  A relativistic collisionless shock propagating into an unmagnetized medium
leaves behind a strong large-scale magnetic field. This seems to follow from
two assumptions: (i) GRB afterglows are explained by synchrotron emission of a
relativistic shock, (ii) magnetic field can't exist on microscopic scales only,
it would decay by phase space mixing. Assumption (i) is generally accepted
because of an apparent success of the shock synchrotron phenomenological model
of GRB afterglow. Assumption (ii) is confirmed in this work by a
low-dimensional numerical simulation. One may hypothesize that relativistic
shock velocities are not essential for the magnetic field generation, and that
all collisionless shocks propagating into an unmagnetized medium generate
strong large-scale magnetic fields. If this hypothesis is true, the first
cosmical magnetic fields could have been generated in shocks of the first
virialized objects.
