  We study the onset of electron heating in intense laser-solid interactions
and its impact on the spectral quality of radiation pressure accelerated ions
in both hole boring and light sail regimes. Two- and three-dimensional
particle-in-cell (PIC) simulations are performed over a wide range of laser and
target parameters and reveal how the pulse duration, profile, polarization, and
target surface stability control the electron heating, the dominant ion
acceleration mechanisms, and the ion spectra. We find that the onset of strong
electron heating is associated with the growth of the Rayleigh-Taylor-like
instability at the front surface and must be controlled to produce high-quality
ion beams, even when circularly polarized lasers are employed. We define a
threshold condition for the maximum duration of the laser pulse that allows
mitigation of electron heating and radiation pressure acceleration of narrow
energy spread ion beams. The model is validated by three-dimensional PIC
simulations, and the few experimental studies that reported low energy spread
radiation pressure accelerated ion beams appear to meet the derived criteria.
The understanding provided by our work will be important in guiding future
experimental developments, for example for the ultrashort laser pulses becoming
available at state-of-the-art laser facilities, for which we predict that
proton beams with ~150 - 250 MeV, ~30% energy spread, and a total
laser-to-proton conversion efficiency of ~20% can be produced.
