Nonlinear optics as a path to high-intensity circular machines
  What prevents us from building super-high intensity accelerators? The answer is case-specific, but it often points to one of the following phenomena: machine resonances, various tune shifts (and spreads), and instabilities. These three phenomena are interdependent in all present machines. In this paper we propose a path toward alleviating these phenomena by making accelerators nonlinear. This idea is not new: Orlov (1963) and McMillan (1967) have proposed initial ideas on nonlinear focusing systems for accelerators. However, practical implementations of such ideas proved elusive, until recently. 
Sergei Nagaitsev, A. Valishev (Fermilab), V. Danilov (SNS Project, Oak   Ridge)
physics.acc-ph