  The space-charge driven envelope instability can be of great danger in high
intensity accelerators. Linear accelerators were designed to avoid this
instability by keeping the zero current phase advance per lattice period below
90 degrees. In this paper, we report on the acceleration effects on the
instability in a periodic solenoid and radio-frequency (RF) focusing channel
and a periodic quadrupole and RF focusing channel using a three-dimensional
envelope model and self-consistent macroparticle simulations. The simulation
results show that the envelope instability can be mitigated with a reasonable
accelerating gradient in both channels. This suggests that the zero current
phase advance might be above 90 degrees in linear accelerators where the
accelerating gradient is sufficiently high and opens additional freedom of
transverse and longitudinal focusing in the accelerator design.
