# Exploiting time varying B field to employ vacuum acceleratio

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1. Aug 7, 2015

### BiGyElLoWhAt

So I've been wanting to build a particle accelerator for a while, and have kind of been brain storming ideas to make it work. I've been recently trying to figure out how to get the actual acceleration to happen.

I have a few ideas, but the one that I like (assuming it's possible) is using a time varying magnetic field to create a circular electric field. Is it possible to create this without a conductor to house the charges?

Also, what would be a reasonable db/dt to expect to get without emplying superconductors if I use electro magnets? Would it be better to use natural magnets? Perhaps rig up a device that drops natural magnets through the loop. If they are transported far enough away before bringing them back up, then I should be able to get a good amount of inductance going on, assuming charges are the only thing necessary to experience said induction, and not that they lie on a conductor.

Really the only other idea that would be coming to mind would be to use conductive loops wrapped around the vacuum tube (chamber) and switch the voltages on a somewhat periodic basis, but this would have to vary as the (likely) electrons or (hopefully) protons accelerate. I'm not sure how to measure that, or calculate it accurately enough to be able to switch the voltages and keep everything accelerating.

Thoughts? Ideas? Critisisms?
Thanks.

2. Aug 7, 2015

### Staff: Mentor

This is the basic idea of the betatron. Have you read up on those yet?

3. Aug 7, 2015

### DEvens

The Maxwell's equation with time derive of $B$ is $\nabla \times E = - \frac{\partial B}{\partial t}$.

"The voltage accumulated around a closed circuit is proportional to the time rate of change of the magnetic flux it encloses."

So, you can get voltage round a loop. But you cannot keep it there indefinitely. Eventually you reach the extreme of $B$ that you can achieve with whatever equipment you have. Then the $E$ field has to drop off. If you have an oscillating $B$ field of some kind, then you get an oscillating $E$ field. Your charged particles go one way for a while, then turn around and go the other way. Assuming they don't smack into the wall at some point.

Also, if you hope to get the charged particles to follow the circular path, then you need something to curve them into that path. Usually that means a magnetic field perpendicular to the path of travel. Otherwise, the force is going to fling the particles out of the loop. If the magnetic field is varying like crazy, then the radius of the orbits is also.

So you have a real balancing act here. You need to have the $B$ field increasing at exactly the right rate so that it provides exactly enough force to keep the charged particles going around the loop. Possibly you can have some extra "play room" if you have a range of radii that are acceptable, by having a disk shaped area for the particles to go round in. Possibly you can do some balancing of the strength of the $B$ field as a function of radius.

Eventually you reach whatever limit on $B$ your equipment enforces. And then you can't go any faster.

4. Aug 7, 2015

### BiGyElLoWhAt

No I have not. I might have to look into it. Do you think it's feasible from a diy point of view?

That was the whole reason I thought about physically dropping natural magnets through the loop, then moving them to the outside, bringing them back up, and dropping them again.

As far as stabalization goes, from what I've seen it's best to use 4 magnet per group and stabalize 1 axis per group. Using a magnet on opposite sides of the tube will create a net zero B field in the center and a B field around it that when mixed with the moving charge acts as a central force. I'm not really concerned with that. Just slap some magnets around the outside and point the north pole in. Alternate axes for centralization. My main concern is the actual acceleration part of it.

5. Aug 7, 2015

6. Aug 7, 2015

### BiGyElLoWhAt

With regards to the betatron, they're talking about pulsed magnets? It seems to me that the momentum imparted would have a time average of zero, so how does that work?

7. Aug 7, 2015

8. Aug 7, 2015

### Staff: Mentor

Please note that PF's policy is to not allow discussion of the actual construction of such a device because of the potential dangers (vacuum, high voltages, etc.). Discussion of the theory of operation is OK.

9. Aug 8, 2015

Noted.