https://doi.org/10.1140/epjp/s13360-022-03290-6
Regular Article
The generalization of Rumsey's reaction concept
1
Institute of Electrical Engineering, Chinese Academy of Sciences, 100190, Beijing, China
2
School of Electronic Electrical and Communication Engineering, University of Chinese Academy of Sciences, 101499, Beijing, China
3
Institute of Electrical Engineering and Advanced Electromagnetic Drive Technology, Qilu Zhongke, 250102, Jinan, China
Received:
11
July
2022
Accepted:
15
September
2022
Published online:
24
September
2022
The concept of reaction was proposed by Rumsey in 1954. The interaction relationship between two complementary sets of time harmonic electromagnetic systems was described by the Rumsey’s reaction. Rumsey explained the reaction of the density of electromagnetic power and the electric field force, but the latter term is not discussed in depth. In 2020, Lindell et al. expanded the Rumsey’s reaction in differential geometry form. The reaction expanded by Lindell includes two items, of which the item of space is the traditional Rumsey’s reaction, which represents the reaction of electromagnetic power density, and the item of time is the reaction of electromagnetic force density. In this paper, the quaternion electromagnetic reaction by the quaternion theory was derived, which further extended the Rumsey’s reaction. The proposed quaternion electromagnetic reaction contains four terms, which correspond to the four reciprocity theorems that have been proposed, namely Lorentz reciprocity theorem, Feld–Tai reciprocity theorem, and two groups of momentum reciprocity theorems. Among them, the imaginary scalar and real vector parts are Lindell reaction, corresponding to Lorentz reciprocity theorem and momentum reciprocity theorem, while the extended terms of this paper are the real scalar part and imaginary vector part, which correspond to Feld–Tai reciprocity theorem and another momentum reciprocity theorem.
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