The TESLA linear collider incorporates an X-ray SASE FEL which demands challenging electron beam parameters (typically transverse emittance of 1.6 mm-mrd and peak current of 5 kA). For a realistic electron beam distribution at the entrance of the undulator, tracking has to be done from the cathode through the whole accelerator. Non-Gaussian beam profiles have to be taken into account as well as nonlinear effects such as space-charge, coherent synchrotron radiation field and wake fields. We have done this with several codes: Astra, for the low energy part (<100 MeV), TraFiC4 for the bunch compressor chicanes where CSR influences the particle trajectories and the code Elegant for the 6D tracking with wake fields in the linacs and transport lines. The so-generated electron phase space density at the undulator entrance can then passed to SASEFEL simulation codes. Results of this integrated modeling is discussed

Limberg, T

Piot, P

Limberg, T.

Piot, P.

DESY Publication Database

Integrated Modeling of the TESLA X-Ray FEL

DESY

CERN Document Server

Integrated Modeling of the TESLA X-ray FELT. Limberg and Ph. Piot ∗, DESY, Hamburg, GermanyAbstractThe TESLA linear collider incorporates an X-ray SASEFEL which demands challenging electron beam parame-ters (typically transverse emittance of 1.6 mm-mrd andpeak current of 5 kA). For a realistic electron beam dis-tribution at the entrance of the undulator, tracking has tobe done from the cathode through the whole accelerator.Non-Gaussian beam profiles have to be taken into accountas well as nonlinear effects such as space-charge, coherentsynchrotron radiation field and wake fields. We have donethis with several codes: Astra, for the low energy part(<100 MeV), TraFiC4 for the bunch compressor chicaneswhere CSR influences the particle trajectories and the codeElegant for the 6D tracking with wake fields in the linacsand transport lines. The so-generated electron phase spacedensity at the undulator entrance can then passed to SASEFEL simulation codes. Results of this integrated modelingis discussed.1 INTRODUCTIONThe TESLA linear collider [1] is foreseen to integratean X-ray FEL user facility producing photons with wave-lengths ranging from 1 to 25 Angstroms. The requiredelectron beam parameters at the entrance of the undulatorsare: for a beam energy range between 13 and 50 GeV,a peak current of 5 kA, and a transverse emittance lessthan 1.6 mm-mrd must be provided. The transverseemittance requirement is specified for a longitudinalbunch slice which length is comparable to the cooperationlength; in the present case less than 1 µm. The FELFigure 1: Schematic rendition of the TESLA X-ray FELdriver-accelerator.driver-accelerator (see Fig. 1) has its own pre-accelerator,necessary to produce the required high brightness beam:it incorporates a photo-injector [2] followed by two com-pressors (CS1, CS2) inter-spaced by accelerating sections(ACC1, ACC2). At ∼ 2.3 GeV, the beam is injected into∗PIOT@MAIL.DESY.DEthe TESLA main linac after traveling through a 15◦ arc1and third compressor (CS3). The momentum compactionof the 15◦ arc is R56 = +8 × 10−4; under the nominaltime-energy correlation of the incoming beam, this arcwill slightly decompress the bunch (∆σz  10 µm). Thesettings of the linac and bunch compressors are gatheredin Table 1. The electron beam can be extracted from theLinacs:parameters ACC1 ACC2 Main LinacGrad (Mv/m) 25 25 18RF phase (◦) -40.0 -7.5 0.0phase adv./cell (◦) - 90 90input E (GeV) 0.14 0.44 2.22final E (GeV) 0.44 2.22 24.6input δp/p (%) 1.60 1.01 0.18final δp/p (%) 1.01 0.18 0.04σz (µm) 300 90 40Compressors:parameters CS1 CS2 CS3type standard S-chic S-chicAngles (◦) 10 2.4|4.8 3|6R56 (mm) -92.4 -22.9 -35.9T556 (mm) 145.7 34.5 53.9E (GeV) 0.14 0.44 2.22δp/p (%) 1.60 1.01 0.18input σz (µm) 1800 300 90final σz (µm) 300 90 40final Iˆ (A) 350 1200 5800Table 1: Linac and bunch compressor parameters. A de-tailed description of the bunch compressors can be foundin Ref [10] (for the “standard”-type) and Ref [11] (for the“S-chic”-type).main linac at two extraction points (E=13 ÷ 27 GeV andE=20÷ 50 GeV) and transported to the undulator sectionsvia a transfer line (∼ 12 km long). The extraction is donewith pulsed bending magnets, arranged in a “dog-leg”(DL) configuration of insignificant momentum com-paction. Optionally the beam can be further compressedby a F0D0-type compressor (CS4) making use of thetime-energy correlation induced by geometric wakes [3] ofthe accelerating structures.The principal effects that degrade the beam in theTESLA X-FEL accelerator are: single bunch self interac-1This arc is required to accommodate a special geometry of the lay-out that supports the “TERA” option where bunches from TESLA couldcollide with HERA protons0-7803-7191-7/01/$10.00 ©2001 IEEE. 2722Proceedings of the 2001 Particle Accelerator Conference, Chicagotion via (1) coherent synchrotron radiation (CSR) fields inbunch compressors section, (2) geometric wake fields inthe TESLA cavities, and (3) resistive wake fields in transferlines and other straight sections. CSR effects are calculatedin a self-consistent manner using the program TraFiC4 [5],while the short range wakes are treated via a “kick approx-imation”, using the code Elegant [6]. In the present study,we only include the longitudinal monopole mode of thewakes using the Green functions provided in Ref. [7] andRef. [8], respectively for the geometric and resistive wakes.2 SIMULATION TECHNIQUEThe low energy (E < 0.14 GeV) beamline has been op-timized with the multi-particle code Astra [4, 2], whichis based on a space charge mesh-type algorithm. Thetransport through the straight sections is modeled withthe single particle code Elegant [6], a six-dimensionalcode that includes an approximative treatment of the wakefields. Tracking through the magnetic bunch compressorsand other dispersive sections is performed with the multi-particle code TraFiC4. Phase space distributions, Φ(x; z),can be passed between Astra and Elegant without anymanipulation. However, this is not the case for the codeTraFiC4, where the use of thousands of field generatingparticles would be prohibitive with respect to CPU-time.Figure 2: The different particles ensembles in TraFiC4.The full ellipses represent the sub-bunches of Φgen en-semble. The dots represent the witness ensembles Φopt (atthe bunch center – outlined here with the red ellipses) andΦsampling (surrounding the whole bunch).TraFiC4 allows the input of various ensembles (seeFig. 2): (1) a generating ensemble ,Φgen, (2) an optic en-semble ,Φopt, and (3) a sampling ensemble, Φsampling .While Φgen is used to compute the electro-magnetic field,Φopt is generally used to study the influence of the field ona center slice (a 6D-Gaussian density distribution internallygenerated populates this ensemble), and Φsampling allowsto study the impact of the field on “real”, user-specified,incoming phase space. For copy Φsgn, of the generatingensemble Φgen, the orbit changes due to the CSR field areapplied and correlated emittance growth is evaluated. Inthe self-consistent mode, fields of the “gen” and “sgn” en-sembles act onto each other. created to reflect the effectof the self-interaction on the generating bunch itself. TheCPU time is ∝ Ngen × (Ngen+Nopt+Nsampling) whereN is the number of sub-bunches (or macroparticles) in eachensemble.A “condensed” copy of the incoming phase space is usedas the Φgen ensemble; it typically contains ∼ 300 − 500macroparticles. The whole incoming phase space ,that canconsists of thousands of macroparticles, is condensed to300-500 macroparticles to set up the Φgen ensemble. Thecondensed phase space is generated as follows (for furtherstudy see Ref. [12]):Φgen(x; z) =Ngen∑i=1qi × e−(s−si)2/(2σ2z)√2πσzδ(δ − δi)×e−[(x−xi)2+(y−yi)2]/(2σ2r)√2πσr× δ(x′ − x′i)δ(y′ − y′i),where δ(...) stands for the Dirac-function. The charge q iand first order moments are obtained by binning the in-coming phase space distribution. The sub-bunches are 3DGaussian charge distribution with fixed length, σz , and ra-dius, σr, which are user-specified parameters. However,we smooth offsets and charge variation with polynominalfits to avoid numerical noise.A few meters downstream of the last dipole, to accountfor co-propagating transient CSR fields, the Φsampling en-semble is then passed, without any operation, to Elegantor Astra (depending on the beam physics dominating thedownstream beamline).3 START-TO-END SIMULATION OF THEX-RAY FELIn this section we present an example of beam dynamicssimulation for the TESLA X-FEL accelerator; the beamis assumed to be extracted from the main linac at the firstextraction point at an energy of E  24.6 GeV. The injec-tor simulation and optimization is discussed elsewhere [2]and the phase space density obtained with Astra at the in-jector front end is our starting point, i.e. 2 m upstreamof CS1. The critical point for avoiding un-tolerable emit-tance growth is to properly match the beam into the bunchcompressors [9]. The typical β-functions along the wholeaccelerator (excluding the photo-injector) are plotted inFig. 3. The evolution of the longitudinal phase space andcharge density profile is presented after each compressionstage in Fig. 4. This figure demonstrates the highly non-Gaussian character of the distribution that arises from theinput distribution but also via CSR and wake fields alongthe beamline. For a 1 nC Gaussian charge density, a peakcurrent of 5 kA would correspond to σz = 25 µm, whilein the present case, for the same peak current achieved, we2723Proceedings of the 2001 Particle Accelerator Conference, ChicagoFigure 3: Lattice along the whole linac, starting fromACC2 entrance up to end of the transfer line.have an rms length of 40 µm. Note that, without using a3rd harmonic rf-section [2] in the injector, the longitudinalprofiles would be even more distorted.Fig. 5 shows peak current and transverse emittance(within a correlation length) along the bunch. Regionswhere the peak current is above ∼3 kA and the transverseemittance below∼ 1.6 mm-mrd will reach saturation in theX-FEL undulator. We estimate, for this set up, that about40% of the beam intensity contributes fully to the lasingprocess.4 SUMMARYUsing the three codes, Astra, Elegant, and TraFiC4,we have performed a thorough integrated modeling of theTESLA X-ray FEL, from the photocathode surface up tothe undulator entrance. Our present efforts are (1) to auto-mate the procedure using a high level interfacing betweenthe codes and (2) to increase the simulation speed. Thislatter point is about to be solved with the availability ofMPP versions of TraFiC4 and Astra along with an effi-cient passing of phase space density to TraFiC4 code [12].5 REFERENCES[1] TESLA TDR, rep. TESLA-01-23, DESY-HH (2001)[2] Flo¨ttmann K., et al. “The TESLA X-FEL injector”, PAC2001[3] Brinkmann R., et al., proc. of PAC’97, pp. 1572-1574 (1997)[4] Flo¨ttmann K., AstraUser Manualhttp://www.desy.de/~mpyflo/Astra dokumentation/[5] Dohlus M., et al., NIM A 445, pp. 338-342 (2000)[6] Borland M., report LS-287, APS/ANL (2000)[7] Novokhatski A., et al., report TESLA-99-16 (1999)[8] Bane K.L.F, et al., report SLAC-PUB-9¯5-7074 (1995)Figure 4: Longitudinal phase space (s,δp/p) and chargedensity Iˆ(s) downstream of CS1, CS2, and CS3 (from topto bottom row).Figure 5: Peak current (top) and transverse emittances(bottom) within longitudinal slice of 1.5 µm width alongthe bunch. The horizontal line indicates the minimum re-quired peak current and maximum tolerated emittances.The vertical lines delimits area of lasing with ε ≤ 1.6 mm-mrd and I > 5 kA.[9] Limberg T. et al., “Optics optimization for multistage com-pression” to be published as a TESLA-FEL report (2001)[10] Limberg T. et al., proc. of FEL2000 in press[11] Loulergue A. et al., proc. of EPAC2000, pp. 754-756 (2000)[12] Dohlus M., et al.,“Beam dynamics simulations in magneticbunch compressors using realistic particle distributions”, sub-mitted to FEL20012724Proceedings of the 2001 Particle Accelerator Conference, Chicago

Integrated modeling of the TESLA X-ray FEL

Abstract

Similar works

Full text

Available Versions

DESY Publication Database

DESY

CERN Document Server