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You wouldn't have to have a 25mile ring if you had 10 to 20 beams
going around in a big sphere!
Instead of having a giant ring, we would have a giant sphere,
like a giant basketball.
Is there some law of magnets that says you can't have a sphere
collider? We would
get way more power!
||There are two beams because a collision happens
between two particles.
||The aim is not to put a lot of energetic particles in
the general area, it is to maximize the energy of
each collision. The beams cross at an angle close
to head-on, so that the kinetic energies add up.
||(The 25 mile ring is necessary to keep a very fast
beam contained in a circular path using a magnetic
field; Tighter rings would require even stronger
magnets, which we can't make, and i believe more
energy loss from the beam through synchrotron
||An interesting idea with two problems.
First, the reason Particle Accelerators are so massive is because they need a ton of space to accelerate up to relativistic speeds. So your basketball needs to be a few kilometers in diameter at least. Plus, by making the think three-dimensional you have to put separate accelerators on each of your vectors, rather than using a single one for both like we do now.
Second, if the above problems can be solved (and they can, being purely logistical), this device won't actually increase the rate of collision exponentially (only it's cost). Think about it: if two adjacent vectors manage to trigger a collision, the particles will be striking at an acute angle rather than smashing into each other head on. I think you'd be lucky to get a real collision rather than a ricochet out of any two vectors that weren't directly in-line with one another. So really all we've done is build more Accelerators in a needlessly complex fashion, you'd be better served to just start building the normal kind in parallel.
Still, it was an interesting idea, and you should be congratulated for thinking in three dimensions- it's not an easy leap to make for most people.
Oh, and yes: Go LHC.