A tomographical analysis of longitudinal phase space during the acceleration phase of the SIS machine cycle

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Nov 16, 2013 (4 years and 8 months ago)




GSI, 23 Okt. 2003

A tomographical analysis of longitudinal phase space during the
acceleration phase of the SIS machine cycle

M. Kirk
, H. G. König, G. Schreiber


This work continues from the previous ex
periments reported in [1]. During this former
experiment, the growth in the longitudinal emittance along the SIS ramps was
determined. The initial and final momentum spreads of the DC beams before bunching
and after debunching, respectively, were measured
in order to determine just the

increase in emittance over the whole machine cycle. During the experiment described in
this report, the longitudinal line charge density profiles were recorded using a BPM and
an oscilloscope. Estimates of the rms emitt
ance of the bunched beam were derived from
these measurements using a tomographic technique [2]. The MEEVA ion source was
chosen and the intensity in SIS prior to RF capture was ~10

ions of U

Experimental setup

A schematic of the experimental s
etup is shown in figure 1. This setup is essentially a
reduced version of that used in the previous experiment, without control of the DDS units
for the cavity frequency, beyond that done by SISMODI. The Timing InterFace (TIF)
central trigger system (
) of the SIS control system defines the reference time
for the measurement process. A pulse delay unit defined, relative to the central trigger,
the start of the first Schottky measurement, before capture. In actual fact 2 triggers are
produced by t
doppel pulser

unit thereby allowing the automatic acquisition of the
Schottky signal in frequency domain before bunching and after debunching respectively.
A second unit for trigger delay was used to define the start of the RF amplitude ramp and
of the
longitudinal beam current profile measurement. As with the previous experiment,
an in
house analogue signal

unit simply added the RF amplitude signal from
the arbitrary signal generator to the reference RF amplitude signal of the SIS control
stem. For most of the results presented herein, 2 cavities were operated together with
phase regulation applied to prevent the phases between the 2 cavities from drifting apart
(that is, no bunch to rf phase regulation). The phase between the 2 cavities de
pends on the
frequency and the maximum discrepancy was, on a previous occaision, found to be
approximately ±10º. The combined gap voltage could be as high as 20kV.


Figure 1
. Schematic of the experiemental layout.

Results and discussion

To begin, the

relative momentum spread from the Unilac had to be reduced to a level
such that the dp/p was considerably less than the final momentum acceptance on the
flattop, i.e. maximum gap voltage. This setup makes the beam sensitive to any non
adiabatic variations

in the gap. If on the other hand the acceptance were too small then a
smaller emittance growth would occur but only due to the fact that the beam completely
fills the longitudinal bucket acceptance. The variation in longitudinal dp/p during the

experiment is shown in figure 2. The initial spread achieved after adjusting the
signal on the frontend RF buncher cavity in the transfer channel
to produce a 90º bunch
rotation in phase space thus reducing dp/p

and adjusting the settings on the

cavity further upstream, was close to the nominal FWHM (±HWHM) of

with a Gaussian like distribution. During the experiment the dp/p gradually
increased and eventually even the form become nongaussian, but somewhat asymmetric
consisting of
a sharp peak with a high frequency ‘shoulder’ in the Schottky spectrum.
Consequently the last (rightmost) FWHM point in figure 2 is exceptionally low, however
the full width at 10% maximum was about ±9.5x10
. It was under these final (initial)

of the injected beam that all the bunch profile measurements were taken.


Closest in

time to the measurement of the Schottky peak which was recorded at the 93

harmonic of the
revolution frequency (figure 3).


Having optimised the dp/p, the SIS RF cavity frequency was adjusted using the

control program. This was done in order minimize the phase space dilution caused
by the mism
atch between the injection energy from the Unilac and the synchronous
energy of SIS. During the RF tuning in SIS, the strengths of the dipole magnets were
fixed (EMODI=1, I meaning injection). To change the RF frequency the

position at inject
ion) parameter was varied.

Figure 2
. Change in relative momentum spread from Unilac during the course of the experiment. Please
note that the rightmost point corresponds to a momentum distribution that is asymmetric and thus non
Gaussian, with a low FW
HM but the rms is still considerably bigger and the full width at 10% of the
maximum is ±9.45x10

As already mentioned, if the SIS frequency is correct then emittance growth should be
minimised during a bunch
debunch cycle. The bunch
debunching was done

during the
injection plateau. Two cavities were used to provide a flattop amplitude of 20kV. The
bunching and debunching with fixed RF frequency was done using the same

ramp, the rise/fall time of the bunch/debunching was 70ms and the 20kV fl
attop lasted
140ms allowing sufficient time for the phase space to reach equilibrium. A consequence
of emittance growth is the increase in dp/p of the debunched DC beam from its dp/p
before bunching. Hence figure 4 shows the variation in dp/p for the fully

beam, plotted against the radial injection offset.


Figure 3
. Longitudinal Schottky measurements on the beam shortly after multi
turn injection into SIS.
Time stamps are given to the nearest minute since the curves are averages of a few measur
ements taken one
straight after the other. The y
scale for the 93

harmonic, which was recorded on a different instrument, is
to the right.

For some unknown reason, even when the Unilac and SIS were considered fully
optimised, there were beam losses duri
ng the RF capture process (figure 5). Furthermore
these losses occurred with stationary RF buckets, and, the acceptance of the 20kV RF
bucket, marked in figure 3, was large enough so as not to be the cause of of the losses.
These losses were also present d
uring the beam time of the following machine
experiment (Spiller et al).

Figure 4
. Optimising dp/p of the debunched beam by varying radial injection offset; the RPOSI parameter.
The optimal setting of 0.3mm (dashed line) was chosen.


Although the metho
d of minimising the dp/p of the fully debunched beam is a sufficiently
effective way to match the SIS frequency to the coasting beam frequency, it is perhaps
unwise to conclude from figure 4, the increase in emittance (i.e. using

For one there are beam losses, and for the other, figures 2 & 3 indicate that during these
measurements the form of the Schottky spectrum must have undergone a transition to an
asymmetric shape. Only the debunched beam was measured upon when making figure
the first pulse in the
doppel pulser

was removed by reprogramming the signal generator.
This was because the data acquisition software application(s) did not allow one to record
and automatically display or analyse the Schottky spectra for each of the 2

triggers from
the doppel pulser.

Instead, an off
line tomographical analysis was attemped on the longitudinal bunch
profiles, which were measured when the SIS was put back to its single cavity operation
and the only RF signals used were produced by SISM
ODI. Since acceleration was now
present, any beam that may have been outside the RF bucket will have been lost to the
walls, thus permitting the use of tomography on the phase space which remains inside the
RF bucket. The results (figures 6 & 7) suggest an

increase in the rms emittance of ~37%
over a period of 250ms during part of the acceleration stage of the cycle. This growth rate
is considerably higher when compared to a former simulation value of approximately
10% increase in the rms (eVs) emittance fr
om the start of capture to the end of the flattop.
The simulation scenario involved the commisioned ramps produced by the GSI ZYKLOP
code, and the initial phase space was gaussian in energy (zero offset) and random
uniform in time relative to the synchrono
us particle.

Figure 5
. Langsamer DC
Trafo measurement along the complete machine cycle in SIS. RPOSI = 0.203mm
i.e., close to the optimal value. Slow extraction begins at about 3000ms. The intensity drops after the start
of the SISMODI capture in 2 sep
arate steps. The first is supposedly due to the RF capture and the second
occurs when the beam is accelerated. Tomographical analysis was undertaken on data sets taken in the
region of 2300ms and just before 2540ms.


Figure 6
. Tomographical reconstuctio
n at 300ms (left) and 542ms after start of RF capture. Shortly after
542ms the beam was slowly debunched before slow resonant extraction occurs. The beam intensity was in
the range 10

of U

with energies in the range of 11.4MeV/u at injection and
250MeV/u at extraction,
thus produced neglible space charge effects. Rms emittances are 4.2eVs (left) and 5.2eVs respectively. The
particle density scale (per eVs) is not quoted since it is arbitrary; space charge was switched off in the
programm. The left

and right phase space density scales are not necessarily the same. The blue line marks
the separatrix.

Time [ms]
4x rms emittance [eVs]

Figure 7
. The 4 x rms emittance calculated at several reconstruction times for 2 data sets in time along the
RF voltage f
lattop stage of the SIS machine cycle. The close proximity, in time, of the points seems to
confirm the stated accuracy of the tomography algorithm to better than ±10%; the size of the error bars.
The bunch of points to the right are at the end of the acce
leration stage, where the frequency is constant.

The last three plots show the bunch profiles as a continuous time
flow representation
(figures 9 & 10: from simulation and from a

BPM), and as a waterfall plot


representation of the same measur
ed signal (figure 8). The longitudinal 1D PIC code
ESME was used for all simulations presented herein [3]. In both simulation and
experiment only as much as the first 20ms of RF capture are shown. There is a clear
discrepancy between the experiment and the

simulation. Figures 8 & 10 show what seems
to be somekind of (unexpected) quadrupolar bunch rotation; the symmetric oscillation in
the bunch profile envelope with a period (ca. 1ms) approximately equals that of the
linearized synchrotron period at those g
ap voltage amplitudes
. There was no
experimentally observed effects of mismatch in the synchronous energy at injection of
the SIS from the Unilac extraction energy, that is, there were no oscillations of the peak
in the longitudinal bunch/line charge dens
ity profiles. Therefore the procedure used to
tune the SIS frequency worked.

Figure 8
. Experiment. Waterfall plot running from 9
19ms after the start of RF capture. RF ramps
generated by SISMODI. This figure corresponds to figure 10.


This envelope oscillation became gradually subdued but then began to increase again as soon as the
debunching phase began. It ma
y be that there was some unwanted phase oscillations which occurred over a
time scale of 1ms thereby squeezing and streching the beam in phase space.


Figure 9
. Longi
tudinal line charge density from ESME simulation. The RF amplitude and B
field (of the
dipole magnets) ramps were derived from the measured gap signal.

Figure 10
. Experiment. Longitudinal line charge density as measured from the pickup. Beam losses were

heavy at during this stage in the machine cycle and persisted upto about 500ms later. This figure
corresponds to figure 8.


The cause behind the beam losses during RF capture can only be, at this moment,
speculated. The cause could have been
some misfunction, on that occaision, of the RF
electronics. Whether the beam losses were due to longitudinal (i.e. the beam was really
‘kicked’ out of the bucket), or transverse effects remains to be proven
If the latter is true


One possibility is that the eigen frequency of the cavity during the pre magnetization of the core is
correctly set until appreciable gap voltage is reached (ca. 500V), thus the soll bahn could be forced out to
the walls as soon as this voltage threshold is crossed. Once crossed, the eigen frequency adjusts to the
correct value. It should also be pointed o
ut that since these experiments a

circuit was
implemented and tested. The function was to average out the initial error in the cavity eigenfrequency over


then it would be reasonab
le to believe in the rms emittances in figure 7, although one
must bear in mind that the change in emittance in such a case would be due to, not just
RF operation, but also due to particles simply ‘leaving’ the phase space, through
absorption at the walls
of the chamber. For the technical details on the recent
developments to the RF regulation hardware one is refered to [4].

A detailed measurement of the phase and amplitude variations along the machine cycle
would be of great assistance as input data to a
computer model (e.g. ESME [3]), to then
hopefully reproduce the experimentally observed emittance growths, and thereby prove
that it is the RF gap voltage signal that is at fault. Furthermore, it may prove worth while
to study the effects of modulations in

the RF phase, which could for example lead to
emittance growth through nonlinear (perhaps chaotic) dynamics. Indeed this has already
been investigated in [5], although at GSI one would have to approach the problem from a
theoretical angle since the RF sys
tems cannot be programmed in such a way at present.


The author wishes to thank: H. Damerau for his support on the installation of his data
acquisition and gap voltage ramp generation software; H.G. König, K. Kaspar, G.
Schreiber, and T.
Winnefeld for their support on the setting up of the RF cavity system;
and C. Wetzel et al. for the setting up of the Unilac operation.



H. Damerau, G. Schreiber, Maschinenexperimente zur longitudinalen
Emittanzentwicklung im SIS (31. Okto
ber/1. November 2002), GSI Arbeitsnotiz


S. Hancock, S. Koscielniak, M. Lindroos, Longitudinal phase space tomography
with space charge, CERN/PS 2000
021 (RF)




H. G. König, Aktuelle Modifikation der SIS
Kavitätenregelung, 08.10.2003, GSI
Arbeitsnotiz (Gruppenordner).


M. Ellison et al., Driven response of the synchrotron motion of a beam, Phys.
Rev. Lett., Vol. 70, Number 5, 1 Feb 1993

several machine cycles. This new regulator module has since been tested and does

reduce this frequency