Simulations for Linear and Fully Nonlinear Thomson Scattering with the TSST Code

1. Simulations for linear and fully nonlinear Thomson Scattering with the TSST code University of Milan • Bacci(1), C. Benedetti (6), A.Giulietti(2), • D. Giulietti(2,3,5), L.A. Gizzi (2), • L. Serafini(1), P.Tomassini(1),V. Petrillo(1) • (1) INFN Sect. of Milano (2) IPCF-CNR, Pisa (3) Dip. Fisica Univ. di Pisa (4) Dip. Fisica Univ. di Milano(5) INFN Sect. of Pisa (6) INFN Sect. of Bologna Tomassini, INFN sez. di Milano

2. Outline • Uncoherent Thomson Scattering in the linear and nonlinear regimes • High-flux source with RF-photoinjector in the quasi-linear regime • Monochromatic source with RF-photoinjector in the quasi-linear regime • Ultra-short quasi-monochromatic fs source with RF-photoinjector • All-Optic Source: Ultra-short fs source with LWFA e-beams 30% of the total time 20% of the total time 10% of the total time 20% of the total time 20% of the total time Tomassini, INFN sez. di Milano

3. Thomson Scattering in the linear and nonlinear regimes q y z X-rays x • Most important parameters: • Particle energy (controls energy and angular distribution of the X-rays) • Laser pulse normalized amplitude a0=eA/mc2 (controls the nonlinearity in the quivering and several other issues) Tomassini, INFN sez. di Milano

4. Thomson Backscattering: relevant issues • 1. Particles in the e.m. field of a plane wave do experience: • 1.a Longitudinal ponderomotive forces at the rising and falling edges of thelaser pulse • 1.bTransverse ponderomotive forces • 1.c Transverse force due to the pulse electric • field in the case of short rising front with • 2. Particles motion is: • 2.a Secolar motion is longitudinal, with a transverse drift. Longitudinal and transverse quivering • Note:In a strong quivering regime several harmonics can be generated (Nonlinear Thomson regime or multiphoton absorbtion regime) -> off axis momentum Tomassini, INFN sez. di Milano

5. The simple case: harmonic or quasi-harmonic quivering Weakly relativistic (g=1.7) on axis particle Weakly nonlinear (a0=1) pulse Tomassini, INFN sez. di Milano

6. A trivial effect: longitudinal ponderomotive force Longitudinal ponderomotive force Weakly relativistic (g=1.7) on axis particle Nonlinear (a0=3.5) pulse Tomassini, INFN sez. di Milano

7. 3D (still) trivial effect: transverse ponderomotive forces Transverse ponderomotive force Weakly relativistic (g=1.7) OFF AXIS particle Weakly nonlinear (a0=1) pulse Tomassini, INFN sez. di Milano

8. Less trivial effect for quasi flat-top pulses Initial phase for non-adiabatic pulses Weakly relativistic (g=1.7) on axis particle Weakly nonlinear (a0=1) pulse Tomassini, INFN sez. di Milano

9. Scattered photons distributions Direction of emission Particle speed and position • The computation of the angular and spectral distribution of the scattered radiation can be performed in the classical dynamics framework (provided that the energy of the electrons is far below 50GeV) by using the retarded potentials: Tomassini, INFN sez. di Milano

10. Scattered photons distributions • Main features of the scattered radiation: • Relativistic effect: It is emitted forward with respect to the direction of the mean speed, within a cone of aperture qc~1/g. • It is blue shifted of a factor depending on the emission angle q, the electron energy and the pulse amplitude: • 2. Nonlinear effects (multiphoton absorption): As the normalized amplitude a0 exceeds unity, a large number of harmonics is produced and a red shift in the mean energy is induced by the longitudinal ponderomotive forces Tomassini, INFN sez. di Milano

11. Fully analytical treatment • An exact but very complex dependence of the X-ray distribution on the scattering angle, initial phase and initial particle momentum has been found. • If the number of cycles is large the spectral distribution can be decomposed as a sum of harmonics, each harmonic having its own energy and intensity dependence upon the output and particle angles. • The exact solution can be simplified if output and particle angles are small or if nonlinearity is weak • For a bunch each particle is processed independently. • First paper with analytical treatment flat-top plane-wave pulses and for an exactly on axis particle: E.Esarey et al. Phys. Rev. E 48 (1993) • First paper introducing the initial phase effect for an exact on axis particle and a perfectly sharp rising front: F.He et. al, Phys. Rev. Lett. 95 (2003) • Full treatement of nonlinear TS for flat-top plane-wave pulses and a generic incidence angle, generalization of the initial phase for non-sharp rising fronts and handling of a realistic e-beam: • P. Tomassini et al., Appl. Phys. B 80, 419 (2005). Tomassini, INFN sez. di Milano

12. Example Emission angle of the main component Head-on collision of a 100 MeV electron against a flat-top pulse of amplitude a0=1.5, l = 1mm , T = 20 fs and rising front giving a_bar=1 Tomassini, INFN sez. di Milano

13. Scattered photons distributions • Tools for simulating the X-ray distribution • Monte Carlo based on the Klein-Nishina formula and its nonlinear generalization • Fully analytical. Full treatement of linear and nonlinear TS for a • plane-wave flat-top laser pulse. • Fully numerical. A numerical integration of the time history can be performed with several high-order schemes. • Semi-analytical. The laser pulse interactong with the particle is decomposed as a sequence of flat-top, slowly varying envelope slices of the pulses. The produced radiation [which is estimatyed analytically for each slice] is then coherently added in a numerical fashion. Extremely slow if a good spectral and angular resolution is needed for a long pulse and 103-104 particles Relatively fast and accurate with most of the TS setup in the linear and nonlinear regimes. Tomassini, INFN sez. di Milano

14. The pulse is not a plane wave (focusing, transverse intensity profile). Phase mismatch and transverse ponderomotive forces can then arise. LASER PULSE Each electron has its own energy and incidence angle. Collective (driven by electrostatic Coulomb forces) effects should also taken into account in the case of dense bunches ELECTRON BEAM Realistic TS simulations A realistic simulation of the TS of a pulse on an electron bunch must take into account consistently a large amount of effects: Tomassini, INFN sez. di Milano

15. A semi-analitic approach: the TSST codeThomson Scattering Simulation Tools • If the laser pulse envelope is adiabatic (rise time>>pulse duration) each electron will interact with a sequence of flat-top slices with slowly varying amplitude, wavevector and phase slice-by-slice. • The amplitude of the scattered radiation A (NOT the intensity) can be computed by summing up (with the correct phase) the amplitude slice by slice Aslice. The X-ray radiation is finally computed as the modulus square of A • With this in mind we can estimate each secular particle trajectory and computing ANALITICALLY the amplitude for each slice, taking account of transverse effects too. • Coherence and a dialog with a self-consistent particle dynamics code are about to be included for very accurate simulations in the case of dense electron bunches. Tomassini, INFN sez. di Milano

16. Lets start with the simplest case:Fundamental relations in the linear regime Particle incidence angles Overlap • Relativistic upshift • For an e-bunch the energy spread of the collected photons depends on • Collecting angle qM • Bunch energy spread • Transverse momentum +front curvature Tomassini, INFN sez. di Milano

17. TS by Relativistic Electron Bunchesthe bunch side • A good electron bunch source is characterized by: • A large number of electrons N>108 • A low energy spread • On focus, the bunch size is as small as possible (few microns the transverse and less of a millimeter the longitudinal size) • The bunch divergence qe is as small as possible qeg<<1. Laser plasma accelerators Standard accelerators Tomassini, INFN sez. di Milano

18. The Bunch Side(More on Bunch Requirements) Not so trivial: Usually the beam normalized emittance is quoted to quantify the goodness of an e-beam. For TS the minimum energy spread is limited by the normalized acceptance angle which should exceeds the normalized mean incident angle of the particles transverse relevant parameter. The relevant parameter is then the rms of the transverse momentum of the bunch and NOT the emittance Tomassini, INFN sez. di Milano

19. Coherence properties • Longitudinal coherence LL=(l/2)(l/Dl) • is negligible unless collective phenomena occur • (->switch to FEL regime…) • However many application [see e.g. contrast phase tomography, contrast phase mammography….] need radiation having some degree of transverse coherence LT=(l/2)(D/r) • Due to the small source size r and large distance D transverse coherence of TS X-rays can be as high as several hundreds of micrometers! Tomassini, INFN sez. di Milano

20. Applications of the TS source • Extremely short duration (approximately as long as the electron beam), usually few femtoseconds for laser-plasma accelerators, few picoseconds for RF accelera-tors and few tens of fs for slice-selected beams by RF accelerators • Extremely small emission spot (few microns!) • Quasi monochromatic and continuosly tunable. • More compactthan synchrotron radiation …why is the TS source interesting for real use? Tomassini, INFN sez. di Milano

21. Thomson Scattering Activities in PLASMONX (coordinator: V. Petrillo, INFN&Univ.MI) We have optimized the TS source aiming at producing • HIGH FLUX quasi-monochromatic X/g radiation (energy in the range 10KeV-600KeV for PLASMONX) for medical imaging (e.g. mammography) with a high-charge (1-2.5 nC e-beam). • MONOCHROMATIC (2%rms) X/g radiation • Ultrashortquasi-monochromatic X beams with a low-charge (20pC) ultrashort (30-50fs) photoinjector e-beam We are currently studying: • All-optical HIGH FLUX-Ultrashort tunable X/g sources with LWFA produced e-beams • Coherent generation of X photons via optical FEL • Finally, we plan to use TS as a diagnostics on the LWFA produced e-beam Tomassini, INFN sez. di Milano

22. TS operating modesin PLASMONX • High-Flux-Moderate-Monocromaticity mode (HFM2) (suitable for applications requiring a high flux quasi monochromatic source) • Moderate-Flux-Monochromatic mode (MFM) (applications where emphasis on monochromaticity and tunability are needed) • Short-Monochromatic mode (SM) (tens of femtoseconds long, monochromatic source) • Laser-Plasma-Ultrashort mode (LPU) [ongoing, laser-plasma accelerated electron bunches are employed producing ultrashort (1fs scale) quasi monochromatic X-rays] Tomassini, INFN sez. di Milano

23. Outline • Uncoherent Thomson Scattering in the linear and nonlinear regimes • High-flux source with RF-photoinjector in the quasi-linear regime • Monochromatic source with RF-photoinjector in the quasi-linear regime • Ultra-short quasi-monochromatic fs source with RF-photoinjector • All-Optic Source: Ultra-short fs source with LWFA e-beams Tomassini, INFN sez. di Milano

24. High Flux operation modeHFM2 • A long (ps scale) laser pulse is employed (weakly nonlinear regime) to reduce harmonics and energy spread • High charge (1-2.5nC) e-beam. Due to the large charge, it is difficult to obtain small beams (length of ps scale) • Current optimization for advanced mammography sources requiring >1011g/s with energy spread <12% rms. Best working point Bunch Pulse • 2.5nC • 8ps long (full size) • 13mm rms tr. Size • 1.5 mm mrad norm emittance • 0.1% energy spread • TEM00 • 6J in 6ps • w0 = 15 mm Tomassini, INFN sez. di Milano

25. Plasmon Thomson quadrupoles dipoles RF deflector collimator 25º solenoid Photoinjector RF sections 25º 11º 5.4 m 1.5m 10.0 m 14.5 m 1-6 Undulator modules Diagnostic PLASMONX LINAC layout • Features: • High brightnss e-beam • Very low transverse momentum

26. High Flux results Reduced overlapping • Optimization of the bunch in progress. Front-to-end simulations from photo-gun to the final focus. • Optimization of the pulse parameters: scan of the distribution with the waist size and duration. Acceptance: Y=g qmax = 0.5 Tomassini, INFN sez. di Milano

27. Second harmonics Third harmonics (E,q) Distribution Tomassini, INFN sez. di Milano

28. 22%FWHM 4.5% FWHM 2.1010g/sec with energy spread 22%FWHM, transverse size 15mm rmsand duration 8ps are produced Tomassini, INFN sez. di Milano

29. Outline • Uncoherent Thomson Scattering in the linear and nonlinear regimes • High-flux source with RF-photoinjector in the quasi-linear regime • Monochromatic source with RF-photoinjector in the quasi-linear regime • Ultra-short quasi-monochromatic fs source with RF-photoinjector • All-Optic Source: Ultra-short fs source with LWFA e-beams Tomassini, INFN sez. di Milano

30. Moderate-Flux-Monochromatic operation mode (MFM) • In the MFM mode the requirement is on monochromaticity so the goal is the optimization of the TS source so as to reduce the energy spread of the X-rays down to few percent. • For an ideal e-beam the energy spread depends only on the acceptance angle: where Y=gqM is the normalized acceptance • To switch in the monochromatic mode just a reduction of the acceptance angle is needed! • UNFORTUNATELY the first consequence of the acceptance reduction is the lowering of the X-ray flux Tomassini, INFN sez. di Milano

31. Minimum TSenergy spread • In the presence of beam energy spread and transverse momentum the minimum energy spread is • With an energy spread 0.1%, emittance 1.5 mm mrad and beam focusing size of 13 mm rms, the contributions are Minimum energy spread of 1.5% rms , with a flux of 1.9.108 photons/s +ponderomotive broadening Y=0.1 Flux: NX=1.9.108g/s DE/E=1.5% rms Y=0.2 Flux: NX=7.3.108g/s DE/E=2.2% rms Y=0.3 Flux: NX=1.5.109g/s DE/E=4.1% rms Tomassini, INFN sez. di Milano

32. Outline • Uncoherent Thomson Scattering in the linear and nonlinear regimes • High-flux source with RF-photoinjector in the quasi-linear regime • Monochromatic source with RF-photoinjector in the quasi-linear regime • Ultra-short quasi-monochromatic fs source with RF-photoinjector • All-Optic Source: Ultra-short fs source with LWFA e-beams Tomassini, INFN sez. di Milano

33. Ultrashort Quasi-monochromatic Source with Photoinjector e-Beam • Ultrashort130MeV, 20pC e-beam Parameters: r (rms)=6mm length (rms)=13mm DE/E=0.1% en=1.2mm mrad Tomassini, INFN sez. di Milano

34. TS Distributions Fundamental at 400KeV First harmonics at 800 KeV • Since the emphasis is on the monochromaticity we choose to collect photons in the “natural-aperture” cone, i.e. the one with Y=Ye=0.2 (approx. 1 mrad). Monochromaticicy requires minimization of the harmonics production. The laser pulse is 5ps long and is focused down to 15 mm of waist size Bunch 45fs long (rms) with 2x108 photons/sec DE/E=4% FWHM energy spread Tomassini, INFN sez. di Milano

35. Outline • Uncoherent Thomson Scattering in the linear and nonlinear regimes • High-flux source with RF-photoinjector in the quasi-linear regime • Monochromatic source with RF-photoinjector in the quasi-linear regime • Ultra-short quasi-monochromatic fs source with RF-photoinjector • All-Optic Source: Ultra-short fs source with LWFA e-beams Tomassini, INFN sez. di Milano

36. All-optical source: LWFA for the e-beam • A route for a drastic reduction of the e-beam size is that of switching to Laser Wake Field Accelerated electrons. • The laser system for the LWFA can either be the same of TS or another dedicate system. In the first case a splitting of the laser pulse is employed Tomassini, INFN sez. di Milano

37. e-beam quality: controlled injection • We are currently exploring controlled self injection with density downramp S. Bulanov et al. [the idea+1D sim.] PRE 58 R5257 (1998) P. Tomassini et al. [First2D sim+optimization for monocromaticity and low emittance] PRST-AB 6 121301 (2003). T. Hosokai et al., [First experimental paper of LWFA with injection by density decrease]PRE 67, 036407 (2003). • Search for working points in the 10-100 MeV energy range, with • ultrashort, • low transverse momentum • quasi monochromatic e-beams Few femtoseconds long For monocromaticity of The X source Tomassini, INFN sez. di Milano

38. 2D PIC results with the ALaDyn codeC.Benedetti, P.Londrillo A.Sgattoni, G. Turchetti developed @ INFN-BO • To increase accuracy, transversally stretched cells have been used in the simulation box. Macro-particles move in a moving-window simulation box of 170x45mm2 with longitudinal and transverse spatial resolution in the center of l/12 and l/4, respectively, and 80 particle per cell. • The plasma density is large (1.1019cm-3) in order to “freeze” the space-charge effects and slippage in the early stage of acceleration. • The density transition was (L~10 mm ~lp). The amplitude of the transition is low (15%), thus producing a SHORT e-beam • The laser pulse intensity (I=8.5.1018W/cm2) 2.5J in 17fs focused on a waist of 32.5 mm) was tuned in order to produce a wakefield far from wavebreaking in the flat regions. • The pulse waist was chosen in order to assure that longitudinal effects do dominate over transverse effects @injection • The accelerating plateau has a negative density gradient in order to induce dephasing in the early stage of the acceleration thus producing quasi-monochromatic e-beams with low transverse momentum Tomassini, INFN sez. di Milano

39. Longitudinal phase-space plot First plateau Tomassini, INFN sez. di Milano

40. Longitudinal phase-space plot Just after transition: particle injection Tomassini, INFN sez. di Milano

41. Longitudinal phase-space plot Particle acceleration Tomassini, INFN sez. di Milano

42. Particles enter in the de-accelerating region: dephasing has started Longitudinal phase-space plot Dephasing Tomassini, INFN sez. di Milano

43. Very low momentum spread Longitudinal phase-space plot Dephasing Tomassini, INFN sez. di Milano

44. Density of particles with pz>0.8 Ez Two dimensional issues Tomassini, INFN sez. di Milano

45. Density of particles with pz>0.8 Ez Tomassini, INFN sez. di Milano

46. Density of particles with pz>0.8 Ez Tomassini, INFN sez. di Milano

47. Density of particles with pz>0.8 Ez Tomassini, INFN sez. di Milano

48. Density of particles with pz>0.8 Ez Tomassini, INFN sez. di Milano

49. Density of particles with pz>0.8 Ez Tomassini, INFN sez. di Milano

50. Density of particles with pz>0.8 Ez Tomassini, INFN sez. di Milano