  We study smooth, global-in-time solutions of the relativistic Vlasov-Maxwell
system that possess arbitrarily large charge densities and electric fields. In
particular, we construct spherically symmetric solutions that describe a thin
shell of equally charged particles concentrating arbitrarily close to the
origin and which give rise to charge densities and electric fields as large as
one desires at some finite time. We show that these solutions exist even for
arbitrarily small initial data or any desired mass. In the latter case, the
time at which solutions concentrate can also be made arbitrarily large.
