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Rumsey's Reaction Concept Generalized

By Ismo Veikko Lindell and Ari Sihvola
Progress In Electromagnetics Research Letters, Vol. 89, 1-6, 2020


The reaction concept, introduced by Rumsey in 1954, describes interaction between time-harmonic electromagnetic sources through the fields radiated by the sources. In the original form the concept was a scalar quantity defined by three-dimensional field and source vectors. In the present paper, the representation is extended to four dimensions applying differential-form formalism. It turns out that, in a coordinate-free form, the reaction concept must actually be a one-form, whose temporal component yields Rumsey's scalar reaction. The spatial one-form component corresponds to a three-dimensional Gibbsian-vector reaction which consists of electromagnetic force terms. The medium is assumed homogeneous and isotropic in this paper.


Ismo Veikko Lindell and Ari Sihvola, "Rumsey's Reaction Concept Generalized," Progress In Electromagnetics Research Letters, Vol. 89, 1-6, 2020.


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