Accelerator size and probe scale relationship?

[C10]

Wondering if anyone has developed a scaling heuristic for the relationship between size of accelerator and smallest size that can be probed with it. With so many data points, something ought to emerge, perhaps a modified power law. Adding a time axis could make a Moore's "law" projection for performance and cost. Also perhaps define a wall more closely related to what a society might ever hope to achieve in this area of research more realistic than the "ring as big as a galaxy" extreme.

It might be interesting as a teaching tool in a few ways. One is to show connections between complexity and cost of real engineering and construction, and the subtlety of what are (in a sense) the intellectual constructs to which the tools are applied. Another is to show in a richer way why it is difficult - and how difficult it is - to observe just the next level down from wherever we are, let alone the "bottom" (if there is one). It might also provide some nice Fermi problems.

I am especially interested in how pre-exponential or power-law factors change with advancing technology in electron, nucleon and heavy-ion accelerators. Do the major leaps in effectiveness from linac to synchrotron to wake-field and beyond represent a progression that is itself more or less linear, rapidly increasing, or (ugh) asymptotic when viewed through this lens?

Thanks-

C10

 

[mfb]

For constant magnetic field strength (proton synchrotrons) or constant acceleration gradient (linear accelerators), energy is proportional to the size of the accelerator, and "smallest size" is proportional to inverse energy.

Technological advantage increases both the possible magnetic field strength and the acceleration gradient, which gives some additional improvement.

For electron/positron synchrotrons, the scaling is bad - LEP will probably stay the largest one ever constructed, linear accelerators are better for higher energy.

Plasma accelerators could improve the acceleration gradient (and therefore the energy) by about 3 orders of magnitude, if the current issues with them can be solved.