# Energy required for particle accelerators

1. Jun 18, 2008

### DSR

This one may sound a little naive, but I hope it is not thought inappropriate for this forum. The amount of energy required in an accelerator to speed an electron up to a sizable fraction of the speed of light is in the MeV range and bigger, more modern accelerators may even go up to the TeV range. One MeV, though, is only 1.602 x 10^-13 Joules, so 1 TeV = 1.602 x 10^-7 J. These seem like pretty small energies. Fermilab is about 4 miles around and uses about 50 MegaWatts a month! Why does it take such large, powerful machines to accelerate such light particles?
Thanks.

2. Jun 18, 2008

### ZapperZ

Staff Emeritus
Fermilab doesn't accelerate electrons. That's why. A proton is many, many times heavier than an electron.

Furthermore, one can't just accelerate one electron using an arbitrarily large gradient. A particle accelerator accelerates a LOT of particles, and it has to do it in stages because we have no accelerating structure that can withstand arbitrarily high accelerating gradient without suffering catastrophic breakdown (that's why the ILC is proposed to be about 20 km long!). So one has to talk about "duty cycle". This is in addition to being able to efficiently transfer the power from the RF source right to the accelerating structures themselves.

BTW, for most practical purposes, an electron reaching MeV energy is already considered to be traveling at c. All our particle tracking code that does beam dynamics assume that.

Zz.

3. Jun 19, 2008

### DSR

A proton is about 1000 times the mass of an electron, but the energy involved, even TeV, is still small, one ten millionth of a joule. So is the great power required because so many particles have to be accelerated together? So why can't you just accelerate a small number of particles to reduce the energy requirements?

I can see why you would want a very long round track. The larger it is, the lower the centripetal force has to be to pull the particles in a circle, so the magnets wouldn't need to be as powerful.

I'm not sure what you mean by gradients. Are you talking about the change in acceleration of the particles? Why can't they be accelerated slowly at a constant acceleration?

4. Jun 19, 2008

### ZapperZ

Staff Emeritus
Then you lose luminosity, meaning you won't get that high of a probability of collision. That was the problem with Run 1 of the Tevatron.

Then you'd need an accelerator that is even LONGER and MORE EXPENSIVE. If you're willing to fork the money out for it (the ILC is now estimated to be around \$10 billion for 20 km), I'll build it.

Zz.

5. Jun 19, 2008

### DSR

Another thing, does cyclotron or synchrotron (or whatever it is) radiation limit the energy that a particle can be accelerated to? Or does it just require increasing levels of energy to keep accelerating the particle? Is there a point at which the particle loses more energy from radiation than what can be put in to accelerate it?

6. Jun 19, 2008

### humanino

Just to add a little point I think to make it clear. One eV is the energy an electron aquires when accelerated by one V on one m. Therefore, to accelerate one electron to 1 TeV, you merely need one cavity one meter long with 1000 billion of V. :tongue2:

7. Jun 19, 2008

### humanino

I would say mostly yes, but Zz knows better than me. Here we have two LINACs with recirculating arcs
To know how much a particle will radiate, the relevant quantity is to compare its mass to its energy (and the radius over which you have it turn).

8. Jun 20, 2008

### malawi_glenn

The bigger the radius, the less syncrotron radiation loss. And the smaller the mass, the bigger loss of syncrotron rad.

The advantages of a circular accelerator is that you can use each unit several times, in a linear accelerator you can only use a unit once. The disadvantages od circular acc is sync rad loss.

9. Jun 20, 2008

### HE_Matt

This has absolutely nothing to do with the question.

10. Jun 20, 2008

### ZapperZ

Staff Emeritus
It does when the OP is using the example of electrons and asking why it takes so much power at Fermilab. Furthermore, if you look at accelerators that accelerate protons versus one that accelerate electrons, the latter is a lot more "simpler" to get to the same energy.

Zz.

11. Jun 21, 2008

### malawi_glenn

The limitation are the magnetic field, you see:

p = 0.3*R*B

the radius R is constant in LHC for instance, so when the momentum (energy) of the particle is increased, you need a higher B-field to keep it in same radius.

And the limitations are today the field from the magnets, we can't make arbitrary strong magnets.

And the loss of syncrotron radiation depends on energy of beam and radius, and mass of particle. So one wants to optimize these conditions. At LHC, this is done by choosing the heavy proton, and not the electron. The procentual loss of syncrotron radiation energy per revolution is always less than 100%.

12. Jul 3, 2008

### ghery

Hi:

I have heard that particle accelerators can produce x-rays, how are these X rays different form for example an x-rays produced in Bremsstrahlung, I know that X rays produced in accelerators are more energetic, but what else besides that..?