The Role of Structured Magnetic Fields on Constraining Properties of
  Transient Sources of Ultra-high-energy Cosmic Rays
  We study how the properties of transient sources of ultra-high-energy cosmic
rays (UHECRs) can be accessed by exploiting UHECR experiments, taking into
account the propagation of UHECRs in magnetic structures which the sources are
embedded in, i.e., clusters of galaxies and filamentary structures. Adopting
simplified analytical models, we demonstrate that the structured extragalactic
magnetic fields (EGMFs) play crucial roles in unveiling the properties of the
transient sources. These EGMFs unavoidably cause significant delay in the
arrival time of UHECRs as well as the Galactic magnetic field, even if the
strength of magnetic fields in voids is zero. Then, we show that, given good
knowledge on the structured EGMFs, UHECR observations with high statistics
above $10^{20}$ eV allow us to constrain the generation rate of transient UHECR
sources and their energy input per burst, which can be compared with the rates
and energy release of known astrophysical phenomena. We also demonstrate that
identifying the energy dependence of the apparent number density of UHECR
sources at the highest energies is crucial as a clue to such transient sources.
Future UHECR experiments with extremely large exposure are required to reveal
the nature of transient UHECR sources.
