# Circular accelerators vs Linear Accelerators

1. Nov 26, 2008

### barnflakes

Can somebody show me the physics of why it's better to have a circular accelerator than a linear accelerator in terms of size? I know that a linear accelerator needs to be a lot bigger than a circular accelerator to produce the same energy, but I can't think of how to show this using physics equations. If anybody could show me I'd be very grateful.

ps. this is for a presentation I'm writing for A-level students, not for homework.

2. Nov 26, 2008

### vanesch

Staff Emeritus
In a linear accelerator, the particles see the accelerating field only once, and the particles that didn't interact are lost. As such, a linear accelerator will have much lower overall luminosity (each time, you need to produce new particles to be accelerated) and will generally not be able to reach the same energies.

In a circular accelerator, the particles see the accelerating field (in the cavities) each time they turn around, so they can be accelerated step by step. Also, the particles remain in the accelerator for many hours, so you only "use up" those that are genuinly interacting (most don't).

However, for electrons, a circular accelerator causes bremsstrahlung, which makes the beams loose energy again, so from a certain amount of acceleration onward, you will loose as much as you win by the accelerating field. A linear accelerator doesn't have that problem. And for protons, you need very strong magnetic fields to curve the path of the protons, requiring a huge cryogenic system and all that.

3. Nov 26, 2008

### barnflakes

So in theory, a truly massive linear accelerator is better? How big would a linear accelerator need to be to produce the same amount of energy that you would produce in say, the LHC, of 27km radius? I want to include some relevant mathematics, so is there a couple of simply formulas I could show them to give them an idea? (I'm thinking along the lines of F = ma here).

4. Nov 26, 2008

### vanesch

Staff Emeritus
Well, in as much as SLAC is a reference, where you have 50 GeV for 3 km, given that the LHC goes up to 7 TeV, that's more than 100 times more energy, so that would be something of 300 km.

Very rough estimation.

5. Nov 26, 2008

### Rajini

Hi,
Usually building such facilities are complicated..It depends on the particle to be accelerated..for e.g., if you consider electrons...Initially they are accelerated in linac (linear acc.) and then sent to circular storage rings..That means after sending the electrons (may be up to 10 GeV) in to circular rings..these electrons stays/circulates/accelerated in these storage rings for few hours (say ~12 hrs)..after 12 h electrons are again injected!
PS: Storage ring is under ultra high vacuum and electrons are usually accelerated (0.9 of c) using magnets/wigglers/undulators etc..(mainly for producing high intense/brilliance X-ray).

gluck
Rajini

6. Nov 26, 2008