Lichtenberg Figures in Acrylic

[Kul69]

http://en.wikipedia.org/wiki/Lichtenberg_figure

Modern Lichtenberg Figures can also be created within solid insulating materials, such as acrylic (polymethyl methacrylate or PMMA) or glass by injecting them with a beam of high speed electrons from a linear electron beam accelerator (or Linac, a type of particle accelerator). Inside the Linac, electrons are focused and accelerated to form a beam of high speed particles. Electrons emerging from the accelerator have energies up to 25MeV and are moving an appreciable fraction (95 - 99+ percent) of the speed of light (relativistic velocities). If the electron beam is aimed towards an acrylic specimen, the electrons easily penetrate the surface of the acrylic, rapidly slowing down as they collide with molecules inside the plastic, finally coming to rest deep inside the specimen. Since acrylic is an excellent electrical insulator, these electrons become temporarily trapped within the specimen, forming a plane of excess negative charge. Under continued irradiation, the amount of trapped charge builds, until the effective voltage inside the specimen reaches millions of volts. Once the electrical stress exceeds the dielectric strength of the plastic, some portions suddenly become conductive in a process called dielectric breakdown.

During breakdown, branching tree or fern-like conductive channels rapidly form and propagate through the plastic, allowing the trapped charge to suddenly rush out in a miniature lightning-like flash and bang. Breakdown of a charged specimen may also be manually triggered by poking the plastic with a pointed conductive object to create a point of excessive voltage stress. During the discharge, the powerful electrical sparks leave thousands of branching chains of fractures behind - creating a permanent Lichtenberg figure inside the specimen. Although the internal charge within the specimen is negative, the actual discharge is initiated from the positively charged exterior surfaces of the specimen, so that the resulting discharge actually creates a positive Lichtenberg figure. These rare and beautiful objects are sometimes called electron trees, beam trees, or lightning trees.

I have a question. Does anyone know if it would be possible to create a "home made" 3D Lichtenberg Figure in Acrylic? The only information I've been able to find about making one of these without a multi-million dollar Linac is using a DC Accelerator. However, I can't find any details about the power/cost of building a DC Accelerator capable of making one.

I think these things are beautiful and I'd like to be able to create my own and I'm just wondering if this is something even worth pursuing. I'm not well versed in electrical physics so it's hard for me to envision what it would actually take to make one.

Surely I'll have to learn a lot more and probably invest a few thousand dollars and I'm willing to do that. As of now I can't even begin to understand how I could calculate the power/cost requirement of making small figures. Just a 1"x1" cube would make me happy.

I just want to know if someday years from now I'll be able to make these things in my garage or if I'm living in a fantasy land.


For now I'll just have to create wood Lichtenberg figures using my 15kV 60mA NST (Neon Sign Transformer) but I dream of the day when I can make 3D figures.

So, is anyone out there that understands this shit who can tell me what to expect if I want to make one of these at home?


Oh and here's an awesome video of a 3D Lichtenberg Figure being created/discharged: http://youtube.com/watch?v=FWOst4VwwEU

 

[johnnyb420]

wow that is really cool


i am not sure if you can do that at home but it looks like it would be extremely dangerous


if you could do thatat home for a reasonable cost i bet you could make an absolute fortune selling them at craft fairs and that sort of place

 

[Kul69]

^^ That's what I was thinking

You can buy them online for like $65 for the cube I showed in the picture. Which is much more than it costs to buy a cube of acrylic that size. The reason they have to charge so much more though is because they rent "beam time" from a particle accelerator to create them so that adds a lot to the price.

If it was possible to make them at home the only cost would be the acrylic and the electricity to fire it up. Could make a total killing selling them for like $10-$20. Even if it look a $5,000 investment in parts I don't think I'd have any trouble selling 500 of them for $20 and making all that money back plus a bit of profit after material expenditures are factored in.

The fact that you could make such a tidy profit for like zero work other than building the accelerator makes me think this isn't something you could do at home really or the people who rent beam time to make them would be doing it.

Nothing is impossible with enough effort/money/time though. I'm more than willing to invest the effort and time I just couldn't see spending more than $10,000 building the accelerator.




I found this guy who made a 100kV linear accelerator at home.

http://www.niell.org/linac.html


The lichtenberg figure image in my original post was made using 5MeV (Million electronvolts)

So, I think I've finally figured out the calculation I need to make to see if this is possible but I don't quite know how to make it.

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.

From the wikipedia page on electronvolt...

It is the amount of kinetic energy gained by a single unbound electron when it passes through an electrostatic potential difference of one volt, in vacuo. In other words, it is equal to one volt (1 volt = 1 joule per coulomb) times the (unsigned) charge of a single electron.

Ok, so is it.. volts * charge of single electon = electronvolts?

From another page on charge of electron...

Electrical charge quantity is not usually measured in terms of the charge on a single electron, because this is an extremely small charge. Instead, the standard unit of electrical charge quantity is the coulomb, symbolized by C, representing about 6.24 x 1018 electrons. The electron charge, symbolized by e, is about 1.60 x 10-19 C. The mass of an electron at rest, symbolized me, is approximately 9.11 x 10-31 kilogram (kg). Electrons moving at an appreciable fraction of the speed of light, for example in a particle accelerator, have greater mass because of relativistic effects.

So, these electrons WILL be moving at an "appreciable fraction of the speed of light" does that mean the values for the "charge of a single electron" change with the mass or is it constant?

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?

 

[zorn]

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.

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.
[...]
Ok, so is it.. volts * charge of single electon = electronvolts?

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.)

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?

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.

 

[Infernal]

Do it the old fashioned way....

But seriously, a link you may find interesting.

Link

 

[Kul69]

^^ Yeah I've seen that link... those people are the only ones I can find that do this and they claim to be the only ones they know of as well.

I'm hoping to shake things up a bit by doing this without renting "beam time" which is what they do. They have no info and probably no experience with doing this without the million dollars linacs.

Thank you for the info zorn, that should allow me to go a bit further in figuring out the logistics of this.

 

[Schizzy]

Would it be possible to do this by setting up a lightning rod and attaching a bunch of acrylic sheets to it?

I am thinking this could work, but it would be important to give the right amount of energy in proportion to the size of the acrylic pieces. Of course lightning is unpredictable, but is there any way to build the rod in a way that only a small fraction of the lightning's energy reaches the acrylic?

I've been looking for an excuse to build a Dr. Frankenstein style lab with a lightning rod ever since I was a kid.

 

[Akoto]

As far as I know, lightning is way way too powerful to work with for any practical application. You'd most likely just end up exploding the acrylic cube and your entire house at the same time.