Use of Recirculation in Short-Wavelength FEL Drivers

Transcription

1 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 Q L ) 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: 1 of 20

2 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 2 of 20

3 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/4π) 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 3 of 20

4 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 (σ δp/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 4 of 20

5 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 E inj (MeV) 10 ΔE linac (MeV) Pass 1 Pass 2 Pass 3 Pass 4 E after pass (MeV) * * Phase during pass -10 o 20 o o o Compactions (m) M 56 T 566 W st arc linac-to-wiggler wiggler-to-linac * lasing at 0.3% extraction efficiency 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 ±2σ in each variable. 5 of 20

6 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 δp/p + 6η FEL ) ; we will require 4-5% 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. Separate beams for recirculation (using a spreader) 2. Bend each beam through 180 o and deliver it to a backleg transport 3. Transport the beam to the other end of the vault 4. Bend back through 180 o 5. Recombine the beam with other passes for futher acceleration/recovery. 6 of 20

7 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 (T 466 and T 566 ). 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 β~16 m, α ~ -1, while reinjection parameters of β~30 m and α ~ 1 are reasonable. Recirculation Arc Following separation of the various passes, we recirculate the beam using a 180 o 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), 7 of 20

8 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 1/6 th integer phase advance in the bending plane and 1/4 th 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 180 o in betatron phase in the bending plane and 270 o in the non-bending plane. They therefore can be used to perform a one-knob dispersion bump and modify M 56 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 T 566 ; 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 8 of 20

9 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: β ~ 30 m, α ~ -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 M 56 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. 9 of 20

10 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. 10 of 20

11 Figure 4b: Beam envelopes through 300 MeV recirculator (based on generic input values of β=16 m, α=-1, match to generic output values β=30 m, α =1). Figure 4c: Beam envelopes through 300 MeV recirculator (based on generic energy recovery input values of β=30 m, α=-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 6σ 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 (Σ 56 ). Results are shown in Figure 7; essentially no emittance growth is observed. 11 of 20

12 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. 12 of 20

13 Figure 7: Results of ray-trace simulation of 6σ beam with 1 mm-mrad normalized transverse emittance and 50 kev-psec longitudinal, with linear chirp equivalent to first pass acceleration through linac 10 o ahead of crest. Top: l-δp/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 Δε ~ 0.01 nm-rad is well below the nominal value, even relative to our ~0.8 nm-rad target geometric emittance (10 nm/4π); the growth in relative momentum spread is of order , 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). 13 of 20

14 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 M 56 >0, and providing isochronicity by recombining the beam with a staircase achromat with M 56 <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 T 566 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 14 of 20

15 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 6σ beam with 1 mm-mrad normalized transverse emittance and 50 kev-psec longitudinal, with linear chirp equivalent to first pass acceleration through linac 10 o ahead of crest and CSR effects. Top: l-δp/p (left), xy (right); bottom: xx (left), yy (right). 15 of 20

16 Figure 10: Simulation of 1 nc 6σ beam with 1 mm-mrad normalized transverse emittance and 50 kev-psec longitudinal, with linear chirp equivalent to first pass acceleration through linac 10 o ahead of crest and CSR effects. Top: l-δp/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). 16 of 20

17 Figure 12: Figure 9 results with linear chirp extracted and CSR-induced curvature compensated using trim on lattice T 566. 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. 17 of 20

18 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 18 of 20

19 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] WiFEL design report: See also the BESSY-FEL design report. [2] M. Billing, Proc. ERL2009 [3] D. Douglas and C. Tennant, Three-Pass Operation of the IR Demo Driver, JLAB-TN , 28 August 2001; D. Douglas, Simultaneous Bunch Length and Energy Spread Compression During Recirculation of Multiple Passes in the IR Demo, JLAB-TN , 4 October [4] C. Tennant, JLAB-TN in preparation. [5] A. Bogacz et al., CEBAF Energy Recovery Experiment Proposal, JLAB-TN , 28 June [6] 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, (2006) [7] C. Tennant, Preliminary Beam Breakup Simulations Using Data for the Jefferson Laboratory MHz Ampere-class Cryomodule, JLAB-TN , 17 January [8] BESSY-FEL design report [9] M. Borland, Proc. PAC2009 [10] G. Neil and G. Williams, JLAMP: A Soft X-ray 4th Generation Light Source for Jefferson Lab, JLab Colloquim, 24 June [11] C. Tennant, JLAB-TN in preparation, op. cit. [12] 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. [13] Schilke: C:\working folders\final backup\faux desktop\se4a\may 2009\se4a nonlinear longitudinal rev 4.xls [14] 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. [15] 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. [16] C. Tennant and D. Douglas, JLAB-TN in preparation op. cit. [17] See Ref. [15]. [18] ibid. [19] 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. 19 of 20

20 [20] D. Douglas, Quantum Excitation Estimates for CEBAF Energy Upgrades, JLAB-TN , 15 October [21] 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 , 19 July [22] D. Douglas, Suppression and Enhancement of CSR-Driven Emittance Degradation in the IR-FEL Driver, JLAB-TN , 24 March [23] D. Douglas and C. Tennant, CSR Management in FEL Driver Linac-to-Wiggler Transport, JLAB-TN , 4 January [24] D. Douglas, Suppression and Enhancement of CSR-Driven Emittance Degradation in the IR-FEL Driver, op. cit. [25] D. Douglas and C. Tennant, CSR Management in FEL Driver Linac-to-Wiggler Transport, op. cit. [26] D. Douglas and C. Tennant, Design Concept for a Scalable High Power FEL Driver, JLAB-TN , 2 September [27] D. Dowell, Compensation of Bend-Plane Emittance Growth in a 180 Degree Bend, Proc. IEEE PAC [28] D. Douglas and C. Tennant, CSR Management in FEL Driver Linac-to-Wiggler Transport op. cit. 20 of 20