1. CERN F. Ruggiero Univ. “La Sapienza”, Rome, 20–24 March 2006 Measurements, ideas, curiosities beam diagnostics and fundamental limitations to the performance of high-intensity accelerators Complement to the lecture on Collective Effects & Beam Measurements Collective Effects & Beam Measurements

2. CERN F. Ruggiero Collective Effects and Beam Measurements Transverse head-tail modes at the CERN PS (E. Metral, 1999, 20 revolutions superimposed) Time (20 ns/div)

3. CERN F. Ruggiero Collective Effects and Beam Measurements Fast vertical single-bunch instability with protons at the PS near transition in 2000 ,  R,  V signals Time (10 ns/div) ~ 700 MHz  Instability suppressed by increasing the longitudinal emittance Head stable Tail unstable (Courtesy E. Metral)

4. CERN F. Ruggiero Collective Effects and Beam Measurements Fast vertical single-bunch instability with protons at injection in the CERN SPS (E. Metral, 2003) ” Instability suppressed by increasing the chromaticity

5. CERN F. Ruggiero Collective Effects and Beam Measurements LONGITUDINAL – HIGH INTENSITY EFFECTS Experiment with a CERN PS proton beam in 1999  Longitudinal Schottky scan spectrogram during debunching Low-intensity beamHigh-intensity beam ~ 200 ms Courtesy R. Garoby

6. CERN F. Ruggiero Collective Effects and Beam Measurements Longitudinal Solitons in RHIC Wall Current Monitor data for a proton bunch freshly injected into RHIC (left) and for the same bunch after 17 minutes (right) Injection is at  = 25.9, i.e. above transition  t = 23.8 These oscillations should be Landau damped When nonlinear effects are included, long lived, stable coherent oscillations become possible for low-intensity beams Long-lived beam “holes” have been observed below transition in the CERN PS Booster “Longitudinal Solitons in RHIC”, M. Blaskiewicz, J.M. Brennan, P. Cameron, W. Fischer, J. Wei, A. Luque, H. Schamel, PAC’03 Longitudinal phase space distribution obtained by a self- consistent solution of the Vlasov equation

7. CERN F. Ruggiero courtesy E. Metral and F. Zimmermann Vertical growth rate of head-tail modes in the LHC as a function of chromaticity at injection energy, for ~3000 bunches of nominal intensity At injection head-tail modes with growth rates up to about 4 sec -1 are stabilized by lattice nonlinearities (assuming an amplitude detuning of 0.002 at 6 sigma). The rigid mode m=0 has to be stabilized by the transverse feedback.

8. CERN F. Ruggiero Collective Effects and Beam Measurements Beam Echo Measurements at CERN 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 re-appearance 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 (i.e., more than 5 millions turns). The picture shows the superposition 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.

9. CERN F. Ruggiero Collective Effects and Beam Measurements Collective Effects: web links & references http://ab-abp-rlc.web.cern.ch/ab-abp-rlc/ (web site of the R&D and LHC Collective Effects team at CERN) “Physics of Collective Beam Instabilities in High Energy Accelerators”, A. Chao, (Wiley, 1993)Physics of Collective Beam Instabilities in High Energy Accelerators “Impedances and Wakes in High-Energy Particle Accelerators”,Impedances and Wakes in High-Energy Particle Accelerators B.W. Zotter and S. Kheifets, (World Scientific, 1998) “Longitudinal holes in debunched particle beams in storage rings, perpetuated by space-charge forces”, S. Koscielniak, S. Hancock, and M. Lindroos, Phys. Rev. ST Accel. Beams 4, 044201 (2001)Longitudinal holes in debunched particle beams in storage rings, perpetuated by space-charge forces “Beam dynamics studies for uniform (hollow) bunches or super-bunches in the LHC: beam–beam effects, electron cloud, longitudinal dynamics, and intra-beam scattering”, F. Ruggiero, G. Rumolo, F. Zimmermann, Y. Papaphilippou, CERN LHC Project Report 627 (2002)Beam dynamics studies for uniform (hollow) bunches or super-bunches in the LHC: beam–beam effects, electron cloud, longitudinal dynamics, and intra-beam scattering “Intrabeam Scattering with Non-Ultrarelativistic Corrections and Vertical Dispersion for MAD-X”, F. Zimmermann, CERN-AB-2006-002 (2006)Intrabeam Scattering with Non-Ultrarelativistic Corrections and Vertical Dispersion for MAD-X