[Animats]

Current record for magnets: 45 teslas.

[mkl]

They need enough for 1000km of accelerator though. LHC has 10,000 superconducting magnets for 26.7km (some can temporarily go up to 7.7 Tesla).

[rcxdude]

There's more than just raw strength that goes into making magnets for a collider. It's the combination of strength, uniformity, and enclosed volume which makes things difficult.