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