Particle Collider Sizing

[Bill Phil]

So I was wondering how to find the size of a circular particle collider with a given energy and magnetic field strength.

Of course the main obstacle I've run into is the relativistic aspect of it. 

But nonetheless I would like to get a rough estimate for the necessary size of a collider for a given energy. 

Any help?

[kerbiloid]

Maybe, https://en.wikipedia.org/wiki/Cyclotron

[Guest]

By "circular particle collider" he means a synchrotron (cyclotron is more of a disk). Equations for that are, admittedly, pretty complex. 

[KSK]

Adding to Kerbiloid’s link, this one might help as well:

https://en.m.wikipedia.org/wiki/Synchrotron_radiation

If I remember correctly, energy lost as synchrotron radiation gives you the practical upper limit of how much energy an accelerator of a given radius can impart to the particles it’s accelerating.

It’s maybe stating the obvious (apologies - I don’t know how much background you have here) but the bigger the radius, the lower the radial acceleration on the particles at a given velocity and therefore the less synchrotron radiation emitted. Eventually you get to a point where any energy you’re adding to the particles to accelerate them is just radiated straight back out again.

 

[farmerben]

4 hours ago, Dragon01 said:

 Equations for that are, admittedly, pretty complex. 

Maybe if Bill Phil specified one specific energy, people here could give rough estimates about it.  

 

The magnets at CERN are about 8 T.  But there is another type of magnet that can go up to 45 T.  https://en.wikipedia.org/wiki/Bitter_electromagnet

The energy comes from Electric fields parallel to the particle's velocity.  The reason to have a ring is to cause the particle to fly through the same electric potential thousands of times.  

Laser Wakefield acceleration has taken over for electron boosting.  It is now able to accelerate electrons to over 4 GeV in a few centimeters.  Adapting this technology for positrons may be possible.  For protons and ions the wakefield is not generated in the same way.  Still anything that lets you generate crazy electric fields means you don't need to worry about the strength of your magnets or the size of your ring as much.  

 

[Bill Phil]

8 hours ago, KSK said:

Adding to Kerbiloid’s link, this one might help as well:

https://en.m.wikipedia.org/wiki/Synchrotron_radiation

If I remember correctly, energy lost as synchrotron radiation gives you the practical upper limit of how much energy an accelerator of a given radius can impart to the particles it’s accelerating.

It’s maybe stating the obvious (apologies - I don’t know how much background you have here) but the bigger the radius, the lower the radial acceleration on the particles at a given velocity and therefore the less synchrotron radiation emitted. Eventually you get to a point where any energy you’re adding to the particles to accelerate them is just radiated straight back out again.

 

That is a concern however it is mostly a problem for electron/positron colliders due to the low mass of the particles. This is part of why a muon collider would be of great interest.

The bigger issue for proton colliders is beam rigidity at higher energies - you need really strong magnets to turn the beam at higher energies or a huge radius. Maybe even both.

[Guest]

1 hour ago, Bill Phil said:

That is a concern however it is mostly a problem for electron/positron colliders due to the low mass of the particles.

This is also why some of the recent large-scale electron/positron colliders were liniacs. They sidestep that problem altogether (though they have their own).

[Rakaydos]

On ‎11‎/‎6‎/‎2019 at 10:41 AM, farmerben said:

Maybe if Bill Phil specified one specific energy, people here could give rough estimates about it.  

 

The magnets at CERN are about 8 T.  But there is another type of magnet that can go up to 45 T.  https://en.wikipedia.org/wiki/Bitter_electromagnet

The energy comes from Electric fields parallel to the particle's velocity.  The reason to have a ring is to cause the particle to fly through the same electric potential thousands of times.  

Laser Wakefield acceleration has taken over for electron boosting.  It is now able to accelerate electrons to over 4 GeV in a few centimeters.  Adapting this technology for positrons may be possible.  For protons and ions the wakefield is not generated in the same way.  Still anything that lets you generate crazy electric fields means you don't need to worry about the strength of your magnets or the size of your ring as much.  

 

There was a talk about "linier partical accelerator around the circumference of the moon", that offhandedly mentioned that, if we REALLY wanted to, a particle accelerator around the track of Neptune's orbit would be able to reach Plank Energy.