Characterizing Electron Beam w/ CMOS-Camera or Faraday Cup

I want to characterize an electron beam using something like a CMOS-camera or maybe just a Faraday cup.

The electron energy is between 1 and 10 keV and the expected total current around 10 microA for 1 keV electrons.

Essentially I want to see whether the beam diameter is around 1 micrometer (or smaller) or much bigger than that, so I would need a resolution or pixel size around 1 micrometer.

The detector should also be reasonably cheap and should last maybe 100 hours.

Does anybody have a suggestion?

Philip Koeck said:

The detector should also be reasonably cheap and should last maybe 100 hours.
Does anybody have a suggestion?

I expect 10 uA through one square um will be destructive to camera technology.

The problem with any imaging array will be with reducing the exposure time. Most image sensors are passivated by a glass insulated surface. The target will need to be a heavy conductive metal, or secondary emission will cover the surface with charge.

Maybe an optical microscope could observe the fluorescence of a metal target, that had been lightly dusted with a phosphor.

Baluncore said:

I expect 10 uA through one square um will be destructive to camera technology.

The problem with any imaging array will be with reducing the exposure time. Most image sensors are passivated by a glass insulated surface. The target will need to be a heavy conductive metal, or secondary emission will cover the surface with charge.

Maybe an optical microscope could observe the fluorescence of a metal target, that had been lightly dusted with a phosphor.

Yes, that sounds very interesting.
I was thinking of a very thin scintillator (maybe a phosphor on thin carbon or metal film) and then lenses behind it, but imaging the phosphor from above might make more sense.

Maybe, rapidly spin a 'T' shaped rotor with a thin cross wire as the head of the T. As the wire passes through the electron beam, a pulse of beam current will pass through the rotor. The pulse width will be dependent on the wire diameter / ( radius * RPM ), but the rise and fall times will depend on beam diameter / ( radius * RPM ). The ( radius * RPM ) will cancel, so the pulse shape is determined by the ratio of wire to electron beam diameter.

Or you could perhaps make the beam move (maybe wiggle a bit?) and use a stationary wire or circuit trace of known size to do the same measurement. Nice idea.

Maybe you can study the beam diameter using diffraction from an edge. If you have deflection plates so you can deflect the beam, you can move it a known amount using voltages in the order of a millivolt. Could you place a razor blade next to the beam and then observe the diffraction pattern on a fluorescent screen as you deflect the beam into contact with the edge?

I am very skeptical that you can achieve these sizes, The "pros" can barely do this, and they are working with relativistic beams.

You are talking a current density of 10 MA/m2, which will likely damage pretty much any material you use, and running it for 100 hours is 4 TC/m2.

You might get away with a small piece of Lexan and then use a microscope to measure the size of the hole, but I strongly suspect the hole will be larger than the beam.

How do the "pros" measure a beam this small? I think they don't. They measure it where it's bigger.

Vanadium 50 said:

I am very skeptical that you can achieve these sizes, The "pros" can barely do this, and they are working with relativistic beams.

You are talking a current density of 10 MA/m2, which will likely damage pretty much any material you use, and running it for 100 hours is 4 TC/m2.

You might get away with a small piece of Lexan and then use a microscope to measure the size of the hole, but I strongly suspect the hole will be larger than the beam.

How do the "pros" measure a beam this small? I think they don't. They measure it where it's bigger.

Would you say that even a phosphor wouldn't last very long in the direct beam?
Maybe diffraction as suggested by Tech99 would be an option.

It sounds like using a Faraday cup with an aperture or edge in front of it should work too.

Thanks for all the ideas!

First, the sort of current densities you are talking about are close to what you get from lightning. No, you're not there, but you're close. So anything you put in needs to survive a lightning bolt.

Second, what's the emittance of your beam. Lets say you get 1mm-mrad. (No gamma factor because you are non-relativistic). This is very very low by Fermilab or CERN standards. A 1 micron beam means a one radian angular extent, which in turn means you need to achieve this focus in one micron in z.

If your final focus is insanely short - say 10 cm - that requires a beam with an emittance 100,000 x better than the best people in the world, KEK in Japan, can do. I thind this unljely. I think we can help you wirh realstic parameters, but this doesn't look even close to realistic.

Being cagey about the device is also not helping.

Vanadium 50 said:

First, the sort of current densities you are talking about are close to what you get from lightning. No, you're not there, but you're close. So anything you put in needs to survive a lightning bolt.

Second, what's the emittance of your beam. Lets say you get 1mm-mrad. (No gamma factor because you are non-relativistic). This is very very low by Fermilab or CERN standards. A 1 micron beam means a one radian angular extent, which in turn means you need to achieve this focus in one micron in z.

If your final focus is insanely short - say 10 cm - that requires a beam with an emittance 100,000 x better than the best people in the world, KEK in Japan, can do. I thind this unljely. I think we can help you wirh realstic parameters, but this doesn't look even close to realistic.

Being cagey about the device is also not helping.

It's really just an electron gun similar to what's used in an SEM, but with a different purpose. I want to use it as a phase plate in a TEM. The idea is actually published, so it's not secret. You can find it on ResearchGate.

At the moment I'm thinking of using a Tungsten filament which gives a source diameter of about 50 μm, a current density around 5 A/cm², a brightness of 10⁶ A/cm² sr and a total current around 200 μA, all at 100 keV electron energy.
At 1 keV the current should be smaller by a factor 10.

So, if I can demagnify the source by a factor 50 without too much loss of electrons I have what I need.

A LaB6 "filament" might be an alternative since it gives a smaller source diameter (more like 10 to 20 μm).

Vanadium 50 said:

First, the sort of current densities you are talking about are close to what you get from lightning. No, you're not there, but you're close. So anything you put in needs to survive a lightning bolt.

With 1000 V and 10 μA I get a power of 10 mW. I think that's no problem for a Faraday cup, at least as far as I can see from data sheets.

Vanadium 50 said:

Second, what's the emittance of your beam. Lets say you get 1mm-mrad. (No gamma factor because you are non-relativistic). This is very very low by Fermilab or CERN standards. A 1 micron beam means a one radian angular extent, which in turn means you need to achieve this focus in one micron in z.

I don't understand what you write above. What's "1mm-mrad"?
Why do I need to achieve the focus in one micron in z?

Vanadium 50 said:

If your final focus is insanely short - say 10 cm - that requires a beam with an emittance 100,000 x better than the best people in the world, KEK in Japan, can do. I thind this unljely. I think we can help you wirh realstic parameters, but this doesn't look even close to realistic.

The lenses I use have focal lengths in the range of 1 cm and I can use object distances up to 10 or 20 cm.

mm-nR are the units of emittance. Emittance is the size of the beam, expressed in appropriate units. In most circumstances, it can only be increased, or decreased by removing particles.

If I have a lens, I can achieve a tight focus only by increasing the beam divergence. Same with the magnetic equivalent.

I don't think this sort of high intensity, non-diverging, tiny spot sized source you described is going to be possible, And if it is, I don't think anything hit by that beam will do anything but make a hole.

Vanadium 50 said:

mm-nR are the units of emittance. Emittance is the size of the beam, expressed in appropriate units. In most circumstances, it can only be increased, or decreased by removing particles.

If I have a lens, I can achieve a tight focus only by increasing the beam divergence. Same with the magnetic equivalent.

I don't think this sort of high intensity, non-diverging, tiny spot sized source you described is going to be possible

Now I see where the misunderstanding is.
I'm not thinking of a parallel beam of electrons.
It will be quite divergent.
Based on the values for a W-filament (see post 10) I would have a divergence half angle of 0.1° at the source, but if I demagnify to a beam diameter around 1 μm the half angle will increase to 5°, which is rather huge in the context of EM. Maybe the LaB6 would be a better choice.

In EM we use brightness, defined as current per area and solid angle, instead of emittance.
Brightness cannot increase in an optical system, but it can decrease due to loss of electrons and diffraction.
So, just as you point out, the more you focus the more the beam diverges.

Vanadium 50 said:

And if it is, I don't think anything hit by that beam will do anything but make a hole.

A faraday cup is just a hollow metal cylinder attached to ground via an Ampere-meter.
If I'm not misunderstanding the data sheets completely even the smallest ones (e.g. https://www.kimballphysics.com/product/fc-70/) should handle the 10 mW from the beam I'm thinking of.

I know what a Faraday cup is. I also know that a micron-size beam spot is a different thing than a centimeter-sized one.

Vanadium 50 said:

I know what a Faraday cup is. I also know that a micron-size beam spot is a different thing than a centimeter-sized one.

I see your point now. The power density is much too high and the heat isn't conducted away fast enough.
There might be other ways.
Maybe do the measurement before and after the focal point instead of in it.
Maybe a Faraday cup that spins quickly and/or measure during short times only.

I wasn't thinking of 100 h continuous use (maybe that was misleading).
100 h should be the total life time of the device, roughly.

I think I might have a feasible design now, based on the suggestions and caveats I got in this discussion.
A faraday cup that's positioned a few cm behind the focus of the beam, where it has a diameter in the order of millimeters and a spinning disk with a sharp edged slit in it placed in the focus.
A fast readout of the current from the faraday cup will give me both the diameter of the focused beam and the total current.

Vanadium 50 said:

I don't think this sort of high intensity, non-diverging, tiny spot sized source you described is going to be possible, And if it is, I don't think anything hit by that beam will do anything but make a hole.

We've done a few simulations and calculations now, with some interesting and even slightly surprising results.
The first simulation shows that we can focus a 1 keV electron beam with a current of about 10 μA onto a spot of just under 2 μm diameter using an electrostatic lens. Unfortunately we can't refocus it equally well after a second lens, possibly due to a combination of electron repulsion, leading to a larger spread of kinetic energies, and chromatic aberration of the lenses.

Another simulation shows that a copper disk (radius 1 cm, thickness 2 mm) heated by a 10 mW heat source on a circular area of 2 μm diameter in the center of one face of the disk and kept at room temperature at its perimeter doesn't actually heat up very much, not even by 1 K.
We confirmed this result with analytical heat conduction calculations for several geometries that we can treat in one dimension.
This is rather strange since it's also known that the anode of an x-ray source gets destroyed after a while although it's rotating.

Any ideas what's going on?
Are x-ray anodes maybe destroyed by some other effect rather than just heating?

Philip Koeck said:

Are x-ray anodes maybe destroyed by some other effect rather than just heating?

In x-ray tubes, the voltages are often higher than 10kV and the current is greater than 10uA.

With electron-beam machining, the energy of the electron impact generates x-rays, and is sufficient to ionise and vaporise individual atoms, ejecting them from the material. That is different to simply melting a puddle on the surface. The anodes of x-ray tubes are made from heavy metals to reduce the electron beam erosion.

Baluncore said:

In x-ray tubes, the voltages are often higher than 10kV and the current is greater than 10uA.

With electron-beam machining, the energy of the electron impact generates x-rays, and is sufficient to ionise and vaporise individual atoms, ejecting them from the material. That is different to simply melting a puddle on the surface. The anodes of x-ray tubes are made from heavy metals to reduce the electron beam erosion.

Maybe the two things are actually quite comparable.

I'm considering a beam of 1 keV electrons (I wrote 10 keV first by mistake) with a 10 μA current giving a power of 10 mW. This should be focused onto a spot with an area in the order of 1 μm².

An x-ray source has around 100 keV and a current around 1 mA (textbook values, not sure how good they are) giving a power of about 100 W.
If the focus area is around 10 000 μm² then the power density is the same for the two.

Philip Koeck said:

An x-ray source has around 100 keV and a current around 1 mA (textbook values, not sure how good they are) giving a power of about 100 W.
If the focus area is around 10 000 μm2 then the power density is the same for the two.

Your x-ray source numbers are about right.
Cathode ray oscilloscopes use 1.5 kV and burn the inorganic phosphor on the screen.
No semiconductor device will survive that high energy environment.

I prefer hutchphd's extension to electrostatic or magnetic deflection of the beam, to scan across one or more, fixed thin-wire targets, that can analyse the profile of the passing current pulse. There is an opportunity there for feedback and self-sharpening of the beam.