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					Linear and nonlinear TS for advanced
     X/g sources in PLASMONX
P.Tomassini(1,2), A. Bacci(1), S.Betti (3), J. Cary (6),
   A.Giulietti(2), D. Giulietti(2,3,5), L.A. Gizzi (2),
           L. Labate(2), L. Serafini(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) U. of Colorado and Tech-X corp.


 University
     of

   Milan




                LPAW07. Tomassini, INFN sez. di Milano                 1
Thomson Scattering Activities in PLASMONX
         (coordinator: V. Petrillo, INFN&Univ. MI)
 We ave 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).

• Ultrashort quasi-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

               LPAW07. Tomassini, INFN sez. di Milano               2
                            Outline

• Uncoherent Thomson Scattering in the linear and
  nonlinear regimes

• High-flux source in the quasi-linear regime

• Ultra-short quasi-monochromatic fs source with RF-
  photoinjector

• High-flux Ultra-short fs source with LWFA e-beams

            LPAW07. Tomassini, INFN sez. di Milano     3
      Thomson Backscattering: relevant issues
1. Particles do experience:
    1.a Longitudinal ponderomotive forces at the rising and
        falling edges of the laser pulse -> lowering of the
        longitudinal momentum inside the pulse
    1.b Transverse ponderomotive forces
    1.c Transverse force due to the pulse            -> off axis
         electric field in the case of short          momentum
         rising edge
2. Particles motion is:
    2.a Secolar motion is longitudinal, with a transverse drift.
        Longitudinal and transverse quivering
    Note: In a strong transverse quivering regime several
        harmonics can be generated (Nonlinear Thomson regime
        or multiphoton absorbtion regime)
               LPAW07. Tomassini, INFN sez. di Milano         4
         Scattered photons distributions
The computation of the angular and spectral distribution of the
scattered radiation can be performed in the classical dynamics
framework by using the retarded potentials:
                  d 2 Ng                 2
                               J (n, )
                  dd 4    2

                                                              n  r (t )
                                                     i (t
                                         dt(t)e
                                                                         )
                  J (n, )  n  (n                              c
                                                                             )

          Main features of the scattered radiation:
1. It is emitted forward with respect to the direction of the mean
          
   speed, within a cone of aperture qc~1/g.
   Full treatement of linear and nonlinear TS for a
2. It is blue shifted of a factor depending on the emission angle q,
   plane-wave laser pulse with analytical expression of
   the electron energy and the pulse amplitude:
   the distributions as well as several approximate
   expressions in P. Tomassini et al., Appl. Phys. B 80,
3. As the normalized amplitude a0 exceeds unity, a large number of
   419 (2005).
   harmonics is produced. INFN sez. di Milano
                LPAW07. Tomassini,                                   5
Example
                     Quasi head-on collision of a 5 MeV electron
                     (qe = 50 mrad, fe = /2) on a flat-top pulse of
                      normalized ampliude a0=1.5, l = 1mm and T = 20 fs

   P. Tomassini et al., Appl. Phys. B 80, 419 (2005)




       LPAW07. Tomassini, INFN sez. di Milano                       6
  Fundamental relations in the linear regime
• Relativistic upshift
                      4g 2        ˜
           EX  E0         ˜    , 2   2   e2  2 e cos(   e )
                   (1 g 22 )

                                                    Particle incidence angles

•
  For an e-bunch the energy spread of the collected photons depends
  on
                                                         2
                                                     n 
   – Collecting angle qM    E X    g
   – Bunch energy spread         2     (g M ) 2              +front
   – Transverse emittance
                             EX     g                 r         curvature


                                     cT  2 2 (1 2  2 4 )
         g M        N()  N e   0 
                                           a              3


              
                                      l         1  
                                                         2 3



           Overlap
                LPAW07. Tomassini, INFN sez. di Milano                          7
              Bunch Requirements
• Trivial: Charge: as large as possible; Size: as low as
  possible; Monocromaticity: as large as possibile
• Less trivial: Usually the beam normalized emittance is
  quoted to quantify the goodness of an e-beam.
  For TS the minimum energy spread is determined by the
  normalized acceptance angle

                 
              g M (1 for monochromaticity)
 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

                    ( INFN sez. di  (
           e  gTomassini,p /mc) Milanon /r)
           LPAW07. e                                          8
         Uncoherent TS Simulation tools
                in PLASMONX
• Nonlinear dynamics in the single-particle approximation:
  (TS)2 (Thomson Scattering Simulation Tools)
  [P.Tomassini, 2004].
  Semi-analytical FAST tools that employes the analytical
  results of P. Tomassini et al., Appl. Phys. B 80, 419 (2005)
  with a generalization to Gaussian pulses. The code accounts
  for
  (i) nonlinear effects,
  (ii) pulse focusing,
  (iii) full effects of beam emittances

 •Linear dynamics in the single particle approximatin [V.
                   Petrillo et al., 2004].
              LPAW07. Tomassini, INFN sez. di Milano         9
                            Outline

• Uncoherent Thomson Scattering in the linear and
  nonlinear regimes

• High-flux source in the quasi-linear regime

• Ultra-short quasi- monochromatic fs source with RF-
  photoinjector

• High-flux Ultra-short fs source with LWFA e-beams

            LPAW07. Tomassini, INFN sez. di Milano      10
             High Flux operation mode
• 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 mammography sources in collaboration
  with the Mammography Monochromatic Beam Outlook
  (MAMBO) I.N.F.N. experiment requiring >1010 g/s with energy
  spread <12% rms.
                         Best working point           Pulse
           Bunch
    •2.5nC                                   •TEM00
    •8ps long (full size)
                                             •6J in 6ps
    •13mm rms tr. Size
    •1.5 mm mrad norm emittance              •w0 = 15 mm
    •0.1% energy spread
             LPAW07. Tomassini, INFN sez. di Milano               11
                              LINAC layout
                               Features:
                         •High brightnss e-beam
                           •Very low emittance




                              quadrupoles
                              dipoles
                              RF deflector
                              collimator            25º
Photoinjector      solenoid
            RF sections             25º

                                     11º
1.5m          10.0 m              5.4 m            14.5 m   1-6 Undulator
                                           Diagnostic
                                                            modules
                 High Flux results

• 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.




                      Reduced overlapping

                 Acceptance: gqmax = 0.5


            LPAW07. Tomassini, INFN sez. di Milano      13
                   (E,q) Distribution




   Second harmonics



Third harmonics




      LPAW07. Tomassini, INFN sez. di Milano   14
22%FWHM

                5% FWHM




  LPAW07. Tomassini, INFN sez. di Milano   15
              Minimum TS energy spread

• The minimum energy spread is
                                       E X      g  n
                                                          
                                                               2
                                                             

                                              2     
                                        E X  in
                                               m
                                                     g  r 
• With an energy spread 0.1%, emittance 1.5 mm mrad and beam
  focusing size of 13 mm rms, the contributions are


    g
           2  103 ,
                                     2
                                  n 
                                   
                                                 2
                                                         0.1
2                                     2  10
    g                             r 

            Minimum energy spread of 2% FWHM ,
                with a flux of 1.3.109 photons/s


                                   
              LPAW07. Tomassini, INFN sez. di Milano             16
                          Outline

• Uncoherent Thomson Scattering in the linear
  and nonlinear regimes

• High-flux source in the quasi-linear regime
• Ultra-short quasi-monochromatic fs source with
  RF-photoinjector

• High-flux Ultra-short fs source with LWFA e-
  beams

          LPAW07. Tomassini, INFN sez. di Milano   17
 Ultrashort Quasi-monochromatic Source
        with Photoinjector e-Beam
• Ultrashort 130MeV, 20pC e-beam

                                                       Parameters:
                                                       r (rms)=6mm
                                                     length (rms)=13mm
                                                        E/E=0.1%
                                                      n=1.2mm mrad



                                         e  (p /mc)  (n /r)  0.2
            LPAW07. Tomassini, INFN sez. di Milano                    18
                  TS Distributions
         Fundamental at 400KeV
• Since the emphasis is on the monochromaticity we
                           Bunch 45fs long (rms)
  choose to collect photons in the “natural-aperture” with
                                2x108 photons/sec
  cone, i.e. the one with e=0.2 (approx. 1 mrad).
  First harmonics at 800 KeV
                                 E/E=4% FWHM
                                   energy spread
Monochromaticicy requires minimization of the
  harmonics production. The laser pulse is 5ps long and is
  focused down to 15 mm of waist size




            LPAW07. Tomassini, INFN sez. di Milano       19
                          Outline

• Uncoherent Thomson Scattering in the linear
  and nonlinear regimes

• High-flux source in the quasi-linear regime

• Ultra-short fs source with RF-photoinjector

• High-flux Ultra-short fs source with LWFA e-
  beams
          LPAW07. Tomassini, INFN sez. di Milano   20
 All-optical source: LWFA self-inj. e-beam

• 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. [2D 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, Few femtoseconds
   – low transverse momentum       For monocromaticity of
   – quasi monochromatic e-beams        The X source
                LPAW07. Tomassini, INFN sez. di Milano     21
         2D PIC preliminary results with
               the VORPAL code
•   Macro-particles move in a moving-window simulation box of
    30x40mm2 with a spatial resolution of 0.05 land 0.15 land
    20ppc
•   The plasma density is large (4.1019cm-3) in order to “freeze” the
    space-charge effects and slippage in the early stage of
    acceleration.
•   The density transition was (L~5 mm ~ lp). The amplitude of the
    transition is low (20%), thus producing a SHORT e-beam
•   The laser pulse intensity (I=7.1018W/cm2) 0.8J in 20fs focused
    on a waist of 12 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 (avoid
    transverse wavebreaking)


              LPAW07. Tomassini, INFN sez. di Milano                22
Steepening@transition->injection
     Main bunch parameters:
          •Charge: 5-20pC
       •Length 0.27mm (rms)
   •Transverse size 0.47mm (rms)
•Transverse momentum 0.58 mc (rms)
•Normalized emittance 0.23 mm mrad
           •Energy 31MeV
     •Energy spread 10% (rms)




   LPAW07. Tomassini, INFN sez. di Milano   23
                  TS Distributions
     Fundamental at 25KeV
• Since the emphasis is on the monochromaticity we
  choose to collect photons in the “natural-aperture”
  cone, i.e. the one with Bunch 1fs long mrad). with
                               e=0.5 (approx. 8 (rms)
 First harmonics at 50 KeV
                                   4x108 photons/sec
  As for the case of the Photoinjector e-beam, FWHM
                                   E/E=15%
                                      energy the
  monochromaticicy requires minimization ofspread
  harmonics production. The laser pulse is 5ps long and is
  focused down to 15 mm of waist size



            LPAW07. Tomassini, INFN sez. di Milano       24
       In the full Nonlinear regime?

• wo=10mm, T=40fs ->ao=7 a huge amount of
  harmonics, including downshots is observed




           LPAW07. Tomassini, INFN sez. di Milano   25
                            Conclusions
•The Thomson Scattering beamline in PLASMONX can be tuned to produce
high flux quasi-monochromatic X rays. With the optimization of the
parameters for mammography a flux of 2.10^10 photons/s @ 20KeV with
22%FWHM enegy spread is obtained. Higher monochromaticity is
obtainable with a lower acceptance angle (with a proportional reduction of
the flux) down to the minimum energy spread of 2% with 109 photons/s.


•The beamline can be tuned to produce ultrashort e-bunches @130MeV.
TS with the PLASMONX parameters can produce 45fs long (rms) X/g rays
with 2x108 photons/sec with E/E=4% FWHM of energy spread

•An all-optical TS source is being investigated. (Very) preliminary
simulations show that the density downramp self-injection scheme is
capable of producing extremely ultrashort (0.3mm->1fs) e-beams thus
allowing the production of a femtosecond-scale tunable quasi-monocromatic
source of 4x108 photons/sec with E/E=15% FWHM energy spread.

                 LPAW07. Tomassini, INFN sez. di Milano                26

				
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