Something bigger than Neptune orbit.
We are ~12 orders of magnitude away from the grand unification energy.
https://www.nature.com/articles/d41586-019-01869-1
And you eventually run into rather fundamental problems of tearing your atoms apart with the magnetic field you create. But I am not up to speed on how close we actually are to these limits.
[0]: https://iopscience.iop.org/article/10.1088/1367-2630/ac4921/...
If you build something in a vacuum then you don’t necessarily need a single continuous piece to create a vacuum. If you specced an accelerator a million miles in diameter, the diameter matters from a standpoint of whether we can accelerate the particle sideways fast enough to keep it in the track, but they are also saying they need 3.1 million miles of accelerator hardware. They are implying they can’t lay it out as a crazy straw, but is that because of the lateral acceleration, the interaction between the coils, or the limits of manufacturing?
What if you built a collider in a spherical arrangement, accelerating in three dimensions at once, but 1/3 the diameter? What if the accelerator were broken into sections to dodge asteroids, with a cumulative segment length that added up to the desired total? What if you laid it out like a Spirograph? What if you laid it out like a truncated Spirograph (just bits of the outer circumference)? What if you laid it out like a 3 dimensional truncated Spirograph?