1. Transverse Mode Coupling Instability in the SPS revealed by SUSSIX Frequency Analysis
E. Métral, G. Rumolo, R. Tomás (CERN Switzerland), B. Salvant (EPFL/CERN Switzerland)
Abstract
Since 2003, high-intensity single-bunch proton beams with low longitudinal emittance have been affected by heavy losses after less than one synchrotron period in the CERN SPS [1]. Measurements of the turn-by-turn evolution of the instability have been compared with HEADTAIL simulations, exhibiting a remarkably good agreement [2]. In both cases, a travelling-wave pattern propagating along the bunch was identified, which was believed to be the signature of a Transverse Mode Coupling Instability. Recently, SUSSIX frequency analysis [3] was applied on tracking data from HEADTAIL. Previous predictions from MOSES [4], which computes the coherent bunched-beam modes, have been confirmed. In particular, using the SPS beam parameters, a coupling between the azimuthal modes -2 and -3 is taking place. The effects of non-zero-chromaticity, linear coupling, chamber shape, amplitude detuning were also investigated, but not reported here. The next step will be to perform measurements in the SPS to verify this prediction, and focus on possible solutions that would prevent modes -2 and -3 from coupling (e.g.linear coupling).
Context
Simulations (HEADTAIL [2])
Measurements (SPS 2003 [1])
Theory (MOSES [3])
Bunch of particles can be considered as a superposition of transverse modes [5].
Modes shift with increasing intensity due to a broadband impedance. This tune shift Q remains real for low intensities. Particle oscillation amplitude is proportional to
At higher intensities, these modes can cross, couple and decouple, which yield imaginary tune shifts Q, leading to damping or instabilities.
MOSES analytically calculates real and imaginary tune shifts in this mode-coupling formalism. In the case of SPS at injection, MOSES predicts a coupling between modes -2 and -3.
Beam Current (normalized)
LHC type Single bunch
intensity=1.15 p/b
low longitudinal emittance
Beam Current (normalized)
Number of turns after injection
 fast transverse instability with Travelling-wave pattern
 Damped by increasing vertical chomaticity
 fast transverse instability with travelling-wave pattern
 Damped by increasing vertical chomaticity
=> is this measured instability a TMCI?
=> is this simulated instability a TMCI?
=> Theory predicts a TMCI for protons
Methods
HeadTail simulation output
Frequency analysis outputs
Comparison of both methods
HEADTAIL simulation parameters:
- SPS injection parameters
broadband transverse impedance
round chambers
FFT of y(s)
Zoom
+ Normalisation to Qs
+ translation of -Qx
SUSSIX
of y(s)+jpy(s)
SUSSIX complex frequency analysis reveals synchrotron sidebands of higher transverse modes with a better resolution
Results
Perspectives
Very good agreement between HEADTAIL simulations and MOSES analytical calculations. Differences are under investigation. - More confidence to use HEADTAIL to predict instability thresholds for more complicated situations (non zero chromaticity, flat chambers, linear coupling, amplitude detuning, space charge), most of which can not be treated by analytical calculations. - A similar frequency analysis on data measured in the SPS machine is under way.
Overview of the evolution of the real part of tune spectrum with increasing current
References
[1] H. Burkhardt et al, proc. EPAC 2004
[2] E.Metral and G. Rumolo, proc. EPAC’06
[3] R. Bartolini, F. Schmidt, A Computer Code for Frequency
Analysis of Non-Linear Betatron Motion, SL-Note AP,
CERN 1998
[4] Y. H. Chin, User’s Guide for New MOSES. Version 2.0,
CERN/LEP-TH/88-05.
[5] E.Metral,Overview of single-beam coherent
instabilities in circular accelerators, Proc. HHH 2004
Coupling between modes -2 and -3 is also predicted by HEADTAIL