Electromagnetic Gravitational Waves Antennas for Directional Emission and Reception
Andr ́e Fu ̈zfa∗
Namur Institute for Complex Systems (naXys),
University of Namur, Belgium November 26, 2018
A successful experiment combining emission and reception of gravitational waves (GWs) would constitute a premiere of gravity control. However, such experiments manipulating gravity would require to compactly store large amounts of energy while using ultra-sensitive detection techniques and hence can be expected to be very difficult to realise. In this paper, we first propose new designs of electromagnetic (EM) generators allowing directional emission of GWs. They are based on the resonant amplification of GWs occuring when EM standing waves couple to an external static magnetic field. The interplay between the EM polarizations, the orientation of the boosting magnetic field and the emitted GW polarizations is studied, as well as the gravitational radiation patterns of the different generators. Then, we develop a new GW directional detection method based on magnetic energy storage. Three possible applications are presented: (i) indirect detection of GW emission by high-accuracy monitoring of the energy loss in the generators ; (ii) direct detection of an incoming plane GW with a high-field magnet and (iii) GW emission-reception experiments. Although current technology allows reaching detection thresholds in these experiments, their practical realisation would still need to over-come several key technical challenges.
Out of the four fundamental interactions, gravitation remains the only one not to be under technological control. This puts limitations on experimental gravity: while we passively explore the permanent natural gravitational fields generated by inertial masses, we do not attempt to artificially bend spacetime at will in our laboratories. Actually, generating gravitational fields does not belong to science-fiction: it is a natural possibility offered by Einstein’s Equivalence Principle. The universality of free fall teaches us that all types of energy, asso- ciated to any of the four fundamental forces, undergo an external gravitational field in the same way. But this also implies that all types of energies produce gravity in the same way. Since we cannot switch off the binding energies of matter (inertial) sources, one should rely on electromagnetic (EM) energies as a source of human-made controllable gravitational fields. Controlling gravity, in an experimental sense, requires not only to generate, but also to detect, artificial gravitational fields.<page1image508115808.png>
The problem of gravity control through the use of EM fields has been considered for decades. While Weber  envisioned the importance of both the generation and detection of gravitational waves (GWs) as early as 1960, Gertsenshtein  discovered in 1962 a wave resonance mechanism allowing to produce GWs from light waves passing through a region of static magnetic field. A decade later, this mechanism has been applied to astrophysics by Zeldovich . Grishchuk and Sazhin then introduced in [4, 5] purely electromagnetic generators of GWs, using transverse magnetic/electric (TM/TE) resonant cavities. Their motiva- tion was also to conduct GW emission-reception laboratory experiments and they concluded they could be feasible experimentally in , considering this as the first necessary step for any future technological application of GW physics . Resonant cavities and EM waveguides were then considered as possible de- tectors of gravitational radiation emitted either by natural or artificial sources [7, 8, 5, 6, 9, 10, 11].
However, due to the faintness of the emission of GWs by foreseeable ex- perimental devices, the strategy to develop GW physics was to use the much stronger astrophysical sources and to attempt detecting them in ground-based specific facilities. But this also meant to postpone the challenge of gravity con- trol with the joint emission and reception of GWs. After decades of widespread effort, this astrophysical strategy has led to the direct measurement (and not mere detection) of the final stage of binary black hole mergers by the LIGO and Virgo collaborations in 2015 .
Detection of astrophysical GWs with laser interferometers such as LIGO allows exploring rather low frequency ranges (typically less than 1 − 10kHz). Electromagnetic detectors of GWs would allow exploring higher frequency range, typically from kHz to 100GHz when using radio-frequencies or from 100GHz to THz when using microwaves. However, there are few expected astrophysical sources above several kHz (cf. ). Yet investigation on electromagnetic de- tectors of GWs started in the 1970’s with the works [7, 8, 5, 14, 9, 10, 16]. Those detectors either make use of the conversion of GWs to photons , the excitation or modification of resonant modes of EM cavities and waveguides in [7, 8, 5, 9, 10, 15], the change of polarization plane of an EM wave due to the passing GWs , or induced birefringence of the interior of the cavity .
Nowadays, GWs emitted from natural sources have been directly detected and with such an accuracy that these messengers can be used to study the Uni- verse in an unprecedented way. However, the emission and reception of GWs in laboratory or for technological applications still remains a great challenge.
Indeed, generating GWs by using oscillating electric fields in a resonant cavity in previous works [4, 5, 17] will produce an amplitude of only 10−44 for an electric field of amplitude 1MV/m in a volume of 1m3. Although we consider here other designs improving this amplitude by three orders of magnitude, this is still about twenty orders of magnitude below the amplitude of GWs from astro- physical sources that are currently detected with laser interferometers. However, GWs from astrophysical sources do arrive at a random rate and, for stellar black hole mergers, on timescales of a few hundred milliseconds. At the opposite, the GWs emitted from EM generators provide a reliable continuous flux of GWs. Different strategies of detection can therefore be developed for the weaker elec- tromagnetically generated GWs to make the most of their stable incoming flux.
The pioneering works [4, 5, 17] on emission and reception of GWs by EM means considered only resonant cavities for both the generation and the detection. Those works finally came up considering a hollow (TM/TE) toroidal microwave cavity , possibly filled with some dielectric material , but their analytical computations were limited to the immediate vicinity of the torus center where standing GWs appear. Detection of the generated GWs was also considered in [5, 6] by placing a hollow cylindrical cavity on the symmetry axis of the gener- ator to try catching the standing GWs through mode excitation in the cavity.
In the present paper, we propose new designs and methods, all based on EM technology, for both the directional emission and reception of GWs as well as three possible applications to GW physics laboratory experiments.
First, we propose to boost the emission of GWs by the use of an external uni- form magnetic field. Indeed, we will show in this paper that, by appropriately orienting the resonant cavity or waveguide carrying an electric field E0 into an external magnetic field B0, specific polarizations of the emitted GW reach an amplitude of order (4GB0E0L2)/(c5μ0), which can be well above the amplitude generated by the cavity or waveguide alone, which is of order (4GE02L2)/(c6μ0) for large external magnetic field (B0 > 10−2T). We also present concepts of GW generators based either on transverse electromagnetic (TEM) waveguides or TM/TE resonant cavities. In addition, while the works [5, 6, 17] limited their analysis of the wave profile in the immediate vicinity of the origin of coordinates, we will also present numerical solutions showing the anisotropy and directional propagation of the GW emission in space for the different polarizations of the gravitational radiation, in relation with the properties of the EM generator (rel- ative orientation of the magnetic field and cavity geometry).
Then, we introduce a new detection method based on a magnetic energy storage device whose energy variation is of order of the GW amplitude h while in [5, 6] the authors considered the energy variation of a resonant cavity which is of order h2. Finally, we consider three possible applications of our results to (i) indirect detection of GW emission from an EM generator ; (ii) directional detection of incoming GW with magnetic energy storage and (iii) GW emission-reception experiments - the equivalent of Hertz experiment for gravity. We show how detection threshold can be reached with current technology while discussing in a non-exhaustive way some expected technical challenges.
The structure of this paper is as follows. In Section II, we model three new types of electromagnetic directional GW antennas, emphasizing notably the interplay between the various EM and GW polarizations at work in the process as well as illustrating the propagation of the generated GWs. In section III, we develop a directional detection method of GWs using intense magnetic fields. Section IV is devoted to three experimental concepts presented as possible ap- plications of the previous results to the development of GW physics in the lab. We finally conclude with some discussions and perspectives in section V.
Controlling gravity, for instance through producing then detecting artificially generated gravitational waves, does not require any new physics nor technology. Indeed, it is in principle achievable within standard general relativity, notably through the Gertsenshtein-Zeldovich effect, and the use of high-field magnets surrounding electromagnetic waveguides and resonant cavities.
However, gravitation is an extremely weak interaction compared to electro- magnetism and nuclear forces. In fact, generating gravitational fields requires to store large amounts of energy on a short scale. Indeed, the amplitude h of the GWs generated from EM devices is of order of magnitude of the following dimensionless constant:
with G the Newton constant, c the speed of light, L the characteristic size of the generator and EEM the total amount of EM energy stored in the GW generator. This dimensionless quantity is analogous to the compactness s = GM/(c2R) of a compact object of size R filled with inertial mass M. This argument Eq.(36) gives a nice interpretation of the Gertsenshtein-Zeldovich number Eq.(7) in terms of EM compactness. Since our technology presently cannot compactly store energy as efficiently as nature does in self-gravitating objects, we are only able to produce tiny gravitational fields and detecting them is a challenge for high-precision physics.
The present paper has examined this question of manipulating gravitational fields in the lab through the introduction of three new improved designs of EM generators of GWs. We have also examined in details the interplay of the EM and GW polarizations in the emission process and the directional propagation of the emitted GWs. We have also developed a new method for directional reception of GW using intense magnetic fields and magnetic energy storage. We have proposed three possible applications under the form of experimental concepts for the development of GW physics in the laboratory. First, one could build an experiment aiming at detecting indirectly the emission of GWs through the cumulated energy loss in the generator. The detection threshold seems to be reachable since it is of the same order of magnitude as the sensitivity of axion dark matter searches , developed in a similar experimental scheme. Second, we show how a magnetic energy storage system can be used as a directional detector of GW coming from outer space, which could be realised with the promising technology of superconducting magnetic energy storage . Finally, we have applied these results to the controlled emission and reception of GWs, a gravitational counterpart of the Hertz experiment for electromagnetism already present in [1, 5, 6, 28]. We showed that the detection threshold can be reached, although with large and very sensitive experimental set-ups and with expected challenging technical difficulties.
Finally, we claim that such gravity control experiments, through the laboratory production of gravitational fields from pure electromagnetic sources, will consti- tute a unique test of the equivalence principle. Indeed, this involves relativistic sources in the weak gravitational field limit while other tests of the equivalence principle mostly involve (i) non-relativistic sources (inertial masses), (ii) composite systems made of different types of binding energies (chemical, nuclear, electromagnetic, gravitational, etc.) and (iii) permanent gravitational fields due to some inertial mass. Implementing gravity experiments as is envisioned here will offer a unique opportunity to test the equivalence principle in the weak field regime but for relativistic sources made of pure electromagnetic energies producing oscillating deformations of space-time.
Harnessing gravity, the last indomitable fundamental interaction, constitutes a true experimental challenge, but will undoubtedly lead to rewarding scientific breakthroughs and new technologies.
Acknowledgments This research used resources of the ”Plateforme Technologique de Calcul Intensif (PTCI)” (http://www.ptci.unamur.be) located at the Uni- versity of Namur, Belgium, which is supported by the F.R.S.-FNRS under the convention No. 2.5020.11.