Transcript and within-bunch modes M. Mehler 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-64291 Darmstadt
2)Hochschule Fulda, Marquardstraße 35, D-36039 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.
Measurement in Time Domain
CH A: URF
Dig itally
Controlle d
Amplifier
Controller
for AGC
Amplitude
Detector
Bandpass
21.4 MHz,
± 250 kHz
REF: URF
Offset-LO
Bandpass
21.4 MHz
Divid er
4:1
ADC
14 bit
Crystal
Oscilla tor
85.6 MHz
Divid er
3:1
CH B: UBeam
Dig itally
Controlle d
Amplifier
Controller
for AGC
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.
Conclusion and Outlook
DSP Unit
Dj
Bandpass
21.4 MHz,
± 250 kHz
Fig. 4: Schematic configuration of the longitudinal feedback system in time
domain [3]
ADC
14 bit
Amplitude
Detector
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 ≈ 3.333 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).
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.
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.1209-1213.
[3] M. Mehler: Quadrupole instability damping in an ion particle bunch based on
RF voltage modulations, GSI internal document, August, 2006