Historical research guide · 0581 · 2012
Gravitational Wave Generator Apparatus
Robert M.L. Baker · Bonnie Sue Baker
In one minute
Robert Baker and Bonnie Sue Baker set out to build a gravitational wave generator on a laboratory bench. Their starting point is Einstein’s quadrupole rule: what radiates a gravitational wave is jerk — the third time derivative of mass motion — and, as Joseph Weber argued, the force producing that jerk does not have to be gravity. Electromagnetic forces are more than a hundred thousand billion billion billion billion times stronger, so the Bakers use them. Their apparatus winds millions of off-the-shelf film-bulk acoustic resonators, the tiny vibrating chips inside mobile phones, into a double helix inside a microwave guide. A phase-coherent wavefront from magnetrons runs up the axis and kicks each opposing pair at the same instant, and each kick radiates a gravitational wave focused between them. Because the pairs fire in step, the beam narrows and the flux grows with the square of the number of elements. They work a full twenty-metre numerical example, and note that the Earth is transparent to these waves — so the receiver could be on the far side of the planet.
Connection
Chapter 4 is about engineering the metric rather than pushing against propellant, and this is the most concrete published bench design for making a spacetime strain on purpose out of ordinary parts. It also sets up chapter 11: the detector and the lens that would close the link are superconducting devices.
From the source
A gravitational wave is radiated by jerk — the third time derivative of mass motion — and the force producing that jerk need not be gravitational. Baker cites Weber’s point that non-gravitational forces play a decisive role in methods for the detection and generation of gravitational waves, and notes that electromagnetic forces are more than 10³⁵ times larger than gravitational ones, so they are what a laboratory generator should use.Section 1, Introduction
The apparatus is a cylindrical array of force-producing elements, preferably a double helix of film-bulk acoustic resonators, energised by a phase-coherent microwave wavefront travelling along the axis of symmetry. As the wavefront moves it fires opposing pairs simultaneously, and each pair radiates a gravitational wave focused midway between the two elements — the laboratory analogue of the changing centrifugal force of a binary star pair.Section 2 and Section 2.1, Double helix
Because the elements fire coherently, the flux grows as the square of the number of generating elements: one factor of N from having N sources, the second from the narrowing of the beam, which concentrates the same power into a smaller cap. Baker follows Dicke’s superradiance and the needle-like radiation computed for a crystal-oscillator array by Romero-Borja and Dehnen.Section 2.2, Superradiance
The worked example is a twenty-metre double-helix array of median radius 20 cm, energised at about 2.5 GHz so that the gravitational wave comes out at twice that frequency, containing 1.55 × 10¹³ resonator pairs each contributing a 2 newton force change. On the standard treatment the generator produces a flux of about 6 × 10⁵ watts per square metre one metre from the end of the array, corresponding to a dimensionless spacetime strain amplitude of about 1.98 × 10⁻²⁵.Section 3, Results, and Section 3.1, Standard approach
The Earth is completely transparent to high-frequency gravitational waves, so the receiver can be on the far side of the planet. At one Earth diameter the conservative calculation gives a strain amplitude of 3.8 × 10⁻³⁹. What to watch: the Li-Baker detector, whose sensitivity is estimated at 10⁻³⁰ to 10⁻³² and which the authors argue can be improved to about 10⁻³⁷ with superconductor resonance chambers, plus Woods’ superconducting lens to concentrate the signal at the receiver.Section 3.2, Conservative approach, and Section 4, Conclusions
Three engineering irregularities set the difficulty: distinguishing the individual resonator pairs, which at first glance demands positioning accuracy of 0.155 picometres; irregularity in the magnetron wavefront; and variation in the delay between the microwave arrival and the mechanical force change. Baker argues each broadens the beam and lowers the flux rather than defeating the effect, and that tight machine winding of the resonator threads in a dust-free environment may hold tolerance to a small fraction of a nanometre.Section 3.3, Irregularities
The way in
https://doi.org/10.1016/j.phpro.2012.08.028How to cite it
Robert M.L. Baker, Bonnie Sue Baker (2012) Gravitational Wave Generator Apparatus doi:10.1016/j.phpro.2012.08.028