Why Magnetic cores contain domains that align with the applied field; once essentially all of them are aligned, the flux density hits the core's saturation level (Bsat) and the core can hold no more flux. Beyond that point the incremental permeability collapses toward that of air, the inductance drops sharply, and current rises much faster than expected. Flux density grows with amp-turns and with applied volt-seconds, so excessive current, too few turns, or too small a core drives an inductor into saturation.
Watch out High frequency is the opposite of the problem: since flux is proportional to applied volts divided by frequency, raising the frequency lowers peak flux, and it is low-frequency or DC-heavy operation that saturates a core. A low-permeability core stores less flux for a given current and so is harder to saturate, and permittivity is a dielectric property that has nothing to do with magnetic cores.
Saturation = too much FLUX (current), not too much frequency. More turns or a bigger core cures it.