Scattering from inhomogeneous plasma spheres in the collisionless approximation

The scattering of electromagnetic radiation from overdense inhomogeneous plasmas in the collisionless approximation is discussed, with a radially varying plasma sphere used as illustration. It is shown that the electric field is singular at points where the local plasma frequency is equal to the incident frequency. In addition, it is shown that absorption takes place even in this limiting case, which cannot be ignored if the approximation is to be valid.