JLAB-TN-09-046
10 August 2009
Use of Recirculation in Short-Wavelength FEL Drivers
D. Douglas and C. Tennant
Abstract
We discuss issues associated with the use of recirculation and energy recovery as costreduction measures in the design of short-wavelength FEL drivers. An example recirculation
transport line is presented.
Introduction
Providing a CW drive beam for a short-wavelength FEL requires:
1. A high brightness electron source
2. An injector and injection line that preserve beam quality
3. A phase space management scenario using the beam provided by the injector; in
particular, there must be a longitudinal matching scenario giving adequate bunch
compression/peak current at the wiggler and appropriate provision for transverse
matching
4. The ability to maintain beam brightness during the acceleration, transport and
compression process by avoiding the impact of lattice aberrations (chromatic and
geometric) and collective effects such as BBU, other wakefield/impedance effects (e.g.
the microbunching instability (MBI), resistive wall, etc), space charge, and coherent
synchrotron radiation (CSR).
These challenges have been/are being met in pulsed systems (LEUTL, VISA, FLASH,
LCLS, FERMI) and there is a consensus that they can be met in a CW FEL driver with “linear”
topology (i.e., without recirculation) such as WiFEL [1]. In this note, we discuss the implications
of using recirculation and energy recovery as a cost-control measure in the design of driver
systems. We detail additional challenges thereby introduced, and present a notional approach for
addressing one of the issues – specifically, the problem of beam quality preservation during
recirculation. This discussion will occur in the context of JLAMP – a proposed upgrade (to short
wavelength) of the JLab IR/UV FEL.
Recirculation, Energy Recovery, Cost Control, and Beam Quality
Use of multi-pass acceleration is universally recognized as an effective cost-control
measure in the design of SRF linacs. Energy recovery provides similar benefit inasmuch as it
simplifies radiation control (by limiting beam energy and power at the beam dump) and
alleviates RF power demands. This is true even in systems running modest (~ 1 mA) current if
they operate at suffiently high gradient: a 7-cell 1497 MHz cavity at 20 MV/m accelerating 2
passes of 1 mA beam (roughly JLAMP parameters) will, for example, draw ~30 kW RF power
without energy recovery, but (depending on the choice of QL) may draw only 1 to 2 kW with
recovery. This represents a savings of ~1/4 MW RF drive– a cost reduction of order 2.5 M$ – per
cryomodule.
Many issues are, however, introduced by the use of recirculation, including:
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1. The need for an appropriate (beam-quality preserving) injection merger
2. The potential impact of additional beam transport length; in particular, the effect of
wakefields, environmental impedances (with their potential to aggravate MBI), and space
charge
3. Additional complexity in longitudinal matching
4. Use of common transport for multiple beams (during energy recovery)
5. Possible BBU limitations, and
6. The impact of lattice aberrations and CSR during recirculation.
Most of these issues appear to be tractable and/or are the focus of ongoing investigation
in a number of projects. Merger design is a critical problem for ERL-based x-ray sources and the
Navy INP FEL. Initial results from these efforts suggest however that this difficulty is
manageable: a JLAMP-class machine can use higher injection energy than either an x-ray ERL
or the INP inasmuch as the lower JLAMP current requires far less RF power, and, in addition,
JLAMP uses much lower charge than the INP and only modestly higher charge than a
conventional ERL.
Wakes/impedances have been investigated as part of the high-energy ERL design
program [2], and appear to be controllable using methods proven in storage rings over the past
few decades. Though the bunch charge involved is lower in a “big ERL" than in JLAMP, the
bunch length is also shorter, yielding similar peak currents; path lengths involved in fact favor
the JLAMP scenario as the machine is much smaller. Similar (and acceptable) impact on beams
of more or less equivalent brightness is thus to be expected. Though a careful characterization
and impedance policy will be required, the integrated effect of these phenomena should be
adequately controlled.
Operation of a multipass ERL will require a rather more complex longitudinal matching
scenario than that used during SRF ERL operation to date. We have limited experience with
“one-and-a-half-pass” operation of the IR Demo [3], and preliminary analysis has yielded a
reasonable solution for a 2-pass up/2-pass down JLAMP-class machine [4]. This will be
discussed in more detail below. In this solution, an isochronous arc is used on the first
(accelerating) pass and final (recovery) pass. This requires the use of common transport for the
two beams; this method was successfully demonstrated with CEBAF-ER [5], wherein two 500
CW MeV beams (one accelerated, one recovered) were transported through a common beamline
for several hundred meters. This requirement is therefore not expected to present fundamental
limitations.
BBU has historically imposed serious limitation on SRF linac performance, but recent
developments render it much less of a concern for JLAMP-class systems. This is due to the
relatively low currents involved, better management of the instability by the transport lattice, and
much better control of SRF cavity HOM spectra available using modern design and construction
methods. An example study is provided in Ref. [6] and typical modeling results available in Ref.
[7]. None of these results suggest that undue concern is warranted.
We therefore focus our attention on the final issue: the impact on beam brightness of
transport through a recirculation arc. In addition to traditional lattice issues (chromatic and
geometric aberrations), we must in this case be concerned with synchrotron radiation (both
incoherent and coherent) driven degradation of beam quality. Though there exists no consensus
on the feasibility of beam quality preservation during recirculation, the potentially significant
cost impact encourages serious investigation of this technique, at least in order to establish limits
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beyond which the use of this technique breaks down. There have, moreover, been initial studies
[8, 9] suggesting that this approach can be successfully applied, at least in somewhat different
regions of parameter space than those envisioned for JLAMP. In the following, we outline a
notional approach to the design of an isochronous (but tunable) recirculation transport that would
preserve beam quality while allowing us to double machine energy in the existing vault.
A JLAMP-Class Recirculator
The following discussion constitutes a design exercise intended to provide an existence
proof of a recirculation arc that fits in the existing JLab FEL vault and preserves beam quality
well enough to drive a short-wavelength FEL. We proceed with this exercise by first stating the
top level design requirements, enumerating the major issues, and addressing them each in turn.
Design Requirements – JLAMP [10] will be a two-pass 600 MeV ERL driver for a short
wavelength FEL in the JLab FEL vault. It will comprise a high-brightness 10 MeV injector, a
300 MeV linac based on three high-gradient (100 MeV) cryomodules and a two-pass recirculator
(300 MeV and 600 MeV beam transport lines), with an FEL embedded in the second pass. The
system will fit in the existing JLab FEL vault (within a ~12 m x ~65 m footprint).
The JLAMP FEL is intended to reach the 10 nm wavelength scale, and thus the electron
beam must present a geometric transverse emittance of (10 nm/4 at 600 MeV, corresponding
to a normalized emittance of 1 mm-mrad. In order to lie within the FEL momentum acceptance
and produce sufficient peak current using the 200 pC design bunch charge, we require a 50 keVpsec longitudinal emittance out of the injector. This would, for example, allow delivery of a 10-3
rms relative momentum spread with 0.5 psec FWHM bunch length to the wiggler
(corresponding to 120 keV-psec at 600 MeV) while providing allowance for modest degradation
of beam quality during acceleration, transport, and compression.
The FEL itself is assumed to have an extraction efficiency of ~0.3%, with a
corresponding full-energy full exhaust momentum spread of 2% (~6 times the extraction
efficiency). During energy recovery, this could (depending on the choice of longitudinal match)
double in the final recirculation pass (at half energy), requiring ~4% momentum acceptance in
the 300 MeV recirculator.
Physics Issues – The technical issues associated with the above requirements are apparent. Most
obvious is the challenge of transporting a 600 MeV beam in a vault with footprint originally
designed for the 210 MeV IR Upgrade. The beam transport system electron-optical design is
therefore of primary concern; particular attention must be provided for the management of
longitudinal and transverse matches and the control of aberrations (which can lead to significant
degradation of beam quality). In addition, the move to high energy by way of multiple passes and
high gradient will require thorough analysis of the BBU instability, although (as noted above)
this is not expected to impose serious limitations. The use of relatively high energy in a small
footprint may result in the generation of significant levels of incoherent synchrotron radiation
(ISR), with attendant and potentially unacceptable levels of emittance excitation. Finally,
considerable care must be taken to insure that CSR does not degrade beam quality.
Longitudinal Matching Scenario – Various longitudinal matching scenarios can in principle
provide an appropriately compressed bunch to an FEL. However, the need to utilize energy
recovery while avoiding parasitic compressions during the acceleration cycle and the necessity
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for adequate momentum acceptance for recovery of the FEL exhaust beam provides considerable
guidance in choice of acceleration/deceleration phases and selection of momentum compactions.
A preliminary study [11] indicates that the following longitudinal match is acceptable.
1. Inject a long, low momentum spread bunch (to avoid LSC effects).
2. Accelerate the first pass beam through the linac ahead of crest (on the rising portion of
the RF waveform).
3. Use an isochronous first recirculation transport
a. Provide 4-5% momentum acceptance to support energy recovery
b. This will retain (future) option of lasing on both passes [12].
4. Dechirp (accelerate on the falling part of the waveform) during the second pass so as to
energy compress the beam to get to small momentum spread.
5. Compress the bunch length in the full energy linac-to-wiggler transport.
6. Decompress the bunch length (to set up energy compression during energy recovery)
using the full energy wiggler-to-linac transport.
a. Select linac reinjection phase and wiggler-to-linac transport compaction to keep
the momentum spread of the recovered beam within the first recirculator
acceptance during energy recovery.
A simple simulation of this process [13] is presented in Figure 1, which shows the
evolution of a longitudinal phase region space as it is accelerated and transported through the
system. The model includes nonlinear RF and compaction terms, but no collective effects. It
gives an existence proof for a longitudinal matching solution taking a 50 keV-psec injected phase
space to a wiggler to deliver ~0.25% rms momentum spread in ~0.120 psec rms (about 150 keVpsec, including nonlinear distortions from the acceleration and bunching process). As indicated
above, the 300 MeV recirculator is isochronous, and the full-energy reinjection phase and
wiggler-to-linac transport compactions are selected to provide energy compression during energy
recovery.
The FEL exhaust energy spread at 0.3% extraction efficiency of ~17 MeV at 600 MeV –
or about 2.8%=1% (core beam) +1.8% (lasing induced) – is compressed to ~9 MeV (or 3%)
during the second transit of the first arc, and then to ~1.5 MeV at the dump energy (here, ~12
MeV). Accelerating phases and compaction values are given in Table 1. We note that the
injected longitudinal phase space is rather similar to that already produced (albeit at 135 pC) in
the JLab IR Upgrade, and the choice of first-pass accelerating phase was made in part based on
Upgrade operational experience (these parameteric choices alleviate LSC [14]) and in the desire
to present to the first arc a beam of moderately large momentum spread (p/p ~ ½%) so as to
assist in CSR management during the recirculation transport.
The simulation locks the phase difference from third to fourth pass to match that from the
first to second (as the common transport has identical time of flight). As the solution straddles
crest from pass to pass on acceleration (to dechirp the phase space on the second pass), the beam
also jumps from one side to the other of trough during recovery. This fundamentally limited the
recovered bunch length (and hence the recovered energy spread) because one or the other
working points will – as the momentum spread (and hence recovered bunch length) increases –
eventually have electrons tailing off into trough and forming a high energy tail. It will therefore
be useful to devise a very large acceptance dump line so as to recover as large a final energy
spread as possible. The solution also tends to be a bit “twitchy”, inasmuch as small phase
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changes can result in large swings of energy spread in the recovered beam. This is not at all
surprising, given the rather large linac energy gain. Note also the system engages in
“incomplete” energy recovery. Care should be taken to define RF drive requirements
appropriately.
Table 1: Longitudinal Matching Parameters
Einj (MeV)
10
304.6
Elinac (MeV)
Pass 1
Pass 2
Pass 3
Eafter pass (MeV)
310
596.3
304.63*
o
o
Phase during pass
-10
20
156.8 o
Compactions (m)
M56
T566
W5666
st
1 arc
0
0
0
linac-to-wiggler
0.38
36
3300
wiggler-to-linac
0.24
7
200
*
lasing at 0.3% extraction efficiency
Pass 4
11.99*
186.8 o
Figure 1: Longitudinal matching scenario for two-pass 600 MeV JLAMP ERL driver while
lasing at 0.3% extraction efficiency. Vertical axis: energy in MeV; horizontal axis: time in 1497
MHz RF degrees. Phase space should be viewed, notionally, as subtending ±2 in each variable.
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Transport System Constraints – The multipass recirculation transport must satisfy numerous
constraints:
1. It must separate each pass for recirculation (implying the need for spreaders and
recombiners)
2. It must provide for betatron matching into/out of the linac on each pass and into/out of
the FEL at full energy
3. It must support the longitudinal matching process by providing path length and
compaction control (through appropriate nonlinear order). The low energy pass must
nominally be isochronous. Tuning range on each longitudinal parameter must be
available.
4. It must avoid parasitic compressions, particularly on the first pass, so as to avoid CSRdriven beam quality degradation
5. It must limit quantum excitation (incoherent synchrotron radiation) to acceptable levels.
6. Each pass must nominally be achromatic
7. Aberrations must be controlled; to maintain beam quality the lattice must provide
suppression of dispersion through second order (at least at the wiggler), manage
chromatic variation of the transfer map and beam (Twiss) parameters, and limit
amplitude-dependent (geometric) effects.
8. The transport momentum acceptance must be adequate to support energy compression
and recovery of the FEL exhaust beam. Given a nominal 0.3% extraction efficiency and
order 1% full momentum spread at full energy, this suggests the full energy transport
must accommodate ~3% momentum spread (beam full p/p + 6FEL) ; we will require 45% acceptance in the low energy recirculator to allow for beam gymnastics during energy
compression/recovery.
9. The system must fit in the existing JLab FEL vault (footprint of ~12 m X 65 m).
10. The design should preserve existing operational capability (and thus must avoid
interferences with existing FEL electron beam and optical transport systems).
Of primary interest here is the low-energy recirculator, as it will serve as an existence proof for a
transport system providing adequate preservation of beam quality during recirculation in an FELvault-sized footprint. In the following sections, we describe a possible design for this line and
analyze its performance.
A Design Concept for the Low Energy Recirculation Arc
As a test of these concepts, we have designed an isochronous 300 MeV transport line
intended to serve as the first (and last) pass(es) of the JLAMP driver. This system must
1.
2.
3.
4.
5.
Separate beams for recirculation (using a spreader)
Bend each beam through 180o and deliver it to a backleg transport
Transport the beam to the other end of the vault
Bend back through 180o
Recombine the beam with other passes for futher acceleration/recovery.
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Spreader – Examination of the installed system reveals that there is space available to slide the
merger and extraction dipoles toward their respective ends of the linac and make available space
to install common dipoles for a JLAMP recombiner and a spreader. There is also enough space
between the installed UV line and the vault south wall to accommodate a set of vertically stacked
transport lines for high energy beams. By “going vertical” at the end of the first pass, we can thus
provide adequate space to match into a recirculator system lying above plane of the existing
IR/near UV machine. This will allow us to service new beamlines to handle the higher energy
beams for shorter wavelengths while retaining essentially all of our existing capability. All that
must be done to switch between the systems is energize/de-energize a common vertical dipole at
each end of the linac and restore appropriate accelerator setpoints for the selected system. A
schematic of the linac back-end (spreader) is given in Figure 2.
Figure 2a: IR Upgrade configuration.
Figure 2b: Notional JLAMP configuration.
The design solution analyzed below has – as the result of optimization – five quads in the
vertical translation (instead of a triplet); these quads use embedded (or nearby) skew sextupole
terms to control nonlinear vertical dispersion (T466 and T566). Various methods can be employed
to provide the required field curvature [15]. After the “return” dipole, the beam will be
transversely matched to a recirculation arc using a five quadrupole telescope. Beam envelopes
using in this matching and optimization process were established during a separate study of linac
optics [16]. This analysis indicates that the first (and last) pass linac optics are similar to those in
the IR Upgrade, while the second (and third) pass is essentially drift-like over the 32 m linac
length. Twiss parameters into the arc are thus ~16 m,  ~ -1, while reinjection parameters of
~30 m and  ~ 1 are reasonable.
Recirculation Arc – Following separation of the various passes, we recirculate the beam using a
180o bending arc comprised of several periods of FODO (quad-dipole-quad) cells. This will
make the arc footprint nearly circular (giving the most efficient utilization of available space),
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will provide periodicity and symmetry for aberration management and tuning capability (e.g.
control of momentum compactions and dispersion), and – given that we are accelerating the first
pass beam on the rising part of the RF waveform – will decompress the bunch length and thereby
alleviate CSR effects.
The specific choice of numerology is driven by the design and optimization process. We
find that adequate performance is provided by using twelve dipole-quad-dipole cells tuned (using
the quad strength as a single family and the field index in the dipoles) to give 1/6th integer phase
advance in the bending plane and 1/4th integer phase advance in the non-bending plane. With this
choice, the arcs are second order achromats, coupling error effects are suppressed (because of the
split tunes), and the system momentum compactions can be tuned using periodically spaced
“subfamilies” of the quads. Specifically, the second, fifth, eighth, and eleventh quads are
separated by 180o in betatron phase in the bending plane and 270o in the non-bending plane.
They therefore can be used to perform a one-knob dispersion bump and modify M56 while
keeping the arc achromatic; the quarter-integer separation in the non-bend plane serves to
suppress perturbation of the out-of-plane betatron match. The specific choice of sixth integer
horizontal phase advance ensures this bump occurs across three dipoles (rather than two as
would occur for a quarter integer tune), providing potentially greater dynamic tuning range.
Sextupoles at these locations can be similarly used to adjust T566; similar multipoles at the
locations of other focusing elements serve to manage linear and nonlinear dispersion.
The use of twelve cells over a roughly 6 m radius transport ensures that the matched
Twiss parameters and dispersions are small. This alleviates aberrations and error sensitivity,
reduces response to CSR, and keeps the beam size relatively small – even during recovery of a
potentially large energy spread beam.
We use dipole fields of ~10 kG, corresponding to a 1 m radius bend over a length of ~1/4
m. The higher energy (600 MeV) line is expected to use similar peak bend field, yielding a 2 m
bend radius and requiring dipoles of length ~1/2 m. These appear to be adequate to limit ISR to
tolerable levels (see following analysis). Aberration management and nonlinear compaction
control will be provided by way of sextupole components in the dipoles and in or near the
quadrupoles. The latter can be the subject of a trade study to determine which of several methods
[17] is most cost effective.
The return arc at the east end of the vault is taken to be identical to the first arc. The
momentum compactions add, debunching the beam without parasitic compression. Observe that
care must be taken to control environmental impedances; the longitudinal phase space is
stretched rather thin over much of this transport and thus susceptible to wake effects. However,
as the bunch is elongated the peak current is very low so there is little driving term to couple to
the environment. Detailed analysis will be required to establish and enforce an impedance policy
and to certify that microbunching effects are not problematic.
Backleg Transport – This line must cleanly transport the beam to the return arc without
introducing aberration effects. It will also provide space for utility functions, such as diagnostic
stations and path length control chicanery. In the full energy arc, the FEL will be embedded in
the backleg as well.
In this exercise, we choose a simple quadrupole FODO array. Phase advance is chosen to
assist in aberration suppression. The first and final two cells are half-length to provide good
beam envelope control while smoothly matching the arcs (with small matched beta, order 2 m
peak) to the backleg transport (with rather larger matched beta, order 10 m peak). The uniform
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transport region comprises 8 FODO cells, with, as mentioned, two upstream and two
downstream half-length cells used as five-quad matching telescopes.
Recombiner – Following the return arc, the beam must be betatron matched (to Twiss parameters
at the reinjection point as given above:  ~ 30 m,  ~ -1) and brought back down to the linac
axis. The bunch must also be partially compressed, inasmuch as the upstream transport will have
lengthened it significantly. For these purposes, we use a clone of the CEBAF staircase, with a
five-quad matching telescope followed by a vertical half-chicane. A second five-quad FODO
array is used to generate a half-betaton-wavelength phase advance (flipping the sign of the
vertical dispersion in the process), whereupon a second half-chicane delivers the matched and
recompressed beam to the linac axis. Aberration control drives the use of five quads – rather than
the CEBAF-style triplet – for this process of dispersion management. The “double half chicane”
structure has a large negative M56 and thus compensates for the naturally positive arc
compaction. By tuning the arc compactions (using quads and sextupole terms as detailed above)
one can adjust the overall recirculator compaction schedule to achieve a range of longitudinal
matches.
Skew sextupoles embedded in the second five-quad channel are invoked to manage
nonlinear vertical dispersion. As in the preceding cases, there are a number of options available
to generate the required fields [18].
Integrated System – The complete linac-to-linac transport thus comprises






a spreader (including aberration control using sextupole terms),
a betaton match (across the spreader) from the linac to a FODO arc,
a first FODO arc (providing aberration and compaction control by trimming quads and
using sextupoles),
matching to/from a FODO backleg transport (in which we assume path-length adjusting
chicanes will be embedded),
a second FODO arc (identical to the first), and
a staircase recombiner
As described above, the longitudinal match can be modified – thorough any desired order – by
adjustment of the appropriate order of multipole at specific sites in the FODO arcs. The
remaining arc multipoles can be used to manage other aberrations and adjust/trim dispersion
(through nonlinear order). Various matching telescopes are available to adjust Twiss parameters
and optimize betatron matching (for machine setup, BBU control, halo/CSR management, and so
forth) just as is regularly performed in CEBAF and the IR Upgrade FEL.
A performance analysis is given below.
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System Performance
Layout – Figure 3 presents a layout of the JLAMP 300 MeV recirculator together with one for
the existing IR Demo. The JLAMP transport roughly fills the available space; a higher-energy
600 MeV recirculator could be laid in below it (but still elevated from the existing machine).
Figure 3: Plan and elevation of JLAMP first pass recirculator layout.
Beam Envelopes – Figure 4a presents (zero charge) optics for the linac [19] (the recirculator arcs
are modeled as zero length matrices at locations denoted by heavy black lines). Figure 4b shows
the propagation of these through the first pass of the 300 MeV recirculation line; 4c shows the
same for the recovery cycle pass. Values are modest, suggesting that error and aberration
sensitivities and halo will be manageable and that BBU thresholds will be reasonable. As one
would expect, there is moderate mismatch in during transitions into/out of the linac, but peak
beam envelopes remain reasonable.
Figure 4a: Zero-charge beam envelopes through linac on each pass; recirculator transforms
denoted by heavy black lines.
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Figure 4b: Beam envelopes through 300 MeV recirculator (based on generic input values of
=16 m, =-1, match to generic output values =30 m,  =1).
Figure 4c: Beam envelopes through 300 MeV recirculator (based on generic energy recovery
input values of =30 m, =-1).
Aberration Analysis – DIMAD analysis of both chromatic and geometric aberrations across the
full recirculation arc (linac to linac) has been performed and suggests that aberration
management is adequate. Figure 5 gives the results of a momentum scan; these indicate that
beam quality of the accelerated beam will be well maintained (as parameters are extremely flat
over ±1% moment spread) and that orbit and Twiss parameters are under reasonable control over
a rather larger range so that energy recovery can be successfully executed. Figure 6 presents the
results of analysis of geometric aberrations. The transverse phase space remains regular out to
100 times the nominal emittance (100 mm-mrad normalized) across a moderately large
momentum range (±1%), indicating the core beam will remain undistorted, halo will propagate
cleanly, and the system should show reasonable freedom from orbit dependences in the optics.
We have, in addition, done a ray-trace simulation of the first pass for a 6 Gaussian beam
with 1 mm-mrad normalized transverse emittance and 50 keV-psec longitudinal emittance. The
longitudinal match is intended to be modeled as above so that the rms momentum spread is ½%.
The linac is simulated by injecting a fully upright beam with this momentum spread and bunch
length appropriate to the longitudinal emittance, and then back-chirping the beam with a (linear)
matrix transform to impose the appropriate length-energy correlation (56). Results are shown in
Figure 7; essentially no emittance growth is observed.
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Figure 5a: Orbit dependence on momentum.
Figure 5b: Lattice function dependence on momentum
Figure 6: Geometric aberration analysis; left: horizontal phase space; right: vertical phase space.
Image of initial phase ellipses regular and only modestly distorted out to 100 times nominal
emittance (100 mm-mrad normalized), across ±1% momentum range.
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Figure 7: Results of ray-trace simulation of 6 beam with 1 mm-mrad normalized transverse
emittance and 50 keV-psec longitudinal, with linear chirp equivalent to first pass acceleration
through linac 10o ahead of crest. Top: l-p/p (left), xy (right); bottom: xx’ (left), yy’ (right).
Incoherent Synchroton Radiation (ISR) Effects – Quantum excitation (ISR) effects are of concern
in the design of any high energy/high brightness electron machine. The analysis methods used
for various CEBAF recirculators [20] are immediately applicable to JLAMP; we find that ISR is
not of concern at the energies anticipated in this case. Figure 8 presents results for estimated
growth in emittance and momentum spread. The ISR contribution of  ~ 0.01 nm-rad is well
below the nominal value, even relative to our ~0.8 nm-rad target geometric emittance (10
nm/4); the growth in relative momentum spread is of order 3×10-6, which is to be compared to
that required by the FEL and produced by the longitudinal match (of order 10-4 or larger).
Figure 8: Estimated ISR-driven emittance growth during acceleration through JLAMP; pass-bypass degradation (blue dots) is small relative to requirement (triangles/red line).
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Impact of Coherent Synchrotron Radiation (CSR) – CSR-driven emittance dilution is the primary
concern for this design study. The design conceptually avoids the issue by chirping the bunch by
accelerating on the rising portion of the waveform (and thereby also alleviating LSC effects),
decompressing the chirped bunch during transport through arcs with M56>0, and providing
isochronicity by recombining the beam with a staircase achromat with M56<0 just prior to
reinjection.
This design uses five…, er…, three methods to manage CSR. First, it relies on a
theological miracle…, uh…, large longitudinal bunch extent to avoid significant CSR effects;
this elongation is imposed both by the magnitude of decompression provided by the positive arc
compactions as well as the relatively large ( ½%) rms momentum spread of the chirped beam,
which spreads the beam out longitudinally not only from the compaction but also from the
transverse offset associated with dispersion [21]. In addition, the high lattice periodicity – with
commensurately small beam envelopes and dispersions – will reduce beam response to CSR
effects. Finally, the symmetry of the transport and the long FODO backleg allow (in principle)
the adjustment of the end-to-end phase advance so as to provide some degree of compensation of
CSR-induced emttance growth [22]. As a fall-back, should the effect prove problematic, we
could introduce a fourth management method [23], at least at the locality of any bending sites
producing significant CSR output.
Effects of CSR in the 300 MeV transport were simulated using a 1-d model in DIMAD
[24]. We find that at 200 pC, the effects are modest, with little transverse effect and moderate but
regular distortion in the longituindal phase space. Results of the simulation (for parameters as
used in Figure 7) are shown in Figure 9. Results are almost indistinguishable between the cases.
However, the computed longitudinal emittance has in fact doubled. The nature of the effect can
be seen if the bunch charge is raised to 1 nC; results for this case are shown in Figure 10, where
the wake-induced distortion of the longitudinal phase space is more clearly visible, as are
transverse effects in the vertical phase space (lower left).
Work with the IR Upgrade and INP designs has given considerable guidance on how to
analyze and mitigate these effects [25, 26]. The nature of the distortion can be more clearly seen
by “dechirping” the longitudinal phase space, as has been done in Figure 11. Here, we reproduce
all of Figure 9 and simply remove the linear correlation in the longitudinal plot. The effect of the
wake is then apparent, as is a palliative measure: we simply adjust the lattice T566 to compensate
for the CSR effects. A simulation of this solution (with the linear correlation again suppressed) is
shown in Figure 12. It is apparent that the distortion of the longitudinal phase space can be
largely compensated, in analogy to the compensation of such effects in transverse phase space
proposed over a decade ago by Dowell [27], although – inasmuch as this transport is common to
both the accelerated and recovered beams - care must be taken to insure this does not adversely
influence the energy recovery process. The compensation can equally well be done at full energy
in the final compression, where it will not influence energy recovery at all.
A few observations and comments should be made about the performance of this design.
First, the CSR tracking results not only indicate that CSR is, to some level, adequately managed,
they also indicate that lattice aberrations are not an issue.
We have made very preliminary runs to determine the sensitivity of the performance to
other operating points. Not surprisingly, given the above discussion, we find that the shorter
projected bunch length that occurs for smaller momentum spread results in more significant CSR
effects in those cases. It is therefore useful to retain a longitudinal matching solution that
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dechirps the beam on the second pass rather than trying to run closer to crest on the first pass and
attempting to repeatedly recirculate a low-momentum-spread beam.
Transverse effects at higher charge (e.g. 1 nC) manifest themselves primarily in the
vertical plane, indicating that it is the recombiner that is driving the effects. This makes sense, as
the recombiner is where the bunch is shortest and beam envelopes largest (thus giving the largest
response to CSR effects). We may therefore consider use of smaller angle bends for the final step
therein and/or use other palliative measures [28]
The longitudinal distortion compensation shown in Figure 12 can be continued to
increasingly higher order simply by invoking higher order (octupole, decapole, …) compaction
trims at the site of the sextupole compaction trims used for the second order correction. In this
manner, the distortion can be further reduced if necessary to provide adequately small emittance.
Of ongoing concern – and not addressed here – are the effects of environmental
impedances, wakes, and other associated phenomena. As the bunch is very elongated,
degradation from self-interactions and environmental sources is of considerable concern.
Microbunching instability (MBI) effects must be evaluated and driving terms properly managed.
As in storage rings, an appropriately draconian impedance policy is of paramount importance!
Figure 9: Results of ray-trace simulation of 200 pC 6 beam with 1 mm-mrad normalized
transverse emittance and 50 keV-psec longitudinal, with linear chirp equivalent to first pass
acceleration through linac 10o ahead of crest and CSR effects. Top: l-p/p (left), xy (right);
bottom: xx’ (left), yy’ (right).
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Figure 10: Simulation of 1 nC 6 beam with 1 mm-mrad normalized transverse emittance and 50
keV-psec longitudinal, with linear chirp equivalent to first pass acceleration through linac 10o
ahead of crest and CSR effects. Top: l-p/p (left), xy (right); bottom: xx’ (left), yy’ (right).
Figure 11: Figure 9 results with linear chirp extracted; CSR-induced curvature evident in
longitudinal phase space (top left).
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Figure 12: Figure 9 results with linear chirp extracted and CSR-induced curvature compensated
using trim on lattice T566.
Operation with Two-Stage Bunch Compression
The operating point invoked in the previous discussion assumes that the beam will be
accelerated rather far off-crest during the first pass, dechirped on the second pass, and bunched
during the full-energy linac-to-wiggler transport. If this nonconventional approach fails (e.g. due
to MBI effects on the long bunch in the first recirculator), we can use the transport system’s
tuning range to employ a rather more conventional multi-stage compression. In this case, the first
recirculator is operated with nonzero compaction and the bunch partially compressed while at
300 MeV. An appropriately configured final compression at full energy can then produce the
desired longitudinal aspect ratio.
We have simulated this use of the first recirculation transport, and find – not
unexpectedly – that CSR effects become more obvious. The reasons are as discussed above: a
shorter bunch traversing the final recombiner dipole is more severely degraded by the CSR
interaction. Results are given in the aptly numbered Figure 13, wherein the case of Figure 12 is
run with a partial compression (to half the incoming bunch length). Longitudinal emittance
grows by ~20%, and the vertical by ~60%. This growth would limit the wavelength reach of
JLAMP, but should be viewed as a result for a non-optimized system. In particular, reduction of
the recombiner bend angles (with attendant reduction in the integrated CSR effects) should help
alleviate this source of beam quality degradation in a more carefully optimized design.
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Figure 13: Figure 12 results with partial (50%) compression of bunch length at reinjection. As
above, the chirp is extract so as to better see structure on the longitudinal phase space. Some
change in the vertical phase space can be seen (in comparison to Figure 12)
Remaining Issues
The preceding discussion ignores a number of issues that must be addressed as part of a
detailed design process. Of particular importance are the following.
1) MBI/environmental impendance/wake control (believed to be manageable for ERLs [M.
Billing, ERL2009] at nearly as high a charge over much longer path length)
2) Merger (open issue for ERLs, solutions in progress at lower energy/higher charge for INP
FEL)
3) Magnet field quality
In addition, two rather more prosaic “housekeeping” issues should be addressed as a part of
this initial design study: we should refit (rematch) the recirculator using more accurate linac
Twiss parameter values rather than just the generic input/outputs used for the simulations
presented above, and we must perform an energy recovery tracking simulation so as to check the
beam behavior at large amplitude and momentum offset (geometric and chromatic aberrations)
during the second (recovery) pass through the recirculator.
Conclusions
We have presented a discussion of issues arising when recirculation and energy recovery
are used as cost-management tools in the design of short-wavelength FEL drivers. A notional
design for a recirculation beam line in such a system was presented and its performance
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analyzed. Although numerous fundamental phenomena are of importance, it is not obviously
impossible to successfully build and operate such a system. Despite some technical risk, the
potential cost-savings return is so high that further work in this area appears warranted.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
WiFEL design report: http://www.wifel.wisc.edu/WiFEL_R&D_Proposal.pdf . See also
the BESSY-FEL design report.
M. Billing, Proc. ERL2009
D. Douglas and C. Tennant, “Three-Pass Operation of the IR Demo Driver”, JLAB-TN01-043, 28 August 2001; D. Douglas, “Simultaneous Bunch Length and Energy Spread
Compression During Recirculation of Multiple Passes in the IR Demo”, JLAB-TN-01048, 4 October 2001.
C. Tennant, JLAB-TN in preparation.
A. Bogacz et al., “CEBAF Energy Recovery Experiment – Proposal”, JLAB-TN-03-006,
28 June 2002.
C. Tennant et al. “Experimental investigation of multibunch, multipass beam breakup in
the Jefferson Laboratory Free Electron Laser Upgrade Driver”, Phys. Rev. ST Accel.
Beams 9, 064403 (2006)
C. Tennant, “Preliminary Beam Breakup Simulations Using Data for the Jefferson
Laboratory 748.5 MHz Ampere-class Cryomodule”, JLAB-TN-08-049, 17 January 2008.
BESSY-FEL design report
M. Borland, Proc. PAC2009
G. Neil and G. Williams, “JLAMP: A Soft X-ray 4th Generation Light Source for
Jefferson Lab”, JLab Colloquim, 24 June 2009.
C. Tennant, JLAB-TN in preparation, op. cit.
By using a beamline that is isochronous linac-to-linac but allowing appropriate internal
modulation of the compaction, it is possible to arrange for bunch compression at full
energy and then again in the low energy recirculator during energy recovery, all the while
retaining the required energy compression needed to decelerate the beam to the dump
without loss. It is then in principle possible to lase at full energy, and again at half energy.
This is somewhat analogous to the simultaneous near- and mid-IR lasing proposed in the
FSU “BigLight” design.
Schilke: C:\working folders\final backup\faux desktop\se4a\may 2009\se4a nonlinear
longitudinal 081309 rev 4.xls
Details of the linac beam dynamics (transverse optics and space charge effects) will be
provided in C. Tennant and D. Douglas, JLAB-TN in preparation.
The required tunable sextupole terms can be generated using sextupoles in the quad-todipole drifts, Saskatoon “EROS”-style multipoles, Advance Magnet Labs helical
multipole elements, and/or the Duke FEL method of asymmetric powering/transverse
displacement of quadrupoles. A mixture of these solutions – depending on the particulars
of operational needs – may be optimum.
C. Tennant and D. Douglas, JLAB-TN in preparation op. cit.
See Ref. [15].
ibid.
Schilke: C:\working folders\final backup\faux desktop\se4a\may 2009\ linac optics rev 5
corrected.xls; see C. Tennant and D. Douglas, JLAB-TN in preparation op. cit.
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[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
D. Douglas, “Quantum Excitation Estimates for CEBAF Energy Upgrades”, JLAB-TN97-038, 15 October 1997.
Note this also puts the system in violation of the basic assumptions of widely available
CSR models; see, e.g., D. Douglas and C. Tennant, “A Remark on One-Dimensional
Models of CSR”, JLAB-TN-08-050, 19 July 2008.
D. Douglas, “Suppression and Enhancement of CSR-Driven Emittance Degradation in
the IR-FEL Driver”, JLAB-TN-98-012, 24 March 1998.
D. Douglas and C. Tennant, CSR Management in FEL Driver Linac-to-Wiggler
Transport”, JLAB-TN-08-048, 4 January 2008.
D. Douglas, “Suppression and Enhancement of CSR-Driven Emittance Degradation in
the IR-FEL Driver”, op. cit.
D. Douglas and C. Tennant, CSR Management in FEL Driver Linac-to-Wiggler
Transport”, op. cit.
D. Douglas and C. Tennant, “Design Concept for a Scalable High Power FEL Driver”,
JLAB-TN-08-052, 2 September 2008.
D. Dowell, “Compensation of Bend-Plane Emittance Growth in a 180 Degree Bend”,
Proc. IEEE PAC 1997.
D. Douglas and C. Tennant, CSR Management in FEL Driver Linac-to-Wiggler
Transport” op. cit.
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