Inverse-scattering theory for the non-spherically-symmetric three-dimensional plasma wave equation

The three-dimensional inverse problem for the scalar time-domain plasma wave equation is discussed using causality and time-reversal invariance. As shown by Balanis in one dimension and by Morawetz and others in three dimensions, the reconstruction of the potential requires only the discontinuity of the wave front at the characteristic surface. A complete solution that can be made rigorous is given for near-field inverse scattering for smooth compact potentials. Two formal methods for far-field inverse scattering from non-spherically-symmetric potentials are presented.