# Particle Accelerators

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1. Aug 9, 2014

### Vacant

If you have two counter-rotating streams of particles traveling at near luminal velocity then is there effective relative velocity on impact not greater than c? Of course it can't be so why bother having the particles strike a pain-stakingly engineered opposing particle stream than say a brick wall?

Last edited: Aug 9, 2014
2. Aug 9, 2014

### ChrisVer

No it's not greater than c, because the relative velocity in SR is not added in the same way as gallilean.
The reason you use 2 beams, instead of a stationary target, is mainly because you want to achieve greater cm energies... For example the beam of protons in LHC will be able to reach about 7TeV each.... the cm energy then will be around 14TeV. You may not reach greater than c, but you'll reach higher relative velocities than by sending a 7TeV proton beam on a stationary target.

ps- i think this should go to High energy physics threads?

3. Aug 9, 2014

### WannabeNewton

Because we are interested in specific scattering processes $1 + 2 \rightarrow 3 + 4 + 5 + ...$ where the numbers represent particle species. This means we very specifically want particle of species $1$ to scatter off of particle of species $2$ to produce the desired outgoing particles with some probability. It isn't enough to have particle of species $1$ aimed at a wall.

4. Aug 9, 2014

### Orodruin

Staff Emeritus
Historically, there have been several beam-on-target experiments. The perhaps most famous of these being that of Rutherford scattering. However, in particle accelerators, energies are extreme and apart from the reasons already mentioned here, the CoM frame would be moving relative to the detector if you did a beam-on-target experiment at those energies. This would result in most of the resulting particles being collimated in the forward direction of the beam, which makes detection a problem. This is much less of an issue when the CoM system is the same as the lab one and the collision products spread in all directions.

5. Aug 9, 2014

### Staff: Mentor

In the laboratory, the "closing velocity" of the two beams (the rate at which the two beams approach each other in the laboratory) is indeed nearly 2c.

However, when we talk of "relative velocity" we specifically mean "the velocity of one stream as 'viewed' by an observer who is traveling along with the other stream". This is the velocity that cannot exceed c in relativity.

Because of the way relativistic kinematics work out, in a fixed-target setup you have to accelerate the beam to a much higher energy than the two beams in a colliding-beam setup, in order to get the same "bang" per collision (center-of-mass energy).

http://pdg.web.cern.ch/pdg/cpep/more_collide.html

Note particularly the answer to the question at the end of that page.

Last edited: Aug 9, 2014