Large-field-strength short-period undulator design

Nuclear Instruments and Methods
Physics Research A318 (1992) 813-tî17
Section A
Large-field-strength short-period undulator design
A.A. Varfolomeev, S.N. Ivanchenkov and A.S. Khlebnikov
1. V. Kurchatc .- !nstitute of Atomic Energy, Moscow 123182, USSR
C. Pellegrini
Departtttent of Physics, UCLA, Los Angeles, CA 90024, USA
G.A. Baranov and V.I. Michailov
D. V. Efremor Scientific Research Institute of Electrophysical Apparatus, St. Pelcrsburg 189631, USSR
A high-quality strong-field hybrid undulator has been designed for an infrared FEL project to be performed at UCLA. The
primary magnetic flux is provided by C-shaped vanadium-permendur yokes and SmCo5 magnets . An additional magnetic flux is
supplied by thin NdFeB magnet blocks placed between the yoke poles . This magnet geometry provides a high saturation limit for
the magnetic field in the gap area. With the 15 mm period and 5 mm gap a peak on-axis field of 7.3 kG has been achieved. The
undulator contains 40 periods . The high accuracy of the yoke poles alignment along with the ability to move the thin permanent
magnet blocks provides an on-axis magnetic field accuracy better than 0.5% .
1. Introduction
The development of compact or short-wavelength
FELs is important to make this laser a widely used
research instrument. One key issue in this program is
the production of short-period high-field undulators
which can provide an electron beam deviation of the
order AW /y . This condition requires that we increase
the peak field B on axis as we decrease the period A W
in accordance with the equation A,,, BO, - 104 G cm. It
poses a challenge to the undulator designers (see, e.g.,
In this paper we describe a hybrid undulator design
that permits the increase of the field saturation limit
above what can be obtained in ordinary hybrid undulator schemes. This undulator has been built for the
compact FEL project "Saturnus" [3] in accordance
with the Kurchatov Institute-UCLA collaboration
2. Scheme of the combined hybrid undulator
The scheme of the combined hybrid undulator with
its main components can be seen from fig. 1. A specific
magnet shape provides two different magnet fluxes.
The primary one produced by samarium-cobalt permanent magnets is directed by the C-shape vanadium-permendur yokes into the gap area along the
plane which is perpendicular to the undulator axis.
Another magnetic flux is induced by the thin
neodymium-boron magnet blocks inserted between the
thin vanadium-permendur poles . It is directed into the
gap area in the same way as in the well-known hybrid
undulator scheme [4]. The main flux direction in this
case remains in the planes parallel to the undulator
axis. This combination of two different magnets provides a wide-aperture capture of the magnetic fluxes
directed to the gap area. As a result the undulator field
strength is raised appreciably at the same undulator
period value .
Different magnet prototypes were investig it v to
find the magnet shapes optimal for short-period undulators. Both computer simulations using the TOSCA
3D code [5] and experimental measurements with the
same period undulator prototype modules [6] were
made. The role of each magnetic flux in providing high
field strength in the gap area was specially investigated . The experimental results of the on-axis field
strength measurements as a function of the variable
magnetic flux provided by an electromagnet inserted
between the half yokes instead of SmCo $ blocks are
given in ref. [6] . It was found that the saturation field
strength for this case being equal to 1.25 kG was the
same as in the case when only the SmCo5 permanent
magnets were used. If only NdFeB magnets were inserted the saturated field strength was equal to 5.3 kG.
But if both magnetic fluxes were provided, i.e., NdFeB
0168-9002/92/$05 .00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
A.A . Varfoloineev et aL / Large-field-strength skort-period undulator design
Fig. l. Drawing of the undulator design cross-section transverse to the undulator axis .
magnet blocks were inserted and the electromagnet
coil was used as well, the saturation field strength
could reach 7.5 kG. The same field limit was achievab!e with both permanent magnet sets being inserted
without any coil. A very important effect is apparent .
The magnetic field strength in the gap provided by two
magnetic sets can exceed the arithmetical sum of the
two field strength values provided by each of magnet
sets separately. This effect was first found in our experiments [6] and then was confirmed by the simulations
The relative contribution of each magnet sc;i to the
gap magnetic field depends very much on the thickness
ratio of the small NdFeB blocks and the vanadiumrmendur poles, respectively [5,6]. For the final design this crucial parameter was selected to be equal 1 .5
(see below).
The results of the mock-up tests and computer
simulations have confirmed the superiority of this combined hybrid undulator scheme over the commonly
used hybrid scheme if high field amplitudes with short
undulator periods are desirable . A 20-25% gain in
comparison with that predicted by the Halbach limit [4]
is possible [6] .
steel frame for support and can be separately moved in
the vertical direction towards or away from the undulator axis with the help of a screw set to adjust the gap
field strength. Both the top and the bottom sets of the
vanadium-permendur yokes are fixed on massive stainless steel frames . The high-precision machining of the
pole tips was done afterwards. The permanent magnet
boxes were also manufactured with high accuracy along
the full undulator length since the undulator magnet
gap value is determined by the thickness of these
At the edges of the undulator two half-cells of
special construction were mounted to provide a wide
range regulation of the magnetic field at the entrance
and the exit of the undulator .
The undulator was mounted on a platform with
adjustable supports as can be seen in fig. 2. The
distance from the bottom of the undulator stack to the
bottom of the platform can be regulated within the
range 15-25 cm and adjusted with the help of micrometer screws on four supporting legs. The upper plate of
the supporting platform carrying the undulator construction as a whole can be moved in horizontal plane
with the help of the lateral adjusting screws. With
these screws and cross-hairs the undulator axis align-
3. The undulator design
Using the results of the prototype model investigation, the Kurchatov compact undulator was designed.
Its main parameters are given in table 1 . A drawing of
the undulator cross section transverse to the undulator
axis iF ¢iven in fia. 1 . The assembled undulator is
shown in fig. 2.
Sets of SmCo. magnets are inserted into common
metal boxes with nonmagnetic stainless steel side walls .
Each of the small NdFcB blocks has its own stainless
Table I
Main parameters of the undulator
Number of periods N
Length of the period A, [mm]
Magnet gap g [mm]
Amplitude of the field Bt) [kG]
Factor of the undulator field, K
Spread in integrals of the field
over one period [G cm]
< 20
A.A. liarfolomeei - et al. / Largefield-strength shortperiod undulator design
Fig. 2. Photograph of the complete undulator assembly.
ment can be done with the accuracy better than 0.1
In accordance with the FEL project the undulator
has no tapering . Its 5 mm gap is fixed with an accuracy
of 10 p.m.
The magnet poles tips have flat faces. No pole face
curvature of the sort considered in ref. [7] has been
used since the expected emittance of the electron
beam is very small [3]. Precise measurements were
made to check the precision of the manufactured and
assembled undulator . It was found that the deviations
of the yoke positions from that predicted for an ideal
periodical structure did not exceed 10 p,m [8] . The
flatness of the pole tip surface over the undulator
length was controlled separately for each platform just
after manufacturing and after shipping. The maximum
deviations did not exceed 40 wm [8] and were appreciably less in the assembled installations .
The parameters of the permanent magnet blocks
used in the undulator are presented in table 2. The
larger SmCoS blocks were inserted into steel boxes
which were placed between the top and bottom halves
of vanadium-permendur yoke. The C-yokes have a
common structure so the sensitivity of the system to
the magnetic properties of the individual magnet blocks
is small . The SmCoS blocks were not specially selected.
However the small NdFeB blocks were carefully controlled and selected. Only those blocks with deviations
from avarage magnetic parameters not exceeding 2%
were selected for installation [8]. The NdFeB magnet
blocks with 25 x 25 X 4.5 mm; dimensions were fixed
between the pole tips. A primary rather crude adjustment of the magnetic field was performed by displacement of the boxes côntaining the SmCos magnets. On
the next stage, the gap field was adjusted by changing
the NdFeB magnet positions. It was possible to change
Table 2
Parameters of the permanent magnet blocks
(mm 3)
Dimensions of the magnet blocks
Remanent induction Br MG)
Maximum energy product (BH)m;, x (MG Oe)
Magnetization dispersion of the selected magnet blocks (%)
Number of used blocks
8 .5-9 .0
10.5-11 .0
A.A . Varfolomeet , et al. / Large-field-strength short-period undulator design
8 .0
7 .8 -I
7 .6 -1
7 .4
7 .2-
7 .01
Period number
Fig . 3 . Magnetic field profile along the undulator axis:
the undulator field in selected cells up to several
percent . At the last stage, a tine tuning up to 0 .5% was
made with the help of shunting screws placed opposite
each pole .
Magnetic field measurements
For measurement of magnetic field in the gap area
a set of Hall probes was used . A small carriage with 4
fixed probes was moved step by step along the undulator axis automatically by a motor-driver . Two of the
probes positioned I mm above and 1 mm below the
central plane - of the undulator were used for vertical
magnet position alignment . The other two probes were
used for magnetic amplitude measurements. An accuracy of 0.1% was provided .
Due to the high accuracy of the construction and
the tuning capability, a highly uniform magnetic field
was obtained . Fig . 3 shows the final results of the
magnetic field amplitude measurements along the undulator axis. One can see that the total spread of the
field amplitudes is less than 0.5% or 40 G . The corresponding spread of the magnetic field integral over the
individual periods is smaller than 20 G cm . This figure
demonstrates the very high accuracy and uniformity of
the undulator magnetic field .
amplitude for even poles, + : amplitude for odd poles.
Another important result is the high magnetic field
amplitude provided by this undulator design at a rather
short undulator period . At the period 15 mm, a field
amplitude of 7.3 kG was obtained . This is not the
absolute maximum . To make the adjustment easier the
nominal amplitude was decreased .
A comparison with the so-called Halbach limit [4],
derived from the experimental data obtained with conventional hybrid undulators shows that our undulator
provides a 20% stronger field than predicted by this
limit along with high uniformity and a short undulator
period .
Our undulator scheme looks similar to but actually
is different from the SEM scheme considered in ref.
[9] . In particular the relative magnetic flux directed by
a pole to the gap midplane with respect to the other
part of the magnetic flux coming through the pole is at
least four times higher for our scheme . This is one of
the reason why the Halbach limit could be exceeded .
[1] Proc . l lth Int. Conf . on Free-Electron Laser, 1989, Naples,
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McMillin and G . Swoyer, Nucl . Instr . and Meth . A296
(1990) 597.
A.A. Varfolomeet- et al. / Largefield-strength .short-period undulator design
[2] 1 . Ben-Zvi and K. Halbach, Summary of Working Group
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(BNL 5227, UC 414, Brookhaven, NY, 1990).
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[4] K. Halbach, J. de Phys. (Paris) 44 (1983) C-1211 .
[5] J.W . Dodd, Yu .Yu. Lachin, C. Pellegrini and A.A. Varfolomeev, Preprint UCLA CAA0072-2/91 (Los Angeles,
CA, 1991).
[6] S.N . Ivanchenkov, C. Pellegrini and A.A . Varfolomeev,
Preprint UCLA-CAA Tech .-note-int .-5/91 (Los Angeles;
CA ; 199!) '
[7] E.T. Sharleman, J. Appl . Phys . 58 (1985) 2154 .
[8] A.A . Varfolomeev, S.N . Ivanchenkov, A.S. Khlebnikov, C.
Pellegrini, G.A . Baranov and V.I . Mikhailov, Preprint
UCLA-CAA0074-3/91 (Los Angeles, CA, 1991).
[9] M.J . Burns, G.A . Deis, R.H . Holmes, R.D. Van Maren
and K. Halbach, IEEE Trans. Magn . 24 (1988) 978.