  We show that strong magnetic fields can be generated at shock waves
associated with formation of galaxies or clusters of galaxies by the Weibel
instability, an instability in collisionless plasmas. The estimated strength of
the magnetic field generated through this mechanism is close to the order of
values observed in galaxies or clusters of galaxies at present, which indicates
that strong amplification of magnetic fields after formation of galaxies or
clusters of galaxies is not required. This mechanism could have worked even at
a redshift of ~10, and therefore the generated magnetic fields may have
affected the formation of stars at the early universe. This model will be
confirmed by future observations of nearby clusters of galaxies. In this
context, we also present the Japanese X-ray missions.
