it would make the electron curve so much that they would return back or do strange stuff, but with the larger diameter the electric field is smaller and so the electron can be bent less and with ease creating a focal spot at a distance of around 10-20cm varying the length of the focusing anode.
This is the setup I built so far:

as you can see the distance between the electrodes now is only 3mm and this has very little effect on the trajectory.
Starting from the first photo, on the top left we have the HV feedthrough to power the filament using a floating air-core transformer, this piece has been made using a 7mm borosilicate glass rod, fixed in place by the white 3d printed plastic part, and then using TorrSeal it has been made a vacuum seal inside the metal connector as can be seen here:

in this rod passes the cable for the filament, and at the top the filament itself is placed, and around the filament is placed the brass cup.
This cup serves the same purpose as the aluminum foil of the previous prototype but at a more precise level, being perfectly cylindrical.
The filament used is this:

I hope it is powerful enough for the emission current I'm hoping to achieve, theoretically, tungsten should be able to emit 5mA/W of power (source Electronics Engineer's Reference Book P36) and I also could coat it with BariumOxide to enhance the emission current.
This piece of fitting is then mounted on the main electron gun (the part on the right) from behind and clamped together using a kf25
This part is also glued using torr seal, the main seal is between the long copper electrode and the inox KF50 fitting, also on the side there are two glass rods that have been made to contact the glue, inside the glass rod there is a copper wire for the middle and end electrode.
At this point I imagine you might ask yourself why to use so much crap like glue and strange stuff, the reason is that the budget for this project is not a lot, so I have to use the KF50 T as the main chamber, to do this I need to fit everything inside without arcing, so it needs to be this compact, the reason for the glue is that HV feedthrough is extremely large compared to what I need, and are also expensive, and not necessary, having a dielectric strength of around 30kV/mm borosilicate glass should be good enough.
The electrodes are centered using a Teflon rod that has a hole in the center of 10mm inside which the filament is placed from behind and through which the electron should travel.
This model can help to understand the current configuration:

The second photo shows the simulated trajectory for the electron coming out of the filament, and on a color scale their energy in different positions, it can be seen the effect of the lens, in constraining the diverging beam to a more or less straight parallel beam.
I found it really useful, during all of this designing, to visually evaluate the electrostatic potential instead of the electric field, along the space inside the model, this is a really cool feature of this simulator and can be used to visually understand what is going on:

It can be clearly seen that the electrostatic potential created by the second electrode, really resembles an optic lens.
One of my biggest concerns are due to the vacuum not being high enough and causing breakdown, with the earlier prototype I could reach 10^-5mBar pretty fast, but not much more, (I should note that in the vacuum chamber was present a part made with PLA, now there is PTFE, and a very little part made in ABS with should be better for vacuum but I'm thinking of changing also the ABS to PTFE).
In particular, the following section is of great concern to me:

It is the side where the filament HV feedthrough is placed, in the first photo it is empty and then it contains the filament (there should also be a glass rod but to make the photo it was easier to meet the copper wire in my hand) I am scared that the small opening remaining between the PTFE and the filament itself is too small to let air molecule pass trough from the previous section, and so that locally there might be a pressure too high that would cause arcing from the filament to the copper tube at the need of the Teflon (near the KF25 connector).
So if anyone has some idea about this problem, I would really appreciate some feedback of any kind to know if I'm going in the right direction or not.
Many thanks and sorry for the long post

[Rich Gorski]

Luca,

Interesting Einzel design. I've designed many of this type for the old CRT industry.

The first problem of the elongated electron spot (prototype #1) as shown on your phosphor plate is as you described. Those large gaps between electrodes exposes the beam to the potential on the brass support rods. The idea is to create an electric field inside the grid structure that is cylindrically symmetric. The potential on those brass rods penetrates into the interior region disturbing the electric field. Reducing the gap between grids to 3mm as on your 2nd prototype should solve most of this problem.

However I see another potential problem. You have insulating materials (plastic??) inside the electrode structure. Insulating material inside the electrode structure is not a good idea. This material can and will charge to unknown potentials again destroying the nice cylindrical electric field as well as causing HV instability. Every electron gun I have seen supports the grid structure from the outside using glass or ceramic support rods. My recommendation is to remove any insulating material from the inside of grids and support the grid structure from the outside. The photo below shows an Einzel electron gun for use in a projection CRT. Note the white glass rods (called beads) that support the electrode structure. Also note that there is no insulating material inside.

My suggestion is to rebuild you electron gun with grid support outside. Then give it a try in your vacuum chamber and post results on what the spot looks like on your phosphor screen and how it behaves under different operating voltages. Then we can go from there to improve the design a step or two at a time.

Rich G.

[Rich Gorski]

I would also advise not to use any type of plastic inside the vacuum chamber if you can help it. Plastic is horrible for achieving a good vacuum. Macor is a machinable ceramic that can be used to fabricate electron gun parts. Unfortunately it's rather expensive. Maybe the easiest and inexpensive way to support the 3 electrode components from the outside is to have them the same outer diameter. Then you can simply Torr seal two or three glass or ceramic rods on the outside. Use an internal mandrel to align the three parts while epoxying then remove the mandrel when epoxy has cured. Internal mandrel methode is a common way to manufacture electron guns as it holds and provides an excellent alignment method for the parts.

Rich G.

[Luca_Cappelletti]

Thank you Rich for the suggestion, I was hoping that the central PTFE would not be a big issue, I have now tried to make some changes to avoid using it:

As you suggested I'm using a temporary plastic rod to keep everything in place, and I have glued those 3 brass objects (I have no idea how to translate their name) but this is a photo to understand better how they are made:

Immagine 2024-06-15 231844.jpg (4.56 KiB) Viewed 6767 times

I glued one on the side of every copper electrode, and in the hole of the brass object, there will be a glass rod that connects the 3 electrodes relative to each other. So that the electrode can be disassembled without the need to break the glue, this can be a temporary solution until everything is working, then as you have suggested a fixed and final support can be made by gluing the glass rod to the electrode directly at the fixed distance.
The reason I tried to use the plastic rod, is that I am afraid of possible arcing between the electrodes, as with my setup it is really hard to get lower than 10^-5mBar and almost impossible to go under 10^-6mBar so with this kind of pressure what do you think is a safe distance for 10 or 30KV?
Also, I read from different sources that oxide-coated cathodes aren't used in high voltage acceleration tubes because ion bombardment on the cathode causes them to degrade, but does this mean that the oxide material is ionized and expelled towards the anode like what is happening at the electron?
In my case, I would like to use an oxide-coated cathode so that a smaller wattage filament can be used, and also the filament can be heated less so it produces less light, which is desirable for collecting light inside the apparatus, it is not a problem if the cathode material is degraded because I can extract the filament and change it periodically, but if the ion being shot are element instead of electron might be a problem.

[Rich Gorski]

Luca,

The vacuum level of your system (10-5 mBar) is mid range vacuum sufficient to support a 20kV potential difference across a 3mm gap. Maybe you can push it to 30kV. CRT electron guns often operate with 30kV across a 3mm gap but the vacuum level in those tubes were 100X better and the electrode surfaces are processed to be a smooth radius with no burrs. Make sure the edges of your cylinders that face the opposing voltage are smooth and have no burrs, sharp points or sharp edges.

On the ion issue you mentioned relating to BaO cathodes and accelerators. This is backward accelerating positive ions created by the electron beam ionizing neutral gas along the beam path. No, cathode material is not expelled toward the anode (unless there's an actual arc to the cathode). These ions, because they are positively charged, will accelerate backward and strike the oxide coating causing burning and contamination of the surface. CRT electrons guns had this problem in the beginning of the industry (poor vacuum) but the tubes of later versions were equipped with Barium getters which allowed CRT tubes to achieve vacuum levels near 10-8 mBar. The problem no longer was an issue.

BaO Cathodes are sensitive to contamination so at your vacuum level I would stick with the reliable simple tungsten filament. You might get away with using a BaO cathode for a while but it may have a short lifetime in your system. Also production BaO cathodes are not such that you can just replace the filament when they go bad. The BaO coating is generally applied to a substrate such as nickel or tantalum which is heated on the back side by the filament (the filament is not coated with BaO) so you will have to replace the entire cathode assembly when it goes bad. I have used BaO oxide cathodes from Kimball Physics. They are a tungsten filament with a 1.5mm diameter Tantalum disk laser welded directly onto the filament. The Ta disk has the BaO coating. Also remember that there is processing that needs to be done to virgin BaO cathodes called activation. This is essentially a slow heating up of the cathode and applying a voltage to coax emission from it. If you let the activated cathode come up to air you will likely have to go through the activation procedure again when back under vacuum. You can only recycle them a few times at most if brought up to air. So if you are looking for a cathode with long life under poor vacuum conditions and that can survive bringing up to air and back down to vacuum many times, the simple tungsten filament is the best choice.

Rich G.

[Luca_Cappelletti]

Update:
today I did a lot of tests, some successful and others less:
First of all, this is the current drawing of the system:

and this is the filament source:

The brass cylinder has a thin copper disc soldered to the other end with a 1mm hole in the center. The light bulb is a 12v 10w halogen type.
The first test was made using A_1_position=5mm, and A_distance=5mm and this is the image I got on the phosphor screen:

spot 150.jpg (39.04 KiB) Viewed 6660 times

the diameter is 7mm at a distance from the filament of 150mm, it was a really good-looking spot, very bright and constant in time the only thing is that the upper left corner was brighter than the under right, but not a big deal, with this I tried varying the voltage applied to the gun going from 3KV to 12KV and there was no difference in the spot position, only the brightness was varying as it should, also by varying the filament voltage the brightness could be controlled.
After this, I tried to simulate what would happen if the filament was moved back and the simulator indicated a really big reduction in the spot size which is my goal. So this configuration was also tested, the anode distance remained the same, but the first anode position was increased to 10mm, so the filament hole, was 10mm behind the exit of the first anode, and the phosphor screen this time was placed at 190mm from the filament as per the simulation this was the distance with the smallest spot:

The simulation was right, the reduction in size was also according to what was predicted by the computer so really good.
At this time I also played with voltage to the filament and to the anode with the same result as before, which can be seen in this video in which the high voltage is constant and the filament is varied:
https://youtu.be/pjrFZditGq0
After some more simulation, I decided to try another configuration, but after testing, I got some disappointing results, i tried to change different parameters and also return to the last successful configuration tested (the one in the video) but I always got bad results, all similar with the following image:

This image was taken with the same parameter that before yielded a spot of 1mm, but this time the spot is very non-uniform and less bright with the same filament voltage, I couldn't understand why and I tried to increase and decrease the anode distance, but always the same result occurred.
After disassembling and verifying the components were good, I found only one possible explanation that I can think of: the filament might be the problem, in the beginning, it was almost perfectly at the center, but now that I have extracted it was shifted more to one side as it can be seen here:

also, the bulb was blue, probably due to the tungsten evaporating.
I tried to move the tungsten gently back to the center, but it broke, I suspect it was more fragile than at the beginning, the time the machine ran was not a lot, less than 40min in total, but once or twice I might have powered the filament with too much power, to see a brighter spot, but only for a fraction of a second, so maybe that was enough to degrade the filament and produce that worse image.
At the moment I don't know if I should try and find another filament source or cut another lightbulb and verify if a new one fixes the problem, those bulbs are really convenient because they fit very tightly in the brass cage and are not big or too powerful.
I was also wondering, what is the smallest spot size I can get? because that should be dictated by the filament dimension, so going under 1mm in spot size with a 1mm filament diameter is impossible?

[Rich Gorski]

Luca,
Looks like your Einzel electron gun is showing some success. It produced a reasonable spot on your phosphor screen and it appears your simulations are leading you in the right directions for the optical design. I have some comments and suggestions about the issues you mentioned in your last report.

1. Problem with the spot showing a large tail after your last configuration trial. This is a typical sign of an electron beam that has gone off axis with respect to the electron optical system (the axis of your cylinders) . It produces a tail in a certain direction which is usually opposite to the direction the beam is off axis or mis aimed. I think you have already found the problem. The mis alignment of the cathode filament WRT the 1mm hole in that first grid. This might have happened due to excessive heating of the filament or it just wasn’t secure in its holder and shifted. With the Anode #1 at 0 volts and the cathode itself at -10kV this is a high E field region and therefore sensitive to misalignments that can mis aim the electron beam. Its also possible that the filament received an arc that damaged it but I think you would be able to see the damage if it actually occurred. So the solution here is to rebuild the cathode with a new halogen bulb and make sure the filament is secure and centered in that 1mm aperture. For now I would continue with the inexpensive halogen bulb cathode since it seemed to perform OK at least for a while. At some point you may want to consider a better production cathode such as a pointed tungsten filament mounted an a ceramic disk like what they use in SEMs.

2. Spot size. The spot size in an electron optical system is not a simple thing to analyze but suffice it to say that the resultant spot size is a function of three things. The magnification of the main lens which magnifies the apparent electron object that is formed by the cathode and first grid, spherical aberration of the lenses and third space charge repulsion which becomes significant in higher current beams. Those three items refer to a properly focused best spot size. In your test you have changed the position of the cathode to achieve a spot size reduction from 7mm to 1mm. This tells me that you are trying to focus the beam by a physical change in the geometry of the electron gun and you likely have not found the best smallest spot size since you only tried two positions. A better way to focus the electron beam is by electrically varying the potential on anode #2 which you currently have fixed at the potential of the cathode. This will require a second HV power supply or at least a focus tap (potentiometer) from a single power supply. In this case the filament is fixed at your -10kV, anode 1 at 0V, but anode #2 can vary say between 0 and -10kV. That will allow electrical focusing of the electron beam. The nice thing about this method is that the final electron beam energy will not be affected by changes in focus potential applied to anode 2. The energy will be equal to the anode #3 potential minus the filament potential or 0- (-10kV) = 10KeV. You can either use a separate -10kV power supply for the anode #2 grid or use a potentiometer to tap a voltage off of your main filament HV supply. Note that the pot will have to be able to handle 10kV. You can get such a pot by salvaging the focus pot from an old CRT television or computer monitor. These pots are hundreds of megohms so it shouldn’t load down you main power supply.

3. How small can the spot get? As explained in #2 above the first thing you must do the know the best spot size of your Einzel design is to be able to properly focus the bean on the target. Physically changing the position of the cathode is certainly a cumbersome and difficult way to do this. I would suggest looking into using the anode #2 grid as a focus grid and leave the cathode fixed in one position. Since you have simulation capability I would suggest trying to simulate the beam focus option using the anode #2 potential.

Rich G.

[Luca_Cappelletti]

Rich thanks for the suggestion, I'm trying to find a schematic for the crt transformer (bsc25-t1010a) so that I can vary the potential on the focusing anode as you suggested.
In the meantime I have tried to fix the following problem: the anode filament is consuming very quickly, and after only some minutes of run time the tungsten is evaporated on the surface of the bulb as can be seen here:

and becomes a lot more fragile than at the beginning, this is probably due to the fact that to get a visible spot size I need to increase the temperature a lot.
So I have tried to add some oxide to the filament to enhance thermionic emission, the first one that was tried is Y2O3 because it is resistant to air contamination and moisture, so when the gun is opened it wouldn't be a problem, but the result was disappointing, there was some improvement in brightness at lower temperature but also degradation in spot size, this last problem I think is due to the method that I have used to deposit the oxide: a suspension of Y2O3 in water was made and using a pipette it was dropped on the filament and then heated slightly to dry so with this method probably the coating is uneven and bigger and result in a image of the filament bigger than the coil of tungsten.
The activation process that I tried was to put the filament in vacuum and heat it to a high temperature for 20-30min, unfortunately, I think that this is the critical part, and I read that it needs to be performed in a reducing ambient (maybe H2?) but I would need more information regarding the activation process.
Because of the little success with Yttrium I tried the other oxide I had on hand just to see if it worked and that was SrO, so a suspension of SrCO3 was deposited on the filament as can be seen here:

and brought under vacuum, then the filament was heated for 20min, the pressure increased momentarily because of the CO2 production, and after I heated the filament for some minutes to a higher temperature than normal operation for oxide-coated anode, but less than the temperature of operation for tungsten, the increase in number of electrons was very clear as can be seen on this photo that compares the different test:

The SrO worked really well because the brightness of the spot was more intense than that of the light produced by the filament glowing, the spot was also bigger, maybe this is due to the bigger filament because the thickness of the oxide coating was probably more than necessary. It is hard to deposit a specific quantity with this method because being the carbonate insoluble it deposits at the bottom of the container so it needs constant agitation to remain suspended. Or maybe the bigger spot is due to electrostatic repulsion by the larger number of electrons.
I think that Y oxide can be further enhanced, but it might have some activation process that I couldn't find information about.
And tungsten alone is too bright and degrades too quickly to be operated for long.
I will try to find out more about rare earth coating composition and more importantly, the activation process, and maybe try also using BaO.

[Rich Gorski]

Luca,

You might have some trouble finding that schematic for the flyback transformer with the focus potentiometer by itself. You might have better luck just by googling CRT circuit diagram. It should show the focus pot as part of the schematic. I know they are 100s of Meg ohms and for the larger CRTs (like 29") the focus range is somewhere around 3kV to 8kV. Maybe just purchase the bsc25 and test it yourself. Remember you don't need the transformer part just the high voltage potentiometer. You can also just hook up a string of high value resistors in series say like ten, 15 megohm each and connect it from your -10kV power supply to ground. then you can simply tap off whatever voltage gives you the best focus. You can at least pin it down to within maybe 500 volts. Then build a new divider to go with even finer voltage steps. Of course getting another -10kV low current power supply would make things really simple over fooling around with a divider or high voltage potentiometer.

As far as the cathode problem all I can say is good luck fabricating your own. The only suggestion I have at this point is to find a small piece of Thoriated tungsten wire and fabricate your own filament. The Thorium lowers the work function so you should be able to run it at a lower power level (less brightness) for the same current (all else being equal).

Rich G.

[Rich Gorski]

Luca,

I have my own electron optics simulation package. I was thinking of running a simulation on your Einzel design and looking at using anode#2 as a focus grid. If you could provide me with a few dimensions I'll give it a try and post results.

1. Filament cage: O.D, length and distance from cage end to screen end of anode1.
2. Position of filament w.r.t screen side of Anode1 cylinder
3. Anode1, Anode2, Anode3: I.D. lengths and A1-A2, A2-A3 gap lengths.

That should be sufficient to run a first simulation.

Thanks,
Rich G.

[Luca_Cappelletti]

Thanks, Rich I would really appreciate your simulation, these are the parameters:
the cage OD is 10mm in length 30mm, distance from A1 11mm,
I attached the complete drawing to avoid confusion, there the tungsten filament is represented by the purple box, it is a coil of thin wire, and the coil has an OD of 1mm and an ID of 0.9mm, a length of around 3mm.

Do you think that the low emission current of pure tungsten might be due to the electric field inside the cage? because in the simulator, I need to set the emission distance, but I have no idea of what that parameter really is so I choose to use 1mm, maybe with another dimensioning more electrons can make it out of the cage?
I also tried measuring the current flowing through the circuit but I didn't have much success, this was done by coating the phosphor on a conductor transparent plate (ITO plate) that was electrically disconnected from the vacuum chamber, this plate was connected to the ground through a uA meter but it didn't read any current at all, not if the HV was on, off, or the filament, even if I could clearly see the light emitted from the phosphor, this was the circuit I tried testing:

The cable of the screen was brought out using an insulated feedthrough, I used a thin enameled wire to run the connection between the feedthrough and the screen but I think that the insulation would prevent the current from flowing into the chamber instead of my multimeter so there should be some current.

[Rich Gorski]

Luca,

Two more questions...

1. What is the distance from the least electrode in the gun (anode #3) to the phosphor screen?

2. Is the filament itself near ground or floating near the filament cage voltage ~ -10kV? If floating then you must be using a HV isolation transformer to power it. The answer might explain why your not reading any electron beam current (maybe you don't have a complete circuit ??).

Rich G.

[Luca_Cappelletti]

The distance from Anode 3 to the screen is 190mm,
the filament is at full anode potential, and yes I'm using a high-frequency air-core transformer with a secondary made of 50kV insulating wire that is also connected to the -HV output of the generator.
This is the circuit:

Also maybe do you know if there is a common type of vacuum tube where I can find the thoriated tungsten filament?

[Rich Gorski]

Luca,

Thanks for the dimension information. I have the simulations started and in the process of fine tuning it as best I can to match your setup. Simulating the cathode is a bit of an unknown. I can't simulate a coil so I'm using thermionic emission from a tungsten disk with temperature of 2900K and 4.5 eV work function. That should be good enough to show results.

Everything looks good in your circuit diagram. You should be reading beam current on you microammeter. Somethings to test for.

1. Does the microammeter work?
2. Check connection to the ITO glass plate. Measure resistance between u-ammeter and ITO by touching ITO surface with probe. You should see a low resistance like 50-100 ohms. Just make sure you have a good connection to the ITO. I've used 1/8" wide copper tape to make that connection in the past and also a clamp mechanism.
3. I guess its possible you could still see the phosphor light up with only 100nA of beam current since its DC and at 10KeV. Maybe you just need a more sensitive micro ammeter?

Rich G.

[Rich Gorski]

Luca,
I’ve completed my simulations on the focusing characteristics of your Einzel electron gun design. Specifically I looked at and found the voltage on Anode #2 that will focus the beam at 190 mm in front of the electron gun. That voltage appears to be about -9100 volts. The five simulation plots below show the beam focus changing for A2 = -10000, -9500, -9125, -9000 and -8875 volts. You can see in the plots that the best focus for 190mm is between the -9125 and -9000 volt simulations. As the voltage on A2 goes more negative the potential difference in the lens region increases causing the lens field to strengthen resulting in a shorter focal length.

Based on this, You can design a simple circuit running from your -10kv supply that will provide a variable focus voltage centered around -9100 volts with a +/- range of maybe 500 volts. Just a simple series circuit consisting of something like a 40Mohm high voltage resistor in series with a 5 Mohm pot in series with a 3Mohm resistor. The 40M resistor must be on the ground side, the pot in the middle and the 5M ohm resistor connected to -10kV. The wiper of the pot should have near the potential range described above (please check my math). The pot and resistors will be at high voltage so it must be mounted inside a insulating box and the knob of the pot also should be a long insulating shaft. Also note that the pot will have to handle about 1000 volts. This is just an example of a simple circuit to provide a variable focus voltage centered around -9100V but of course you can design your own. It draws about 200uA from the -10kV power supply (2 Watts). There should be no current collected on the A2 grid as long as no beam is hitting it.

The cathode in the simulation is a 2mm diameter tungsten disk and the current is derived from the Richardson equation based on the electric field in front of the cathode at each mesh point. I have the temperature set at 2700K with a 4.5eV work function. The cathode generated 1.2mA in my simulation. I also noted that at the cathode position of 2mm behind the cage aperture, the surface is very near the edge of the positive electric field. In other words if you pulled the cathode back to 3 or 4mm the electric field would turn negative and the cathode would be cut off (with the cage at -10kV). So, if you wanted to reduce the distance from 2mm to maybe 1mm you might get more current out of the cathode but you are also closer to creating a short to the cage.

Good luck and keep me informed on how things go and if you have any questions.
Rich G.

A2 = -8875V

A2 = -9000V

A2 = -9125V

A2 = -9500V

A2 = -10,000V