The Diffractive Quantum Limits of Particle Colliders

Abstract

Quantum Mechanics places limits on achievable transverse beam spot sizes of particle accelerators. We estimate this limit for a linear collider to be Δx > \hbar c f/Eδ_0 where f is the final focal length, E the beam energy, and δ_0 the intrinsic transverse Gaussian width of the electron wave-function. δ_0 is determined in the phase space damping rings, and we find δ_0 \approx \sqrt{\hbar c /eB} where B is the typical wiggler magnetic field strength in this system. For the NLC δ_0 = 25 nm, and Δx = 0.06 nm, about two orders of magnitude smaller than the design goal. We can recover a crude estimate of the classical result when we include radiative relaxation effects. We also consider a synchrotron and obtain Δx > \sqrt{\hbar c f/E} = O(1.0) nm. We discuss formulation of quantum beam optics relevant to these issues.