Beam dynamics performances and applications of a low-energy electron-beam magnetic bunch compressor
aa r X i v : . [ phy s i c s . acc - ph ] F e b Beam dynamics performances and applications of a low-energyelectron-beam magnetic bunch compressor
C. R. Prokop a , P. Piot a,b , B. E. Carlsten c , M. Church d a Northern Illinois Center for Accelerator & Detector Development and Department of Physics,Northern Illinois University, DeKalb, IL 60115, USA b Accelerator Physics Center, Fermi National Accelerator Laboratory, Batavia, IL 60510, USA c Acceleration Operations and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA d Accelerator Division, Fermi National Accelerator Laboratory, Batavia, IL 60510, USA
Abstract
Many front-end applications of electron linear accelerators rely on the production of temporally-compressed bunches.The shortening of electron bunches is often realized with magnetic bunch compressors located in high-energy sectionsof accelerators. Magnetic compression is subject to collective e ff ects including space charge and self interactionvia coherent synchrotron radiation. In this paper we explore the application of magnetic compression to low-energy( ∼
40 MeV), high-charge (nC) electron bunches with low normalized transverse emittances ( < µ m). Keywords:
Photoinjector, Linear accelerator, Electron beam, Magnetic bunch compressor, Space charge, Coherentsynchrotron radiation, Flat beam
1. Introduction
Most of the photoinjectors being used for generation ofbright electron bunches for, e.g., free-electron laser (FEL)applications consist of generating and rapidly acceleratingthe electron bunch to high energy and subsequently short-ening the bunch using a magnetic bunch compressor [1].The only deviation to such a design is the combined ac-celeration and compression using velocity bunching [2].Attempts to operate low-energy magnetic bunch compres-sors have to date been inconclusive [3] or deemed incom-patible with the production of low-emittance beams [4].In this paper we explore and demonstrate via numeri-cal simulations that low-energy bunch compression per-formed on a ∼ ff curves between transverse emittance and peak currentfor several cases of electron-bunch charge. In addition,our simulations are performed with several computer pro-grams thereby enabling a benchmarking of very di ff erentapproaches for modeling collective e ff ects and especially coherent synchrotron radiation (CSR) [5, 6]. Our studyconsiders the magnetic bunch compression planned in the40-50 MeV photoinjector of the Advanced Superconduct-ing Test Accelerator (ASTA) currently under constructionat Fermilab [7, 8].
2. Accelerator beamline overview
The compression of a ∼ Te) photocathode located onthe back plate of a 1 + / ∼ Preprint submitted to Elsevier today unches are further accelerated up to 50 MeV by two1.3-GHz superconducting RF (SCRF) accelerating cav-ities (labeled as CAV1 and CAV2 in Fig. 1). A thirdSCRF cavity (CAV39) operating at 3.9 GHz will even-tually be incorporated to correct for nonlinear longitudi-nal phase space distortions [10–12]. Because of its su-perconducting nature, the ASTA facility produces elec-tron bunches repeated at 3 MHz arranged in a 1-ms 5-Hz RF macropulse. The downstream beamline includesquadrupoles, steering dipole magnets, and diagnostics sta-tions. A skew-quadrupole channel can be set up as around-to-flat-beam transformer (RFBT) to convert an in-coming angular-momentum-dominated beam into a flatbeam with high transverse emittance ratio [13, 14]. Thebeamline also incorporates a four-bend magnetic bunchcompressor (BC1) which, consists of four 0.2-m rectan-gular dipoles (B1, B2, B3, B4) with respective bendingangles of ( + ,-,-, + ) 18 ◦ . The longitudinal dispersion ofBC1 is R = − .
19 m. Finally a single-shot longi-tudinal phase space diagnostics combining a transverse-deflecting cavity (TDC) with a vertical spectrometer willbe installed [15].
Figure 1: Injector configuration at ASTA. The “RF gun”, “L1” and “L2”respectively correspond to the gun cavity and surrounding solenoid mag-nets, “CAV1”, “CAV2”, and “CAV39” are superconducting RF cavities,“RFBT” is the round-to-flat beam transformer, and “BC1” refers to themagnetic bunch compressor, and B1-4 are the dipoles of the chicane,with distance between the dipoles marked in the figure. The numberbelow the beamline indicates the axial positions in meters w.r.t. the pho-tocathode surface.
The beam dynamics through CAV2 were simulatedwith astra and optimized using a genetic optimizer forseveral cases of charge and photocathode drive-laser con-figurations; see Ref. [16]. The resulting phase spacedistributions are used as a starting point for transportand compression through the beamline downstream ofCAV39. The quadrupoles settings were optimized forthe various operating charges using the single-particle dy-namics program elegant [17]. The evolution of the nom- inal betatron functions downstream of CAV39 up to thecryomodule entrance is plotted in Fig. 2.
10 12 14 16 18 20 22 s (m) (cid:0) ( m ) Figure 2: Evolution of the horizontal (blue) and vertical (red) betatronfunctions through the ASTA injector. The green rectangles indicate thelocation of quadrupole and dipole (smaller rectangles) magnets. TheBC1 compressor is located at s ∈ [11 . , .
1] m. The origin of thehorizontal axis ( s =
3. Modeling methodology
The bunch-compression performance of BC1 was ex-plored via numerical simulations using impact - z [18] and csrtrack [19]. Both programs model the beam as anensemble of interacting macroparticles and integrate theequations of motion to advance the macroparticles alonga user-specified beamline.In impact - z the space-charge (SC) interaction is mod-eled using a mean-field quasi-static particle-in-cell (PIC)algorithm and the (point-like) macroparticles are ad-vanced through the beamline using high-order transfermaps. Each beamline element is segmented into axialslices modeled by transfer maps. Between each transfer-map segment, impact -Z applies a space-charge “kick”evaluated from the mean-field PIC SC algorithm [18].CSR e ff ects are included in impact -Z using the one-dimensional formulation described in Ref. [20]. The one-2imensional model is valid provided [21] D ( s ) ≪
1, with D ( s ) ≡ σ x ( s ) σ z ( s ) s σ x ( s ) R ( s ) , (1)where R ( s ) is the trajectory’s radius of curvature and σ x ( s )and σ z ( s ) are respectively the transverse and longitudinalroot-mean-square (RMS) sizes at the curvilinear beamlineposition s .In impact - z the longitudinal charge distribution neededfor the 1D CSR model is obtained from a longitudinal bin-ning of the macroparticle ensemble. Convergence studieswere carried out in order to determine the optimal num-ber of longitudinal bins, N z , to be used for both the SCand CSR calculations. Low values of N z generally under-estimated the peak-current and therefore the collective ef-fects, while large values of N z introduce numerical noisethat can lead to artifacts (e.g. numerically-induced mi-crobunching) [22]. The convergence study [23] revealedan appropriate value of N z =
256 for a bunch representedby N = × macroparticles. The number of bins inthe transverse dimensions was set to N x = N y =
16. The impact - z simulations presented in the rest of this paper usethis set of parameters.The program csrtrack was specifically developed toe ffi ciently simulate the impact of bunch radiative self-interaction via CSR. C srtrack incorporates several mod-els including a 2D particle-to-particle (P2P) model thatdirectly computes the forces on macroparticles from theLi´enard-Wiechart potentials evaluated at retarded times.These calculations are self-consistent and enable the com-putation of both the transverse and longitudinal forcecontributions from SC and CSR e ff ects. Since the P2Pmodel is computationally intensive, (the calculation timescales as N ), csrtrack also includes an improved one-dimensional model referred to as the 1D Projected (1DP)model. The 1DP model uses the 1D projection of thesmoothed charge distribution convoluted with a kernelfunction [24]. Compared to the model of Ref. [20], the1DP model is not limited to the ultra-relativistic regime.C srtrack ’s P2P model treats each macroparticle as a 3DGaussian charge distribution (referred to as “sub-bunch”)in the ( x , y , z ) space with distribution g ( x , y , z ) = π ) / σ h σ v σ || e − x σ h − y σ v − z σ || , (2) where σ h , σ v and σ || are respectively the horizontal, ver-tical and longitudinal RMS sizes of the sub-bunches. Theresulting beam’s spatial charge distribution is Φ ( x , y , z ) = P Nj = Q j g ( x − x j , y − y j , z − z j ) where Q j and ( x j , y j , z j )are respectively the i -th sub-bunch charge and LPS coor-dinates. In csrtrack , σ v and σ || may be defined relative tothe vertical and longitudinal RMS bunch sizes, σ y and σ z ,respectively, and are adjusted along the bunch compres-sor as the dimensions of the bunch change. Due to thecomputational intensiveness of the P2P model, only 10 sub-bunches were used compared to 2 × used with the1DP model. This relatively-low number of sub-bunchesrequires a large σ || of 5% of the longitudinal bunch length σ z for the 1DP simulations and 10% for the P2P simula-tions; for a detailed study see Ref. [23]. The P2P modelrequires parameters for the sub-bunches in the horizontaland vertical dimensions, σ h and σ v . We chose σ v = σ y and σ || = σ z . However, csrtrack does not allow σ h tobe set as a variable of the horizontal RMS width, so we in-stead chose 0.1 mm, which is on the order of 10% of theRMS size σ x for all four of the bunch charges presentedhere. Both of csrtrack ’s models neglect collective forcesin the vertical dimension.The astra simulations of the beam generation and ac-celeration simulated up to s = . python program, gluetrack [25], was used to manip-ulate the beam distributions and generate macroparticledistributions suitable for impact - z and csrtrack . For allthe bunch-compressor studies, impact - z was used to trackthe bunch distribution from s = . s = . ff ects.Simulations were performed for four cases of bunchcharges ranging from 3.2 nC to 20 pC. For each chargethe transverse emittance was optimized with astra [16].The distributions were manipulated using gluetrack toadjust several parameters including their Courant-Snyder(C-S) parameters, and longitudinal phase space (LPS)chirp C ≡ −h z i δ i i /σ z , i where ( z i , δ i ) are the coordinates inthe LPS, the h u i indicates the statistical averaging of vari-able u over the LPS distribution and σ z , i ≡ h z i i / . We3lso modeled the e ff ect of CAV39 by numerically remov-ing the second order correlation in the LPS distribution. Table 1: Transverse and longitudinal beam parameters 0.1-m upstreamof B1 dipole entrance face. Only the Courant-Snyder parameters werefixed while the other parameters depend on the bunch charge or upstreambeamline settings.
Parameter Value Units β x , i α x , i β y , i α y , i -1.6 - C [1.0,6.0] m − total energy 38.6 MeVThe charge-independent beam parameters computed0.1-m upstream of dipole magnet B1 are summarized inTab. 1. The beam distribution was matched to achieve thetransverse C-S parameters listed in Tab. 1 (see discussionbelow) upstream of BC1. The initial LPS chirp was tunedby removing the second-order correlation and scaling thefirst-order correlation between δ i and z i . The other LPSparameters and emittances (shown for the four charges inTab. 2) are inherent to the generation process and werenot adjusted. The initial LPS distribution for each of thefour charges appears in Fig. 3 with its linear correlationremoved. The S -shaped LPS is a remnant of space chargee ff ects during the bunch generation and transport beforeacceleration in CAV1 and CAV2 [26]. As expected largercharges yield higher total fractional momentum spread. Table 2: Initial normalized transverse ε x / y , i and longitudinal ε z , i emit-tances and RMS bunch length σ z , i for the four cases of charge consideredin this paper. The parameters are computed 0.1-m upstream of dipolemagnet B1’s entrance face. Q (nC) ε x , i ( µ m) ε y , i ( µ m) ε z , i ( µ m) σ z , i (mm)3.2 4.43 4.58 82.19 2.561.0 2.20 2.22 33.41 1.950.250 0.580 0.576 14.37 1.930.020 0.296 0.297 2.54 1.26 Figure 3: LPS distributions 0.1-m upstream of dipole magnet B1’s en-trance face for 3.2 (a), 1.0 (b), 0.25 (c) and 0.02 nC (d) bunches. Thedistributions were obtained from simulations of the photoinjector beamdynamics in astra ; see Ref. [16]. The ordinates z > Simulations were performed for LPS chirps
C ∈ [1 . , .
0] m − with the bulk of the simulations performedaround the maximum-compression value C = − / R ≃ . − , corresponding to enhanced collective e ff ects.The initial values for the betatron functions were se-lected such that the beam experiences a waist betweenthe third and fourth dipole [27]. Simulations performedwith the 1DP csrtrack model also confirmed there is a setof horizontal C-S parameters that minimizes the bending-plane emittance growth as displayed in Fig. 4. The up-stream magnets were tuned to provide the incoming hor-izontal C-S parameter ( β x , i , α x , i ) = (8 . , .
0) shown inFig. 2. Lastly, the final RMS bunch lengths as a func-tion of the initial LPS chirp are given in Fig. 5 as ob-tained using impact - z ’s SC + CSR model. In addition, thereare slight variations in the bunch length between the fourdi ff erent models due to their collective e ff ects inhibitingcompression to varying degrees.
4. Benchmarking of numerical models
The beam dynamics simulations throughout BC1 wereperformed for several degrees of bunch compression (con-trolled with the LPS chirp) for the four cases of bunch4 (cid:1) x,i (m) (cid:2) x , i Figure 4: Contour plot of the final normalized horizontal emittance ( ε x in µ m) as a function of the C-S parameters β x , i and α x , i csrtrack ’s 1D-Projected model and a bunch charge of 3.2 nC . From this data, weselected the values for our simulations, ( β x , i , α x , i ) = (8 . , . .charges that will be used at the ASTA. Four simulationalgorithms were used as described earlier. Because ofits computational e ff ort, crtrack ’s P2P model simulationswere restrained to a smaller range of values for C .The LPS 1.0-m downstream of the B4 dipole simu-lated with impact -Z (SC + one-dimensional CSR mod-els) and csrtrack (P2P model) are shown in Fig. 6 [(a)-(d)] and [(e)-(f)] respectively for the four charges listedin Tab. 2. Despite the vastly di ff erent algorithms used bythese two programs, the LPS distributions displayed verysimilar distortions including those at the small-scale lev-els. Figure 7 summarizes the evolution of peak current asa function of the initial LPS chirp for the four numericalmodels. Likewise the longitudinal emittances computedwith impact - z (SC + CSR) and csrtrack (P2P) for the caseof maximum compression are in decent agreement; seeTab. 3.The transverse-emittance after compression is shownin Fig. 8. C srtrack ’s P2P model consistently o ff ersthe greatest emittance growth, followed by impact - z ’s (cid:3) )0.00.51.01.52.02.5 (cid:4) z ( mm ) Figure 5: RMS bunch length σ z downstream of BC1 as a function of theLPS chirp for various bunch charges using I mpact -Z’s CSR + SC modelmodel, for 3.2-nC (blue), 1.0-nC (red), 250-pC (green), 20-pC (ma-genta) bunch charges. The inset plot corresponds to a close-up aroundchirp values that achieve minimum RMS bunch lengths. (color online)Table 3: Final normalized longitudinal ε z at maximum compression( C = . − ) simulated with impact-z (SC + CSR) and csrtrack (P2P). impact - z csrtrack SC + CSR P2PQ (nC) ε z ( µ m) ε z ( µ m)3.2 267 2611.0 118 1050.250 61.5 57.80.020 10.5 11.6SC + CSR model, as these are the only two models thataccount for both SC and CSR e ff ects. However, theP2P model also includes transverse CSR forces and amore elaborate model for longitudinal CSR. Our previ-ous study [23] showed that the influences on final emit-tance from using too-few macroparticles as well from asthe randomization in the down-sampling of initial dis-tributions were both much smaller than the discrepancy5 igure 6: LPS at BC1 exit for impact - z ’s (a-d) and csrtrack ’s (e-h) 3Dmodels, for 3.2-nC (a,e), 1-nC (b,f), 250-pC (c,g), and 20-pC (d,h) bunchcharges, zoomed in to show details, for C = . − . (Red line) longi-tudinal current projection, with arbitrary scale and o ff set. Note that thehorizontal and vertical axis ranges are di ff erent for each plot. The ordi-nates z > between the SC + CSR and P2P models. The emittancegrowth observed from csrtrack ’s 1D and impact - z ’s SC-only model, indicates that CSR accounts for most of theemittance dilution at higher charge. For the low-chargesimulations ( Q =
250 and 20 pC) the relative importanceis reversed, with SC contributing more to the emittancedegradation than CSR. Of the models presented here, only impact - z ’s include SC in both the vertical and the horizon- Figure 7: Peak currents ˆ I versus energy chirp for impact - z ’s SC + CSR(green), impact - z ’s SC (blue), csrtrack ’s 1DP (red), and csrtrack ’s P2P(magenta) models, for 3.2-nC (a), 1.0-nC (b), 250-pC (c), and 20-pC (d)bunch charges. (color online) tal planes, and are shown in Fig. 9. As vertical emittancegrowth is entirely the result of SC, the inclusion of impact - z ’s CSR model reduces vertical emittance growth due tothe reduced compression.Finally, the evolution of the slice parameters duringcompression were explored. For this analysis the beamis divided into axial slices of equal longitudinal length δ z = µ m. A statistical analysis on the population con-tributing to each slice was performed to yield the sliceemittances, energy spread and peak current. A com-parison of the slice bending-plane emittance and energyspread between impact - z and csrtrack ’s P2P model ofslice-emittance as the chirp is varied appears in Fig. 10.The level of agreement between the two programs is ofthe same order as what observed for the bunch parameters.Fig. 11 summarizes the evolution of the slice horizontalemittance in the slice with the highest peak current withinthe bunch. When the beam is greatly over-compressed( C = . − ), the LPS may be double-peaked, and thetransverse brightness as defined here may not be an appro-priate measure of the bunch’s utility. The curve demon-strates how little slice emittance growth occurs for partial6 (cid:5) x ( (cid:6) m ) (a) (b) (cid:7) )024681012 (cid:8) x ( (cid:9) m ) (c) (cid:10) )0.00.51.01.52.02.53.03.5 (d) Figure 8: Final horizontal emittances for each of the di ff erent bunchcharges with impact - z ’s SC-only model (blue), csrtrack ’s 1D CSR-model (Red), impact - z ’s SC + CSR model (Green), and csrtrack ’s P2Pmodel (magenta), for 3.2-nC (a), 1-nC (b), 250-pC (c), and 20-pC (d)bunch charges. (color online) compression.
5. Expected beam dilution and trade-o ff s A large number of accelerator applications re-quire beams with high-peak-currents and low-transverse-emittances. These requirements conflict with each otheras collective e ff ects, which dilute the beam’s phase spaceand emittances, increase with peak current. A commonly-used figure of merit is peak transverse brightness B ⊥ ≡ ˆ I π ε x ε y [28]. Figure 12 summarized the evolution of B ⊥ as function of the LPS chirp for the four cases of bunchcharges. The figure combines the data provided in Fig. 7and Fig. 8. Despite the lower-charge bunch result insmaller peak current at lower charges (see Fig. 7), thetransverse brightness increases with lower bunch charges.The main factor at play in this reduction is the lower initialtransverse emittances, and more importantly, the reduceddilution of the transverse emittances during compressionin BC1 due to the weaker collective e ff ects (CSR and SC). (cid:11) y ( (cid:12) m ) (a) 4.0 4.5 5.0 5.5 6.012345 (b)4.0 4.5 5.0 5.5 6.0LPS Chirp (m (cid:13) )0.51.01.52.0 (cid:14) y ( (cid:15) m ) (c) 4.0 4.5 5.0 5.5 6.0LPS Chirp (m (cid:16) )0.10.20.30.4 (d) Figure 9: Final vertical emittances for each of the di ff erent bunchcharges with impact - z ’s SC-only model (blue) and impact - z ’s SC + CSRmodel (Green), for 3.2-nC (a), 1-nC (b), 250-pC (c), and 20-pC (d)bunch charges. C srtrack does not compute vertical forces, so the emit-tance remains roughly constant along the bunch compressor. (color on-line)
In addition we note that the maximum achieved trans-verse brightness does not necessarily occur at maximumcompression. This is due to the larger peak currentsat maximum compression that drive collective e ff ects,wherein the relative emittance growth driven by collectivee ff ects is greater than the relative increase in peak current,a trade-o ff similar to that of going down to lower bunchcharges. A summary of the achieved maximum value of B ⊥ appears in Fig. 13.The trade-o ff between obtained peak current and ε x isshown in Fig. 14; only data associated to LPS chirp upto maximum compression at C ≤ . − are displayed,as over-compression results in lower peak currents withgenerally larger emittance dilutions.The simulation data points to several conclusions aboutthe parametric trade-o ff s that must be considered. First,the emittance growth, particularly the slice emittance, isgreatly reduced at lower degrees of compression, partic-ularly C < − , which corresponds to compression7 (cid:18) (cid:19) (cid:20) x ( (cid:21) m ) (a) (cid:22) (cid:23) (cid:24) z (mm) (cid:25)(cid:26) (c) (cid:27) (cid:28) (cid:29) (b) (cid:30) (cid:31) z (mm) (d) Figure 10: Example of final normalized transverse slice emittances (toprow) and energy spread (bottom row) evolution within a 1-nC bunch forfour cases of compression C = .
0, 5.0, 5.25, and 6.0 m − respectivelyshown as blue, green, red and turquoise traces). Plots (a) and (c) cor-respond to impact - z simulations while plots (b) and (d) are results from csrtrack ’s P2P model. Emittance and energy spread values associatedto slices that contain too-few number of macroparticle for meaningfulstatistical analysis are set to zero. The heads and tails of the bunchesare sparsely populated (see Fig. 6 for reference), particularly for the P2Psimulations which use only 5 % of the number of particles used in the impact - z simulations. to around one-third of the initial bunch length. Second,using lower bunch-charges is preferred for experimentsthat require high transverse brightnesses, due to the loweremittance growth from collective e ff ects justifying thelowered peak current. For the 20-pC bunch charge, theregime with C < . − results in horizontal emittancegrowth that is under 10% of the initial horizontal emit-tance, regardless of which of the simulation codes is used.Under-compression is discussed further in section 6.1.
6. Applications
The main motivation that led to the inclusion of BC1 inthe ASTA’s photoinjector is to provide a weak compres-sion necessary to avoid significant energy spread to be ac-cumulated during acceleration in subsequent cryomodule. s li c e ! x ( " m ) (a) 1 2 3 4 5 6051015202530 (b)1 2 3 4 5 6LPS Chirp (m )0246810121416 s li c e $ x ( % m ) (c) 1 2 3 4 5 6LPS Chirp (m & )0.00.51.01.52.02.5 (d) Figure 11: Final normalized transverse slice emittances ε x , M in the slicewith the highest peak current computed with impact - z ’s SC-only model(blue), csrtrack ’s 1D CSR-model (red), and impact - z ’s SC + CSR model(green), and csrtrack ’s P2P model (magenta), for 3.2-nC (a), 1-nC (b),250-pC (c), and 20-pC (d) bunch charges.
It is anticipated that a second-stage bunch compressor willeventually be installed at higher energy to compress thebunch to high peak current while mitigating phase-spacedilution. However, in light of the studies presented in theprevious Sections it is worth investigating other possibleapplications of the BC1 compressor as discussed below.
One of the motivations for exploring low-energy bunchcompression is to moderately compress the bunches be-fore injection in an accelerating structure and then furthercompress at high energy [4]. In Ref. [4], the low-energybunch compression was accomplished at ∼
15 MeV andresulted in intolerable beam degradation at the Tesla TestFacility I (TTF1) and consequently dismantled from thebeamline during its upgrade as the Free electron LASer inHamburg (FLASH) user facility. The requirement on thefirst-stage bunch compression is to provide bunch lengthsthat satisfy σ z ≪ λ/ (2 π ) (where λ is the wavelength ofthe RF wave associated with the subsequent accelerating8 B ’ ( A / m ) (a) 1 2 3 4 5 610 (b)1 2 3 4 5 6LPS Chirp (m ( )10 B ) ( A / m ) (c) 1 2 3 4 5 6LPS Chirp (m * )10 (d) Figure 12: Peak transverse brightness B ⊥ = ˆ I π ε x ε y versus energy chirpfor impact - z ’s SC + CSR (green), impact - z ’s SC (blue), csrtrack ’s 1DP(red), and csrtrack ’s P2P (magenta) models, for 3.2-nC (a), 1.0-nC (b),250-pC (c), and 20-pC (d) bunch charges. (color online) structure). The latter condition insures that no significantLPS quadratic distortion is imparted during accelerationin the subsequent linac. For the L-band linac of ASTAthis sets the upper requirement σ z ≤ µ m [4]. Fora Gaussian distribution this requirement corresponds to aˆ I ≃
500 A at Q = . C ∼ . − resulting inthe tolerable bending-plane emittance dilution as shownin Tab. 4 along with compression to σ z ≃ µ m for eachof the other bunch charges. Relative emittance growth issignificantly smaller for 1-nC bunch charge and below. Despite their relatively poor transverse emittance, fullycompressed bunches could be used to generate copiousamounts of radiation via a given electromagnetic process.The spectral-angular fluence emitted by a bunch of N ≫ d Wd ω d Ω (cid:12)(cid:12)(cid:12) , via d Wd ω d Ω (cid:12)(cid:12)(cid:12) N ≃ d Wd Ω d ω (cid:12)(cid:12)(cid:12) [ N + N | S ( ω ) | ] , (3) B + ( A / m ) Figure 13: Maximum peak transverse brightness B ⊥ = ˆ I π ε x ε y versusbunch charge for impact - z ’s SC + CSR (green), impact - z ’s SC (blue), csr - track ’s 1DP (red), and csrtrack ’s P2P (magenta) models. Each datapoint is a maximum from each line in Fig. 12. (color online) where ω ≡ π f ( f is the frequency) and S ( ω ), the bunchform factor (BFF), is the intensity-normalized Fouriertransform of the normalized charge distribution S ( t ) [29].The former equation assumes the bunch can be approxi-mated as a line charge distribution and is practically validas long as the rms bunch duration σ t and transverse size σ ⊥ satisfy σ ⊥ ≪ c σ t /γ where γ is the Lorentz factor and c is the velocity of light. When the BFF approaches unity, d Wd ω d Ω (cid:12)(cid:12)(cid:12) N ∝ N and the radiation is termed “coherent radia-tion”.At ASTA the availability of a superconducing linaccoupled with a non-interceptive radiation-generationmechanism (e.g. di ff raction radiation [30]) could lead tothe production of single-cycle THz pulses repeated at 3MHz over 1-ms. As an example we consider the worst-case scenario of a fully compressed 3.2-nC bunch; the de-pendency of the BFF over frequency appears in Fig. 15(left plot). The BFF starts to take o ff at frequency lowerthan f ≃ -1 , x ( - m ) (a) 10 -2 -1 (b)10 -2 -1 ˆI (kA) -1 . x ( / m ) (c) 10 -3 -2 -1 ˆI (kA) -1 (d) Figure 14: Final normalized transverse emittances ε x versus peak cur-rents ˆ I for LPS chirps using impact - z ’s SC + CSR (green), impact - z ’s SC(blue), csrtrack ’s 1DP (red), and csrtrack ’s P2P (magenta) models, for3.2-nC (a), 1.0-nC (b), 250-pC (c), and 20-pC (d) bunch charges. Onlydata corresponding to chirp values C ∈ [1 . , .
2] m − are displayed.(color online) spot RMS size below the required σ ⊥ /γ value. Howevera statistical analysis indicates that the central part of thebeam containing approximately 15% of the beam popu-lation (or 500-pC out of the original 3.2-nC bunch) hasemittances below 10 µ m resulting in beam σ ⊥ ≤ µ m;see Fig. 15 (right plot). It should be pointed out that thelower-charge cases investigated in the previous sectionwould result in shorter pulses with associated BFFs thatcontain higher-frequency content (see also Fig. 5). An important asset of the ASTA photoinjector is itscapability to generate beams with high-transverse emit-tance ratios known as flat beams. Immersing the photo-cathode in a magnetic field introduces a canonical angu-lar momentum h L i = eB σ c , with B the magnetic fieldon the photocathode surface, and σ c the RMS transversesize of the drive-laser spot on the photocathode [31]. Asthe beam exits the solenoidal field provided by lenses L1and L2, the angular momentum is purely kinetic result-ing in a beam coupled in the two transverse planes. Three Table 4: Final normalized transverse ε x / y and longitudinal ε z emittancesfor the four cases of charge considered in this paper. The initial LPSchirp ( C ) was optimized for each charge to yield a final bunch length σ z ≃ µ m, based on the scan presented in Fig. 5. The simulationswere performed with impact - z ’s SC + CSR model. The values displayedin this Table should be compared with the pre-compression values sum-marized in Tab. 2.
Q (nC) C (m − ) ε x ( µ m) ε y ( µ m) ε z ( µ m)3.2 3.7 10.56 4.24 88.71.0 3.2 3.03 1.98 34.20.250 3.1 0.623 0.594 14.70.020 1.9 0.296 0.293 1.83 -2 -1 frequency (THz)10 -6 -5 -4 -3 -2 -1 b un c h f o r m f a c t o r -1 radius (mm)10 -1 ( m ) p e a k c u rr e n t ( A ) Figure 15: Bunch form factor associated to the 3.2-nC fully-compressedelectron bunch (left plot) and final horizontal (blue), vertical (red), andlongitudinal (green) normalized emittances (left vertical axis) and peakcurrent (dashed black line, right axis) of the bunch within a selectedtransverse radius (right plot). These simulations were performed nearmaximum compression with C = . − and 3.2-nC. (color online) skew quadrupoles in the beamline can apply the torquenecessary to cancel the angular momentum [32, 33]. Asa result, the final beam’s transverse emittance partition isgiven by ( ε x , i , ε y , i ) = ε u βγ L , βγ L ! , (4)where ε u is the normalized uncorrelated emittance of themagnetized beam prior to the transformer, β and γ theLorentz factors, L ≡ h L i / p z , and p z is the longitudi-10al momentum. Note that the product ε x , i ε y , i = ( ε u ) .If compressed these flat beams may have applications inSmith-Purcell FELs [34] or for beam-driven accelerationtechniques using asymmetric structures [35]. It may alsobe possible to mitigate the emittance growth in BC1 byhaving a beam that is wide in the direction of the chicanebend.In this section, we explore the behavior of flat beamsin the low-energy bunch compressor at ASTA, for the dif-ferent initial emittance ratios ρ ≡ ε x , i /ε y , i . In order toproduce these bunches, we took the 3.2-nC bunch pre-sented earlier and numerically scaled the macroparticlecoordinates to produce the desired transverse emittanceratios while constraining the product ε x , i ε y , i = µ m .Due to the large transverse aspect ratio of the bunches,the criterion given in Eq.1 is generally not satisfied andit is therefore anticipated that the projected CSR model isinadequate, thus we use CSR track ’s P2P model to sim-ulate the flat beams and neglect the 1DP model. Theparameters used for flat beam simulations follow thoseused in the previous section, with the exception of themacroparticle horizontal size used in the csrtrack P2Pmodel. Due to the much greater transverse dimension weset σ h = . impact - z SC + CSR sim-ulations were also performed to evaluate the emittancegrowth in the vertical plane. The simulated emittancegrowth is shown in Fig. 16 for a 3.2-nC bunch with aninitial LPS chirp of C = . − . As expected the rela-tive emittance dilution is reduced as the initial emittanceratio ρ increases. The agreement between csrtrack and impact - z for the bending-plane emittance dilution is re-markable (within ∼
30 %) given the large transverse hori-zontal beam sizes. I mpact - z predicts that the vertical emit-tance increases by a factor of 1.5 to 1.8 over the range ofconsidered initial emittance ratios ρ ∈ [1 , ε ≡ √ ǫ x ǫ y ismitigated for the larger initial flat-beam emittance ratios. The production of shaped electron bunches has a largenumber of applications including the investigation ofwakefield and beam-driven acceleration techniques. Op-erating the low energy bunch compressor with LPS chirp C > . − leads to over compression and results ina structured longitudinal charge distribution. Figure 17confirms, for the case of Q = . x x , i Figure 16: Bending plane transverse emittance ε x ε x , i growth in BC1 (red)simulated with csrtrack (dashed line) and impact - z (solid lines) as func-tions of the initial emittance ratio ρ ≡ ε x , i ε y , i . Corresponding impact - z results for the vertical emittance ( ε y ε y , i , blue solid line), and four-dimensional transverse emittance ( ε ε , i , magenta solid line). (color on-line) distribution could be generated with a separation betweenits peaks ( ∼ µ m) consistent with requirements frombeam-driven acceleration such as plasma-wakefield anddielectric-wakefield acceleration techniques. In additionthe distance between the peaks could be controlled tosome degree by slight changes over the initial LPS chirp.The full-bunch and slice-at-peak-current horizontal emit-tance at C ∼ . − are 67.0 and 75.1 µ m, respec-tively, compared to 106 and 107 µ m for the maximum-compression case ( C ∼ . − ). These bending-planenormalized emittances of ∼ µ m can still be focused toa sub-mm or sub-100- µ m transverse spot size at respec-tively ∼
40 MeV and ∼
250 MeV (the latter energy cor-responds to acceleration of the 40 MeV beam into one ofASTA accelerating cryomodules).11 igure 17: LPS distribution (gray colormap in left plot) and current pro-jection (red trace and right plot) associated to over-compressed buncheswith an incoming LPS chirp of C = . − . The ordinates z >
7. Summary
In this paper we presented numerical studies of a low-energy magnetic bunch compressor similar to the one be-ing installed at the ASTA facility at Fermilab. Our re-sults indicate that low-energy compression can be a vi-able path as a first stage compressor for a multistage com-pression scheme. In addition the capability of such alow energy compressor to provide high-peak currents atlow energy ( ∼
40 MeV) could have important applica-tions when combined with the long-macropulse capabil-ity of the ASTA’s superconducting accelerating modulesuch as, e.g. the production of single-cycle THz radi-ation from di ff raction radiation. As part of our investi-gation we used several computer programs and observedan acceptable agreement when simulating the evolutionof the LPS distributions during compression. The sim-ulated transverse-phase-space parameters downstream ofthe bunch compressor have discrepancies that are inherentto the capabilities of each of the model but provide simi-lar emittance growth and trade-o ff curves. Based on theseobservations, simple (and faster) models could be used tooptimize the bunch compression design with a quick turnaround while first-principle model could provide high-fidelity simulations of the optimized designs. The instal- lation and commissioning of the BC1 bunch compressoralong with the available diagnostics at ASTA will pro-vide a unique experimental platform for benchmarkingthe simulation codes currently available in regimes wherethe CSR and SC e ff ects can play similar roles. Acknowledgments
This work was supported by LANL Laboratory Di-rected Research and Development (LDRD) program,project 20110067DR and by the U.S. Department of En-ergy under Contract No. DE-FG02-08ER41532 withNorthern Illinois University and Contract No. DE-AC02-07CH11359 the Fermi Research Alliance, LLC.
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