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Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

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## FREE-SPACE RELATIVISTIC LOW-FREQUENCY SCATTERING BY MOVING OBJECTSBy D. Censor
Abstract:
The present study brings together two aspects of electromagnetic theory: the recently discussed low-frequency series expansions based on the concept of Consistent Maxwell Systems, and Einstein's Relativistic Electrodynamics. Combined, this facilitates the analysis of pertinent low-frequency scattering problems involving objects moving with arbitrary constant velocities in free space. The low-frequency series expansions start with leading terms that are prescribed by solutions of the vector Laplace equation, thus significantly simplifying the conventional analysis in terms of the Helmholtz wave equation. The method is demonstrated by deriving relativistically exact explicit results leading terms for perfectly conducting circular-cylindrical and spherical scatterers. The results apply to arbitrary reference frames where the objects are observed in motion. For simplicity of notation expressions are given in terms of spatiotemporal coordinates native to the object's restframe. Subsequent substitution of the Lorentz transformation for the coordinates is then a straightforward matter. Previous exact relativistic results for scattering by moving objects have demonstrated the existence of velocity induced mode coupling. It is shown that the low-frequency expansions used here display the same effects for various orders of the partial fields appearing in the series.
2. Van Bladel, J., 3. Venkov, G., M. W. McCall, and D. censor, "The theory of lowfrequency wave physics revisited," 4. Censor, D., "Application-oriented relativistic electrodynamics (2)," 5. Stratton, J. A., 6. Sommerfeld, A., 7. Censor, D., "The mathematical elements of relativistic free-space scattering," 8. Twersky, V., 9. Twersky, V., "Multiple scattering by arbitrary configurations in three dimensions," 10. Twersky, "V. Multiple scattering of electromagnetic waves by arbitrary configurations," 11. Morse, P. M. and H. Feshbach, 12. Stevenson, A. F., "Solution of electromagnetic scattering problems as power series in the ratio (dimension of scatterer/wavelength)," 13. Werner, P., "On the exterior boundary value problem of perfect reflection from stationary electromagneitc wave fields," 14. Asvestas, J. S. and R. E. Kleinman, "Low-frequency scattering by perfectly conducting obstacles," 15. Dassios, G. and R. Kleinman, 16. Censor, D., I. Arnaoudov, and G. Venkov, "Differential-operators for circular and elliptical wave-functions in free-space relativistic scattering," 17. Censor, D., "Broadband spatiotemporal differential-operator representations for velocity-dependent scattering," 18. Censor, D., "Scattering in velocity dependent systems," |

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