Autoresonant Transition in the Presence of Noise and Self-Fields

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Abstract
A sharp threshold for resonant capture of an ensemble of trapped particles driven by chirped frequency oscillations is analyzed. It is shown that at small temperatures T, the capture probability versus driving amplitude is a smoothed step function with the step location and width scaling as alpha(3/4) (alpha being the chirp rate) and (alphaT)(1/2), respectively. Strong repulsive self-fields reduce the width of the threshold considerably, as the ensemble forms a localized autoresonant macroparticle.