1. CSFI 2008 - Rimini - Maggio 29, 2008 All Optical Free Electron Lasers : una nuova sfida per i codici di simulazione FEL, Plasma e Fasci A. Bacci, V. Petrillo, A. R. Rossi, Luca Serafini, P. Tomassini* - INFN/MI (*and CNR-Pisa), C. Benedetti, P. Londrillo, A. Sgattoni, G. Turchetti - Univ. di Bologna and INFN/BO Bubble regime and self-injection schemes with density downramp analyzed Generation of electron beams for FEL’s applications with plasma injectors, targeting FEL simulations showing fs to 100 attosec X-ray pulses (1 Å - 1 nm) using optical undulators

2. CSFI 2008 - Rimini - Maggio 29, 2008 CO 2 envelope TiSa envelope e - beam TiSa pulse plasma L sat =10L G =1.3 mm (  =0.002) CO 2 focus Z [m] r  m] las =1  m  x,y,z =1  m  mesh < 50 nm

3. CSFI 2008 - Rimini - Maggio 29, 2008 Compare vs. RF Linac driver: SPARX lay-out 160 m80 m Fully consistent e.m. simulation: N mesh =10 16, N part =10 8-10, N step =10 7

4. CSFI 2008 - Rimini - Maggio 29, 2008 What is a SASE-FEL Radiation Source? a Bright Electron Beam propagating through an Undulator Spontaneous Radiation:  peaked at  r  u (1 + K 2 ) / 2  2 ; K=B u u ;  ≥ 2. 10 3 Beam rms divergence  ’  1/   rad (Compton Backscattering of undulator virtual photons) I r  e ;  e number of electrons per bunch (  10 9 ) 1-25 GeV electrons 100-0.5 Å photons und. period  u

5. CSFI 2008 - Rimini - Maggio 29, 2008 Interaction of e - with Spontaneous Radiation causes Microbunching and SELF-AMPLIFICATION of Spontaneous Emission (SASE) In the SASE mode the Intensity: I ph  e   > 4/3 ;  e of electrons (  10 9 ) Amplification gives extraordinary High Photon Flux (diffraction limited beam) Beam rms divergence  ’   2  e  few  rad Interaction of a bright electron beam with noise in an undulator magnet results in a density modulation of the electron bunch at the optical wavelength: SASE instability leads to COHERENT EMISSION Resonance Condition

6. CSFI 2008 - Rimini - Maggio 29, 2008  n [  m] 10 13 10 14 10 15 10 16 10 17 I [kA] 10 18 AOFEL SPARX SPARC SPARX 1 pC The Brightness Chart [A/(m. rad) 2 ]

7. CSFI 2008 - Rimini - Maggio 29, 2008 Issues of transporting Ultra-high Current e - beams with brightness preservation Longitudinal space charge debunching and correlated energy chirp Transverse time-dependent space charge oscillations and rms emittance compensation/preservation Linear Model for Plasma Beams (HOMDYN) invariant envelope vel. bunch.

8. CSFI 2008 - Rimini - Maggio 29, 2008 SPARC 640  m AOFEL 3  m SPARX 580  m acceleration focusing beam plasma emittance laminarity parameter Beam-plasma wavelength betatron length transition spot-size

9. CSFI 2008 - Rimini - Maggio 29, 2008 Transverse beam plasma wavelength : uncontrolled oscillations over distances > lead to rms (projected) emittance blow-up

10. CSFI 2008 - Rimini - Maggio 29, 2008 Longitudinal space charge length  p (full debunching)

11. CSFI 2008 - Rimini - Maggio 29, 2008 So we would like to operate a SASE FEL with ultra high beam currents, I p > 10 kA, yet in the usual regime Emittance dominated beam through undulator

12. CSFI 2008 - Rimini - Maggio 29, 2008 We started exploring two self-injection schemes: a) self-trapping in the bubble regime and b) controlled self injection with density downramp. Bubble injection [ A. Pukhov, J. M.-ter-Vehn, Appl. Phys. B 74, 355 (2002)] has been widely investigated, both experimentally and numerically and it has been proved to be able to produce high energetic (GeV- scale), high charge and quasi monochromatic (few-percent) e-beams. Self injection with density downramp Main idea+1D sim. [S. Bulanov et al., PRE 58, 5 R5257], First 2D sim+optimization for monocromaticity and low emittance [P. Tomassini et al. PRST-AB 6 121301 (2003)], First experimental paper of LWFA with injection by density decrease [T. Hosokai et al., PRE 67, 036407 (2003)]. It has been (numerically) proved to be able to produce very low emittance and quasi monochromatic e-beams Beam Generation

13. CSFI 2008 - Rimini - Maggio 29, 2008 2.5D PIC results with the VORPAL code Macro-particles move in a moving-window simulation box of 50x60  m 2 with a spatial resolution of 0.05  and  0.15  and 20particle/cell The plasma density is large (7-12. 10 18 cm -3 ) in order to “freeze” the space- charge effects and slippage in the early stage of acceleration. The density transition was (L~5-10  m ~ p ). The amplitude of the transition is low (20%-40%), thus producing a SHORT e-beam The laser pulse intensity (I=7. 10 18 W/cm 2 ) 2J in 25fs focused on a waist of 18  m) 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 (avoid transverse wavebreaking that will increase the emittance of the bunch) A Multi-plateau (three contiguous accelerating regions with increasing densities along the pulse path) is adopted to fix punch slippage along the bucket

14. CSFI 2008 - Rimini - Maggio 29, 2008 2.5D PIC results with the VORPAL code RISING Region

15. CSFI 2008 - Rimini - Maggio 29, 2008 2.5D PIC results with the VORPAL code Plateau I Region

16. CSFI 2008 - Rimini - Maggio 29, 2008 Transition Region Wave-breaking->injection

17. CSFI 2008 - Rimini - Maggio 29, 2008 2.5D PIC results with the VORPAL code Injected bunch Accelerating Region

18. CSFI 2008 - Rimini - Maggio 29, 2008 2.5D PIC results with the VORPAL code

19. CSFI 2008 - Rimini - Maggio 29, 2008 2.5D PIC results with the VORPAL code

20. CSFI 2008 - Rimini - Maggio 29, 2008 2.5D PIC results with the VORPAL code

21. CSFI 2008 - Rimini - Maggio 29, 2008 Best portion of the beam 2.5D PIC results with the VORPAL code Beaming (x long. axis, y transv.)

22. CSFI 2008 - Rimini - Maggio 29, 2008 Slice analysis: length of each slice Best slices

23. CSFI 2008 - Rimini - Maggio 29, 2008 CO 2 envelope TiSa envelope e - beam TiSa pulse plasma L sat =10L G =1.3 mm (  =0.002) CO 2 focus Z [m] r  m]

24. CSFI 2008 - Rimini - Maggio 29, 2008 In a conventional FEL the electron beam is generated in the space charge dominated regime (  TR ) and is brought, by acceleration and focusing, into the emittance dominated regime (  TR ), where the FEL interaction occurs In the AOFEL the electron beam is generated in the emittance dominated regime (  TR ) and is left diffracting within the plasma (and in vacuum) into the space charge dominated regime (  TR ), where the FEL interaction occurs

25. CSFI 2008 - Rimini - Maggio 29, 2008 ASTRA simulation (solid lines) for AOFEL beam in vacuum 20 kA, 1  m focal spot size, 0.3 mm. mrad Red: no space charge Black: space charge Black dashed: numerical integration of rms envelope equation with space charge Red dashed:

26. CSFI 2008 - Rimini - Maggio 29, 2008 Longitudinal Phase Space distributions show violent blow-up of uncorrelated energy spread due to transverse space charge field 158  m from plasma exit, about 3 gain lenghts

27. CSFI 2008 - Rimini - Maggio 29, 2008 Longitudinal Phase Space after removal of correlation

28. CSFI 2008 - Rimini - Maggio 29, 2008 518  m from plasma exit, about 10 gain lenghts

29. CSFI 2008 - Rimini - Maggio 29, 2008 RETAR simulations, 20 kA, 1  m focal spot size drift inside plasma and exit through plasma-vacuum interface focus PLASMAVACUUM

30. CSFI 2008 - Rimini - Maggio 29, 2008  <><> <><> Selection of best part in the bunch: 40 pC in 2 fs (600 nm) Longitudinal phase space and density profile projected rms  n = 0.7  m

31. CSFI 2008 - Rimini - Maggio 29, 2008 at plasma exitafter 1 mm drift  x = 5  m = 0.5 spherical wave front x pxpx plane wave

32. CSFI 2008 - Rimini - Maggio 29, 2008 Average power (L sat =2.5 mm) Peak power 0.7 GW s (micron) GENESIS Simulations uniform beam over 0.5  m averaged rms beam parameters Check 3D effects

33. CSFI 2008 - Rimini - Maggio 29, 2008 60 nm <><> <><>  GENESIS Simulations with averaged rms transv. beam parameters Actual profiles of current, energy and energy spread

34. CSFI 2008 - Rimini - Maggio 29, 2008 Simulation with real bunch GENESIS Simulations starting from actual phase space from VORPAL (with oversampling)  =2.5  m (CO 2 laser focus closer to plasma) After 1 mm : 0.2 GW in 200 attoseconds L beff < 2 L c

35. CSFI 2008 - Rimini - Maggio 29, 2008 GENESIS Simulations for laser undulator at 1  m to radiate at 1 Angstrom Simulation with real bunch  =3.5  m Average power (L sat ~500  m, P sat ~10 MW) Peak power 100 MW in 100 attoseconds Field

36. CSFI 2008 - Rimini - Maggio 29, 2008 ALADYN vs. VORPAL High resolution  z= /24=33 nm  x= /10=80 nm 20 particles per cell 63000 particles in red circle (160 pC bunch) z [  m] x [  m]

37. CSFI 2008 - Rimini - Maggio 29, 2008 W 0 =23  m, T=17 fs I=8.5*10 18 W/cm 2, E=2.4 J nota che abbiamo ancora energia laser che possiamo usare per aumentare un po’ la durata fino a valori piu’ realistici oppure il waist per diminuire ulteriormente le forze trasverse e quindi aumentare il raggio del beam

38. CSFI 2008 - Rimini - Maggio 29, 2008

45. ALADYN vs. VORPAL

46. CSFI 2008 - Rimini - Maggio 29, 2008

47. Slice 8, I=25 kA

48. CSFI 2008 - Rimini - Maggio 29, 2008 Slice 9, I=15 kA

49. CSFI 2008 - Rimini - Maggio 29, 2008 Conclusions Feasibility study for exp. at LNF with FLAME (200 TW TiSa laser available in 2008): perspectives for ELI (600 PW in 2015) We presented an exploratory analysis ( raising the plasma density we reached 250 kA,  3%, and  n 1.5  m, 50 MeV ) We must set up a reliable start-to-end simulation from plasma to X-rays (ALADYN3D+GenesysEM?): see C. Benedetti’s talk Computational challenge: turn a plasma-code into an accelerator-code, from plasma vomit to partice beams It’s worth to envision and study the future generation of high brightness beam injectors

50. CSFI 2008 - Rimini - Maggio 29, 2008