https://doi.org/10.1140/epjc/s10052-023-12304-1
Regular Article - Theoretical Physics
Lorentz force detuning in heterodyne gravitational wave experiments
1
II. Institute for Theoretical Physics, University of Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany
2
Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607, Hamburg, Germany
Received:
5
September
2023
Accepted:
23
November
2023
Published online:
19
December
2023
Heterodyne cavity experiments for gravitational wave (GW) detection experience a rising interest since recent studies showed that they allow to probe the ultra high frequency regime above 
. In this paper, we present a concise theoretical study of the experiment based on ideas from the former MAGO collaboration which already started experiments in turn of the millenium. It extends the former results via deriving an additional term originating from a back-action of the electromagnetic field on the cavity walls, also known as Lorentz Force Detuning. We argue that this term leads to a complex dependence of the signal power 
on the coupling coefficient between the mechanical shell modes and the electromagnetic eigenmodes of the cavity. It turns out that one has to adapt the coupling over the whole parameter space since the optimal value depends on the mechanical mode 
and the GW frequency 
. This result is particularly relevant for the design of future experiments.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
