Beam Dynamics and FEL Simulations for FLASH Igor Zagorodnov and Martin Dohlus Beam Dynamics Meeting, DESY

FLASH I parameters ACC39 FLASH I layout is considered. But the results are equally applicable for FLASH II (SASE). short gain length (for the optimal beta function) high peak current short radiation wavelength high electron energy ~ 6.5 nm In accelerator modules ACC1, ACC2,..., ACC6 the energy of the electrons is increased from 5 MeV (gun) to 1000 MeV (undulator). In compressors the peak current I is increased from A (gun) to 2500 A (undulator).

FLASH I parameters Electron beam properties for good lasing High peak current ~ 2500 A. Small slice emittance  (0.4-1  m). Small slice energy spread  E  (< 300 keV). short gain length (for the optimal beta function) small energy spread small emittance high peak current High harmonic module in 2010

FLASH I parameters ACC39 energy 1 GeV radiation wavelength ~ 6.5 nm Only SASE mode of operation is investigated. Charge tuning ( pC) allows to tune - the radiation pulse energy (  J), - the pulse width FWHM (2-70 fs).

FLASH I parameters ACC39 r 56  mm Technical constrains V 1  150 MV V 39  26 MV V 2  360 MV How to provide (1) a well conditioned electron beam and (2) what are the properties of the radiation? (1) Self consistent beam dynamics simulations. (2) FEL simulations.

FLASH I 3d simulation method (self-consistent) ACC39 W3W3 2W 1 TM 3W 1 TM W 1 TM ASTRA ( tracking with space charge, DESY) CSRtrack (tracking through dipoles, DESY) W1 -TESLA cryomodule wake ( TESLA Report , DESY, 2003 ) W3 - ACC39 wake ( TESLA Report , DESY, 2004 ) TM - transverse matching to the design optics ( V2+, V.Balandin &N.Golubeva ) ALICE (3D FEL code, DESY )

FLASH I simulation methods (looking for working points) 1d tracking with space charge and wakes compressor 3d tracking with all collective effects Astra CSRtrack quasi 3d tracking with all collective effects accelerator matrix transport for x & y CSRtrack ~ 10 h (46 cpu-s) ~ seconds (1 cpu) ~ 30 min (1 cpu) 1d analytical solution without collective effects (8 macroparameters -> 6 RF settings) initial guess ~ 5 iterations final result

FLASH I before and after upgrade rollover compression vs. linearized compression ~ 1.5 kA ACC39 ~2.5 kA slice emittance > 2  m slice emittance ~  m Q=1 nC Q=0.5 nC

new Optics correction M.Dohlus, T. Limberg, Impact of optics on CSR-related emittance growth in bunch compressor chicanes, PAC 05, 2005 V2+ a small transverse bunch size before the last dipole

Working points (8 macroparameters) ? What is the optimal choice? s - particle position before BC2 s 1 - particle position between BC2 and BC3 s 2 - particle position after BC3 s=s 1 =s 2 =0 for the reference particle

Working points (8 macroparameters) What is the optimal choice? V 1  150 MV V 2  360 MV 5% reserve 10% reserve

Working points (8 macroparameters) - low compression in BC1 and high compression in BC2 - maximal energy chirp transported through BC1for the same C 1 (it looses the voltage requirements on RF system ACC2/ACC3)

Working points (8 macroparameters)

working point 5% reserve

Working points (8 macroparameters) Too strong compression! Local maximum of compression!

Working points (8 macroparameters) Tolerances (10 % change of compression) working point

Working points (8 macroparameters) working point

Working points (8 macroparameters) - a free parameter to move the peak

Charge Q, nC Energy in BC2 E 1, [MeV] Energy in BC3 E 2, [MeV] Deflecting radius in BC2 r 1, [m] Deflecting radius in BC3 r 2, [m] Compression in BC2 C 1 Total compression C First derivative p 1, [m -1 ] Second derivative p 2, [m -2 ] e e e e (12) e3 Working points (8 macroparameters) scaling for different charges we have used another scaling

Working points (6 equations => 6 RF parameters) Analytical solution without self-fields* 8 macroparameters define 6 equations nonlinear operator (defined analytically) *M.Dohlus and I.Zagorodnov, A semi analytical modelling of two-stage bunch compression with collective effects, (in preparation)

Analytical solution without self-fields Solution with self-fields nonlinear operator (tracking with self-fields) numerical tracking analytical correction of RF parameters residual in macroscopic parameters

FLASH I simulation methods (looking for working points) initial guess ~ 5 iterations final result

Working points (6 equations => 6 RF parameters) Charge, nC V 1, [MV]  1, [deg] V 39, [MV]  39, [deg] V 2, [MV]  2, [deg] RF settings in accelerating modules Analytical solution without self-fields + iterative procedure with them ACC39 8 macroparameters define 6 equations

Q=1 nC Phase space Current, emittance, energy spread

Q=0.5 nC Phase space Current, emittance, energy spread

Q=0.25 nC Phase space Current, emittance, energy spread Space charge impact

Q=0.1 nC Current, emittance, energy spread Phase space

Q=0.02 nC Current, emittance, energy spread Phase space

Q=0.02 nC ACC39 CSR impact

Q=0.02 nC ACC39 r 56 =0 [m], t 566 =0.06 [m] Space charge impact

Tolerances (analytically) without self fields (10 % change of compression) Tolerances (from tracking) with self fields agree with this table Q, nC ACC1 |  V|/V ~O(C -1 ) |  |, degree ACC39 |  V|/V |  |, degree ACC2/3 |  V|/V ~O(C 2 -1 ) |  |, degree

FLASH parameters How to provide (1) a well conditioned electron beam and (2) what are the properties of the radiation? (1) Self consistent beam dynamics simulations. We are able to provide the well conditioned electron beam for different charges. But RF tolerances for small charges are tough. (2) FEL simulations (next slides).

Charge Q, nC Longitudinal electron beam size  s,  m Transverse electron beam size  r,  m Slice parameters for SASE simulations slice emittance Slice parameters are extracted from S2E simulations for SASE simulations current

Radiation energy statistics ( runs) nC 1 nC Mean energy nC 1 nC 0.25 nC 0.02 nC Radiation pulse width (RMS) Charge, nC Mean radiation energy,  J Pulse radiation width (FWHM), fs

Radiation energy statistics   Gamma distr. Q=0.02 nC     Q=1 nC z=10m z=20m

Temporal structure Q= 1 nC Q=0.02 nC z=10m z=20m

Summary with harmonic modulewithout* Bunch charge, nC Wavelength, nm 6.56 Beam energy, MeV 1000 Peak current, kA Slice emmitance,mm-mrad Slice energy spread, MeV Saturation length, m Energy in the rad. pulse,  J Radiation pulse duration FWHM, fs Averaged peak power, GW Spectrum width, % Coherence time, fs *) E.L.Saldin at al, Expected properties of the radiation from VUV-FEL at DESY, TESLA FEL , 2004.

FLASH Simulation results (1) Self consistent beam dynamics simulations We are able to provide the well conditioned electron beam for different charges. But RF tolerances for small charges are tough. (2) FEL simulations The charge tuning ( pC) in SASE mode allows to tune - the radiation pulse energy ( mJ) - the pulse width (FWHM 3-70 fs).