  In this paper we generalise our previous results [1] concerning scattering on
the exterior of collapsing dust clouds to the charged case, including in
particular the extremal case. We analyse the energy boundedness of solutions
$\phi$ to the wave equation on the exterior of collapsing spherically symmetric
charged matter clouds. We then proceed to define the scattering map on this
spacetime, and look at the implications of our boundedness results on this map.
  More specifically, we first construct a class of spherically symmetric
charged collapsing matter cloud exteriors, and then consider solutions to the
wave equation with Dirichlet (reflective) boundary conditions on the surface of
these clouds. We then show that the energy of $\phi$ remains uniformly bounded
going forwards or backwards in time, and that the scattering map is bounded
going forwards but not backwards. Therefore, the scattering map is not
surjective onto the space of finite energy on $\mathcal{I}^+\cup\mathcal{H}^+$.
Thus there does not exist a backwards scattering map from finite energy
radiation fields on $\mathcal{I}^+\cup\mathcal{H}^+$ to finite energy radiation
fields on $\mathcal{I}^-$ for these models.
  These results will be used to give a treatment of Hawking radiation in a
companion paper [2].
