LONGITUDINAL DISPERSION MEASUREMENTS AT THE S-DALINAC
USING RF MONITORS*
F. Hug #, C. Burandt, R. Eichhorn, M. Konrad, N. Pietralla
TU Darmstadt, Darmstadt, Germany
Abstract
The superconducting electron accelerator S-DALINAC
is a recirculating linac with two recirculations. Currently
the effect of different longitudinal working points on the
resulting energy spread of the linac is investigated in
order to provide an electron beam with a lower energy
spread for the experimental setups in future. For this
purpose it is necessary to know the properties of the beam
transport system exactly, especially the effects of
different settings on the longitudinal phase space. We will
report on the lattice optimizations in the recirculation arcs
and on a new setup for the measurement of their
longitudinal dispersion using rf phase measurements on
beam intensity monitors and the time of flight method.
INTRODUCTION
The Superconducting DArmstadt LINear Accelerator
(S-DALINAC) is provides electron beams of up to 130
MeV for nuclear- and astrophysical experiments at the
university of Darmstadt since 1987 [1]. It can accelerate
beams of either unpolarized or polarized electrons [2]
with beam currents from several pA up to 60 A. The
layout of the S-DALINAC is shown in Fig. 1.. The
superconducting cavities are operating at a frequency of 3
GHz with a maximum accelerating gradient of 5 MV/m.
After having passed the injector linac the beam has an
energy of up to 10 MeV and can either be used for a low
energy experimental area or be bent 180 degrees and
injected into the main linac. The main linac consists of 8
standard 20-cell cavities and can achieve an energy gain
of 40 MeV. So the maximum energy of 130 MeV can be
achieved by recirculating the beam twice before directing
it to the adjacent experimental hall. The experimental
setups located there require an energy spread of + 1·10-4.
Figure 1: Floor plan of the S-DALINAC.
___________________________________________
*Work supported by BMBF under contract 06DA9024I
#
hug@ikp.tu-darmstadt.de
Figure 2: Hill plot of the resulting energy spread of the
beam as function of the longitudinal dispersion and the
synchrotron phase.
NON-ISOCHRONOUS RECIRCULATION
The original design of the S-DALINAC uses an
isochronous recirculation scheme and electron
acceleration in the maximum of the accelerating field (on
crest) in every turn. Isochronicity is a property of beam
optics and can be described as dl/dE = 0 meaning that the
length of the flight path of all electrons is independent
from their energy. The acceleration on crest is the
common mode for linacs. Unfortunately in this case rf
jitters can add up causing an increase in energy spread.
For that reason the usability of a non-isochronous
recirculation scheme with acceleration on edge of the
accelerating field for the S-DALINAC has been
investigated. In such a scheme the electrons would
perform synchrotron oscillations in longitudinal phase
space which can cancel out the errors caused by the rf
jitters if a half or full integer number of oscillations can
be achieved. [2,3]
In numerical simulations the usability of such a nonisochronous recirculation scheme at the S-DALINAC has
been verified already and a new longitudinal working
point has been determined. Figure 2 shows the results
found in these simulations. The optimized working point
(DL = -1.5 mm/% and ΦS = -9.5°) would lead to a
reduction of the energy spread to E/E = 6.03∙10-5 which
satisfies the requirements mentioned above. (for more
details see [4,5] )
Figure 3: Optimized lattice for the bending sections of the first (left) and second. (right) recirculation. At the end of
each bend D (red) and D’ (green) vanish while DL (purple) reaches the envisaged value of -1.5 mm/%.
Measurement Principle
LATTICE OPTIMIZATIONS
In order to tune the S-DALINAC to a different
longitudinal working point optimizations at the
quadrupole lattice of both recirculation arcs had to be
carried out. [5] The optimized lattice allows changing the
value of DL easily while the transverse dispersion D and
the transverse angular dispersion D’ both equal zero at the
end of every recirculation arc. The manipulation of DL is
done by changing the quadrupole gradients in the arcs.
In the first recirculation arcs (Fig. 3 left) the two
quadrupoles are set always to the same gradient and by
changing this gradient the longitudinal dispersion can be
manipulated while D and D’ always remain at zero. The
dispersion changes by gradient like:
dDL /dG = -0.18 mm/% / T/m
For the second recirculation (Fig. 3 right) one more
quadrupole in the arc is needed to compensate an
asymmetry of the bending angles of the dipoles. The
quadrupoles are not set to the same gradient like in the
first recirculation arc but it is possible as well to
manipulate the longitudinal dispersion while D and D’
remain at zero at the end of the arcs. To do so the
quadrupole gradients are changed in a fixed ratio:
dDL /dG1 = 0.19; dDL /dG2 = 0.11
dDL /dG3 = 0.7 mm/% / T/m
For the determination of the longitudinal dispersion in
the arcs the time of flight of the electron bunches is the
matter of interest as changes of beam energy are related to
changes of this time when DL ≠ 0. Instead of measuring
the time of flight of every bunch directly it is more
appropriate to determine the phase of the 3 GHz
oscillation excited by the beam in an rf monitor. In that
way it is possible to detect changes in time of flight by
measuring a difference in phase of the 3 GHz oscillation.
A certain phase difference corresponds to a difference in
time of flight and can be converted to a difference in path
length dl easily using the 10 cm wavelength of the 3 GHz
operation frequency of the S-DALINAC. Finally DL can
be determined from dl:
d
deg
dl
 3.6
 DL 
dl
mm
dE
Measurement Setup
The setup for longitudinal dispersion measurements at
the S-DALINAC makes use of rf intensity monitors
located at the end of the recirculation arcs. Usually, these
intensity monitors, which are pillbox cavities at a 3 GHz
resonant frequency (see Fig. 4 left), are used for nondestructive measurement of the beam current during
operation. The passing beam excites an oscillation in the
TM010 mode whose rf signals can be coupled out by an
MEASUREMENT OF LONGITUDINAL
DISPERSION
Even though the idea of improving the energy spread at
the S-DALINAC using non-isochronous recirculation was
presented many years before [4], the realisation,
especially tuning the machine to the new longitudinal
working point, still was not possible. The main reason
was a lack of diagnostics developed meanwhile and
described in the section below.
Figure 4: Measurement setup consisting of rf monitor
(left) and rf board with FPGA board (right).
antenna. As the power coupled out of the cavity is in
the order of some nWs these signals are amplified by 35
dBm
before they are sent to the rf electronics located outside
of the accelerator hall. The rf electronics consist of a rf
board and a FPGA board (see Fig. 4 right) and is part of
the newly developed digital LLRF system of the SDALINAC [6]. The signals coming from the rf monitor
are mixed with the signals coming from the local
oscillator on the rf board and converted down to the base
band using an I/Q-demodulator. The I/Q values represent
the relative oscillation phase of the monitor in respect to
the local oscillator. In addition the magnitude of the rf
signal is detected by a diode. The analogue signals for
I,Q and A are transferred to the FPGA-board and
digitized (see Fig. 5). Inside the FPGA an iterative
algorithm called coordinate rotation digital computer
(CORDIC [7]) converts I and Q into phase. The
communication with the FPGA board is done via USB
and CAN-Bus. The PC runs an EPICS IOC and the
measured values can be read out as well as the offsets on
the rf board can be adjusted on a GUI.
Figure 6: Measured I/Q values of the beam for different
dipole and quadrupole settings (top) and resulting
longitudinal dispersion (bottom) of the first recirculation.
The red arrows mark the correction of beam losses which
appeared only at very low quadrupole gradients in the arc.
Figure 5: Schematic view of the measurement setup.
Results for the First Recirculation
The quadrupole lattice of the recirculation arcs has been
optimized for providing a non-zero longitudinal
dispersion as mentioned above. Afterwards an experiment
in the first recirculation arc has been carried out to test the
measurement setup as well as the accuracy of the results
of the beam dynamics simulations. To determine DL the
magnetic field of the dipoles in the arc have been set to
different values changing the energy of the reference
trajectory. For every dipole setting the I/Q-values have
been measured. Afterwards, the arc has been tuned to a
different longitudinal dispersion by changing the
quadrupole gradients. The pairs of I/Q values for every
measurement are plotted in the upper part of Fig. 6. The
bending system accepted a large range of quadrupole
gradients. Only at very low gradients the transverse
extension of the beam caused beam losses in the arc. The
lower part of Fig. 6 shows the obtained values of DL for
the measurement and a linear fit of the data points. The
results fit very well with the simulation results. In
addition it is obvious that DL can be changed over a large
interval without the appearance of beam losses including
the envisaged value of DL = -1.5 mm/%.
SUMMARY AND OUTLOOK
A setup for measuring longitudinal dispersion in the
recirculation arcs has been tested successfully. This
allows to tune the accelerator to different longitudinal
working points now and to investigate the effects on
resulting energy spread of the beam.
REFERENCES
[1] A. Richter. “Operational experience at the SDALINAC”, EPAC ’96, Sitges (1996) 110.
[2] H. Herminghaus, NIM A305 (1991) 1.
[3] H. Herminghaus, NIM A314 (1992) 209.
[4] R. Eichhorn et al., “Methods to reduce the electron
beam energy spread at the S-DALINAC”, LINAC
’06, Knoxville, Tennessee (2006) 73.
[5] R. Eichhorn et al., “Reducing the Energy Spread of
Recirculating Linac by Non-Isochronous Beam
Dynamics”, LINAC ’10, Tsukuba, (2010) 64.
[6] A. Araz et al., Phys. Rev. ST Accel. Beams 13,
082801 (2010).
[7] J. Serrano, “FPGA Technology in Instrumentation
and Related Tools”, DIPAC ’05, Lyon, (2005), 132.