Solution of the Electromagnetic Scattering Problem from an Electrically Large Random Dielectric Medium
The time-harmonic electromagnetic scattering problem from a random inhomogeneous dielectric medium (here a turbulent plasma wake created by the atmospheric reentry of a vehicle) is considered. The electronic density of the plasma, that gives rise to its dielectric permittivity, has a fluctuating part εf (r), the variance and correlation function of which are known a priori. Because the electrical dimensions of the wake can be very large, the numerical solution of Maxwell's equations via a full-wave calculation performed with a boundary element and finite element method is prohibitive when statistical quantities such as the mean Radar Cross Section (RCS) and its variance are required, that necessitate a large number of random realizations. To remedy this difficulty, two approximations are considered and illustrated for a 2D scattering problem. First, a Mie series approach is adopted where the medium is discretized with small disks, thus reducing considerably the number of unknowns for a given random realization of εf (r), and a domain decomposition method is proposed to further reduce the complexity of the numerical solution of the corresponding system. Second, the statistical mean and the variance of the RCS are derived in closed-form from the Born approximation and yield accurate results when, as expected, the statistical mean of the relative dielectric permittivity is close to unity and |εf (r)| is small. Conversely, it is shown how these expressions can be used to validate the results obtained with the Mie series approximation. Numerical examples are presented that illustrate the potentialities of these techniques.