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What prevents us from building super-high intensity accelerators? The answeris case-specific, but it often points to one of the following phenomena:machine resonances, various tune shifts (and spreads), and instabilities. Thesethree phenomena are interdependent in all present machines. In this paper wepropose a path toward alleviating these phenomena by making acceleratorsnonlinear. This idea is not new: Orlov (1963) and McMillan (1967) have proposedinitial ideas on nonlinear focusing systems for accelerators. However,practical implementations of such ideas proved elusive, until recently.

Nonlinear optics as a path to high-intensity circular machines