  For high-intensity linear accelerators, space-charge halo mechanisms are
largely classified into two families: particle resonances and parametric
instabilities. The dominance between the fourth-order particle resonance and
the envelope instability has been argued and studied. Our studies and previous
literatures indicate the dominance of particle resonances over parametric
instabilities in high-intensity linear accelerators. Any counter evidence has
not been found yet. Also all the studies indicate that parametric instabilities
are unlikely to be observed in actual linear accelerators unless waterbag or KV
beams are generated. We propose a way to overcome the previous design rule to
avoid the zero-current phase advance sigma_o > 90{\deg} for the high-intensity
linac. The interplay is presented of the envelope instability and the
fourth-order parametric instability.
