1. Basic concept for a SIS100 longitudinal feedback system damping coupled- and within-bunch modes
M. Mehler1), H. Klingbeil1), B. Zipfel2)
1)GSI, Gesellschaft für Schwerionenforschung, Planckstraße 1, D Darmstadt
2)Hochschule Fulda, Marquardstraße 35, D Fulda
Abstract
Simulation of Operation Principle for m = 2
For SIS100, a bunch-by-bunch feedback system and a higher order mode damping system are planned. Flexible solutions using DSPs (Digital Signal Processing Systems) and FPGAs (Field Programmable Gate Arrays) are desirable in order to cope with different types of instabilities. Therefore, a generic approach is discussed here and first simulation results for the quadrupole mode are presented.
Problem Definition
Fig. 3: ESME simulation result for understanding the physical principle. Left: Particle start configuration (length 14°); Right: Bunch length after 4 synchrotron periods (length 6°) in phase space [3]
During oscillation the ion bunch becomes longer and shorter in time domain with 2 fS. In phase space this is equivalent to a rotation.
Starting where the ion bunch has its maximum length ΔΦmax in phase space leads to the requirement to transfer the outermost particles to a lower constant Hamiltonian H to get a lower ΔΦ.
The solution is to decrease the RF voltage during the first and third quarter of the synchrotron rotation and to increase it during its second and fourth quarter. This leads to a phase shift of 90° between the measured beam amplitude signal and the modulation voltage.
An example for the effect of such an RF voltage modulation with 2 fS RF amplitude modulation is displayed in Fig. 3.
Proposed System Topology
Fig. 1: Within-bunch modes m = 1 to 2, coupled-bunch mode pattern n = 4. a) Mountain-range display; b) Superimposed; c) Phase space [1]
Synchrotrons accelerating more than one bunch with high particle beam intensities are susceptible to coupled-bunch (CBM) and within-bunch coherent oscillation modes (n = 0...number of bunches - 1, m arbitrary). This causes an emittance blow up or may in the worst case destroy the ion bunches. Therefore such oscillations should be damped.
Within-bunch modes with m odd lead to phase modulations of the bunch compared to the RF voltage phase. Within-bunch modes with m even lead to a length modulation of the ion bunch compared to its reference length. The oscillation frequency is a multiple of the synchrotron frequency (m fS).
Coupled-bunch modes are defined by the phase correlation n of a special instability mode (e.g. m = 1) between the adjacent bunches.
Fig. 4: Schematic configuration of the longitudinal feedback system in time domain [3]
For amplitude oscillation detection one dedicated DSP system for every bunch in SIS100 (for h = 10 where 8 buckets will be filled, 8 separate systems will be needed) may be used. This will lower the required performance of each detection system.
It is planned to use a system similar to the beam phase control system but with its own signal generation instead of the RF cavity DDS. The correction signal will be led to an additional broadband kicker cavity which shall modify the total RF voltage.
Measurement in Time Domain
Conclusion and Outlook
The ESME simulations have shown that amplitude modulations of the RF voltage are in principle capable of damping quadrupole oscillations. During machine experiments it could be shown that the DSP system is usable to detect amplitude oscillations of the beam.
Concerning the simulations the next step is to simulate more realistic situations like the damping of small deviations of the bunch from a matched one and to incorporate closed-loop control.
Machine experiments are planned to establish a method to excite reproducible oscillations and to influence growth rates of quadrupole instabilities in SIS18 for future tests of the longitudinal feedback damping system.
Fig. 2: Left: Block diagram of the DSP-based phase and amplitude detector [2] as basis for the amplitude detection in time domain; Right: Measured beam signal amplitudes (2 fS ≈ kHz)
In time domain within-bunch instabilities with m odd can be measured through their phase shift compared to the adjacent bunches (n > 0). For n = 0, m = 1 a beam phase control system will soon be commissioned..
Instabilities with m even can be measured through the amplitude modulation of the beam signal.
The DSP subsystem usable for high-precision phase and amplitude detection and for fast closed-loop control algorithms shall be the basis for the detection of within-bunch amplitude oscillations. It includes analogue pre-processing in the IF range, ADC and DAC modules, suitable digital interfaces and comfortable diagnostics features.
The picture on the right in Fig.2 shows an example for such an amplitude measurement of excited quadrupole modes (m = 2) that was accomplished on August 17, 2006 (SIS18).
References
[1] F. Pedersen, F. Sacherer: Theory and Performance of the Longitudinal Active Damping System for the CERN PS Booster, IEEE Transactions on Nuclear Science, Vol. NS-24, No.3, June 1977
[2] H. Klingbeil: A Fast DSP-Based Phase-Detector for Closed-Loop RF Control in Synchrotrons, IEEE Trans. Inst. Meas., Vol. 54, No. 3, June 2005, p
[3] M. Mehler: Quadrupole instability damping in an ion particle bunch based on RF voltage modulations, GSI internal document, August, 2006