# Beam Echo Measurements at CERN

#### The last few hours of SPS running in 1995, devoted to machine studies, delivered the first longitudinal echo signals in a coasting proton beam stored at 120 GeV (CERN Bullettin, January 1996). Echo phenomena have been well known in plasma physics for many years. However the effect has only been observed recently in accelerators. The first measurements were made at the beginning of 1995 in the 8 GeV anti-proton accumulator at Fermilab, but it was not clear whether the effect would be observable in a big machine like the SPS. The implications could be promising, both for the SPS and for the LHC. Potential applications of this new technique are the fast detection of weak longitudinal diffusion, beam energy spread measurements and possibly impedance measurements.

An echo is formed by the interference of two consecutive RF pulses with slightly different frequencies. Each RF excitation induces a well defined pattern of particle energy along the machine circumference, rapidly destroyed by the revolution frequency spread. However, the long lasting memory of the proton beam allows the reappearence of an ordered structure long after the initial excitations. The timing of the echo response depends on the frequency of the kicks and their separation; the longer the separation, the later the echo: in the SPS we have observed echo delays up to two minutes (corresponding to more than 5 millions turns). The left-top picture shows the super-imposition of 22 echo measurements with different time separations between the two RF-kicks, ranging from 5 to 220 ms. The vertical axis shows the absolute value of the echo amplitude on a linear scale and the horizontal axis shows the time measured from the first RF-kick. The horizontal scale is 50 s. The solid line shows the analytical estimate for the echo envelope assuming a diffusion coefficient of $10-13$ s$-1$: in order to observe such a small diffusion with the Schottky signal, one would have to wait more than one day.

Following the links in this page you can get full information about analytic calculations, numeric simulations and echo measurements performed at CERN, including measurements in LEAR and bunched beam echoes recently observed in the SPS.

Background bibliography:
• T.M. O' Neil and R.W. Gould, Phys. Fluids 11, 1 (1968).
• E.M. Lifshitz and L.P. Pitaivskii, Physical Kinetics, Pergamon Press, Oxford, 1981.
• G.V. Stupakov, Echo Effect In Hadron Colliders, SSC Report SSCL-579, July 1992.
• G.V. Stupakov and S. Kauffmann, Echo Effect in Accelerators, SSC Report SSCL-587, September 1992.
• P.L. Colestock, L.K. Spenzouris and J.-F. Ostiguy, Nonlinear Wave Phenomena in Coasting Beams, Proc. IEEE Particle Accelerator Conference, Dallas, 1995, pp. 2757-2761.
• L.K. Spenzouris, J.-F. Ostigy, P.L. Colestock, Direct measurement of diffusion rates in high energy synchrotrons using longitudinal beam echoes, Phys. Rev. Letters 76, 620 (1996).

21/05/1997 Francesco.Ruggiero@cern.ch