# Initial design of a global fast orbit feedback system for the alba synchrotron

D. Beltran, M. Muñoz, CELLS, Bellaterra, Spain

Abstract

This paper presents the initial design of the Global Fast Orbit Feedback
(FOFB) system for the ALBA Storage Ring. The FOFB system is designed to
reach a submicron stability of the electron beam working at frequencies
of at least 100 Hz. It compensates the small perturbations produced by
vibrations, electromagnetic noise and changes in the gap or phase of the
insertion devices, etc. A description of the model is shown. The
different subsystems have been identified and modeled: the BPM
processor, the iron lamination and the vacuum chamber. The power
converters for the correctors play an important role in the system, and
they have been designed (strength, resolution, bandwidth, voltage
output) accordingly with the FOFB requirements. We have also studied the
latency of the system (communication network, processing times). The
orbit correction is computed by a PID controller. The simulations of the
closed loop response show a damping of the perturbation between 0 and
100 Hz, although the system also introduces a small amplification of the
noise just after this bandwidth. Finally the paper presents the initial
design of the hardware architecture of the FOFB system.

## introduction

ALBA is the first Spanish Light Source which is intended to provide
Spain with a powerful source of X-rays. The project is funded by the
Spanish and Catalan Governments at equal parts. The first phase includes
the construction and commissioning a linear accelerator, a booster
accelerator, a storage ring and 7 beamlines, with the start of operation
planned for 2010.

ALBA is a 3rd generation 3 GeV light source, with a perimeter of 268 m,
With such an energy the brilliance at 20 keV reaches 10^19^
Ph/s/mm2/mrad2/0.1%BW for in-vacuum undulators with 5 mm gap.

The lattice has 16 cells with a 4-fold symmetry in order to increase the
number of available straight sections for experiments, providing 16
medium straight sections of 4.2 m, 4 longs ones of 8 m and 12 short ones
of 2.2. For more information see reference \[1\]

## Orbit correction basics

In order to provide a stable beam for the experiments, the electron beam
has to be stable to values smaller than 10% of the beam size. In the
vertical plane, where the beam size is of the order 5 to 10 µm in the
medium straight section, this corresponds to a sub-micrometer stability
of the electron beam. The closed orbit correction system is in charge of
keeping the beam stable. The system is composed of two conceptual parts:
The slow and the fast orbit feedback. The two components share most of
the hardware, and could be integrate in a single loop in the future. The
main components of the orbit correction system are the Beam Position
Monitors (in charge of reading the position of the electron beam around
the ring), the Corrector Magnets (that introduce displacement in the
beam to bring back the orbit to the desired one) and a system of CPUs
that predict the settings of the corrector magnets based in the readings
of the BPMs.

The slow orbit feedback takes care of the correction of the orbit
created by "large" static perturbation, such as misalignment of magnets,
etc. It would compensate errors up to a few mm, with corrector strength
up to 1 mrad, and is mostly a static system, taking care also of
adjusting the frequency of the RF to have a centred horizontal orbit.

The fast global orbit feedback system is in charge to stabilize the
electron beam up to frequencies of at least 100 Hz, compensating the
small perturbations produced by vibrations, electromagnetic noise and
changes in the gap or phase of the insertion devices. Typically, the
maximum corrector strength needed will be of circa 50 µrad at 50 Hz. The
elements involved in the FOFB are the BPM detectors and the BPM
electronics, the corrector power supplies, the corrector magnets, the
vacuum chamber, the frequency of the RF system, and a computer system
and network, that collects the information from the BPM electronics,
runs correction algorithms and acts on the storage ring corrector
magnets and in the frequency of the RF. Those elements are described in
the next section.

## Fast orbit feedback subsystems

This section describes the influence of the different subsystems
involved in the FOFB:

• BPM electronics.

• The Power supply.

• Iron lamination, corrector coil, and vacuum chamber.

Figure 1 shows the model of the correction loop.

  -----------------------------------------------------------------------
  ![](media/image1.png){width="3.245138888888889in"
  height="1.3034722222222221in"}

  Figure 1: Model of the FOFB correction loop.
  -----------------------------------------------------------------------

### BPM Electronics: Libera Electron Processor

Libera Electron \[2\] is a standalone device composed of a RF analogue
front-end, four ADCs, a FPGA, and a Single Board Computer. The electron
beam is determined by sampling at 118.2218 MS/s the signals from the
four BPM buttons for the storage ring and by processing the samples in a
multiple-stage filtering and decimation scheme.

We have measured the step response of the fast acquisition data path,
which is shown in Figure 2.

![](media/image2.wmf)

Figure 2: Libera Fast acquisition response, with a sampling rate of 10
kHz.

This is a second order underdamped system, with a damping ratio of 0.47
and an undamped natural frequency of 11918 rad/s. We have to add the
latency of the digital system, as we could correlate this value with the
turn-by-turn acquisition (1 us resolution). This gives a latency of 350
µs. So, the transfer function, including the group delay of the digital
calculation is:

$H(s) = e^{- \text{st}_{o}}\frac{w_{n}^{2}}{s^{2} + 2{\zeta w}_{n} + w_{n}^{2}}$,

where *t~o~*=350 µs, *w~n~*=11918 rad/s, ζ=0.47.

### Iron Lamination and Vacuum Chamber

The Storage Ring sextupoles of ALBA will have additional coils to
provide horizontal and vertical corrections to the beam. Due to the fact
that the vacuum chambers are made with metal, eddy current will appear,
therefore, the magnitude of the magnetic field will be reduced for high
frequencies. The ALBA vacuum chamber is made of 3 mm thick stainless
steel, but there is a reduction of the vacuum chamber thickness (2 mm)
at the location of correctors only at the location of the sextupole
poles instead over the whole width of the corrector. Also, the thickness
of the laminations of the sextupoles is 0.5 mm, in order to reduce the
Eddy currents in the core of the sextupoles.

The document \[3\] has a simulation of the magnetic field attenuation of
the Vertical corrector field in the vacuum chamber. Those simulations
take into account the effect of the iron losses on the iron core and the
vacuum chamber. A step has been used to measure the bandwidth of the
vacuum chamber \[4\]. The rise time (10-90%) for the vertical field is
1.2 ms, so the cutoff frequency is 290 Hz if a first order system is
assumed. The rise time for the horizontal field (vertical correction) is
0.155 ms, and the cutoff frequency is 2.4 kHz. It was also simulated the
effects of the eddy current currents due to a sinusoidal waveform. The
field attenuation is shown in Figure 3.

![](media/image3.wmf){width="2.5590277777777777in"
height="1.7583333333333333in"}

Figure 3: Attenuation of the magnetic field.

The -3 dB attenuation measured in this case is 235 Hz for the horizontal
correction and 1551 Hz in the vertical correction. We have adjusted the
transfer function for both plots. The vertical correction field has a
slope of 40 dB/dec, which corresponds to a second order filter. We have
fitted the curve (up to 4 kHz), and it has the following transfer
function:

$H_{\text{CV}} = \frac{1}{(s2{\pi f}_{c} + 1)^{2}}$ , with f~c~=2.3 kHz.

The response for the horizontal correction is neither a first order
filter. It has a slope of 8.5 dB/dec (the first order filter is 20
dB/dec). We could take a conservative approach, and consider a first
order filter with a cut-off frequency of 235 Hz

### Corrector Power Supply

This section shows the specification of the power supplies, according to
the simulations done in the vacuum chamber and the measurements done by
the corrector coil manufacturer.

When the project of the FOFB started, the Libera electron processor, the
magnet coils and the vacuum chamber where already decided. The only
components that we have designed for the optimization of the FOFB system
are the corrector power supplies.

The corrector magnets were designed for higher correction fields in
static mode. In order to avoid the need of cooling the coils, the
magnets present a small resistance but a large inductance. The vertical
correction coils have (according to the measurements made by the magnets
manufacturer) an inductance of 211 mH and a resistance of 2.24 Ohms. In
the dynamic mode requested by the FOFB system, we have to dimension the
power supply accordingly, in order to produce current with the
appropriate strength and bandwidth the power supply.

Following the experience in other light sources (SLS, Elettra), the
dominant noise sources that the fast orbit feedback should cancel are in
a range up to 100 Hz, and the highest component is related with the
mains network (50 Hz). The correction signal will be the addition of
sinusoidal waveforms, and the highest component is 50 Hz. So we
calculate the required voltage for a correction of 80 µrad at 50 Hz in
the vertical plane, for our load (L=220 mH and R=2.2 Ohms):
$V = L \ast I_{\text{peak}}\text{*cos}(\omega t)$ = 55 V. We have to add
to this voltage the DC component, which is 1 mrad (10 A). The resistance
of the magnet is 2.2 Ohms, and the resistance of the cable is 0.5 Ohms,
so the total DC voltage is 2.7\*10=27 V. The total voltage will be
55+27≈ 85 V.

The bottom line is a power supply with ± 12 A and ± 85 V. This power
supply allows DC corrections of ±1 mrad (10 A) and in addition an AC
correction of ±80 µrad (0.8 Apeak) at 50 Hz (or ±40 µrad at 100 Hz) in
the vertical plane. The same power supply will be used for the
horizontal correction and it will provide a correction of ±115 µrad
(1.16 Apeak) at 50 Hz (or ±58 µrad at 100 Hz) in the horizontal plane.

## Fast orbit feedback COrrection

The FOFB system is closed loop system. The beam position is measured by
the BPM, and compared with the reference orbit (set point). The error
signal is applied to a PID controller, which computes the correction and
it generates a control signal for the corrector power supplies.

The target of the FOFB is to cancel (or attenuate) perturbations below
100 Hz. In our system, the perturbation is modelled as the input signal,
and the output is the attenuation of the perturbation.

We simulate the sensitivity transfer function, which is defined by:

(x_beam_position)/(x_noise)=1/(1+H)

where H = HLibera \* Htransport_delay \* HPower supply \*
Hmachine_optics.

This transfer function gives the suppression of possible disturbances
over the frequency range. The idea is the get the larger and higher
attenuation in the stopband. We consider the bandwidth of the system, as
the attenuation lower than 3 dB.

Figure 4 shows the Simulink model with the models of the different
subsystems involved the in FOFB. The transport delay models the latency
of the system: BPM position distribution, processing times, corrector
settings distribution.

![](media/image4.wmf){width="3.2527777777777778in"
height="1.0993055555555555in"}

Figure 4: Simulink model of the FOFB.

Using a PI controller
$\text{PID} = K_{p}\left( \frac{T_{i}s + 1}{s} \right)$ with *K~p~*=0.2
and *T~i~*=1/(2\*π\*50), the frequency response of the sensitivity
function is shown in Figure 5. With these moderate values of the PI
parameters, the 0 dB point is in the range desired (between 100 and 200
Hz), and the system can compensate realistic values of the noise under
100 Hz.

![](media/image5.wmf){width="2.452777777777778in"
height="1.8659722222222221in"}

Figure 5: Amplitude and phase response of the sensitivity function.

## conclusion

We have studied the different subsystems involved in the FOFB. We have
measured their response and simulate their behaviour, in order to
produce precise model that will help us study the behaviour of the
system. With this complete model, we have adjusted the PID parameters in
order to get the desired bandwidth, with the highest attenuation. The
idea is to use this model, and together with the real noise measurements
in our accelerator, decide the final parameters of the PID. The next
steps are to decide in the communication model for the data sharing
between the Liberas, the corrector magnet power converters and the CPUs
in charge of the PID.

## Acknowledgments

We would like to thank Thomas Schilcher and Michael Boge from SLS for
the discussions in our visit to their facility.

## References

\[1\] D. Einfeld, "Status of the ALBA Project", Proceedings of EPAC-06,
Edinburgh 2006.

\[2\] http://www.i-tech.si/.

\[3\] M. de Lima "Eddy current studies on the ALBA SR sextupoles",
Internal report, 2007.

\[4\] M. de Lima "Field attenuation and delay at SR correctors dune to
eddy currents in the sextupoles vacuum chamber", Internal report, 2007.