CSFI 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

CSFI 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

CSFI 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 = , N step =10 7

CSFI 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 ;  ≥ 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 Å photons und. period  u

CSFI 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

CSFI Rimini - Maggio 29, 2008  n [  m] I [kA] AOFEL SPARX SPARC SPARX 1 pC The Brightness Chart [A/(m. rad) 2 ]

CSFI 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.

CSFI 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

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

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

CSFI 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

CSFI 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 (2003)], First experimental paper of LWFA with injection by density decrease [T. Hosokai et al., PRE 67, (2003)]. It has been (numerically) proved to be able to produce very low emittance and quasi monochromatic e-beams Beam Generation

CSFI Rimini - Maggio 29, D 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 ( 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= 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 (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

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

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

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

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

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

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

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

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

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

CSFI 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]

CSFI 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

CSFI 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:

CSFI 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

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

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

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

CSFI 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

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

CSFI 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

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

CSFI 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

CSFI 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

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

CSFI 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

CSFI Rimini - Maggio 29, 2008

ALADYN vs. VORPAL

CSFI Rimini - Maggio 29, 2008

Slice 8, I=25 kA

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

CSFI 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

CSFI Rimini - Maggio 29, 2008