  As an extension of previous theoretical study on the coherent structure
resonance due to space charge effects [Chao Li and R. A. Jameson, Phys. Rev.
Accel. Beams 21, 024204, 2018], this paper aims to demonstrate how the beam, as
a whole, is spontaneously affected when the predicted mixed coherent 2nd/4th
order structure resonance stop band around $90^{\circ}$ phase advance is
crossed. The beam characteristics during the structure resonance crossing, such
as the rms emittance growth and the appearance of 2-fold/4-fold structure in
phase space, are well explained by the mixture characteristic of different
orders of structure resonance. The related `attracting' and `repulsive' effects
in the structure resonance stop band from below and above crossing are
considered as a natural beam reaction to the coherent structure resonance that
the beam spontaneously moves to a structure resonance free region then the
space charge takes a weaker importance. In the PIC simulation, it is found that
the emittance growth is positively related to the time that the beam spends
inside the structure resonance stop band. As a potential candidate mechanism,
the incoherent particle-core resonance also has been checked. It is found that
this incoherent resonance has basic difficulties in explaining the results
obtained from the self-consistent PIC simulation. The incoherent particle-core
resonance might lead to phase space distortion, emittance growth, or beam halo
formation only on a long-time scale. This clarity of the discrepancies between
coherent and incoherent resonance mechanisms will lead to a better
understanding of the numerical study and experimental researches obtained
recently. In addition, similar understanding can be extended to the study of
higher order structure resonance.
