Bane, K.

Emma, P.

Huang, Z.

Iverson, R.

Raubenheimer, T.

Stupakov, G.

Wang, L.

UNT (University of North Texas) Digital Library

SLAC-PUB-15853LCLS-II-TN-13-02December 2013A Possible Dechirper Device for the LCLS and LCLS-IIK. Bane, P. Emma, Z. Huang, R. Iverson,T. Raubenheimer, G. Stupakov, L. Wang (SLAC)Work supported in part by US Department of Energy under contract DE-AC02-76SF00515.SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA  94025INTRODUCTIONThe purpose of this note is to investigate the use of a metallic pipe withsmall corrugations [1] for passively dechirping, through its wakefield, the LCLSbeam. Similar dechirper systems have been tested in Pohang and Brookhavenat relatively low energies (< 100 MeV) and with relatively long bunches (> 1ps) [2, 3]. A recent proposal from RadiaBeam is to build a 2-m dechirperand install it in the LCLS for a GeV, femtosecond beam test. Such a devicecan be used to either reduce or increase the amount of energy chirp in ashort electron bunch prior to the FEL interaction in the undulator, and henceprovide a flexible control of the LCLS FEL bandwidth. The results can be usedto guide the design of the LCLS-II dechirper, where it is important to removeunwanted electron energy chirp from the LCLS-II superconducting acceleratorand to provide independent controls of x-ray properties in each of the twoparallel beamlines.Details of the longitudinal and transverse wake calculations in a flat, cor-rugated pipe, as well as Figs. 2-4 of this note, can be found in Ref. [4]. In thisnote in Fig. 1 we give a sketch of the dechirper in longitudinal view, showingthe parameters half-gap a, corrugation period p, t = p/2, and depth h. Thebeam and structure parameters that will be used in the example calculationsof this note are given in Table I. Note that corrugation parameters in the tableare at the moment initial suggested values only, and that the calculated wakeeffects are obtained using approximate analytical formulas. For deciding onthe actual corrugation parameters of a dechirper to be built, one will need toperform numerical calculations of the wakes, by e.g. using the field matchingprogram described in Ref. [5]. Such calculations are not within the scope ofthis note.2zy2atphFIG. 1. Geometry in longitudinal view of the vacuum chamber with corrugatedwalls. A rectangular coordinate system is centered on the symmetry axis of thechamber. The blue ellipse represents an electron beam propagating along the zaxis.TABLE I. Beam and structure parameters used in the example calculations in thisnote. Here the structure parameter t is taken to be equal to p/2.Parameter name LCLS LCLS-II UnitBeam energy, E 6.6 4.0 GeVBeam charge, Q 250 100 pCPeak current, Î 1.2 1.0 kAStructure:Length, L 2 10 mDepth, h 0.25 0.5 mmPeriod, p 0.25 1.0 mmExample gap, 2a 1.6 4.0 mm3DECHIRPER DESIGN PARAMETERS AND EXPECTED EFFECTSON THE BEAMThe choice of dechirper parameters is determined from the following con-siderations. A smaller dechirper gap generates a stronger longitudinal wake(which scales as the inverse square of the gap), and allows one to shorten thedevice for the required size of energy chirp. However, an extremely small gapmakes the transverse dipole and quadrupole wakes stronger (they scale as theinverse fourth power of the gap) and leads to projected emittance growth andtight tolerances on the beam offset in the dechirper.In Fig. 2 we plot the energy difference between the tail and head of thebunch due to the dechirper as function of half-aperture a. This function de-pends on a as a−2. For the plot we assume that the charge Q = 250 pC andstructure length L = 1 m. We see that for a = 0.7 mm, ∆E = −10 MeV.We illustrate the strength of the transverse wakes in Figs. 3 and 4. In Fig. 3we plot the relative project emittance increase (ε/ε0)−1 for a bunch traversingthe structure on axis vs. half-aperture a. The emittance growth is due to thequad wake. The parameters used are ones that could apply to the LCLS:bunch charge Q = 250 pC, focusing function βy = 10 m, rms bunch lengthσz = 10 µm, length of structure L = 1 m, and beam energy E = 6.6 GeV.We see that for these parameters, the half aperture of the dechirper needs tobe kept to a & 0.6 mm. As a becomes smaller, the emittance grows steeply.However, if one made a dechirping structure composed of two identical parts,with the second half rotated by 90 degrees with respect to the first half, andwith equal beta functions (βx = βy) then the quad wake effect will cancel(assuming the beta function is large compared to the structure length).If the beam enters the structure vertically offset from the axis by y = y0,it will excite both dipole and quadrupole wakefields. Let us denote the jitter4FIG. 2. Energy difference at tail of a short bunch compared to the head due to thewakefield of a flat dechirper vs. half-aperture a [4]. Here charge Q = 250 pC andstructure length L = 1 m.amplification factor by the symbol ξ (for details of the meaning of this factor,see Ref. [4]). The jitter amplification factor ξ as function of half aperture a isplotted in Fig. 4. Note that the other parameters are the same as those usedin the earlier quad wake calculations. We see that one needs to keep the halfaperture of the dechirper jaws to a & 0.7 mm in order to keep ξ . 1.2.The results presented above indicate that the transverse wake limit theminimal gap 2a between 1 and 2 mm (smaller beam charge would allow asomewhat smaller gap). Given that, in the typical setup, we would like thesize of the corrugations to be a small fraction of the minimal gap, we suggest aflat corrugated pipe with these parameters: depth (h) = period (p) = 0.25 mm,t = p/2 = 0.125 mm, and length of pipe L = 2 m. The gap is tunable, withminimum full gap 2a = 1 mm. It is desirable to split the 2-m-long dechirper5FIG. 3. Relative emittance growth due to the quad wake in a flat dechirper vs. half-aperture a [4]. Here charge Q = 250 pC, energy E = 6.6 GeV, rms bunch lengthσz = 10 µm, and structure length L = 1 m. The beam is on-axis; it has a lon-gitudinal uniform distribution, and initially an uncorrelated, bigaussian transversedistribution in yy′ phase space.into two segments of 1 m length each, rotated by 90 degrees relative to eachother. Note that the longitudinal wakefield generated by such a 2-m device isalready 25% stronger than the 553 m of Linac L3 in the LCLS.LCLS CONSIDERATIONSA possible location for the 2-m-long dechirper is the LCLS LTU area, justupstream of QDL34 (as close to XCDL4 as possible). XCDL4 is at z=3377.706in linac z coordinates. The beta functions are βx = 5 m, and βy = 17 m. It isconceivable to make βx = βy there but this has not been studied carefully.Using a linac longitudinal beam dynamics tracking code (LiTrack [6]), we6FIG. 4. Jitter amplification factor ξ due to the dipole wake in a flat dechirper vs.half-aperture a [4]. Here charge Q = 250 pC, energy E = 6.6 GeV, rms bunch lengthσz = 10 µm, and structure length L = 1 m. The beam has a longitudinal uniformdistribution, and initially an uncorrelated, bigaussian transverse distribution in yy′phase space.give two examples of possible uses of a dechirper in the LCLS. We considera 250-pC beam that is accelerated to 6.6 GeV, in order to generate soft x-rays at the 2 keV photon energy. In Fig.5 (a) we show a possible outcomeof longitudinal phase space at the end of L3. [Here and in following figures,we show a group of 3 or 4 plots giving: phase space (upper right), beamcurrent (lower right), (sometimes) longitudinal wake of dechirper (lower left),and beam energy spread (upper left).] The longitudinal phase space has aresidual chirp with a FWHM energy spread of 0.17%, which means the FELbandwidth will be 0.34% determined by the energy chirp. By setting the fullgap of the dechirper to 2a = 1.58 mm, the residual chirp can be removed to a7large degree, as shown in Fig. 5 (b). The FEL bandwidth can be reduced to0.1-0.2% level, set by the intrinsic SASE bandwidth. The spectral brightnesswill be increased by a factor of 2 accordingly.As another example, we consider producing large bandwidth FEL radi-ation for femtosecond x-ray nanocrystallography [7]. In such experiments,nanocrystals are randomly hit by XFEL pulses, producing diffraction patternsat unknown orientations. One can determine these orientations by studyingthe diffraction patterns themselves, i.e. by indexing the Bragg peaks. Thenumber of indexed individual images and the SASE bandwidth are inherentlylinked, because increasing the number of Bragg peaks per individual image re-quires increasing the bandwidth of the spectrum. This calls for a few percentSASE bandwidth, resulting in an increase in the number of indexed images atthe same number of hits.Large bandwidth FEL has been generated by over-compressing electronbunches in BC2, and 1-2% bandwidth (FWHM) has been observed using softx-ray spectrometers [8]. In Fig. 6 (a), we show an example of an over-compressed 250-pC bunch at 6.6 GeV (L3 end), the FWHM electron energyspread is 1.55%. By closing the full gap of the dechirper to 1 mm, this energyspread can be increased to 2.33%, as shown in Fig. 6 (b). There could beemittance growth associated with this extreme gap and further studies arerequired to quantify this effect.Note BPMDL4 is adjacent to the proposed dechirper device and existingdownstream BPMs can be used to detect the beam kick from the de-chirper.Projected emittance, spectrum, XTCAV and FEL diagnostics are already inplace in the LCLS.8(a)Without dechirper.(b)With dechirper (2a = 1.6 mm).FIG. 5. LiTrack results of a 250-pC bunch at L3 end in the LCLS (6.6 GeV). Thebunch core current is slightly above 1 kA.9(a)Without dechirper.(b)With dechirper (2a = 1 mm).FIG. 6. LiTrack results of a 250-pC bunch at L3 end in the LCLS (at 6.6 GeV). Thebunch is over-compressed to 3 kA peak current in order to generate a large chirp.10FIG. 7. In LCLS-II after the bypass line, for the nominal (100 pC) electron bunch:longitudinal phase space (upper right), energy spread profile (upper left), and cur-rent profile (lower right). This is the result without a dechirper, and we see asignificant, residual energy chirp in the bunch.LCLS-II MOTIVATIONThe LCLS-II accelerator also uses a series of magnetic bunch compressors togenerate 1 kA of peak current. With a very large iris, the longitudinal wakefieldof the TESLA-type superconducting L-band linac section following the finalmagnetic compressor is very weak, leaving a large, linear energy chirp in thebeam, which will increase the FEL bandwidth significantly. Fortunately, beforeit reaches the undulator, the beam passes through a 2.2-km-long, stainless steelbypass transport line, where the resistive wall wake removes much of the energychirp. However, a large chirp still remains, as is shown in Fig. 7 below; herethe bunch charge is (the nominal) 100 pC, with a peak current of 1 kA.Adding a 10-m long adjustable gap, rectangular dechirper after the linacallows control of the final linear energy chirp as the beam enters the FEL11undulator. Possible dechirper parameters are a = 1—30 mm, p = 1 mm, andt = h = 0.5 mm. The final energy chirp after this structure, with 2a = 4 mm,is shown in Fig. 8 (a).Since LCLS-II can provide high-repetition rate bunches to multiple FELbeamlines (at least two beamlines, SXR and HXR, are in the baseline design),it is desirable to have independent controls of x-ray properties, such as band-width and pulse duration, while in the same accelerator configuration. Addinga dechirper prior to the individual FEL beamlines can achieve some of thesegoals. For example, if the gap is adjusted down to 2a = 2 mm, the final chirpcan be increased as shown in Fig. 8 (b); this may satisfy some user requests forlarge FEL bandwidth (close to 0.6% FWHM). Another potential applicationis the seeded x-ray pulse length shortening by a chirped electron beam, sinceonly the portion of the bunch within the amplification bandwidth will be am-plified in the seeded section. Continuing the example of Fig. 8 (b) for an SXRself-seeded beam, assuming the amplification bandwidth at 1 keV is 1 × 10−3(FWHM), the final x-ray pulse length is estimated to be ∼ 10 fs, instead ofthe 60-fs level obtained when there is no energy chirp [as in Fig. 8 (a)].CONCLUSIONWe have calculated the strength of the longitudinal and transverse wake-fields in a flat dechirper as function of gap, and estimated the resulting inducedchirp and effect on projected emittance in a short electron bunch. In addition,through LiTrack simulations, we have demonstrated some ways in which suchdechirpers can be used in chirp control in the LCLS and in LCLS-II.We should note, however, that the corrugation parameters given in Table Ifor the dechirpers are meant to be suggestive only. The strength of the wakes ofthe dechirper that are assumed here use analytical approximations. It is known12(a)Full gap 2a = 4 mm(b)Full gap 2a = 2 mmFIG. 8. Longitudinal phase space in LCLS-II after the bypass line, and now includinga 10-m long dechirper with: (a) full gap 2a = 4 mm, (b) 2a = 2 mm. The bunchcharge is the nominal 100 pC. The plot at lower left is the wakefield-induced chirpof the 10-m long structure.13that the real interaction strengths for a given geometry will be somewhatless. Before actually building a dechirper, one needs to calculate the trueinteraction strength (especially important for the longitudinal wake) by e.g.using a numerical field matching program [5], and then possibly modify thecorrugation parameters.ACKNOWLEDGEMENTWork supported by Department of Energy contract DE–AC02–76SF00515.[1] K. Bane and G. Stupakov, SLAC-PUB-14925 (2012).[2] P. Emma et al, “Experimental demonstration of energy-chirp control in rela-tivistic electron bunches using a corrugated pipe,” submitted to PRL, December2013.[3] M. Harrison et al, “Removal of Residual Chirp in Compressed Beams Using aPassive Wakefield Technique,” presented at NaPAC13, Pasedena, CA, Septem-ber 2013, paper MOPHO25.[4] K. Bane and G. Stupakov, SLAC-PUB-15852 and LCLS-II TN-13-01 (2013).[5] K. Bane and G. Stupakov, Phys. Rev. ST Accel. Beams 6 (2003) 023301.[6] K. Bane and P. Emma, Proc. 2005 Part. Accel. Conf., Knoxville, TN, 2005, p.4266.[7] S. Serkez et al, DESY 13-109, 2013.[8] J.Welch et al, Proc. FEL2011, Shanghai, China, 2011, p. 461.14

A Possible Dechirper Device for the LCLS and LCLS-II

K. Bane

P. Emma

Z. Huang

R. Iverson

T. Raubenheimer

G. Stupakov

L. Wang

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A Possible Dechirper Device for the LCLS and LCLS-II

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