  Radio Frequency Knock Out resonant slow extraction is a standard method for
extracting stored particle beams from synchrotrons by transverse excitation.
Classically, the beam is excited with an RF field comprising a frequency band
around one of the betatron sidebands. This article demonstrates that the
third-integer resonance commonly used for the slow extraction induces nonlinear
motion, resulting in the appearance of additional sidebands of higher order at
multiples of the betatron tune. Measured and simulated beam spectra are
presented, revealing these sidebands and the beam's response to being excited
at first and second order sidebands. The feasibility of using a second order
sideband for the purpose of slow extraction is demonstrated. This results in a
significant improvement in the temporal structure (spill quality) of the
extracted beam, but at the cost of higher excitation power requirements. This
is observed both experimentally and in tracking simulations. The mechanism
behind the observed improvement is explained using beam dynamics simulations.
