  When a moderately intense, few-picoseconds long laser pulse ionizes gas to
produce an underdense plasma column, a linear relativistic plasma wave or wake
can be excited by the self-modulation instability that may prove useful for
multi-bunch acceleration of externally injected electrons or positrons to high
energies in a short distance. At the same time, due to the anisotropic
temperature distributions of the ionized plasma electrons, the Weibel
instability can self-generate magnetic fields throughout such a plasma on a few
picosecond timescale. In the present paper we first show using simulations that
both these effects do indeed co-exist in space and time in the plasma. Using
our simulations, we make preliminary estimates of the transverse emittance
growth of an externally injected beam due to the Weibel magnetic fields. We
then present results of an experiment that has allowed us to measure the
spatiotemporal evolution of the magnetic fields using an ultrashort
relativistic electron probe beam. Both the topology and the lifetime of the
Weibel instability induced magnetic fields are in reasonable agreement with the
simulations.
