  Generation of wake fields by a short electromagnetic pulse in a plasma with
an inhomogeneous background magnetic field and density profile is considered,
and a wave equation is derived. Transmission and reflection coefficients are
calculated in a medium with sharp discontinuities. Particular attention is
focused on examples where the longitudinal part of the electromagnetic field is
amplified for the transmitted wave. Furthermore, it is noted that the wake
field can propagate out of the plasma and thereby provide information about the
electron density profile. A method for reconstructing the background density
profile from a measured wake field spectrum is proposed and a numerical example
is given.
