Autoresonant transition in the presence of noise and self-fields

A sharp threshold on the driving amplitude for transition to adiabatic nonlinear phase-locking (autoresonance) is characteristic of a single, electrostatically trapped particle starting in equilibrium and driven by a chirped frequency perturbation. In the presence of a weak noise or a small temperature ($T$) initial distribution of trapped particles, the threshold develops a width, scaling as $T^{1/2}$. The inclusion of repulsive self-fields makes the width of the autoresonant transition narrower.