On the detection of gravitational waves through their interaction with particles in storage rings

It is shown that the interaction between a gravitational wave and ultra-relativistic bunches of particles in storage rings can produce a measurable effect on the non-Euclidean geometry of the space -time manifold of high energy rotating particles. Such an interaction causes simultaneous correlated deflections of bunches at different locations in a collider beam around the storage ring. T he radial deflection of a bunch of particles in a beam caused by a gravitational wave perpendicular to the surface of the ring is predicted to have a frequency equal to twice the revolution frequ ency of the bunch, and be modulated by the frequency of the gravitational wave. Using a system of beam position monitors (and possibly a streak camera), every bunch of particles can be monitored and its oscillations reconstructed so that a clear picture of the complete ring can be achieved at any moment. If the storage ring has two counter-rotating beams, noise effects can be reduced by measuring the difference, at a given point all along the beam, of the relative bunch deflections at both rings. The amplitude and frequency of the gravitational wave (and polarisation, if any) ca n then be deduced. Coincidence at different storage rings, with correlated radial deflection amplitudes and frequencies, are also expected. The position of the source can then be deduced. For gravitational waves with frequencies of the order of 100-1000 Hz and amplitudes of the order of $10^{-20}$-$10^{-23}$ the amplitude of the radial deflection can be as large as a milimeter, depen ding on the quality factor as a gravitational wave antenna and the parameters of the collider.