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arXiv · 1909.08506

Rumsey's Reaction Concept Generalized

Ismo V. Lindell·Ari Sihvola
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Abstract

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.

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Ismo V. Lindell, Ari Sihvola. 2019-09-18. Rumsey's Reaction Concept Generalized. https://arxiv.org/abs/1909.08506

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