Nonradiating sources with connections to the adjoint problem

Journal Article · Wed Sep 01 04:00:00 EDT 2004 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.70.037601· OSTI ID:20636612

Marengo, Edwin A; Devaney, Anthony J ^[1]

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1. Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115 (United States)

A general description of localized nonradiating (NR) sources whose generated fields are confined (nonzero only) within the source's support is developed that is applicable to any linear partial differential equation (PDE) including the usual PDEs of wave theory (e.g., the Helmholtz equation and the vector wave equation) as well as other PDEs arising in other disciplines. This description, which holds for both formally self-adjoint and non-self-adjoint linear partial differential operators (PDOs), is derived in the context of both the governing PDE and the corresponding adjoint PDE of the associated adjoint problem. It is shown that a necessary and sufficient condition for a source to be NR is that it obeys an orthogonality relation with respect to any solution in the source's support of the corresponding homogeneous adjoint PDE. For real linear PDOs, this description takes on a more relaxed form where, in addition to the previous necessary and sufficient condition, the obeying of a complementary orthogonality relation with respect to any solution in the source's support of the homogeneous form of the same governing PDE is also both necessary and sufficient for the source to be NR.

• OSTI ID: 20636612
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 3 Vol. 70; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ELECTROMAGNETIC FIELDS
ELECTROMAGNETIC RADIATION
HELMHOLTZ THEOREM
MATHEMATICAL SOLUTIONS
VECTORS
WAVE EQUATIONS