Couldn’t we use a Möbius strip design through magnetic fields in a vacuum and magnetic guard rails around both circumferences to make them orientable? It would double the travel surface area meaning up to x times the speeds possible as long as the magnetic fields were maintained unevenly or not on a rigid surface to allow the möbius time to “jiggle” a little until collision while still being held in place by the magnetic fields in play. It also means the cooling would be almost halfed because you could cool a smaller denser area.
First you would need to make the Möbius strip magnetic troughs on both “sides” of the material. Doable by inverting one half against the other in a v shaped pattern. Then you’d need an upper housing to keep the atoms in place so they could be accelerated. What would that be? Another Möbius strip.
I was just basing it on deflection interpretations shown form collisions in the past, they strike out straight, at slight and significant angles and then otherwise curl away.
But if you did build one there would be some trouble building a magnetic trough as it would be a v at first and at ^ where it met itself if done around once, I think—So would it pay to start with two troughs going in separate directions as many times as needed (Minimum 2 opposing lines traveling in opposite directions meeting somewhere along that line [midpoint possible but anywhere achievable if speeds are attainable]) and then converging at a point. For that matter do they accelerate the materials to the same speeds or relative speeds to the masses of the isotopes being intertwined? I realize they would need different accelerations and magnetic field densities.
Now the question becomes can you house a Möbius strip within a housing that allows proper collision. The answer is yes. Just A custom magnetic housing. The other question is, is there a need for a Möbius strip collider? It’s more maths to get the collisions right, but you get twice the distance per round before collision for a similar amount of space.
Also according to google if you search for Möbius strip benefits it seems to say that they last twice as long as a loop because they wear down evenly. Who’s to say that the collision points wouldn’t need retuning after each use but it may minimize the amount of maintenance needed.
Anyway, that’s the basic idea.