Simulations on a potential hybrid and compact attosecond

Simulations on a potential hybrid and compact attosecond X-ray source based on RF and THz technologies Thomas Vinatier, Ralph Assmann, Ulrich Dorda, François Lemery, Barbara Marchetti, DESY, Hamburg, Germany EAAC 2017, Wednesday 27 th September 2017, Working group 3 Special thanks to the entire AXSIS collaboration, especially A. Fallahi for useful discussions on the AXSIS guns and the general design The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007 -2013) ERC Grant Agreement n. 609920

Frontiers in Attosecond X-ray Science: Imaging and Spectroscopy AXSIS Franz Kärtner University of Hamburg Ralph Assmann DESY, Hamburg Henry Chapman University of Hamburg Petra Fromme Arizona State University (call to University of Hamburg) And Associated Scientists from Mid-Sweden University, DESY, and MIT MSU www. cfel. de www. rle. edu

Outline > Introduction: • Motivations and objectives of the study • General assumptions > From the cathode to the THz linac entrance: • Assumptions for selecting suitable cases • Influence of the UV laser transverse dimension and focusing solenoid > In the THz linac: • Influence of the accelerating frequency • Influence of the interaction length between the electron bunch and the THz field • Balance between the solenoid focusing and the transverse forces in the linac > Focusing to a potential ICS point: • Presentation of result for a selected potential working point • Limitations of the scheme and possible solutions

Introduction: Motivations and objectives > Particle acceleration and bunch compression to the femtosecond level or below currently require large infrastructures due to relatively low frequencies (a few GHz) and field amplitudes (a few tens of MV/m). > THz fields in dielectric-loaded waveguides (DLW) Higher frequencies (0. 1 to 10 THz) and field amplitudes (0. 1 to a few GV/m) Accelerator beamline shorter by a factor around 100. > AXSIS project: Electron bunch photo-emitted and accelerated in a gun driven by THz fields up to ≤ 1 Me. V Acceleration up to 15 -20 Me. V and compression down to ≤ 1 fs rms in a THz-driven DLW (THz linac). Goal: Produce attosecond X-ray pulses by Inverse Compton Scattering (ICS). See talk of N. Matlis on Monday and F. X. Kaertner et al. NIMA 829 pp. 24 -29 (2016) for details

Introduction: Motivations and objectives > All-optical scheme Intrinsic desirable features (self-synchronized, compact, potentially k. Hz repetition rate). However, THz guns aim to work in a regime never explored by the other electron sources. Field amplitude Emg normalized to the frequency f = kc/2π Tells how quick the bunch is accelerated compared to the field wavelength and determines the longitudinal dynamics. Plot by T. Vinatier & R. W. Assmann See K. Floettmann PRSTAB 18, 064081 (2015) & K. J. Kim NIMA 275 pp. 201 -218 (1989) for details on the α parameter. See A. Fallahi et al. PRSTAB 19, 081302 (2016) for details on the AXSIS THz guns.

Introduction: Motivations and objectives > Some aspects of the THz guns development are challenging and currently addressed by the AXSIS team: • Reduced transverse aperture (120 µm Ø) Challenge for extracting significant charge (≥ 1 p. C). • High frequency Challenge for controling energy spread and non-linearities of the longitudinal phase-space. > Objectives: • Characterize THz linac capabilities, which looks very promising for reaching AXSIS requirements, by replacing the THz gun with an S-band gun. • Also an investigation for a potential dedicated hybrid layout. Charge Mean kinetic energy Rms length Rms transverse dimension ≥ 1 p. C 15 -20 Me. V ≤ 1 fs ≈ 10 µm AXSIS requirements at the ICS point

Introduction: General assumptions Parameters for ASTRA simulations Values UV laser 3 D Gaussian with 75 fs rms duration Bunch charge Q 1 p. C & 5 p. C Gun type 1. 6 cells at 2. 9985 GHz (S-band) Gun field amplitude Emg 110 MV/m & 140 MV/m Solenoid type 2 coils with reversed polarities THz linac frequency f 150 GHz & 300 GHz THz linac length (≡ interaction length) L 6. 4 cm & 12. 8 cm

Outline > Introduction: • Motivations and objectives of the study • General assumptions > From the cathode to the THz linac entrance: • Assumptions for selecting suitable cases • Influence of the UV laser transverse dimension and focusing solenoid > In the THz linac: • Influence of the accelerating frequency • Influence of the interaction length between the electron bunch and the THz field • Balance between the solenoid focusing and the transverse forces in the linac > Focusing to a potential ICS point: • Presentation of result for a selected potential working point • Limitations of the scheme and possible solutions

From the cathode to the THz linac entrance > Production of (sub)-fs bunch by velocity bunching in high frequency field is limited by curvature induced on the longitudinal phase-space Shortest bunch length σt possible required at the THz linac entrance to limit it at maximum. § Gun RF-phase as close as possible from the zero crossing (with full extraction) § Minimization of distance between cathode and THz linac entrance Different from photo-injectors classical design Challenge for mechanical integration. Two options: 60 -65 cm and 85 -90 cm from the cathode. > Solenoid strength and transverse dimension of the UV laser pulse also have a, coupled, influence on the achievable bunch length at the THz linac entrance. > Solenoid strength fixed to have a bunch rms transverse dimension = 10% of linac diameter (100 µm at 300 GHz and 200 µm at 150 GHz).

From the cathode to the THz linac entrance Conditions: Q = 5 p. C; Emg = 110 MV/m; Linac entrance at 89 cm; Bunch focused at 100 µm rms. > Optimum value of the UV laser transverse dimension: § Too small Space-charge forces No bunch compression in the RF-gun, especially close from the cathode. § Too large Radial dependency of the RF-gun accelerating field induces a correlation between the electron energy and its transverse position Increase of σt in the gun and following drift space (non ultra-relativistic energy). > Solenoid-induced bunch lengthening: Electrons with larger transverse offsets travel longer paths in the solenoid magnetic field and have lower energies.

From the cathode to the THz linac entrance Case G-1 Case G-2 Case G-3 Case G-4 Emg (MV/m) 110 140 140 Linac entrance (cm) 85. 6 85. 0 61. 0 60. 9 f (GHz) 300 300 150 Rms length σt (fs) 39. 0 28. 7 24. 1 22. 6 Including all relevant physical effects (space-charge forces, etc. ) > Gun field amplitude increase from 110 to 140 MV/m -25% to -30% on the bunch length at the linac entrance due to decrease of space-charge forces. > Linac closer from the gun -13% to -20% on bunch length Bunch lengthening due to higher required solenoid field more than compensated by decrease of spacecharge forces and optimum transverse dimension of the UV laser pulse. > Around -5% on bunch length at the linac entrance if f = 150 GHz compared to f = 300 GHz, due to the lower required solenoid field.

Outline > Introduction: • Motivations and objectives of the study • General assumptions > From the cathode to the THz linac entrance: • Assumptions for selecting suitable cases • Influence of the UV laser transverse dimension and focusing solenoid > In the THz linac: • Influence of the accelerating frequency • Influence of the interaction length between the electron bunch and the THz field • Balance between the solenoid focusing and the transverse forces in the linac > Focusing to a potential ICS point: • Presentation of result for a selected potential working point • Limitations of the scheme and possible solutions

In the THz linac: General considerations > Field amplitude Eml in the linac Maximum output kinetic energy of 20 Me. V 220 MV/m for L = 6. 4 cm and 115 MV/m for L = 12. 8 cm. > Femtosecond bunch at 15 -20 Me. V σt quickly increases after the point of maximal compression Ballistic bunching needed to matches it with the transverse focal point (by adjusting dephasing between bunch and THz field) at the ICS point. > Assumption: 30 cm needed for transverse focusing after the linac exit Ballistic bunching adjusted to provide shortest bunch length at this point. Case L-1 Case L-2 Q (p. C) 1 1 f (GHz) 300 150 150 Eml (MV/m) 115 220 115 L (cm) 12. 8 6. 4 12. 8 Linac entrance (cm) 85 85 85 61 σt (fs) (30 cm after linac exit) 2. 2 0. 97 1. 0 3. 7 234 (1. 34%) 197 (1. 32%) 233 (1. 66%) 80 (0. 55%) σE (ke. V) (30 cm after linac exit) Case L-3 Including all relevant physical effects (space-charge forces, etc. ) Case L-4

In the THz linac: Influence of frequency Conditions: Q = 1 p. C; L = 12. 8 cm; Eml = 115 MV/m; THz linac entrance at 85 cm. Energy gain gradient: -e. Emlcos(ϕ) ϕ: Phase of the reference particle > f = 300 GHz to f = 150 GHz Energy spread decrease (same input bunch length covers a two times smaller fraction of the field wavelength) and of bunch length after compression (less non-linearities induced during compression due to the smaller field curvature experienced by the bunch). > f = 300 GHz to f = 150 GHz Bunch energy decreases because after off-crest injection, necessary for compression, bunch phase slippage towards more accelerating fields is two times slower.

In the THz linac: Influence of interaction length Case L-1 Case L-2 Q (p. C) 1 1 f (GHz) 300 150 150 Eml (MV/m) 115 220 115 L (cm) 12. 8 6. 4 12. 8 Linac entrance (cm) 85 85 85 61 σt (fs) (30 cm after linac exit) 2. 2 0. 97 1. 0 3. 7 234 (1. 34%) 197 (1. 32%) 233 (1. 66%) 80 (0. 55%) σE (ke. V) (30 cm after linac exit) Case L-3 Case L-4

In the THz linac: Influence of interaction length Conditions: Q = 1 p. C; f = 150 GHz; THz linac entrance at 85 cm > Increase of L Energy spread decreases due to lower field amplitude + Final σt decreases (especially at 5 p. C) due to lower field amplitude and slower rate of compression in the linac (similarity with adiabatic velocity bunching in TWS). > Increase of L Increase of the output energy due to possible phase-slippage towards more accelerating fields after off-crest injection.

Outline > Introduction: • Motivations and objectives of the study • General assumptions > From the cathode to the THz linac entrance: • Assumptions for selecting suitable cases • Influence of the UV laser transverse dimension and focusing solenoid > In the THz linac: • Influence of the accelerating frequency • Influence of the interaction length between the electron bunch and the THz field • Balance between the solenoid focusing and the transverse forces in the linac > Focusing to a potential ICS point: • Presentation of result for a selected potential working point • Limitations of the scheme and possible solutions

Focusing to a potential ICS point: Working points > Conditions: Q = 1 p. C; Emg = 140 MV/m; Linac entrance at 85 cm; L = 12. 8 cm; Eml = 115 MV/m; f = 150 GHz; Focusing: quadrupole triplet (+8. 5, -19 and +29. 4 T/m). > Start-to-end ASTRA simulation including all relevant physical effects (including space-charge forces) > Demonstration that transverse and longitudinal focal points can be matched through ballistic bunching

Focusing to a potential ICS point: Working points > Longitudinal phase-space without spike + Gaussian transverse profile. > Bunch properties fulfilling or very close to the AXSIS requirements at ICS point. > Work in progress for further optimization of bunch properties and more bunch charge. Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (µm²) 1 14. 9 153 1. 24 10. 5*10. 6 0. 37*0. 28 5 15. 2 292 7. 9 1. 05*1. 13 19. 5*24. 1 εx*εy (π. mm. mrad)² Work in progress

Conclusions > THz linac is very promising to fulfil the AXSIS requirements in terms of bunch properties at the ICS point (including final transverse focusing). > Dedicated hybrid layout mixing S-band gun and THz technologies Great potential to be a compact ICS X-ray source delivering fs and sub-fs pulses. Further investigations ongoing for increasing bunch charge and overcoming limitations: Reduce bunch length, emittance and energy spread and control of final focusing. > Technical limitations to be included for fixing distances and parameters. > Study with THz gun is also ongoing.

In the THz linac: Influence of field balance Case L-1 Case L-2 Q (p. C) 1 1 f (GHz) 300 150 150 Eml (MV/m) 115 220 115 L (cm) 12. 8 6. 4 12. 8 Linac entrance (cm) 85 85 85 61 σt (fs) (30 cm after linac exit) 2. 2 0. 97 1. 0 3. 7 234 (1. 34%) 197 (1. 32%) 233 (1. 66%) 80 (0. 55%) σE (ke. V) (30 cm after linac exit) Case L-3 Case L-4

In the THz linac: Influence of field balance Case 1 Case 2 (dashed) vs Case 4 (full) > Improper balance between solenoid focusing and transverse forces in the linac (defocusing in the velocity bunching regime) Potentially improper transverse properties for final focusing to the ICS point (Case 1). > Can also deteriorate the bunch length if a transverse focal point is located just before the longitudinal one (Case 2 vs Case 4). > Possibility to counteract that with tunable magnets around the linac should be studied.

Limitations of the scheme: From fs to sub-fs > Presented working point not in the sub-fs regime Use of a focusing device with shorter focal length (Example: Active plasma lens) ICS point closer from linac exit σt shorter. Triplet Plasma lens Quadrupole triplet Active plasma lens Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (µm²) εx*εy (π. mm. mrad)² 1 14. 9 153 1. 24 10. 5*10. 6 0. 37*0. 28 1 12. 1 160 0. 80 4. 8*4. 8 0. 31*0. 31

Limitations of the scheme: Reduction of emittance > Quite high transverse emittance considering that Q = 1 p. C. Due to the quite large transverse dimension of UV laser pulse for optimizing velocity bunching. > Start with Q = 1. 1 p. C and use of a transverse collimator before the linac to cut 0. 1 p. C Significant transverse emittance reduction + tighter focusing. Transverse collimator Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (µm²) εx*εy (π. mm. mrad)² 1 14. 9 153 1. 24 10. 5*10. 6 0. 37*0. 28 1 14. 8 155 1. 35 8. 3*8. 3 0. 25*0. 21

Limitations of the scheme: Decrease energy spread > Quite high relative energy spread (≈ 1% rms) for an ICS source ( +2% bandwidth). Intrinsic to the compression by velocity bunching. > Increase the THz phase velocity above c (value assumed in the study) Optimization of bunch phase-slippage Decrease of energy spread. > Use a second shorter linac between the first one and ICS point Possibility to remove part of the correlated energy spread (but risk of bunch lengthening).