Hi Kul,
Unfortunately I'm not sure how much luck you will have. It really depends on the level of energy and luminosity you need. It's not too hard to set up a simple DC linear accelerator -- basically, you just get a high voltage power supply, put a voltage across two plates/electrodes with a vacuum in between, and let electrons get ripped off one plate and accelerated towards the other. Of course it's not
easy, but it is apparently something you can build at home if you are really dedicated.
The problem is this doesn't easily scale up. It's difficult to get electrons accelerator to large (several MeV) voltages this way. The Tevatron at Fermilab -- the world's top accelerator, at least until next year -- has as its first stage a simple electrostatic linear accelerator that runs at about 1 MeV. But the thing takes up an entire (very large) room and God only knows how much it cost. Of course it produces an obscene amount of electrons; you certainly don't need anything close to that many.
For higher-energy acceleration what's generally used are oscillating electromagnetic fields. Now, normally an oscillating electric field will just push a charged particle back and forth, back and forth. However, if you divide up the particles into bunches, and set up a sequence of oscillating electric fields timed so that each bunch passes through them at exactly the right time, then you can get it so that each field gives the particle a forward kick (by the time the field reveres the bunch has already passed through it, and the next one won't arrive until the field points forward again.) It's the same way you can speed up someone on a swing if you push them at exactly the right time. Or -- a better analogy -- the same way a surfer gets pushed forward by an ocean wave.
But I don't think an accelerator like this is going to be buildable at home for a reasonable cost. There's too much in the way of power supplies, waveguides, klystrons, etc. required; and more importantly everything has to be tuned properly to work. It's that second part that I suspect would make it difficult and expensive. Medical linacs typically run at ~10 MeV or so; I believe they cost on the order of $1,000,000.
So the question is how high-energy and high-luminosity can you get with a simple home-built linac? And how high do you need to make this patterns? I'm not sure.
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Originally Posted by Kul69
How can I determine the electronvolt potential of a beam? I'm assuming there is some simple calculation I can do based on the amount of energy pushing the beam.
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Ok, so is it.. volts * charge of single electon = electronvolts?
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Yup, that's right. For a DC accelerator it's very simple. Basically the voltage difference you accelerate across is the energy of your beam in eV.
Charge is invariant: the charge of an electron (or anything else!) does not change with velocity, ever.
(As a matter of fact, it's not really a good idea to say that mass changes either. What happens is that when particles move with relativistic speeds, they do become harder to accelerate. So one way to think of this is that their mass is increasing, since acceleration=force/mass. *But,* relativistic particles are much harder to accelerate along their direction of motion than perpendicular to it. So if you want to think of mass as changing with faster motion, you have to let there be two different masses for the same particle, one that applies when you accelerate it along its direction of motion (speeding it up/slowing it down) and one that applies when you try and turn it. That's very odd.)
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If it's constant than I just need to do volts * charge of electron = electronvolts and I know that 5MeV is enough to make these, right? So, I have a number of volts that will work.. but then how do I calculate the minimum number of volts that will work?
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You'd need to know a bit about the process involved and about the acrylic material you have. I'd guess that you just need enough energy for the electrons to penetrate throughout the acrylic.
If that's true, what you'd need to do is calculate the penetration depth (as a function of energy) for electrons in acrylic. You need it to be around the thickness of the acrylic you want to use. To calculate it, you'll want to first look up the
absorption cross-section for electrons in acrylic. You can typically find graphs of these as a function of energy. Using this and the density of acrylic, it's not hard to calculate the average distance an electron of some energy will travel through acrylic.
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