Particle accelerators

Mar 2020
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I've been looking int Large Electron-Positron collider at CERN (an experiment which ended in the year 2000), groups of electron and positrons were accelerated along a circular tunnel so that they collided. Electromagnets were used to keep the particles moving in a circle.

could someone tell me how the strength and direction of the magnetic field would need to be adjusted to:

One: keep a particle traveling in a circle while it is increasing its speed

Two: bend the paths of both positrons and electrons which are traveling in opposite directions in the same tunnel
 

topsquark

Math Team
May 2013
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The Astral plane
I've been looking int Large Electron-Positron collider at CERN (an experiment which ended in the year 2000), groups of electron and positrons were accelerated along a circular tunnel so that they collided. Electromagnets were used to keep the particles moving in a circle.

could someone tell me how the strength and direction of the magnetic field would need to be adjusted to:

One: keep a particle traveling in a circle while it is increasing its speed

Two: bend the paths of both positrons and electrons which are traveling in opposite directions in the same tunnel
It would help if I were more of an experimentalist but let's give it a go.

The radius of curvature of the path of a charged particle in a constant magnetic field is \(\displaystyle r = \dfrac{mv}{qB}\) so the magnetic field must manage to maintain that magnetic field in order for the particle to stay in its orbit in the collider ring. In principle, that's it.

However it's a tad more complicated than that. In order for the particles to speed up the magnetic field is pulsed to give the particle a bit of a kick. In addition there is not just one particle but a whole pack of them in one general location in the ring so the pulsing magnetic field will work on all of them.

However it is more complicated still because we also have the anti-particles (at least in colliders) going around in the opposite direction to deal with.

However it is more complicated than that. There are several such packets circling around at the same time and the magnetic field is adjusted so that only two of these packets, one particle and the other the anti-particle, will be set to collide with each other in the detector. A large number of these packets are smashed together at different intervals to form the whole experiement.

In short, the answer to your question is the radius equation I mentioned above. But it's a rather tricky problem to get all of this set up and working properly.

-Dan
 
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