Conceptual Design of a Superconducting Undulator System for the LCLS-II
Hard-X-Ray FEL
P. Emma, W. Craddock, C. Emma, J. Frisch, H.-D. Nuhn, C. Pellegrini, SLAC, Stanford, CA 94309, USA;
D. Arbelaez, J. Corlett, M. Leitner, S. Myers, S. Prestemon, R. Schlueter, LBNL, Berkeley, CA 94720, USA;
C. Doose, J. Fuerst, Q. Hasse, Y. Ivanyushenkov, M. Kasa, G. Pile, E. Trakhtenberg, M. White, E. Gluskin, ANL,
Argonne, IL 60439, USA
Dec. 11, 2014
1. Introduction
Undulators serve as the primary source of radiation for modern storage rings, and more recently for
the advent of Free-Electron Lasers (FELs). The performance of future FELs can be greatly enhanced
using the much higher magnetic fields of superconducting undulators (SCU) [1]. For example, the upper
limit of the spectral tuning range of the LCLS-II hard x-ray (HXR) FEL can be extended from just under
5 keV, using a hybrid-permanent magnet undulator (PMU), to 7 keV using an SCU of similar length. In
addition, SCUs have no permanent magnet material and are therefore expected to be orders of magnitude
less sensitive to demagnetization through radiation dose; a major issue at LCLS-II with its nearly 1-MW
electron beam power. Here we present a conceptual design of a full-scale SCU system to possibly replace
the LCLS-II HXR PMU, based on R&D already underway through collaboration with SLAC, ANL, and
LBNL [2]. The R&D effort aims to demonstrate, by July of 2015, the viability of superconducting
undulators for FELs by building, testing, tuning, and measuring two 1.5-m long planar SCU prototypes
using two different superconducting wire technologies: NbTi at ANL and Nb3Sn at LBNL.
The LCLS-II [3] FEL project at SLAC aims to construct a new continuous wave (CW), 4-GeV
superconducting linac (SC-linac) [4], to feed either or both of two new undulators: 1) the Soft X-ray
Undulator (SXU), or 2) the Hard X-ray Undulator (HXU). The HXU will replace the existing LCLS-I
fixed-gap undulator and can be optionally fed by the existing 3-15 GeV copper (Cu) linac (120 Hz),
presently used to drive the LCLS-I FEL. The spectral requirements for the SXU are 0.2-1.3 keV (SASE
and self-seeded), while the HXU requires 1 keV to  5 keV (both SASE and self-seeded where possible)
when driven by the SC-linac. The HXU spectral range, when driven by the Cu-linac, requires 1-25 keV.
The baseline design use two adjustable-gap, planar PMUs (NdFeB) with 39-mm (SXU) and 26-mm
(HXU) periods and a minimum 7.2-mm full magnetic gap, gm. At 4 GeV (limited by SC-linac costs) the
PMU’s reach these requirements, but with little margin, especially for the HXU which barely produces
5-keV SASE photons, and cannot exceed 4 keV when self-seeded, due to a limited undulator hall length.
To address these performance limitations, we propose a short SCU undulator (77 m) for the HXU
FEL, which is nearly half the length of the baseline PMU device (140 m), while still producing the same
spectral tuning range as the PMU baseline, but allowing a future SCU extension to fill the existing 140-m
undulator hall, then providing up to 7-keV photons with the same 4-GeV electron beam (see Figure 4). In
addition, the full-length SCU (140 m) can provide > 1 TW peak FEL power when self-seeded, tapered,
and driven by the Cu-linac (see Figure 2 and Table 1 – “Cu-linac”).
Several SCUs have been built in the recent past [5], and some are operating in existing storage rings
[6], [7], but technical issues such as precise field measurements, phasing corrections, and alignment
procedures have set the challenge which needs to be accepted to push FEL performance into the future.
1
2. Motivation
The motivations for SCU’s, especially in comparison to PMU’s (“in” or “out” of vacuum), are listed
below.






Higher magnetic fields allow superior FEL performance, or a reduced undulator length.
No permanent magnetic material to be damaged by radiation, allowing longer life and smaller gaps.
Somewhat reduced resistive wakefield with a cold bore [8,14,14].
Much lower vacuum pressure, which limits gas scattering.
Smaller footprint and simpler K-control than the typical massive adjustable-gap PMU.
Easily oriented for vertical polarization, if desired.
Figure 1 shows calculations [9] for the LCLS-II HXU (using the SC-linac at 4 GeV) with vertical axis
as the full undulator system length (including breaks), versus the upper-limit SASE photon energy that
saturates within 80% of that undulator length. The “system length” uses 1.5-m long undulator magnet
segments and 0.33-m (average) breaks between segments (see Figure 18), with a beam position monitor
(BPM), a quadrupole magnet, and a phase shifter. The lower-limit photon energy setting (at 4 GeV) is 1.5
keV for all curves, while the electron beam parameters are listed in Table 1 under “SC-linac”. The figure
shows (for example) that an SCU using Nb3Sn technology, with a 5-mm vacuum chamber aperture, can
produce from 1500 to 7250 eV at 4 GeV, using a 140-m long SCU. It also shows the PMU is tunable
from 1500 eV to only 4800 eV with the same undulator length.
Figure 1: Undulator system length (with 1.5-m magnet segments and 0.33-m average break lengths) versus the
upper-limit SASE photon energy which saturates in 80% of that undulator length at 4 GeV. (Note the baseline PMU
uses 3.4-m segments and 1-m breaks: a 5% smaller packing factor). The lower-limit photon energy in all cases is
1.5 keV. A suffix of “-5” or “-4” indicates the full vacuum chamber aperture in millimeters. In addition, the
existing 140-m undulator hall length is indicated as a limit (maximum installed undulator length), as is the upper
limit photon energy for self-seeded operation (intersection with the “93 m” line [ 140/1.5]).
2
Table 1: Electron beam parameters used for FEL calculations (SC-linac and Cu-linac).
Parameter
Sym.
SC-linac
Cu-linac
unit
E0
4.0
3-15
GeV
Emittance
x,y
0.4
0.4
m
Slice energy spread, rms
E
0.5
1.5
MeV
Peak current
Ipk
1
4
kA
Bunch charge
Q
0.10
0.15
nC
Bunch length (rms)
z
8.7
3.3
m
Mean beta function

16
16
m
fb
930
0.12
kHz
Electron energy
Max. electron bunch rate
The lower-limit photon energy is chosen at 1.5 keV for all curves (at 4 GeV), so once the magnet gap
and undulator technology (e.g., NdFeB-PMU, NbTi-SCU, or Nb3Sn-SCU) are chosen, the period is then
exactly given by the FEL resonance condition,
𝜆𝑟 =
𝜆𝑢
(1 + 𝐾 2 ⁄2) ,
2𝛾 2
where r is the FEL wavelength, u is the undulator period,  is the electron energy in units of rest mass,
and K is the undulator parameter (K  0.93B[T]u[cm]), where the peak field, B, is a known function of
the magnet gap, gm, period, and the precise undulator technology applied. Note that the lower-limit
photon energy can be set to 1 keV by lowering the electron energy to ~3.5 GeV.
All “5” labels (e.g., “PMU-5”) in Figure 1 have 5-mm vacuum chamber apertures (7.3-mm magnet
gaps – see Figure 3), while “4” labels (e.g., “PMU-4”) are 1-mm smaller, with a 6.3-mm magnet gap.
The “in-vacuum” case is the same PMU technology and has the same (4-mm and 5-mm) vacuum chamber
aperture for a fair comparison, but 2-mm smaller magnet gaps, since no vacuum chamber is needed here.
The various undulator periods are listed for all eight cases with appropriate color coding.
The SCU performance is clearly superior to the PMU, both “in-vac” and “out-of-vac”. (Note that invacuum devices have improved performance primarily by allowing a smaller magnetic gap.) Clearly the
“in-vacuum” performs better than “out-of-vacuum”, but neither reaches the attractive performance levels
of SCUs. (Note also that an in-vacuum device, with its permanent magnets approaching even closer to
the high-power electron beam, is not an attractive choice for the LCLS-II FELs.) The Nb3Sn technology
promises the best performance, but involves more risk with a 650C heat treatment cycle required after
winding the coils. Note that self-seeding requires at least 50% more undulator length, so the highest selfseeded photon energy is the intersection of these curves with the 93-m line (e.g., 6.3 keV for Nb3Sn-5).
Figure 1 can be used to estimate the length of SCU needed. For example, the “NbTi-5” solid-green
curve intersects the 5-keV line at Lu  75 m, while the “Nb3Sn-5” solid-red curve intersects the 5-keV line
at Lu  65 m. This is about half the length of the PMU device (solid-blue curve), which might offset the
somewhat higher costs of an SCU and still allow future extension to fill the hall (140 m) in the future.
Finally, in addition to the spectral tuning range extension, when the “Nb3Sn-5” or “NbTi-5” fulllength undulators are driven by the Cu-linac (see Table 1, “Cu-linac”) at 6.6 GeV with self-seeding [10]
and a step-wise field taper is applied (~20% total field taper needed over the fill undulator), a peak FEL
power of ~1.6 TW at 4 keV is possible (see Figure 2, where the self-seeding monochromator is located at
3
z = 0). This was run using a 1.5-m undulator segment length and 0.5-m breaks. This power level is only
possible with the full-length SCU system upgrade of 140 m.
Figure 2: Peak FEL power (~1.6 TW) at 4 keV using the “Nb3Sn-5” undulator (red) and the “NbTi-5” undulator
(green) of Figure 1, but now self-seeded, tapered, and driven by the Cu-linac at 6.6 GeV with 4 kA. Segment
lengths are 1.5 m here with 0.5-m breaks, allowing an efficient step-wise field tapering with this 1-m FEL gain
length. The self-seeding monochromator is located at z = 0 (above) and the beam parameters are listed in Table 1
under “Cu-linac” (at 6.6 GeV). This power level is only possible with the full-length SCU system of 140 m.
In addition to a broader tuning range, and less radiation sensitivity, the SCU magnet can easily be
rotated in its cryostat (before installation) to produce either horizontal or vertical polarized light, allowing
polarization control by interfering the radiation fields from two adjacent planar undulators in a crossed
configuration. A phase shifter between them controls the final polarization. This crossed-undulator
scheme [11] might easily be implemented in the SCU by rotating a few of the final undulator sections.
3. FEL Requirements
The HXR undulator system at LCLS-II should have an adjustable K-value and should generate FEL
light into saturation when driven by either the new superconducting linac (4 GeV) at up to 1 MHz, or the
existing copper linac (3-15 GeV) at 120 Hz. The required photon energy tuning range in each case is
listed in Table 2. The HXU needs to be designed for both of these cases, operated at separate times, not
simultaneously. Note also that self-seeding should be available for as much of the tuning range as
reasonably possible.
Table 2: Photon energy SASE tuning range required by the HXU system when driven by each linac.
Parameter
Electron energy
Maximum bunch repetition rate in undulator
Photon energy tuning range (SASE)
* The
SC-linac
Cu-linac
unit
4
3 - 15
GeV
930
0.120
kHz
1.5* - 5.0
1 - 25
keV
lower-limit photon energy (SC-linac) is set to 1 keV by lowering the
4
e
energy to ~3.5 GeV.
Parameters for LCLS-II HXU
An HXU parameter list which meets these requirements, while using the electron beam parameters of
Table 1, is shown in Table 3, allowing for two possible SCU technologies (NbTi or Nb3Sn) with a planar
undulator.
Table 3: Planar undulator parameters for the NbTi and the Nb3Sn SCU technologies based on the electron beam
parameters of Table 1 and the photon energy tuning requirements of Table 2. The last seven items are based on an
undulator beamline length of 77 m (or a 140-m long tunnel-filling option in parenthesis as future expansion).
Parameter
symbol
values
unit
Undulator technology
-
Nb3Sn
NbTi
-
Undulator period
u
18
20
mm
Maximum on-axis peak magnetic field (80% short-sample limit)
Bmax
1.91
1.71
T
Maximum K value (80% short-sample limit)
Kmax
3.21
3.20
-
Full magnetic gap (in field direction)
gm
7.3
mm
Full vacuum chamber aperture (internal, in field direction)
gvc
5.0
mm
Magnetic undulator segment length
Lseg
1.5
m
-
3
-
Lcry
5.5
m
Long break length between every 3 segment (BPM, quad, PS)
Lbrk3
0.7
m
Short break length between 1st/2nd and 2nd/3rd segments (PS)
Lbrk12
0.15
m
Mean break length (average over one cryostat)
Lbrk
0.33
m
p
0.82
-
LFODO
11
m
LQ
8
cm
|GLQ|max
7
T
Number of cryostats
Ncry
14 (25)
-
Number of undulator segments
Nseg
42 (75)
-
Number of cavity BPMs needed
NBPM
14 (25)
-
Number of quadrupole magnets needed
Nquads
28 (50)
-
Nps
42 (75)
-
Lu,mag
63 (112)
m
Lu
77 (140)
m
Number of undulator segments per cryostat
Cryostat length
rd
Packing factor: p = Lseg/(Lseg + Lbrk)
FODO cell length (2 cryostats)
Magnetic length of quadrupole magnet (example value)
Integrated quadrupole gradient (15 GeV,   16 m)
Number of magnetic phase shifters needed
Total magnetic length of undulator (Lseg×Nseg)
Total length of undulator beamline, with breaks but no self-seeding
The two undulator periods have been chosen by assuming a 7.3-mm fixed magnetic gap (5 mm
vacuum chamber aperture – see Figure 3 for gap stack-up) and a fixed electron energy of 4.0 GeV from
the SC-linac, along with the required lower-limit photon energy (in SC-linac operational mode) of
1.5 keV. This choice is based on the maximum field (K) attainable with each technology using an
excitation current which is 80% of the quench limit. For the two technologies proposed (Nb3Sn or NbTi)
this results in an 18-mm undulator period for Nb3Sn and a 20-mm undulator period for NbTi. (These
5
periods are rounded to integer values giving a lower-limit photon energy at 4.0 GeV of 1375 eV for
Nb3Sn, and 1250 eV for NbTi.) Lower values of photon energy can be reached by reducing the electron
energy (e.g., 4.0  ~3.5 GeV, producing ~1 keV). The 5-mm chamber aperture is chosen in order to
control resistive-wall wakefields of the undulator chamber (see next sections), to allow insertion of tuning
circuits etched on high-temperature superconducting tape (HTS), to provide clearance and thermal
insulation between the slightly warmer vacuum chamber and the magnet core (as shown in Figure 3), and
also to allow enough room for the passage of Hall probes in the undulator measurement process [12].
Figure 3: Cross-section (not to scale) of undulator showing vacuum chamber and gap stack-up with a full chamber
aperture of 5 mm (shown vertically here) and a full magnetic gap of 7.3 mm. The ‘horizontal’ aperture will likely be
3-4 times larger than the vertical to form a quasi-rectangular aperture. The 0.5-mm vacuum gaps at top and bottom
provide thermal insulation from the magnet core to the slightly warmer vacuum chamber. High-temperature
superconductor (HTS) tape contains magnetic field tuning circuits and is mounted on each side of the chamber.
FEL Performance
The performance of the HXU SCU FEL when driven by the SC-linac or the Cu-linac is listed in Table
4 for both the Nb3Sn and the NbTi technologies, while the electron beam parameters for both linacs are
listed in Table 1, with undulator parameters in Table 3. Note for the “Cu-linac” parameters in Table 4
below, the number of photons per pulse at the low-photon-energy limit (1-keV) is estimated based on the
maximum value of K (~ 3.2), which is set by the field limit for the chosen gap and period, and with the
electron energy appropriately reduced (~3.5 GeV). For the high-photon-energy Cu-linac limit (25 keV),
the electron energy is set to its maximum (15 GeV) and the K-value is appropriately reduced (~2.7). For
the “SC-linac” parameters, the energy is fixed at 4.0 GeV, but a 1-keV photon energy can be reached by
reducing the electron energy (e.g., 4.0  ~3.5 GeV). Note that the values in Table 4, except where noted
as “Lu = 140 m”, are calculated based on the short (Lu = 77 m) undulator beamline length, not the tunnelfilling future expansion with Lu = 140 m.
6
Table 4: FEL performance parameters with the SC-linac energy fixed at 4 GeV and the Cu-linac energy variable
from 3 to 15 GeV. The abbreviation “SS” is for the “Self-Seeded” mode of operation and “nt” indicates “no taper”
included here. The upper-limit of the photon energy tuning range is listed for both the short undulator beamline
length (Lu = 77 m) and the long undulator upgrade (Lu = 140 m), which are described in Table 3. All other
parameters are listed for the short undulator beamline length (Lu = 77 m).
Parameter
symbol
SC-Linac (4 GeV)
Cu-Linac (3-15 GeV)
unit
Undulator technology
-
Nb3Sn
NbTi
Nb3Sn
NbTi
-
SASE photon tuning range (Lu = 140m)
-
1.4-7.2
1.3-6.5
1-25
1-25
keV
SASE photon tuning range (Lu = 77m)
-
1.4-5.6
1.3-5.0
1-25
1-25
keV
Photon energy tuning range (SS, est.)
-
1.4-3.2
1.3-3.8
4-12
4-12
keV
Nph
0.8-0.07
1.0-0.09
2.8-0.12
3.1-0.12
1012
FEL pulse energy (SASE, nt)
ErNph
170-63
200-72
450-480
500-480
J
Peak FEL power (SASE, nt)
PFEL
6.8-2.5
8.0-2.9
13-14
14-14
GW
Est. X-ray pulse length (FWHM)

25
25
35
35
fs
Power gain length (3D, magnetic)
LG
1.3-2.9
1.3-2.9
0.75-2.4
0.80-2.6
m
FEL parameter (3D, SASE)
3D
8-4
8-4
13-4.6
14-4.7
104
Bandwidth (FWHM, SASE)
BWSASE
2-4
2-4
3-23
3-23
eV
Beam rate in this FEL (max.)
fFEL
930
930
0.12
0.12
kHz
Avg. e power (max., nt)
Pe
120
120
0.2
0.2
kW
Avg. x-ray power in FEL (max., nt)
Px
160-60
190-70
0.1-0.1
0.1-0.1
W
Spontaneous energy spread (Lu = 77m)
E/
0.6-0.1
0.5-0.1
0.5-1.7
0.4-1.5
104
Spontaneous energy loss (Lu = 77m)
/
6-0.6
5-0.5
5-15
4-12
104
Spont. cryo heat load
dP/ds
1.1-0.05
0.9-0.04
~0.002
~0.002
W/m
Num. photons/pulse (SASE, nt)

Figure 4: Average FEL x-ray power (300 kHz, 100 pC), as a function of photon energy, when driven by the SClinac for the PMU (blue), NbTi (green), and Nb3Sn (red). Undulator periods are 26 mm, 20 mm, and 18 mm,
respectively, and the full vacuum aperture is 5 mm (7.3-mm full magnetic gap). Beam parameters are in Table 1 and
undulator parameters are in Table 3.
7
The average x-ray power for the PMU and the two SCU technologies is shown in Figure 4 (vertical
log scale). The SCU curves are shown for both the Lu = 140 m case (solid), and the Lu = 77 m case
(dashed), where the PMU FEL output with Lu = 140 m (baseline plan) drops very rapidly before 5 keV
since the 140-m undulator length is not long enough to support SASE saturation at 5 keV. However, the
two SCUs, with 140-m upgraded undulator system, perform well out to 6-7 keV and with somewhat
higher power over the full tuning range. The dashed lines show the short undulator case, with Lu = 77 m,
demonstrating that even in this case both of the SCU technologies provide at least 5 keV photons
(including a 20% safety factor applied in all cases) and with about half the undulator length. Note that a
5% smaller packing factor was used for the PMU case, although this is a small adjustment.
Undulator Tolerances
The various tolerances for the SC undulators, shown for each linac, are listed in Table 5. The tolerances
are not so sensitive to the conductor technology. The undulator parameters for each case are listed in
Table 3. The width of the magnetic poles should be based on the field roll-off tolerance listed in Table 5.
Table 5: Undulator tolerance estimates for each linac.
Parameter
symbol
Segment-to-segment mean K variation (at Kmax)
K/K
0.03
0.03
%
Phase shake error (rms over segment)

5
5
deg
Max. field roll-off at ±1 mm (in bend plane)
B/B0|
0.2
0.2
%
Segment misalignment in x (in bend plane, rms)
xrms
150
150
m
Segment misalignment in y (in field plane, rms)
yrms
80
80
m
Break length error (rms)
Lbrk
2
2
mm
st
I1x
40
40
T-m
nd
Total hor. 2 field integral over one segment
I2x
50
50
T-m2
Total ver. 1st field integral over one segment
I1y
40
40
T-m
Total ver. 2nd field integral over one segment
I2y
50
50
T-m2
Total hor. 1 field integral over one segment
SC-Linac
Cu-Linac
unit
Longitudinal Wakefields
The resistive-wall wakefield of a long undulator vacuum chamber can limit the FEL power by
changing the energy of the different time-slices along the electron bunch during the exponential gain
regime. This wakefield is well known for a short bunch in a warm-bore vacuum chamber [13], but the
physics for a cold-bore chamber is different when the mean free path of electrons in the conductor is
longer that the skin depth. In this case the wakefield is dominated by the anomalous skin effect, where
the high conductivity at low temperatures does not contribute significantly to the wake. The wakefield of
a cold-bore has recently been calculated [14] and is shown for the SC-linac case (4 GeV) in Figure 5 for a
100-m long (total magnetic length which is easily scaled), aluminum rectangular vacuum chamber with
5-mm full aperture, a Gaussian bunch, and beam parameters listed on the plot. The warm-bore wake is
also shown for aluminum using the model for an AC-conductivity presented in Ref. [13]. The cold-bore
wake for aluminum is seen to be smaller than the warm-bore, a small advantage for the SCU. Note that a
8
copper chamber with the same aperture would increase the wakefield with respect to aluminum by about
20%.
To evaluate the significance of the wakefield, the energy loss at any point along the bunch, z, should
be compared to twice the FEL parameter (2  0.12% for the SC-linac case with 4 keV photons). Figure
5 shows that the cold-bore energy loss in the core of the beam does not exceed this level, especially when
including an appropriate taper (as shown in green and biased by 0.04%), suggesting a small impact of
the wake. Note that a 4-mm vacuum chamber aperture would have an increased cold-bore wakefield of
about 5/4 = 1.25, suggesting that a 4-mm chamber aperture may also be possible. The cold-bore
wakefield for this same SCU, when driven by the existing Cu-linac, will be somewhat reduced from the
warm-bore wakefield observed at LCLS-I, which has not been a major operational limitation.
Figure 5: The resistive-wall wakefield over a 100-m long aluminum rectangular vacuum chamber (5 mm full
aperture) for a cold-bore (blue-solid), and a warm-bore (red-dashed). The Gaussian peak current electron profile (Q
= 100 pC, z  8.7 m, Ipk 1 kA) used here is shown on an arbitrary scale (gray-dotted). The FEL bandwidth
boundaries (±2, plus a small taper of 0.04%) are also shown (green-dash-dot). The relevant undulator and beam
parameters are listed on the plot.
In addition to the energy spread generated by the wakefield (shown in Figure 5), the energy loss will
add to the cryogenic load, depending on the vacuum chamber temperature and isolation. This load can be
estimated by calculating the average loss in Figure 5, which is about 0.08%. With a 120-kW average
electron power as a maximum (SC-linac only), limited by the electron dump, this is a maximum heat load
along the chamber of 1 W/m (100 pC charge with 1 kA peak current). Note that with a 300-pC bunch
charge, but with a bunch length which is three times longer (z  25 mm), producing the same peak
current of 1 kA, the loss per meter and the induced energy spread are both reduced by about a factor of
two. In addition, RRR values (residual resistivity ratio) of aluminum from 10 to 200 have no significant
impact on the wakefield, suggesting that higher temperatures of the vacuum chamber up to 40K or more
should not change this result. From this wakefield assessment, and for other reasons described above, we
choose a 5-mm vacuum chamber aperture in this design rather than the more aggressive 4-mm value.
9
4. Undulator Magnet Design
The planar undulator magnet designs are based on the parameters in Table 3, depending on which
SCU technology is selected. This selection will be made after the two 1.5-m long SCU R&D prototype
undulators are built and tested (July 2015). Until then, we describe here the design for each case (NbTi
and Nb3Sn), where the Nb3Sn provides higher fields, but includes more technical risk.
The undulator magnet segment lengths for a production undulator system are chosen, in part, based
on providing an efficient, but discrete field tapering over the full undulator. When the HXU SCU is
driven by the copper linac at 6.6 GeV (for example), tuned to 4-keV with self-seeded photons, the peak
FEL power can be enhanced a factor of > 10 by strongly tapering the undulator fields after saturation (see
Figure 2). Since it is most practical to generate a taper in a step-wise fashion (segment-by-segment), the
segment lengths should be made similar to, or shorter than the FEL gain length (~1 m in this 4-keV case)
in order to approximate a smooth and efficient taper. Studies of a tapered, self-seeded FEL at 4 keV and
8 keV (based on an SCU with parameters described in Table 1 and Figure 2) are shown in Figure 6, where
a discretely tapered undulator with a 1.5-m segment length appears to be a reasonable compromise in
maintaining an aggressive packing factor and minimizing the engineering issues of a very long segment,
while maximizing peak FEL power. Each 1.5-m segment must then be powered separately to allow this
strong taper (~20% over the full undulator system length). Note that this TW-power level is only possible
with a 140-m tunnel-filling SCU undulator length.
Figure 6: FEL peak power in a self-seeded, discretely tapered undulator (described in Figure 2) for various values
of the magnet segment length, where the red trace is for 4-keV photons (6.6 GeV) and the blue (dashed) is for 8-keV
photons (9.4 GeV). In this case, with a 1-m FEL gain length at 4 keV (1.4-m at 8 keV), a compromise segment
length is about 1.5 m long. This FEL power level is only possible with the full undulator system of Lu = 140 m.
From this study, and the desire to build reasonable length SCU segments to minimize accumulated field
errors and to allow more convenient measurements and corrections, we choose a 1.5-m magnet segment
length as a compromise between engineering issues and the best tapered FEL performance. This length is
also the same as the prototype undulators being developed at present, requiring less new development.
Three of these 1.5-m long undulator segments will be included in each cryostat, as described below.
10
The NbTi Magnet
The NbTi magnet (1.5 m) is a scaled-up version of the 1.1-m long SCU1 magnet, the second
superconducting undulator currently being built at the Advanced Photon Source (APS) of ANL. The
magnetic design is similar to that of SCU0 [6], the first SCU currently in operation at the APS. It consists
of a pair of identical magnets, or jaws, separated by a gap where a beam chamber is accommodated. Each
jaw is a series of vertical racetrack superconducting coil packs wound with a round NbTi wire, and
separated by magnetic poles, with currents flowing in opposite directions in adjacent coil packs. The
winding form is made of low carbon steel to increase the undulator peak field. Each jaw has a main coil
and two pairs of correction coils that are wound on top of the main coil in the last two end grooves. The
correction coils are separately powered and are used mainly for tuning the second field integral, since the
first integral is automatically zeroed due to a chosen asymmetric magnetic configuration.
Preliminary magnetic simulations of the NbTi magnet having the period length of 20 mm and the
magnetic gap of 7.3 mm, which is wound with a commercially available 0.7-mm round NbTi wire,
suggest that a design peak field of 1.73 T can be reached at current of 623 Amperes corresponding to the
80%-level of a short sample critical current (see Figure 7). The design model of the magnet is shown in
Figure 8. The superconducting coils are indirectly cooled by liquid helium passing through the channels
in the cores; the flanges of the LHe circuit are also visible in the Figure 8.
Figure 7: Calculated dependence of the undulator peak field on the NbTi magnet current.
Figure 8: NbTi magnet design model with 1.5-m length.
11
The Nb3Sn Magnet
A prototype undulator magnet using the low-field superconductor Nb3Sn is being fabricated at LBNL.
The high transport current provided by Nb3Sn conductors is being leveraged in order to attain the highest
possible magnetic field in this superconducting undulator. Nb3Sn is an intermetallic compound with an
A15 lattice structure, and is very brittle in nature. To avoid damage, the material is drawn in an
unprocessed state and wound prior to subjecting the material to a heat treatment cycle that produces the
intermetallic Nb3Sn. This reaction process, which occurs at approximately 650 °C, adds an additional
processing step to the fabrication process when compared to the NbTi device, but Nb3Sn provides a
higher field.
The magnetic design is based on a solid low-carbon steel mandrel structure into which grooves are
machined to accommodate the coils. The result is a single structure that provides all of the magnetic and
structural characteristics of a half-undulator (top or bottom). The half-undulator is wound from a single
continuous length of wire with alternating winding directions in neighboring coil packs. Insulation in the
form of a glass braid with a thickness of 55 μm is used to electrically isolate the wire (see Figure 9).
Figure 9: Glass braid insulation with 55-m thickness on 0.6-mm diameter Nb3Sn wire.
Two sets of end correction coils are used to cancel dipole fields inside the undulator and to correct for
the end kicks. The second field integral is zero by the choice of a symmetric magnetic configuration.
The Nb3Sn magnet prototype design is shown in Figure 10. This includes the single-piece undulator core,
an external end-kick corrector that is decoupled from the main core, and a joint section where the brittle
Nb3Sn conductor is soldered to an NbTi cable to provide more flexible power leads.
Figure 10: Nb3Sn undulator design including the main undulator cores, the NbTi splice sections, and the external
end-kick corrector.
12
For a given period length, magnetic gap, wire diameter, and insulation thickness, the size of the poles
and pockets are optimized with respect to the load line margin for the superconductor. The left plot of
Figure 11 shows the load line for the Nb3Sn undulator (red curve) along with the corresponding magnetic
field on the axis of the undulator (blue curve). The solid black line shows the critical current of the
Nb3Sn wire. The design point is chosen at approximately 80% of the point where the load line intersects
the critical current of the superconductor. The right plot on Figure 11 shows the results of the coil pack
size optimization. The contours represent the load line margin as a function of the number of wire turns
and layers in the coil pack. The optimal coil size is chosen near the minimum of the margin plot along the
Number-of-Turns axis. The number of layers is chosen at a point where there is no longer a significant
reduction in the load line margin as more layers are added.
Figure 11: The left plot shows the Nb3Sn undulator load line with the 80% design point indicated with a blue
marker. The right plot shows a contour that represents the load line margin as a function of the coil dimensions.
This is used to optimize the coil dimensions for a given period length.
The starting point for the end design aims to set the pole potentials to an ideal pattern given by {0, ¼,
¾, 1, 1, …} from the entrance of the device. For an ideal device, which assumes perfect periodicity
and infinite permeability of the core, the fraction of the coil pack with respect to the periodic sections is
given by {1/8, 1/2, 7/8, 1, 1, …}. In the ideal case, this pattern leads to zero-steering and zerodisplacement ends. As the poles saturate, the potentials deviate from the ideal case and displacement and
steering errors become present. By the choice of a symmetric field (even number of coils) the net
displacement at the end of the device is cancelled when the entrance and exit steering errors are corrected.
The end design incorporates steering correctors at each end of the device. These steering correctors
are referred to as local end-kick correctors. Another set of corrector coils, which are directly wound in
the first pocket of the undulator core, is used to cancel dipole fields that can be present due to differential
saturation in the end sections. These end correctors are referred to as global field end corrector.
Figure 12 (left) shows the magnetic field that is produced when the global field end correctors are
energized. Note that this corrector produces both local kicks as well as a global dipole field in the center
of the device. To produce this symmetric field configuration, the four coils are wired in series and
powered with a single power supply. The highlighted coils in Figure 12 (right) represent the global field
end corrector coils. These coils are wound in the first undulator pocket directly below the main undulator
13
windings. Within the correction strategy, these coils are used to cancel the global dipole field only and
the remaining end kick errors are removed with the local end-kick correctors. Figure 13 (left) shows the
magnetic field that is produced by the local end-kick correctors. These correctors produce only local
kicks with zero global dipole fields in the center of the device. These correctors will be operated
independently, requiring one power supply for each end. The image on the right of Figure 13 shows the
location of the coils at the ends of the undulator. Note that field clamps are used for these coils in order to
minimize the interaction between the local end-kick correctors and the undulator cores.
In operation, the end correctors will be tuned in unison with a given undulator strength, controlled
with a pre-measured look-up table. This corresponds to one master power supply and three slave power
supplies for end corrections. A single power supply will be used for the global field end corrector, and
one power supply will be used for each of the two local end-kick correctors. From the end-design
simulations, the maximum current that is expected for the end correctors is less than 10 A for the global
field end corrector, and less than 30 A for the two local end-kick correctors.
global field
local
kicks
Figure 12: A global field end corrector is used to cancel the dipole field in the undulator which is present due to
differential saturation of the core near the ends. This corrector is co-wound with the main coil in the first pocket of
the undulator core as seen on the picture at right.
no global
field
local kicks
Figure 13: Two local end-kick correctors are used (one on each end) to correct entrance and exit steering errors.
These are fully decoupled from the central core, and therefore produce no global field effects when energized.
14
Radiation Sensitivity
Background radiation generated by the electron beam scales with the beam repetition rate. For the
LCLS-II, this results in an increase of 103-104 over LCLS-I. A number of measures can be taken to
mitigate beam-based radiation, including reducing the dark-current, improving beam collimation, and
refining beam vacuum. Nevertheless, we note that superconducting undulators are expected to be
significantly more tolerant of radiation damage than hybrid permanent magnet systems.
Two communities have studied the radiation tolerance of superconducting materials in detail:
 High Energy Physics, where superconducting magnets are critical to the LHC, and in
particular to the interaction region where significant radiation dose is anticipated; peak total
fluence reaches ~5×1017 n/cm2 (~20 MGy) over a 10-year span.
 Nuclear Sciences, where superconducting magnets are critical to the International
Thermonuclear Experimental Reactor (ITER); total fluence over the experiment lifetime is
expected to reach 1018-1019 n/cm2.
Detailed experiments on low-temperature superconductors indicate that the materials do not degrade
at these flux levels. For superconducting magnets, the primary concern with radiation is in the
mechanical properties of associated magnet materials, in particular the epoxy used in the vacuumimpregnation process. Many epoxies contain organics whose chemical links can be broken by energetic
particles, resulting in reduced mechanical strength, particularly in tension and in shear.
For the most demanding radiation environments, such as ITER, cyanate ester-based insulation
systems are used. For less demanding environments, a commonly used epoxy resin system in accelerator
magnets is CTD-101K (Composite Technology Development, Inc.). For radiation doses on the order of
25 MGy or less, CTD-101K is competitive with cyanate esters in terms of strength retention, and up to
these dose levels we do not anticipate any impact on magnet performance. We note that a similar dose
level is currently being used by CERN in the specification of the LARP-developed high-field quadrupoles
for the high-luminosity upgrade project; the magnets, developed by the US DOE laboratories LBNL,
FNAL, and BNL, use CTD-101K as epoxy resin. Such a Br reduction is already roughly an order of
magnitude more than could be tolerated, based on FEL field quality requirements. We anticipate 2-3
orders of magnitude less sensitivity to dose for superconducting undulators as compared to permanent
magnet undulators [15].
5. Undulator Measurement and Correction
The performance of all magnetic components will be measured and corrected, as necessary, prior to
installation into the LCLS tunnel. Below we discuss possible techniques for measuring and correcting the
undulator magnets.
Magnetic Measurements
The SCU magnets will be measured with a variety of techniques in order to ensure that the magnetic
field requirements are satisfied. The required accuracy of the measurements will be driven by the
stringent requirements on the variability in the effective field between segments, as well as trajectory and
phase error requirements. Hall probe measurements will be critical for accurately determining the
effective field of the undulator as a function of current. Hall probe (along with integral corrections) and
15
pulsed wire methods can be used to determine trajectory and phase errors in the device. Integral coil and
pulsed wire methods can be used to determine the first and second field integrals for the device. In the
following section, the various measurement systems that have been developed will be described.
As the 1.5-m SCU segments are fabricated, preliminary magnetic field measurements and device
“training” will be performed. The performance of SCU magnets will first be measured during the initial
cold test in a vertical LHe cryostat. A Hall probe mounted on a vertical stage will be used for these
measurements.
The final, precise measurements will be done with a horizontal measurement system, which could be
based on a ‘warm tube’ concept implemented at the APS for measurements of SCU0 [16]. In this
concept, shown in Figure 14, a titanium guiding tube is located in the cold beam chamber of the cryostat.
It is thermally isolated from the beam chamber and is self-heated by passing electrical current through it.
The guiding tube bore is open to air and accommodates a carbon fiber stick with Hall probes or wire
measurement coils. In this design, the temperature of the Hall sensors is kept close to room temperature.
The wire coils are of rectangular or ‘figure-8’ types to measure the first and the second field integrals.
The mechanical parts will include a guiding tube inside the cryostat and two stages externally
mounted on the cryostat flanges. A horizontal 6-m long linear stage will be used to drive the Hall probe
inside the cryostat under the test. A custom-made Hall sensor assembly will be mounted on a carbon
fiber holder, and the guiding tube. Relatively small 5.0-mm aperture of the SCU beam chamber would
require custom made Ti tube and carbon fiber holder as well as miniature Hall sensors. A possible vendor
of such sensors is Arepok Ltd in Slovakia. The existing LabVIEW-based data acquisition system that
has been developed and successfully used for measurements of the SCU0 and SCU1 could be employed
for the SCU measurement.
Cold (20K) Al
beam chamber
Warm (300K) Ti
guiding tube
Y
X
Vacuum
Warm (300K)
carbon fiber
Hall probe holder
Air
Figure 14: Cross-section of vacuum chamber with titanium guiding tube located in the cold beam chamber.
Besides traditional undulator measurement systems using hall probes and moving coils or wires,
pulsed or vibrating wire measurements can be readily incorporated into the precise measurement system.
These methods are straightforward to implement in small gap devices or where space restrictions make
other measurement methods more difficult. For pulsed and vibrating wire methods, a wire is stretched
along the length of the undulator and current is passed through the wire, generating either a local
disturbance (pulsed wire method) or a global wire vibration (vibrating wire method) due to the Lorentz
16
force. For the pulsed wire technique, the shape of the disturbance can be related to the first and second
field integrals of the magnetic field (depending on the length of the current pulse), making this an
attractive candidate for field-integral measurements. A pulsed-wire measurement system has been
constructed at LBNL and will be applied to the measurement of the superconducting undulators.
Significant effort has been placed in the improvement of the pulsed wire method in order to obtain
accurate measurements in undulators, especially those with short period lengths. Specifically, algorithms
that correct for finite pulse width and dispersive effects in the wire motion have been developed in order
to obtain accurate field integral and phase error measurements [17].
Magnetic Corrections
The SCU magnet must deliver a high quality magnetic field with tight tolerances specified in Table 5.
Non-superconducting undulators are usually magnetically tuned to achieve such a precise field. Tuning
an SCU in a similar way is a challenging task due to a fact that a superconducting magnet is contained
inside a cryostat. The fabrication approach that is being pursued for the SCUs relies on very precise and
controlled fabrication and winding processes, which could potentially lead to a shim-free magnet.
Nevertheless, a novel technique for tuning of SCUs is being developed in parallel in order to mitigate the
risk of not meeting the stringent FEL requirements.
The SCU0 and SCU1 magnets at APS have been successfully built using a precision fabrication
approach, both with quite successful results. The measured deviation of the magnet core dimensions from
nominal values is within 10 µm rms for the 0.33-m long SCU0 magnet, and within 30 µm rms deviations
for the 1.1-m long SCU1 magnet. The precise winding of SCU magnets has also been achieved at the
APS, as seen in Figure 15, where a cross-section of a typical SCU1 winding pack is shown. As a result, a
phase error of about 2 degrees rms was measured in SCU0, and about 4 degrees rms (preliminary
measurements) in SCU1. The strict quality control will be implemented at various steps of the LCLS
SCU magnet fabrication to insure that the mechanical tolerances are kept within 30 µm rms, resulting in a
required high precision magnetic field. Nevertheless, there is provisional space included in the design to
accommodate HTS shims on each side of the surface of the vacuum chamber, if required (see Figure 3).
Figure 15: Cross-section taken through a typical SCU1 winding pocket showing precision winding.
Along with the focus on precise fabrication, a tuning scheme using single-turn coils and
superconducting switches is also being developed for field correction in the periodic section of the
undulators. All of the single-turn coils will be wired in series such that, when activated, the current
17
through all coils is the same. The coils can be activated by using heater switches, which divert the current
from a bypass path to the individual single-turn coils. Therefore, the correction is performed with a single
variable current source and variable on/off single-turn coils which can be activated at the desired
locations along the length of the device. This type of concept has the advantage that it can be used to tune
the undulator in-situ while magnetic measurements are performed on the device. In [18] the effect of
various types of machining imperfection on the resulting trajectory and phase errors in the undulator was
investigated. Based on this analysis, the proposed correction scheme should be adequate for correcting
machining errors that are representative of those measured on previous prototypes.
A switching network and corrector scheme using patterned superconducting (YBCO) tapes and
sputtered heaters has previously been developed at LBNL [19]. For this switching method, two heaters
are needed at each switching location with one heater being constantly powered. A new scheme that uses
resistive joints has been developed for the tuning of the undulator prototypes. This method can
significantly reduce the heat input since heaters are only activated in the locations where the field
correction is desired. Figure 16 shows a diagram of this concept, which includes the main tape, the
soldered single-turn coil tapes, and the switching heaters. As shown in the figure, when the heaters are off
the current bypasses the single-turn coils. When the heater is turned on, a majority of the current (> 99%)
passes through the single-turn coil, applying a local field correction as necessary.
Figure 16: Superconducting switch concept using YBCO tapes with resistive joints and activation heaters. When a
heater is activated, >99% of the current is diverted from the bypass path to the patterned loops that are placed below
the undulator poles.
The single-turn correction coils will be placed on the each side of the vacuum chamber under the
undulator poles (see Figure 17). The coils will be placed in a pattern that allows for positive and negative
kick corrections as well as positive and negative phase error corrections. During testing, the locations
where correction is necessary will be determined and the heaters at those locations will be activated. The
main current in the corrector network will also be adjusted for optimal phase error and trajectory
correction at various values for the main undulator current. An additional power supply and current leads
with a maximum capacity of 100 A will be required to operate the periodic field corrector. In the end, a
measured look-up table will be produced that relates the current for the corrector network to the main
current in the undulator. The heater switch network will be used in the testing phase only. Once the
correction locations are determined, a hard-wired corrector will be fabricated specifically for each device
without the use of heaters. This is done to avoid any long term reliability issues that might arise due to
18
having heaters in the system. Insertion of this hard-wired corrector into the assembled undulator may
require some disassembly, and therefore added risk.
Figure 17: Periodic section field tuner on both sides of chamber.
6. The Full Undulator System
Magnetic System Layout
As listed in Table 3, the full magnetic length of the initial (short) SCU undulator is chosen at Lu,mag =
63 m, which is composed of 42×1.5-m undulator segments (i.e., a beamline length of Lu  77 m when
including breaks with a packing factor of 0.82). The installation of a longer undulator system is possible
(e.g., 75×1.5-m segments, plus breaks, will nearly fill the 140-m tunnel and produce up to ~7 keV SASE
photons), but here we describe the minimum SCU system length which still allows up to 5-keV photons
at 4 GeV in a very shorter undulator length (see Figure 1).
Each cryostat will contain three 1.5-m long undulator segments, each terminated magnetically, and
with a cold, adjustable magnetic phase shifter between each segment, as shown in Figure 18. One
quadrupole magnet will be located at the entrance of the first undulator segment and one at the exit of the
third segment. These quadrupole magnets are each permanently and precisely aligned transversely (< 50
m rms in the direction of the undulator’s field) to their adjacent undulator segments. The first of these
quadrupoles is a special alignment magnet which is only powered during beam-based alignment (BBA) to
find its magnetic center with respect to the beam. The second quadrupole is a focusing and alignment
magnet, which is powered during both BBA and FEL operations, as described below.
The three undulator segments are spaced by two short break lengths with 15-cm long (or less)
magnetic phase shifters (2×2). The third (long) break includes the two quadrupole magnets, a highresolution cavity BPM (~1 m rms position resolution), and a third phase shifter, all of which should fit
in a length of 0.7 m or less (see Figure 18). The magnetic packing factor is: p = (31.5 m)/(31.5 m +
0.15 m + 0.15 m + 0.7 m)  0.82, which should be slightly more efficient than the PMU baseline design
(p0  3.4/4.4 = 0.77). The long break also includes a pair of steering correction coils (x and y) which can
be integrated into the one focusing quadrupole magnet, as in LCLS-I, adding no additional length.
Motion control stages are included to allow remote adjustment of the horizontal and vertical position of
19
each end of the cold mass or cryostat (quadrupoles and undulator segments as a unit), with the corrections
guided by a BBA procedure (see below).
This layout scheme, with a set of three 1.5-m long, independently powered undulator segments,
allows the full undulator system to be tapered more smoothly, as shown in Figure 6, where it is clear that
a much longer segment (e.g., 4.5 m) would produce 10-times less FEL power than a 1.5-m segment. In
addition, the 1.5-m length is more convenient to construct, measure, and correct, with smaller
accumulated errors, and is closer in length to the 1.5-m long prototypes presently being developed at ANL
and LBNL.
Figure 18: A concept cryostat (one of 14) with three 1.5-m long independently powered undulator segments,
alignment and focusing quadrupoles, a cavity BPM, a set of three magnetic phase shifters, and motion control pads
at each end. Horizontal and vertical steering coils are integrated into the focusing quadrupole.
Alignment Strategy and Motion Control
The SCU has the disadvantage of limited access to the magnetic array after cool-down. Therefore the
system alignment considerations are even more important and must be supplemented by a well-prepared
beam-based alignment procedure in order to attain the final precision alignment using the electron beam.
The cryostat and cold-mass designs must include special features to enable this procedure.
The cryostat will be designed to allow precise component alignment before tunnel installation,
although this engineering has not been developed yet. In addition to this, a final high-precision beambased alignment (BBA) procedure will be used during beam operations, which uses beam position
readings from the BPMs, and takes advantage of the quadrupole field gradients in order to center the
undulator segments and quadrupoles onto the electron beam trajectory [20], as has been done routinely at
LCLS-I since 2009. This method finds the magnetic centers of the focusing quadrupoles with respect to
the beam by varying the electron beam energy by large factors (3-4) and measuring the induced beam
kicks generated by a series of off-axis quadrupoles, using all BPM position readings. The magnet movers
(x and y position control stages at each end of the cryostat) are then used to apply an alignment correction.
This should work well for the quadrupole magnets but it leaves the undulator segments potentially
misaligned. However, if the focusing quadrupole is also precisely and permanently aligned transversely
to the magnetic center of its adjacent undulator segment (to < 50 m rms, as at LCLS-I), then both the
focusing quadrupole and its adjacent undulator segment will be aligned when the local magnet movers are
20
adjusted. If a second quadrupole magnet, the “alignment quad”, is added (see Figure 18), and is also well
aligned to the upstream end of the adjacent undulator segment, then a final step in the BBA procedure
will be to turn on and off the alignment quadrupole, record the induced kick in each plane, and correct its
x and y position, which is pinned to the upstream end of its adjacent undulator segment. Note that the
special alignment quadrupoles are only switched on during beam-based alignment, and are switched off
during FEL operations (set to zero within ±2% of nominal field). Only the focusing quadrupole magnets
at the end of each cryostat are switched on during FEL operations (i.e., used for electron focusing).
Each of two motion control platforms will allow ±1-mm independent x and y position adjustment at
each end of the cryostat, providing control with at least four degrees of freedom (x, y, pitch, and yaw) of
the three joined undulator segments and their adjacent quadrupoles as one rigid structure. The three
undulator segments within the cryostat must be well aligned to a straight line (to ~50 m rms in the field
direction and somewhat looser in the orthogonal direction). In this way, when the position adjustments
are used to center the quads onto the electron beam, the set of undulator segments within one cryostat will
then be aligned all along its length. The BBA procedure is global and therefore also aligns the full multicryostat undulator system to a straight line. In addition, all BPM readings are re-calibrated (in terms of a
readback offset) so they all read zero in both x and y after BBA is complete, as routinely done at LCLS-I.
Break Sections
The long break sections separate the cryostats and include the focusing quadrupole, the alignment
quadrupole, the cavity BPM, and one of three magnetic phase shifters, as shown in Figure 18. Steering
coils are also included, for each plane, inside the focusing quadrupole magnets, requiring no additional
space (as at LCLS-I). This long break section is estimated to require no more than 0.7 m in length, but
might be shorter with a more advanced design. The break can be cold or warm and should be chosen by
the cryostat designer based on the efficiency of cold-to-warm transitions and other issues. A vacuum
isolation valve would be preferable between cryostats, but is not absolutely required. A concept drawing
of the quadrupole magnet is shown in Figure 19, attached directly to the undulator cold mass.
Figure 19: A concept for a quadruple magnet aligned and pinned to the undulator segment.
21
The short break sections (two per cryostat) are estimated to be 15 cm in length and include only a
magnetic phase shifter. Preliminary design studies of this phase shifter suggest this break may be as short
as 12 cm in length and adjusted by one power supply, as shown in Figure 20. Table 6 lists the various
components in the break sections with an indicator (in parenthesis) as to whether they are in the “(long)”
or the “(short)” breaks.
Table 6: Components within the break sections. Those in the long breaks might be cold or warm.
Device
Quantity per
Cryostat
Comment
Cavity type BPM
1
< 1 m rms position resolution (long)
Focusing quadrupole magnet
1
8-cm long with ±7 T integrated gradient (long)
Alignment quadrupole magnet
1
4-cm long with ±4 T integrated gradient (long)
Phase shifters (one in long break)
3
2×2 magnetic phase shifter (long & short)
x-steering coils
1
x-correctors inside quad, with BL  ±0.0005 T-m
y-steering coils
1
y-correctors inside quad, with BL  ±0.0005 T-m
Figure 20: A concept for a magnetic phase shifter between two undulator segments with 124-mm of length required.
Cold Beam Position Monitors
High-resolution (~1 m) beam position monitors (BPMs) are required adjacent to each focusing
quadrupole in order to support beam-based alignment [20]. These cavity BPMs are presently designed for
room temperature undulators and should also work without modification for the SCU. The frequency
change for cold operation can be compensated by choosing a different down-mix frequency in the BPM
electronics. The standard ceramic RF feed-throughs, typically used for BPMS, are rated to operate at
liquid helium temperatures; however specific feed-throughs have not yet been chosen for the warm
BPMs. The cryogenic BPM cables will be the same as those used for the HOM couplers in the LCLS-II
linac cryo-modules.
22
Beam-Induced Heat Loads
The electron beam can be operated at up to 120 kW in the HXU and will deposit some of this power
into the cold mass of the SCU, requiring enough refrigeration power to hold the temperature at about 4K.
Two sources of beam-induced heat loads are identified and estimated here.
The spontaneous radiation of the electron beam passing through the undulator will deposit some of
this power into the cold vacuum chamber. The relative energy loss per unit length over an undulator with
strength K, period u, and electron energy E, is
∆𝐸⁄𝐸 1
𝐸 2𝜋 2 2
= 𝑟𝑒
( ) 𝐾 ,
𝐿
3 𝑚𝑐 2 𝜆𝑢
where re is the classical electron radius, and mc2 is the electron rest mass. Only the SC-linac delivers high
a beam power so we do not need to consider the Cu-linac here. At E = 4 GeV, with an 18 mm period, and
Kmax  3.2, the worst-case relative energy loss is 9×10-6 /m. With a 300-kHz beam rate (100 pC bunch at
the 120 kW dump limit), this is an average power of about 1 W/m. Some of this radiation will travel
down the undulator freely and not impinge on the vacuum chamber, but we ignore this reduction factor
and list this 1-W/m value as an absolute worst-case estimate. This loss per meter value is also listed in
Table 4, along with the induced energy spread.
The second source of beam-induced heat load is the resistive-wall wakefield, which adds another
1 W/m in the worst case (again from the SC-linac only, with 100 pC, 1 kA, and 120 kW as the electron
beam power limit). This estimate is described in the “Longitudinal Wakefields” section above. Table 7
summarizes the worst-case beam-induced heat loads in the SCU when using the SC-linac.
Table 7: Worst case beam-induced heat loads per meter.
Device
dP/ds
units
Resistive-Wall Wakefield
1
W/m
Spontaneous Radiation
1
W/m
Total
2
W/m
Cryostat Layout – Option-A
At this conceptual design stage, two separate options are being studied for the cryostat layout (named
“Option-A” and “Option-B” temporarily and pursued independently by ANL and LBNL, respectively).
Option-A follows the “minimal segmentation” concept used for the superconducting linac, where long
strings of cryostats share cold interconnects, common insulating vacuum, and an integrated cryogenic
distribution system running the length of the undulator string. Minimal segmentation means that the
removal of any individual cryostat requires a room-temperature warmup of the entire undulator string, or
at least up to the room-temperature self-seeding section (see below). This option makes sense if the
undulator magnets and associated components represent a low failure risk, and/or if the risk is suitably
mitigated by the presence of installed spares in the undulator array. Benefits should include lower system
costs due to simpler cryostat geometry and the absence of a separate, external distribution system with Utube bayonet connections to each cryostat.
23
In the limit, this concept is envisioned as two independent strings of undulator cryostats separated at
the room-temperature self-seeding section (see below) of the undulator array. If finer segmentation is
desirable, the concept can be adjusted to add additional insulating vacuum breaks and an external
distribution system with connections to each cryostat string in the undulator array. Finer segmentation
approaches the concept described as Option-B in the next section.
Cryostat
The cryostat concept follows similar accelerator magnet cryostat designs and consists of a cylindrical
vacuum vessel (shown as a 16” diameter pipe) containing a thermal radiation shield which surrounds a
cold mass. Cryostats join to each other via flexible interconnects similar to the SC linac. The cold mass
operates at 4.5 K and includes three undulator magnets, three phase shifters, alignment and focusing
quadrupole magnets, and a beam position monitor all aligned with the requisite precision to a rigid
strongback. The strongback is supported from the vacuum vessel by low-heat-leak supports. With the
cryostats installed and at operating temperature, cold mass alignment is possible either by re-positioning
the individual vacuum vessels or by shifting the cold mass with respect to the vacuum vessel (if the lowheat-leak support system is so designed). Figure 21, Figure 22, and Figure 23 show the cryostat concept.
Figure 21: Option-A: Representation of 60-meter undulator array in two cryogenic strings (left) and a cross-section
of the cryostat (right).
Figure 22: Option-A: Side view of a single 3-magnet superconducting undulator cryostat (left), and cryostat with
vacuum vessel removed showing thermal radiation shield (right).
24
Figure 23: Option-A: Isometric view of the cold mass assembly with 3 magnets.
Cryogenics
Cryogenic refrigeration will be supplied by a small commercially available helium refrigeration plant
in the several-hundred Watt class for both magnet and thermal shield cooling. The refrigerator would be
separate and independent of the 2K linac system for reasons of operational flexibility, differences in
cooling requirements, and physical system location. The distribution system is integral to each undulator
cryostat except for the transfer lines that connect the refrigerator to the feed boxes of each undulator
string. The end of each string (2) is terminated by an end box containing valves for cool-down and steady
state operation. Figure 24 shows a simplified schematic of the refrigeration and distribution system.
Figure 24: Option-A: A simplified schematic of the refrigeration and distribution system.
25
Cooling channels within each undulator magnet connect to a helium reservoir pipe that runs the
length of the string. The pipe operates in the “2-phase” regime at a prescribed liquid helium level, which
is maintained by a regulating supply valve. Saturated helium gas is returned to the refrigerator through
the vapor space in the pipe.
Cryostat Layout – Option-B
A second cryostat layout has been pursued at LBNL, which is called the “Segmented Cryostat
Concept”. The goal of this approach is to provide modularity, facilitate fabrication/assembly, and
simplify operation, making full use of technical solutions that have been developed for recent large-scale
DOE SC projects. Specific design goals include:
 Modularity: The cryostat layout should accommodate three 1.5-m long superconducting
undulator magnets, with the full magnetic system meeting field strength, trajectory wander,
and phase shake requirements. The entire cold mass should act as a rigid structure so that
external fiducials, identified on the exterior of the vacuum vessel, can be used to position the
cryostat on the FEL line within alignment tolerances.
 Assembly: The design should minimize the amount of measurements and effort required
during and after final cryostating, as that phase of assembly is likely to be on the project’s
critical path. To this end, the proposed design is based on assembly of the three 1.5-m
magnets onto a rigid structure, with direct, rigid structural support connections from cold to
warm such that the location of the cold mass after cool-down is accurately known.
Measurements of Keff and field tuning (addressing phase shake and internal trajectory wander,
if needed) are performed on the individual 1.5-m undulators prior to assembly in the final
cryostat. Measurements in the final cryostat may then be limited to validation that the
trajectory through the cryostat module meets FEL trajectory and phase-shake wander.
 Operational Considerations: The proposed design results in parallel cryogenic feed-lines to
each cryostat, allowing the operations team to warm up and remove an individual cryostat
without impacting the rest of the ~100 m FEL line. Such an approach minimizes beam downtime in case of module replacement, since the other cryostats remain cold, and only the local
vacuum is broken.
A conceptual layout of the FEL line, based on this approach is presented in Figure 25. The spatial
layout of a periodic section of the FEL line is shown in Figure 26 and Figure 27. A short, roomtemperature section containing bellows, vacuum pumps, and vacuum valves, which together allow for
individual cryostat removal without impacting the rest of the line, separates consecutive cryostats.
26
Figure 25: Option-B: Conceptual undulator layout, showing more than four 5.5-m long cryostats, based on the
Segmented Cryostat Concept.
Figure 26: Option-B: Cryostat layout with three 1.5-m long undulator magnets, focusing quadrupole, alignment
quadrupole, BPM, isolation valve, and one phase shifter (of three) between each pair of undulator magnets. The
long break section, which includes the focusing and alignment quadrupoles, is 716 mm long allowing an 82%
packing factor.
Cryostat
The design of the cryostat leverages many developments from the FRIB cryomodules [21] and is
shown in Figure 28. The outer vacuum vessel is a welded, box-like structure, composed of major
components that can be fabricated in advance of assembly. Its final closure is the last step in the cryostat
fabrication process.
27
Figure 27: Option-B: Spatial layout of a periodic section of the FEL line based on the Segmented Cryostat Concept.
Figure 28: Option-B: Spatial layout of a periodic section of the FEL line based on the Segmented Cryostat Concept.
28
The complete cryostat fabrication process is composed of the following steps:
1. A stainless steel strongback, supporting the three 1.5-m long undulator segments, is prepared. The
strongback will remain at room temperature during operation and serves to provide the requisite
rigidity to the cold mass assembly.
2. Pre-assembled fiberglass posts are positioned on a linear bearing assembly attached to the strongback
as shown in Figure 29. The fiberglass posts are designed to provide rigid transverse support of the
cold mass, while allowing for longitudinal dimensional changes associated with cool-down. The
thermal contraction of the posts is known to high accuracy, and the heat load of each post is wellestablished (0.15 W to 4.5K).
3. Thermal shielding (~50 K) is installed to reduce the radiation load and to thermally intercept heat on
each of the posts. Cooling lines are attached to the thermal shield.
4. Each of the undulator coil sections are assembled on the posts, together with the vacuum chamber.
Each of the undulator sections will have previously been measured, tuned, and fiducialized, so that
accurate alignment of the three undulator segments can be performed during this step. Note that the
three segments will be rigidly connected to each other, with each connection incorporating a phase
shifter with sufficient phase range (nominally 4π).
5. Critical ancillary equipment is installed, including cold beam position monitors and focusing
quadrupoles. The vacuum chamber thermal transitions are installed, and the vacuum chamber
aligned.
6. The pre-fabricated LHe header is welded to the structure and thermally linked to the undulator cold
mass.
7. The remaining three sides of the thermal shield are assembled, with multi-layer insulation (MLI) wrap
on both sides to minimize radiation heat load. Note that at this point the full cold mass is assembled
on a rigid warm strongback structure.
8. The cold-mass/strongback assembly is placed in the bottom-half vacuum vessel. Note that at this
point there is still full access to the cold mass.
9. Current feedthroughs and diagnostic wiring are routed and connected at the bottom vacuum chamber.
10. The cryogenic feedbox, incorporating Bayonet mounts (as used on the FRIB cryomodules), is
installed. At this point technicians continue to have good access to make the requisite welded
cryogenic connections.
11. The upper vacuum vessel is finally installed, closing the cryostat.
12. Pressure relief valves are installed in the upper vacuum vessel.
13. Interstitial vacuum equipment is then installed on the ends of the cryostat, resulting in a fully modular
assembly for installation on the FEL line.
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Figure 29: Option-B: Pre-assembled fiberglass posts are positioned on a linear bearing assembly attached to the
room-temperature strongback. The fiberglass posts are designed to provide rigid transverse support of the cold
mass, while allowing for longitudinal dimensional changes associated with cool-down.
The complete cryostat can then be placed on two support mounts, each providing remote x-y position
control. Since the cold mass is rigidly supported by the strongback, the central axis of the undulators in
the cryostat can be aligned with the other cryostats via the support-mount x-y controls. This process is
essentially the same as used in the current LCLS-I.
Cryogenics
The cryogenics in the segmented cryostat configuration are based on a primary liquid distribution line
feeding each of the cryostats in parallel through low-loss, bayonet connections (each 0.06 W at 4.5K).
Figure 30 shows a conceptual piping and instrumentation diagram. The bayonets would remain in place
during operation, but can be extracted to allow removal of a single cryostat. Due to the parallel cryogenic
circuit, all other cryostats remain cold, as they are connected to the primary cryogenic feed. Over the life
of the FEL, this approach should significantly reduce the number of thermal cycles each cryostat
experiences. Due to an efficient bayonet and distribution line design the overall system heat load is
dominated by radiative and beam-loss heat loads. Commercial refrigeration units as described in section
7 will be able to provide sufficient cooling capacity.
30
Figure 30: Option-B: Conceptual piping and instrumentation diagram for the Segmented Cryostat Concept.
Comparison of the Two Layout Options
The two cryostat design options (Option-A and Option-B) are quite different and have “pros” and
“cons” which are briefly summarized here:
Option-A:
 Pro: Lower system costs are possible due to simpler cryostat geometry and the absence of a
separate, external distribution system.
 Con: The removal of any individual cryostat requires a room-temperature warmup of the
entire undulator string, or at least up to the room-temperature self-seeding break section.
Option-B:
 Pro: The Segmented Cryostat Concept provides modularity, facilitates fabrication and
assembly, and simplifies operation.
 Pro: Parallel cryogenic feed-lines to each cryostat allow the warm-up and removal of an
individual cryostat without impacting the rest of the ~100 m FEL line.
 Con: The static heat loads will likely be higher due to the many bayonet connections.
 Con: The total system cost may be higher due to the more complex design.
Self-Seeding Section
In addition to SASE operation, the LCLS-II HXR undulator should have the capability to run in selfseeded mode. For hard x-rays (4-12 keV) this will need a special diamond crystal-based monochromator
and electron bypass chicane, as was constructed and successfully tested at LCLS-I [10]. This will require
31
the addition of one more 5.5-m long drift section, but without a cryostat. This warm drift section, which
includes the x-ray monochromator and electron bypass chicane, would be located about half-way down
the undulator system, following perhaps the 6th or 7th cryostat. This extra 5.5 m length is not included in
the 77-m long undulator beamline descriptions above and 14 cold cryostats will still be required as a
minimum. The warm self-seeding section will require a cryogenic bypass line as well.
7. Cryogenics System
A Linde LR280 refrigerator is selected as a reference baseline for cost estimating purposes. This
baseline choice does not preclude other vendors from making proposals in the bidding process. With the
largest size helium compressor (250 kW), this refrigerator can provide 640 W and 900 W with LN 2 at 4.4
K. This is more than adequate for the full 140 meter undulator. Smaller refrigerators from Linde or other
vendors can be an option to reduce initial cost. Delivery time is expected to be 16 – 18 months. The
helium refrigerator with its ancillary equipment will be located in a small new build just outside and to the
south of Building 921 which is directly above beam line. Liquid helium transfer lines will be routed to
the undulator through existing penetrations in Building 921.
The 325 HP (250 kW) helium compressor will be located inside or just outside on an existing
concrete pad at Building 127 (SLAC’s deactivated Helium Compressor Facility, aka CHF). The decision
to locate the helium compressor at Building 127 instead of at Building 921 was made for the following
four reasons. 1) There is insufficient excess power at Building 921. Power upgrades will be very costly.
2) Helium lines from the CHF run right under Building 921. 3) Required ancillary equipment such as
adsorbers, LN2 cooled charcoal traps, regeneration heaters and a MCC are located at Building 127 and
might be used. 4) Any vibration issues or noise problems at Building 901 are eliminated. This baseline
design assumes that a new Linde compressor is part of the purchase package to make it a turnkey
operation and increase reliability over the use of existing 25 year old Sullair compressors.
A highly integrated turnkey system such as the one referenced above is required to minimize the
burden on cryogenic technicians and engineers who will be fully engaged with the main LCLS II
refrigeration system. The total installed system cost including refrigeration, transfer lines, dewars,
utilities and civil construction with contingency is expected to be $3.5 million. A complete cost
spreadsheet is available.
8. SCU Development Schedule
Bringing superconducting undulator technology to a level of technology readiness for consideration
as the baseline for the LCLS-II project will require an aggressive, focused effort by the SLAC, ANL, and
LBNL teams. A detailed schedule has been developed (Figure 31), with the goal of minimizing project
risk, while expediting development time for earliest project completion. This technically-driven schedule
assumes immediate start of work and the availability of appropriate funding in January 2015. The
schedule developed here is intentionally optimistic and leaves little margin for error.
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Figure 31: The superconducting undulator development schedule (bottom, red), and the existing LCLS-II
permanent magnet undulator schedule (top, green). The SCU schedule is optimistic and leaves little margin for
error.
Key elements of the schedule include:
1) A design and prototype phase, culminating in a complete prototype cryostat, which meets LCLSII requirements. The prototype performance demonstration will serve as input for a possible
decision to re-baseline the undulator technology for the LCLS-II project (see “Critical Decision:
baseline selection” in 2017). This phase incorporates a number of parallel efforts that are critical
for risk reduction, and includes test infrastructure investments in preparation for production
articles. Industrial partners are identified and first contracts are placed to qualify vendors.
2) A first-article phase, where possibly two production lines are qualified, results in two fullyqualified articles. The industrial partners are fully integrated in these first articles. During this
phase all measurement systems are completed and commissioned.
3) A production phase, where the remaining 12 articles (of 14 total) are produced in two parallel
assembly lines. Industrial partners are used in most fabrication efforts; only the final assembly,
tuning, and cold testing of the devices is performed by the laboratory partners.
4) An installation phase, where the articles are installed on the FEL line. The installation time is
estimated at 9 months, and is designed to minimize the LCLS down-time.
5) The schedule shown in Figure 31 shows the high-level elements of the schedule, including
milestones representing critical hardware performance tests or critical decision points.
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9. Cost Estimate
A cost estimate for a 77-m long SCU system (fourteen 5.5-m-long cryostats) is shown in Figure 32,
including a large 60% contingency at this early stage of development. The system total is estimated at
68M$ with escalation but no contingency, and includes one pre-production cryostat, one first-article, 13
production cryostats (assuming first article is usable), the main cryo-plant, and full installation.
The estimated costs (pre-conceptual design) are based on ANL’s existing procurements for SCU0 (a
0.33-m long SCU installed in APS on January of 2012), SCU1 (a 1.1-m SCU to be installed in APS on
December of 2014), and the SCU-LCLS R&D prototype (in progress). Additional input comes from
budgetary quotes, extrapolations of existing procurements, or engineering judgment based on similar
experience. ANL estimates were cross-checked with LBNL estimates for consistency, where available.
No spares, except construction spares, are included in the estimate. Construction spares are included only
for subcomponents likely to be damaged or destroyed during the normal production process.





SLAC (LCLS-II) superconducting linac estimates were used for some components.
Cryostat mover system cost is not yet included, but can be similar to LCLS-I, possibly re-using
LCLS-I components.
A quantity discount of 10% was applied to manufactured parts beyond the prototype; learning
curves were applied to effort but not yet consistently.
Burden was calculated using Argonne rates.
Management is shown as a flat 10% of total.
Successful completion of the pre-production prototype will reduce risk and allow contingency reduction
at CD-2.
Figure 32: Cost estimate for a 77-m long SCU with 14 cryomodules. The costs include a large 60% contingeny at
this stage.
34
In addition to this full-system cost estimate, we also present an estimate of the required short-term
funding necessary to begin the effort to the “Critical Decision” point in 2017, providing a full 5.5-m
cryostat with all subsystems, and leading to a possible decision to re-baseline the undulator technology
for the LCLS-II project. The short-term funding needed is 4.8M$/yr for 2.5 yrs (12M$ total), starting in
early FY2015.
Figure 33: Short-term cost estimate to advance the project to the “Critical Decision” point in 2017, providing a full
5.5-m cryostat and all subsystems, leading to a possible decision to re-baseline the undulator technology for the
LCLS-II project. The short-term funding needed is 4.8M$/yr for 2.5 yrs (12M$ total).
10. Summary
A proposal has been described to replace the project baseline, hard-x-ray, permanent magnet
undulator (PMU) at LCLS-II with a superconducting undulator (SCU) of approximately half the length
initially (77 m), with a full-length replacement at a later time (140 m). Such a half-length system can still
produce SASE photons over the required tuning range of 1.5-5 keV using the 4-GeV LCLS-II electron
beam with parameters in Table 1 (SC-linac). This undulator can be expanded in the future to fill the
existing LCLS undulator hall (140 m), eventually providing up to 7 keV SASE photons and self-seeding
capabilities out to nearly 6 keV or more, depending on the conductor technology chosen in the Fall of
2015 (NbTi or Nb3Sn). When driven by the copper linac, this expanded SCU can also provide more than
1 TW of peak FEL power at 4 keV when self-seeded and optimally field-tapered. Finally, with no
permanent magnet materials, the SCU will be 2-3 orders of magnitude less sensitive to demagnetization
through radiation dose; a major issue at LCLS-II with its very high average electron beam power and
small undulator vacuum chamber. A conceptual design is presented along with a draft schedule and cost
estimate to design, test, build, and install such a system for LCLS-II, possibly as early as September 2020,
with a mid-2017 “go” or “no-go” critical decision point.
35
11. References
[1]
J. Bahrdt, Y. Ivanyushenkov, “Short Period Undulators for Storage Rings and Free Electron Lasers”, Journal
of Physics, Conf. Series, 425 (2013), 032001.
[2]
P. Emma et al., “A Plan for the Development of Superconducting Undulator Prototypes for the LCLS-II and
Future FELs”, in Proc. of 36th Int. Free-Electron Laser Conf., Basel, 2014, THA03.
[3]
T. Raubenheimer, “The LCLS-II, a New FEL Facility at SLAC”, in Proc. of 36th Int. Free-Electron Laser
Conf., Basel, 2014, WEB001.
[4]
P. Emma et al., “The Linear Accelerator Design for the LCLS-II FEL Facility”, in Proc. of 36th Int. FreeElectron Laser Conf., Basel, 2014, THP025.
[5]
D. Dietderich et al., “Fabrication of a Short-Period Nb3Sn Superconducting Undulator”, IEEE Trans. on
Applied Superconductivity, Vol. 17, No. 2, June 2007, pp. 1243-1246.
[6]
Y. Ivanyushenkov et al., “Experience of Operating a Superconducting Undulator at the Advanced Photon
Source”, In Proc. of 2011 Part. Acc. Conf., New York, NY, pp. 2053-2055, WEPRO049.
[7]
R. Rossmanith et al., “A Year’s Experience with a Superconducting Undulator in the Storage Ring ANKA”, in
Proc. of 2006 EPAC, Edinburgh, Scotland, pp. 3571-3573, THPLS123.
[8]
B. Podobedov, “Resistive Wall Wakefields in the Extreme Anomalous Skin Effect Regime”, Phys. Rev. ST AB, 12, 044401, 2009.
[9]
M. Xie, “Design Optimization for an X-Ray Free Electron Laser Driven by SLAC Linac”, in Proc. of 1995
Part. Acc. Conf., Dallas, TX, pp. 183-185, (1995), TPG10.
[10] J. Amann et al., “Demonstration of Self-seeding in a Hard-X-ray Free-electron Laser”, Nature Photonics, 6,
693-698, 2012.
[11] K.-J. Kim, Nucl. Instrum. Methods A 445, 329 (2000).
[12] Y. Ivanyushenkov et al., “Development Status of a Magnetic Measurement System for the APS
Superconducting Undulator”, In Proc. of 2011 Part. Acc. Conf., New York, NY, pp. 1286-1288, TUP243.
[13] K.L.F. Bane and G. Stupakov, “Resistive Wall Wakefield in the LCLS Undulator”, Presented at the US
Particle Accelerator Conference (PAC’05), Knoxville, TN, May 16-20, 2005.
[14] K.L.F. Bane and G. Stupakov, to be published (Sep. 2014).
[15] S. Okuda, K. Okashi, N. Kobayashi, Effects of electron-beam and ã-ray irradiation on the magnetic flux of NdFe-B and Sm-Co permanent magnets, Nucl. Instrum. and Meth. B94 (1994) 227.
[16] C. Doose, M. Kasa, “Magnetic Measurements of the First Superconducting Undulator at the Advanced Photon
Source”, in Proc. of 2013 Part. Acc. Conf., Pasadena, CA, pp. 1238-1240, THPBA06.
[17] D. Arbelaez et al., “A Dispersion and Pulse Width Correction Algorithm for the Pulsed Wire Method”, Nucl.
Instrum. Meth. A716 (2013) 62-70.
[18] E. Rochepault et al., “Error Analysis and Field Correction Methods in Superconducting Undulators”, IEEE
Trans. on Applied Superconductivity, 24 (2014) 4101005.
[19] D. Arbelaez et al., “Magnetic Field Correction Concepts for Superconducting Undulators”, IEEE Trans. on
Applied Superconductivity, 23 (2013) 4100104.
[20] P. Emma et al., “Beam-based Alignment of the LCLS Undulator”, Nucl.Instrum.Meth. A429 (1999) 407-413.
[21] M. Johnson et al., “Design of the FRIB Cryomodule”, in Proc. of 2012 International Part. Acc. Conf., New
Orleans, LA, USA, pp. 2507-2509, WEPPD006.
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