  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.
