Coulomb09, Senigallia, Ultra-High Brightness electron beams from laser driven plasma accelerators Luca Serafini, INFN-Milano Brightness Degradation due to Chromaticity blow-out in ultra-focused beams (  p/p> 1% is a danger) 6D Phase Space Density of beams produced by self-injection mechanisms (Brightness, Brilliance) Ultra-high brightness in step density gradient plasma injectors (A look at the particle beam beyond the source) Fs to As pulses of Coherent X-rays (the AOFEL)

Coulomb09, Senigallia, Vittoria Petrillo Università degli Studi, Milano (Italy) Alberto Bacci, Andrea R. Rossi, Luca Serafini, Paolo Tomassini INFN, Milano (Italy) Carlo Benedetti, Pasquale Londrillo, Andrea Sgattoni, Giorgio Turchetti Università and INFN Bologna (Italy)

Coulomb09, Senigallia, Brightness and Brilliance 5D and 6D phase space density Figures of Merit for Particle Beams

Coulomb09, Senigallia,  n [  m] I [kA] AOFEL SPARX SPARC X-ray 1 pC The Brightness Chart [A/(m. rad) 2 ] Self-Inj

Coulomb09, Senigallia,  [  ] BnBn SPARX SPARC The 6D Brilliance Chart [A/((m. rad) 2 0.1%)] Self-Inj Ext-Inj AOFEL X-ray 1 pC

Coulomb09, Senigallia, Rapidity

Coulomb09, Senigallia, electron beam Physical Principles of the Plasma Wakefield Accelerator Space charge of drive beam displaces plasma electrons Transformer ratio Wake Phase Velocity = Beam Velocity (like wake on a boat) Plasma ions exert restoring force => Space charge oscillations Wake amplitude Ez Courtesy of T. Katsouleas Plasma acceleration experiments with SPARC/X e - beams

Coulomb09, Senigallia, Self-Injection beams seem to have low phase space density but high rapidity (suited for relativistic piston applications)

LNF – 29/05/2009 C. Benedetti

x envelope and emittance free diffraction in vacuum RETAR (A. Rossi) no description of plasma vacuum interface

Bunch length and average current

Energy spread

Transverse and longitudinal phase and configuration 1 cm

Transverse and longitudinal phase and configuration 92 cm

LNF – 29/05/2009 SPARC  n =1 mm. mrad,  0 = 200  m,  =300,  =0.6%, d=10 m  n =0.005 mm. mrad Self-Inj  n =2 mm. mrad,  0 = 1  m,  =2000,  =2%, d=1 m  n =40 mm. mrad Emittance Dilution due to Chromatic Effects on a beam emerging from a focus of spot size  0, drifting to a distance d

LNF – 29/05/2009 ASTRA (A. Bacci) : matching with a triplet

LNF – 29/05/2009 Space charge energy spread No Space charge energy spread

LNF – 29/05/2009 No Space charge No energy spread SPARC beam Space charge energy spread

Coulomb09, Senigallia, How to measure this emittance blow-up? No trace on beam envelope… energy selection?

LNF – 29/05/2009 SPARC 640  m AOFEL 3  m SPARX 580  m acceleration focusing beam plasma emittance laminarity parameter Beam-plasma wavelength betatron length transition spot-size Bubble-self.inj  m

Coulomb09, Senigallia, Coherence and Time Duration

Coulomb09, Senigallia, 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]

AOFEL injection by longitudinal nonlinear breaking of the wave at a density downramp looks one of the most promising since it can produce e-beams having both low energy spread and low transverse emittance. electromagnetic undulator made by a laser pulse counter propagating respect to the electron beam

First stage:LWFA with a gas jet modulated in areas of different densities with sharp density gradients. Energy (J)2 Waist (  m) 20 Intensity (W/cm 2 ) Duration (fs)20 n 01 (cm -3 ) L R (  m) 10 n 02 (cm -3 ) p (  m) 13

Coulomb09, Senigallia,  <><> <><> 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

VORPAL C. Nieter J. R. Cary J.Comp.Phys (2004) New results by ALADYN Numerical Modelling Formation of the plasma Formation of the bunch Acceleration stage Astra Retar Beam-CO2 laser Interaction FEL instability Genesis 1.3 EURA Transition Plasma-undulator First stage Second stage Third stage

Second stage: Transition from the plasma to the interaction area with the e.m. undulator (analysis by ASTRA) With space charge Without space charge

FEL interaction with a e.m. undulator Pierce Parameter I A = Amp L g1d = u /(  Ideal 1d model L g  u     Three-dimensional model E rad =  E beam = 1.35nm

, <1

Generalized Pellegrini criterion Requirements for the growth

50 20 kA  X m m  =

L g1d =76  m  z =0.2  m L g =200  m

Transverse coherence d= L sat * /  x = 10*L g * /  x = 10* *10 -9 / =0.4  m Longitudinal coherence L c = /(  (1+  ) =0.04  m 1 spike each 10 L c

Third stage: FEL radiation = u (1+a w 2 )/4  2 by uploading the particles by VORPAL Superradiant structure 0.1  m=330 as Single spike structure Monochromatic pulse

First peakSaturation P max (W) E (  J) L R  m) L sat  mm) R (nm) 1.35 d R/ R 0.81% 25 micron Laser requirements: 250 GW for 5 mm R=30  m E=4.16J

Coulomb09, Senigallia,

I=31 KA  z =1.5  m  x =0.6 um  n =0.1  m  =45  E/E=0.3% a 0 =0.8  =0.162 nm

Conclusions All optical free-electron laser are possible with e-beam produced by LWFA in density downramp + electromagnetic undulators Characteristics of radiation: small energy/pulse, quasi transverse coherent, very short pulse, longitudinal coherence, monochromaticity Injection of the beam, control of the exit from the plasma, requirements of power and structure of the e. m. undulator

Coulomb09, Senigallia, Conclusions Beams produced by Self-Injection in the bubble regime look affected by strong chromaticity: serious emittance dilution after the source, loss of beam brightness Possible cures: prompt focusing in mm (plasma lenses?), energy selection (charge loss), emittance compensation schemes? Maximum brightness with step downramp density injection (1D mech., localized injection) Needs new targets, shock wave gas jets AOFEL: table top X-FEL delivering fs to as quasi-coherent bright X-ray pulses

Coulomb09, Senigallia,

Scattered photons in collision  Scattered flux  Luminosity as in HEP collisions  Many photons, electrons  Focus tightly  Short laser pulse; <few psec (depth of focus) Thomson X-section Coulomb09, Senigallia,

Rapidity

Coulomb09, Senigallia,

This last group tries to realize the scheme proposed by Gruener et al. (1.74 GeV, 160 kA, 1mm mrad,  E/E=0.1%,  x =30  m) where an electron beam generated by LWFA in the bubble regime is driven in a static undulator  u =5 mm, =0.25nm, L sat =5m, L rad =4fs,P sat =58 GW,

The technology of ultra short, high power lasers has permitted the production and the study of high- brightness, stable, low divergence, quasi mono- energetic electron beams by LWFA. These beams are now an experimental reality ( for instance: Faure et al.,Leemans et al., Jaroszinski et. al, Geddes et al., ecc.) and can be used in applications for driving Free- electron lasers Last experimental results, see, for instance: J.Osterhoff et al. PRL (2008) (mono-energetic fraction: 10 MeV, divergence=2.1 mrad FWHM) Koyama, Hosokai MeV and density downramp N. Hafz, Jongmin Lee, Nature photonics THCAU05 FEL Conf 2008

electron beam Ti:Sa pulse Ti:Sa envelope Gas jet Lsat≈10 Lg CO 2 envelope AOFEL Lg=10.1 x (  x 2/3 /I 1/3 )x( w /K 0 /JJ 2 ) 1/3

Coulomb09, Senigallia, 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

Coulomb09, Senigallia, 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 Coherence Time duration

Coulomb09, Senigallia,

Slice 8, I=25 kA Equivalent Cathode