X-band FEL beam dynamics issues A. Latina (CERN) for the X-band FEL and CLIC collaboration Many thanks for their inputs to A. Aksoy (Ankara), A. Charitonidis (NTUA), S. Di Mitri (Elettra), D. Schulte (CERN) LCWS2014 – Oct 9, 2014 – Belgrade

Table of contents Introduction Beam dynamics issues X-band and FEL Beam dynamics issues Design optimisation procedures Longitudinal Transverse Sensitivities Static and dynamic imperfections Phase space profiles Conclusions and to-do work

X-band and XFEL Normal conductive X-band (12 Ghz) offers several advantages w.r.t. traditional S-band, or C-band. E.g.: High-gradient acceleration (>100 MV/m already achieved) Higher repetition rate (kHz) Power efficiency Ultimately, these advantages offer: reduced costs, compactness, affordability For instance, if one imagines an LCLS-like machine based on X-band technology, the length of both the accelerator and the undulators could be about 250 meters This figure has to be compared with the length of the actual LCLS, which is about 1230 meters including 1100 meters of accelerator and 130 meters of undulators.

X-band and XFEL X-band acceleration has some drawbacks: Technical difficulties, due to novelty of this technology Geometric wakefields scale as: These impart: -> Transverse deflection -> Longitudinal energy chirp Transverse WF can lead to instabilities Longitudinal WF induce energy spread, but can be exploited

Transverse constraints D. Schulte Small a/λ: strong lattice. Simplified wakefield model (K. Bane) Stability of beam with initial jitter requires to stay above red line Emittance growth with 100um tolerances: We need dispersion free steering or CLIC-style alignment for FEL

Machine layout Main subsystems: RF gun, injectors (two boosters), a laser heater, two linacs, two bunch compressors, spreaders (doglegs). Typical input bunch parameters in Booster 2: 125 MeV, 200 pC beam charge, 2.5 ps RMS duration (750 micron), 0.15 m rad transverse normalized emittance (slice and projected), 15 keV RMS uncorrelated energy spread Typical target parameters: 6 GeV, ~25 fs duration (~7 μm bunch length), sliced energy spread: <0.01%

RF gun & Injector optimization A. Aksoy Laser Booster -1 Booster -2 X-band structure 75 cell, ~0.9 m, 65MV/m 3 GHz Photo Cathode RF (PHIN) Gun 2.6 Cell, 100 MV/m 3 GHz Traveling wave structures (PSI type) 120 cell, ~4 m, max 18 MV/m Optimization goal  minimum projected emittance, minimum sliced emittance minimum bunch length Laser parameters Laser pulse length? Laser spot size? Gun parameters Gradient-phase? Bunch charge? Solenoid fields and positions? Injector structure Gradient? Position of structure? Phase of structure?

Injector Optimisation A. Aksoy Acceptable projected emittance has been observed Sliced emittance can be optimized with mismatch parameter..

Linacs Design Beam dynamics Issues: Design: Single-bunch wakefields Longitudinal space-charge and CSR (micro-bunching instability) Geometric and chromatic aberrations ISR induced emittance growth Bunch profile Static errors: Beam break-up instability Emittance growth due to misalignments Dynamic errors: Longitudinal stability

Longitudinal Linac Optimisation Must take into account: longitudinal short-range wakefields, RF curvature, CSR, ISR, sensitivity, … X-band structures have a/λ = 0.125, and a gradient G=70 MV/m Start from Booster 2: there is a total of 10 degrees of freedom Booster2: S0.V, S0.Phi, X0.V, X0.Phi Linac1: X1.V, and X1.Phi Linac2: X2.V, and X2.Phi BC1: R56 BC2: R56 We use the simplex.

Semi-analytical Optimisation Degrees of freedom can be reduced using some analytical considerations. E.g. BC1: 1) S-band RF curvature linearisation: Taylor-expand Ef to vanish the 2nd-order terms: 2) Analytically compute R65s in order to find R56s. 3) Fix intermediate parameters, such as: Bunch length after BC1: from 55 to 70 μm Energy after BC1 and BC2: e.g. 250/300 MeV, and 2.5 GeV

Longitudinal Linac Optimisation A fast C++ 1d code has been developed for optimization: RF nonlinearities, Wakefields Chicanes’ T566 are taken into account It is integrated within Octave, to access available optimization toolboxes It allows fast tracking of the longitudinal phase space: simplex optimisation of a merit function

Optimisation procedure Total of 10 degrees of freedom: Booster2: S0.V, S0.Phi, X0.V, X0.Phi Linac1: X1.V, X1.Phi Linac2: X2.V, X2.Phi BC1: R56, BC2: R56 Optimize BC1 and BC2 independently (**) BC1: S0.Phi = between 0 and 45 degrees X0.Phi = between 150 and 220 degrees S0.V, X0.V chosen to achieve the desired intermediate energy, and to linearize bunch R56 is computed to achieve the desired intermediate bunch length, within ±10% (*). BC2: X1.Phi = between 0 and 30 degrees R56 is computed for full compression, and varied within ±10% X2.Phi = between -15 and 30 degrees (*) Full compression not required. (**) Alternative: fix R56 to optimal values and optimise both linacs and BCs

Optimisation procedure Initial curvature from S-band injector is taken into account Merit function to be optimised: Achieve desired intemediate and final bunch lengths (55 / 65 um, and 7 um) Sliced energy spread is the theoretical miminum Longitudinal distribution is as flat / symmetric as possible Target parameters: Final energy: 6 GeV Total energy spread < 2% Sliced energy spread: < 0.01 %

Solution to the Optimisation (I) S0.Phi = 32.686 deg ; S0.V = 0.225667 GV; X0.Phi = 219.5 deg ; X0.V = 0.0257602 GV ; X1.Phi = 23.4869 deg ; X1.V = 2.39917 GV ; X2.Phi = 5.5 deg ; X2.V = 3.5166 GV ; BC1.R56 = -0.082 m BC2.R56 = -0.0110615 Intermediate_blength = 56 um intermediate_energy = 300 MeV intermediate_energy2 = 2.5 GeV final_bunch_length = 9.6 um final_energy = 6 GeV final_espread = 0.02 % final_slice_espread = 0.01 % total_RF_length = 102.227 m

Transverse Linac Optimisation Check bunch compression Definite energy sections and R56 of BCs (include longitudinal Wakefield and 2nd order effects at BCs) Define lattice Optimize cost, number of structures per module et… Optimize lattice (include longitudinal & transverse Wakefield, 2nd order effects at BCs and CSR) Check longitudinal tolerances Optimize R56 and energy error tolerances Check Transverse tolerances Optimize lattice and alignment tolerances

1st optimisation criteria: the wake effect A. Aksoy Strong wake field plays main role on bunch charge distribution and its length along beamline. Longitudinal wake potential changes linearity on chirp uniform bunch distribution and no tail is preferred Transverse wake potential causes deflection along bunch Longitudinal wake potentials experienced by bunch (which has σ=100 um) in x-band structure Transverse wake potentials experienced by bunch (which has σ=100 um) in x-band structure

Transverse beam dynamics A. Aksoy However the transverse deflection is proportional FODO type of lattice is proposed. In order to get minimum deflection. We propose different number of structures per one FODO cell The most critical section is linac 2 since the energy is low and bunch length is long

Transverse deflection in Linac 1 Plots show the transverse deflection of coordinate (x) and angle (x’) of slices along the bunch in linac 1 for a Gaussian bunch. σz= 100µm σz= 150µm For compression of lattices and bunch profile we check A. Aksoy

The amplification on Linac 1 The amplification for different bunch charge distributions on a lattice that has FODO cell with 6 structure per cell and 16 structure per cell The uniform charge distribution has lowest amplification. In order to get lower amplification factor than 1.5 we need to have bunch length σz < 70 µm A. Aksoy

The amplification on Linac 1 The amplification of uniform charge distribution on different type of lattices In order to get lower amplification factor than 1.5 we are allowed to use the FODO lattice with 6 or 8 structure per cell A. Aksoy

The lattice We have proposed FODO type of lattice on which 8 structures located in one cell Linac 1: 40 x-band strcuture, phase 25 degre Linac 1: 80 x-band strcuture, phase 3 degre BC1 R56=-0.082 m BC2 R56=-0.011 m

Bunch compression

Sensitivity Studies A. Charitonidis Theoretical / Analytical formulation (in progress): Arrival time jitter Final bunch length variation due to phase jitter Compression factor (BC1)

Longitudinal coherent errors We have checked only linac coherent phase error (≡ beam phase error) and gradient error. A. Aksoy ΔΦ < 10 fs required (bunch length is ~25 fs)

Solution to the Optimisation (II) S0.Phi = 25.5482 deg ; S0.V = 0.151403 GeV ; X0.Phi = 189.569 deg ; X0.V = 0.0167787 GeV; X1.Phi = 24.1816 deg ; X1.V = 2.46678 GV ; X2.Phi = -12.7467 deg ; X2.V = 3.61694 GV ; BC1.R56 = -0.07 m ; BC2.R56 = -0.01 m ; intermediate_blength = 70 um intermediate_energy = 250 MeV intermediate_energy2 = 2.5 GeV final_bunch_length = 10.3266 um final_energy = 6 GeV final_espread = 0.05 % final_slice_espread = 0.004 % total_RF_length = 99.7272 m

Fermi @ ELETTRA Upgrade Existing FEL is based on injector for synchrotron (FERMI) Upgrade with X-band to increase beam energy for FEL

Emittance S. Di Mitri Normalized RMS projected emittance at the entrance of BC2 (left) and linac exit, as function of the linac-to-beam RMS misalignment and the horizontal betatron function in the BC1 (left) and BC2 (right). The left-hand plot assumes an initial emittance of 0.15 m, the lower, 0.5m.

Conclusions & further work Beam dynamics poses some known issues Semi-analytical / numerical tools are being developed Optimisation procedures Preliminary designs have been produced We are trying to reduce the R56 of bunch compressors in order to relax longitudinal tolerances.. Include analytical sensitivities in optimisation procedure We need to derive tolerances Phase stability is alerting We have several unknown parameters Tolerance of bunch arrival time Tolerance for bunch length variation Tolerance for energy jitter.. Transverse jitter? Tools for FEL simulation are ready