jats:titleAbstract</jats:title> jats:pIn this paper we generalise our previous results (Alford 2020 jats:italicAnn. Inst. Henri Poincare</jats:italic> jats:bold21</jats:bold> 2031–92) 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 jats:italicφ</jats:italic> 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 jats:italicφ</jats:italic> 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 jats:inline-formula jats:tex-math</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:msup mml:mrow <mml:mi class="MJX-tex-calligraphic">I</mml:mi> </mml:mrow> mml:mo+</mml:mo> </mml:msup> mml:mo∪</mml:mo> mml:msup mml:mrow <mml:mi class="MJX-tex-calligraphic">H</mml:mi> </mml:mrow> mml:mo+</mml:mo> </mml:msup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cqgad259aieqn1.gif" xlink:type="simple" /> </jats:inline-formula>. Thus there does not exist a backwards scattering map from finite energy radiation fields on jats:inline-formula jats:tex-math</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:msup mml:mrow <mml:mi class="MJX-tex-calligraphic">I</mml:mi> </mml:mrow> mml:mo+</mml:mo> </mml:msup> mml:mo∪</mml:mo> mml:msup mml:mrow <mml:mi class="MJX-tex-calligraphic">H</mml:mi> </mml:mrow> mml:mo+</mml:mo> </mml:msup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cqgad259aieqn2.gif" xlink:type="simple" /> </jats:inline-formula> to finite energy radiation fields on jats:inline-formula jats:tex-math</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:msup mml:mrow <mml:mi class="MJX-tex-calligraphic">I</mml:mi> </mml:mrow> mml:mo−</mml:mo> </mml:msup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cqgad259aieqn3.gif" xlink:type="simple" /> </jats:inline-formula> for these models. These results will be used to give a treatment of Hawking radiation in a companion paper (Alford 2023 arXiv:2309.03022).</jats:p>