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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

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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

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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

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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

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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

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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 ]

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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.

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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

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

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

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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

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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

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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

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

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

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

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

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

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

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

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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.)

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

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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]

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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

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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:

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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

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

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

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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

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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

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

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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

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

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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

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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

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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]

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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

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CSFI 2008 - Rimini - Maggio 29, 2008

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ALADYN vs. VORPAL

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CSFI 2008 - Rimini - Maggio 29, 2008

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Slice 8, I=25 kA

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

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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

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CSFI 2008 - Rimini - Maggio 29, 2008

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