Challenges and tolerances for a compact and hybrid

Challenges and tolerances for a compact and hybrid ultrafast X-ray pulse source based on RF and THz technologies Thomas Vinatier, Ralph Assmann, Ulrich Dorda, François Lemery, Barbara Marchetti, DESY, Hamburg, Germany EAAC 2019, Wednesday 18 th September 2019, Working group 3 The authors would like to thank K. Flöttmann and the entire AXSIS collaboration for fruitful discussions 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, and by the Laserlab-Europe Grant Agreement n. 654148.

Outline > Introduction > Tolerance study > Other challenges > Conclusions

Outline: Introduction > Introduction • Presentation of the concept • Simulation of e- bunch properties • Simulation of X-ray properties > Tolerance study > Other challenges > Conclusions

Presentation of the hybrid concept > S-band RF-gun: ≈ 6 Me. V e- bunch with 0. 1 to a few p. C charge. > THz linac (THz-driven dielectric-loaded waveguide): Acceleration to 15 -20 Me. V & compression to the single femtosecond order or below. > Quadrupole triplet: Transverse focusing to below 10 μm rms. > Collision with ps laser: 3 to 12 ke. V ultrafast X-ray pulses via ICS. ps IR laser (400 m. J) Details in T. Vinatier et al. , Nucl. Instr. Meth. A 909, p. 185 (2018) & T. Vinatier et al. , J. Appl. Phys. 125, 164901 (2019)

Simulation of e- bunch properties > Start-to-end beam dynamics simulations, up to the ICS point, performed with ASTRA for two frequencies in the THz linac (150 and 300 GHz). Typical properties at the ICS point for f = 300 GHz (115 MV/m) and a 1 mm vacuum diameter Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (μm 2) εx*εy (μm 2) 0. 1 17. 7 42 0. 4 4. 5*5. 9 0. 11*0. 11 1 17. 5 130 1. 3 6. 8*7. 9 0. 23*0. 19 2 17. 6 190 1. 9 8. 9*9. 7 0. 32*0. 24 Typical properties at the ICS point for f = 150 GHz (115 MV/m) and a 2 mm vacuum diameter Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (μm 2) εx*εy (μm 2) 1 15. 0 45 1. 8 6. 0*6. 2 0. 21*0. 19 4 15. 0 130 3. 1 8. 7*8. 6 0. 38*0. 29 Details in T. Vinatier et al. , Nucl. Instr. Meth. A 909, p. 185 (2018) & T. Vinatier et al. , J. Appl. Phys. 125, 164901 (2019)

Simulation of X-ray properties > Simulation of the X-ray generation via ICS simulated with the Monte-Carlo code CAIN for two laser wavelengths (1048 and 524 nm) and 1 ps rms length. θcoll = 4 mrad σνγ/νγ = 1. 5% EX: Mean X-ray energy; θcoll: Collimation angle; Nγ, θcoll: Number of collimated photons/shot; σνγ/νγ: rms bandwidth Details in T. Vinatier et al. , J. Appl. Phys. 125, 164901 (2019)

Outline: Tolerance study > Introduction > Tolerance study • Approach and tools • RF-gun, solenoid and UV laser jitters • THz linac field amplitude and phase jitters • THz linac misalignments • Quadrupoles gradients jitters • Quadrupoles misalignments • ICS laser imperfections and misalignments > Other challenges > Conclusions

Approach and tools > Tolerance study performed with ASTRA parameter scanning and a self-written Matlab code (influence of a single imperfection/jitter) and with the ERROR namelist of ASTRA (simultaneous influence of several imperfections/jitters). Field amplitude & phase jitters Amplitude jitter Energy & pointing jitters Pointing jitter and arrival timing jitter at the THz linac entrance Field amplitude & phase jitters Gradients jitter 3 D translation (x, y, z) & 2 D rotation (x, y) 3 D translation (x, y, z) & 3 D rotation (x, y, z) Waist & duration Transverse offset Timing jitter > Not all results shown in this talk, only those most affecting the e- bunch properties.

RF-gun, solenoid and UV laser jitters Reference electron bunch properties at the ICS point Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (μm 2) εx*εy (μm 2) 1 17. 65 123 1. 31 10. 6*10. 5 0. 226*0. 189 > RF-gun: 0. 01% rms peak field jitter & 0. 006˚ (≡ 5. 5 fs at 3 GHz) rms laser/RF-field phase jitter assumed. > UV laser: 35 μm rms pointing jitter & 3% energy jitter assumed. > Solenoid: 0. 04% rms peak field jitter assumed. • Simultaneous study of all the jitters show that σt and especially σE are the most affected properties. σt variation under the assumed jitters σE variation under the assumed jitters > The assumed jitters, at the state-of-the-art for the RF-gun, are needed to keep the longitudinal properties under control, although not totally satisfactorily for σE. Decoupling all the jitters is needed to determine which one has the strongest influence and if it can be improved.

THz linac field amplitude and phase jitters Reference electron bunch properties at the ICS point (f = 300 GHz) Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (μm 2) εx*εy (μm 2) 1 17. 65 123 1. 31 10. 6*10. 5 0. 226*0. 189 > Phase: 1˚ rms jitter assumed. Especially affects bunch length (σt), energy spread (σE) and mean energy (<E>). > Field amplitude: 1% rms jitter assumed. Especially affects σt, σE and the bunch transverse size (σx and σy). σE variation under a 1° rms phase jitter σy variation under 1% rms amplitude jitter > A 1% rms amplitude jitter looks reasonable for the stability of the e- bunch properties. On the opposite, the phase jitter would have to be reduced significantly below 1˚.

THz linac misalignments y Reference electron bunch properties at the ICS point Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (μm 2) εx*εy (μm 2) 1 17. 65 123 1. 31 10. 6*10. 5 0. 226*0. 189 z x > Offsets: x and y up to +/- 0. 6 mm. z up to +/- 1 mm. A y offset affects σE and σt. > Rotations: around x and y up to 9 mrad (≈ 0. 52˚) w. r. t. linac entrance and 13 mrad (≈ 0. 75˚) w. r. t. linac center. All rotations affects σE and σt. A rotation around x (y) strongly affects σx (σy) and εx (εy). Charge losses vs rotation angle σE and σt variations vs rotation around y w. r. t. linac center σy and εy variations vs rotation around y w. r. t. linac entrance > Transverse offset should be kept below 200 µm and rotations below 1 mrad. > This is well within theoretical accuracy of positioning devices (e. g. hexapodes). However, the practical accuracy rely on a beam-based alignement procedure and has to be determined.

Quadrupoles gradients jitters Reference electron bunch properties at the ICS point Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (μm 2) εx*εy (μm 2) 1 17. 65 123 1. 31 10. 6*10. 5 0. 226*0. 189 > Gradient detuning studied independently for the 3 quadrupoles up to around +/- 2%. Bunch properties more affected by a detuning of the 2 nd quadrupole. σx and especially σy are the most affected properties. > Simultaneous jitter of 0. 5% rms for all the gradients also studied. σy variation vs gradient detuning of the quadrupoles σy variation under a 0. 5% rms gradient jitter > Keeping the gradient jitter of the 2 nd quadrupole below 0. 5% (reasonable) would allow to keep the e- bunch properties variation below 15% (max. for σy).

Quadrupoles misalignments y Reference electron bunch properties at the ICS point Q (p. C) <E> (Me. V) σE (ke. V) σt (fs) σx*σy (μm 2) εx*εy (μm 2) 1 17. 65 123 1. 31 10. 6*10. 5 0. 226*0. 189 z x > Offsets: x and y up to +/- 0. 5 mm. z up to +/- 1 mm. A y offset of the 3 rd and especially 2 nd quadrupoles affects σE, σt, σy and εy. > Rotations: around x, y and z up to 20 mrad (≈ 1. 15˚). A rotation around z of the 2 nd (1 st) quadrupole affects σx (σy) and εx (εy). σt variation vs offset along y εy variation vs rotation around z (skew) > Quadrupole rotation around z (skew) should be kept below 0. 5˚ (9 mrad) (reasonable) and y offset below 100 µm for the 2 nd quadrupole (more challenging).

ICS laser imperfections and misalignments Reference X-ray pulse properties at the ICS point Case EX (ke. V) θcoll (mrad) Nγ, θcoll σνγ/νγ (%) SPD (ph/e. V) Laser σr at focus (µm) Laser σt (ps) 1 5. 9 4 2*104 1. 4 90 10. 5 1 2 4. 3 4 4*104 1. 1 300 6. 1 1 EX: Mean X-ray energy; θcoll: Collimation angle; Nγ, θcoll: Number of collimated photons/shot; σνγ/νγ: rms bandwidth; SPD: Spectral photon density ≡ number of photons/e. V within the rms bandwidth (figur of merit) > Transverse misalignment studied up to 3σr of the laser at focus. Time offset with the e- bunch studied up to 10σt (≡ 10 ps) of the laser. Nγ, θcoll variation vs transverse misalignment Nγ, θcoll variation vs time offset > Synchronization with the ICS laser at the ps level required (reasonable). Transverse alignment e- bunch/ICS laser of a few μm required (study of e- bunch pointing jitter is ongoing).

Outline: Other challenges > Introduction > Tolerance study > Other challenges • THz requirements and generation • Dielectric-loaded waveguide manufacturing > Conclusions

THz requirements and generation > Quartz dielectric loading assumed (εr = 4. 41). > vph & vg : THz pulse phase & group velocities. > T: THz pulse duration; > <P> & ETHz : THz pulse average peak power & energy. f (GHz) a (μm) b – a (μm) vph (c-1) vg (c-1) T (ps) <P> (MW) ETHz (m. J) 300 500 90. 35 1 0. 5132 407 23. 3 9. 5 150 1000 180. 71 1 0. 5132 407 93. 9 38. 2 150 800 201. 53 1 0. 4143 607 47. 4 28. 8 > None of the schemes studied for THz generation (laser-based, gyrotrons, CSR/FEL, wakefields) is currently able to fulfil all these requirements at once. > Research ongoing on efficient laser-based THz generation in non-linear crystals shows THz power (close to) fulfiling the requirement in short pulses (≈ 10% T). Research still has to be done to produce longer pulses.

Dielectric-loaded waveguide manufacturing > Requirement from beam dynamics simulations: Control of the phase velocity at a level better than 1‰. > Problem: This requires a very tight manufacturing accuracy for the waveguide (dielectric thickness accuracy better than 150 nm). Phase velocity as a function of the dielectric thickness variation for f = 300 GHz, a = 500 μm and εr = 4. 4 > Solution: Adjustment of vph by tuning the frequency of the THz field (feasible by tuning the temperature of the non-linear crystal in the case of laser-generated THz) could compensate waveguide production errors. 1‰ control level on vph corresponds roughly to 1 K control level on the crystal temperature. Temperature dependent Phase velocity as a function of the frequency variation for a = 500 μm, b – a = 90. 4 μm and εr = 4. 4 n. THz & nlaser: refractive indices for THz/laser in the crystal. Λ: Crystal poling period

Outline: Conclusions > Introduction > Tolerance study > Other challenges > Conclusions

Conclusions > A tolerance study has been performed (and is continued) to determine what are the requirements in terms of jitters and misalignments for an ICS-based compact ultrafast X-ray pulse source mixing RF (gun) and THz (linac) technologies. Some of them were found to be particularly challenging or still to be investigated. At least: 0. 01% peak field jitter & 0. 006° phase jitter (≡ 5. 5 fs) (≤ state-of-the-art). ≤ 1% peak field jitter & < 1° phase jitter. Dependent on THz source (e. g. laser). To be studied. Offset < 200 μm & rotation < 1 mrad (dependent on beambased alignment). Offset < 100 μm. Phase velocity fine-tuning THz requirements Transverse misalignment ebunch/ICS laser ≤ few μm (e- bunch pointing jitter study ongoing).