It is shown that magnetic fields in the Sun and astrophysical accretion disks are of a spatially intermittent nature. The intermittent flux fragments can be found all over the Sun, showing that more than 90% of the flux occurs in strong-field form with strengths of 0.1－0.2 T and sizes of 50－300 km in the photosphere. And the fluctuating magnetic field can be orders of magnitude stronger than the global one in accretion disks. A reconnective annihilation of the magnetic field leads to the formation of magnetic flux loop cells with small scales, followed by the enhanced transverse plasmons occurring in the thin current sheet. The nonlinear interaction between the flux and plasmons results eventually in self-similar collapse, giving rise to more spatially intermittent, collapsing magnetic loop cells. And the self-generated magnetic fields by the transverse plasmons are modulationally unstable, leading to magnetic flux collapse and forming the highly intermittent magnetic flux. Such a magnetic collapsing instabilities are analyzed in both cases of magneto-hydrodyna-mics and kinetic plasma physics, with their applications to solar intermittent flux and anomalous viscosity in astrophysical accretion disks, respectively.