1. X-ray Generation in Plasma Using Laser-Accelerated Electrons Rahul Shah, F. Albert, R. Fitour, K. Taphuoc, and A. Rousse Laboratoire d’Optique Appliquée (LOA) LOA laser (similar to what we will see at NN)

2. Intense Light Fields Cause Electron Motion Along Propagation Direction Z+ - Bound Atomic Optics Light magnetic field negligable Non-linearities arise from atomic potential longitudinal transverse both transverse and longitudinal 0 1a  0 ~1a 0 1 a  Relativistic Optics Magnetic field causes electron moves in direction of light wave Non-linearities for free electrons Relativistics harmonics, Effective force manipulates plasma a0~E/ωa0~E/ω

3. 1. Ultrafast studies (femtosecond) ~Å~Å Bright and Short-Pulse X-rays for Diffraction, Imagery, and Diagnostic

4. 1. Ultrafast studies (femtosecond) ~Å~Å Bright and Short-Pulse X-rays for Diffraction, Imagery, and Diagnostic x-ray (normal) phase-contrast x-ray 2. Phase Contrast X-rays of laser-fusion interaction Be shellfuel layer

5. 1. Ultrafast studies (femtosecond) ~Å~Å Bright and Short-Pulse X-rays for Diffraction, Imagery, and Diagnostic x-ray (normal) phase-contrast x-ray 2. Phase Contrast X-rays of laser-fusion interaction Be shellfuel layer 3. Diagnostic of process (laser-wakefield acceleration) 1 mm z simulation 1 wave e - laser electron energy ~10 µm trapped e - 1 A. Pukhov and J. Meyer-ter-Vehn Appl. Phys. B, 74, (2002)

6. magnetic field electron ρ (radius of curvature) Synchrotron Radiation Broad spectrum, narrow beam, 10-100 picoseconds E X-ray  γ 3 /ρ keV hν m GeV e - laser solid x-rays electrons Laser on solid targets/K α femtosecond but low-brightness electron Relativistic Electrons Provides Desirable X-ray Qualities Absent in Line-emission Sources

7. Laser Wakefield Acceleration Provides MeV-GeV Electrons in Millimeters + + + + + + + + + + + - - - + - - - - - - - - laser plasma - 10 µm 100 GeV/m Electrons pushed by laser force Pulled back by ions creating plasma wave Electrons accelerated by electrostatic field, 3 orders larger than conventional

8. Laser Wakefield Acceleration Provides MeV-GeV Electrons in Millimeters 1 mm + + +++++ + ++ + -- - + -- - - - - - - laser plasma - 10 µm 100 GeV/m Experimentally simple Various regimes;varying energies State of the art: GeV, tunable and monochromatic x y < 1° fluorescent screen electron beam

9. Relativistic Harmonics Laser & Plasma Can Generate Low-divergence Ultrafast X-rays from Laser-Accelerated Electrons Laser overlaps accelerating electrons Light intensity causes free-electron harmonics

10. Laser & Plasma Can Generate Low-divergence Ultrafast X-rays from Laser-Accelerated Electrons Laser creates ionic cylinder Plasma field causes synchrotron radiation from accelerating electrons Synchrotron Radiation due to Plasma

11. Synchrotron motion in Plasma Laser & Plasma Can Generate Low-divergence Ultrafast X-rays from Laser-Accelerated Electrons ion field ρ (radius of curvature) relativistic electron Relativistic electrons collimate radiation Synchrotron radiation Relativistic Harmonics

12. longitudinal transverse both transverse and longitudinal 0 1a  0 ~1a 0 1 a  Relativistic Harmonics laser plasma θ (deg) normalized intensity a 0 =0.01 rest electron Relativistic Intensity results in higher order radiation fundamental 6 th harmonic 11 th harmonic 16 th harmonic

13. longitudinal transverse both transverse and longitudinal 0 1a  0 ~1a 0 1 a  Relativistic Harmonics laser plasma θ (deg) normalized intensity a 0 =2 rest electron Relativistic Intensity results in higher order radiation Previously 2 nd, 3 rd reported fundamental 6 th harmonic 11 th harmonic 16 th harmonic

14. longitudinal transverse both transverse and longitudinal 0 1a  0 ~1a 0 1 a  Relativistic Harmonics laser plasma θ (deg) normalized intensity a 0 =2 1 MeV electron copropagating fundamental 6 th harmonic 11 th harmonic 16 th harmonic Relativistic Intensity results in higher order radiation Energetic electrons result in forward peaking

15. Relativistic Harmonics: Experimental Setup Laser parameters: 400 fs, 1.053 µm, 2 J laser plasma

16. Relativistic Harmonics: Experimental Setup Laser parameters: 400 fs, 1.053 µm, 2 J laser plasma

17. Even Harmonics Consistent with Relativistic Process Relativistic harmonics Linear n e scaling, even orders He at a~2, linear polarization ≈5x10 18 e - /cm -3 13 th harmonic 12 11 wavelength source image Atomic harmonics n e 2 scaling, no even orders Signal vs. Density laser plasma

18. I = 5x10 17 W cm - 2 n = 10 18 cm -3 Linear Pol. I = 4x10 18 W cm -2 n = 10 19 cm -3 Circular Pol. RELATIVISTIC i. Even orders ATOMIC i. Odd orders only Relativistic Process Occurs with Circular Polarization laser plasma

19. I = 5x10 17 W cm - 2 n = 10 18 cm -3 Linear Pol. I = 4x10 18 W cm -2 n = 10 19 cm -3 Circular Pol. laser plasma RELATIVISTIC i.Even orders ii.Lin/Circ polarization ATOMIC i.Odd orders only ii.Lin pol. only Relativistic Process Occurs with Circular Polarization

20. I = 5x10 17 W cm - 2 n = 10 18 cm -3 Linear Pol. I = 4x10 18 W cm -2 n = 10 19 cm -3 Circular Pol. 4 μm focal spot laser plasma RELATIVISTIC i.Even orders ii.Lin/Circ polarization iii.Generate only at focus ATOMIC i.Odd orders only ii.Lin. pol. Only iii.Large volume of generation Relativistic Process Occurs with Circular Polarization

21. 1112 source slit grating detector wavelength image laser plasma Angular Profile Shows Role of Accelerated Electrons Take into account energetic electrons and divergence of laser and electrons Using a 0 ~6 (10x more power) order 100 harmonic radiation observed. Angular profile similarly depended on 1 MeV electrons.

22. Banerjee et. al. POP 20:182, 2003 Taphuoc et al. PRL 91: 195001, 2003 laser plasma Relativistic High Harmonics 1,2 Laser light itself creates non-linearity in electron motion Observe characteristics in the radiation supporting relativistic harmonic generation Laser-accelerated electrons collimate radiation X-rays though would require a 0 ~10, and the higher harmonics have even broader angular distribution…

23. Synchrotron radiation 1 50 GeV electrons, n e ~10 14 /cm 3, 5-30 keV x-rays E x-ray  γ 2 n e r 0 X-ray Generation from Electron Beam Propagation in a Plasma Beam coulomb field repels ambient electrons Electron beam self charge and magnetic force cancel 1 Esarey et. al. PRE 65,056505, 2002 amplitude Joshi, et. al. Phys. Plas., 9:1845, 2002. plasma D. Whittum. Physics of Fluids B, 4:730, 1992 Ion channel r0r0 F=mω p 2 r/ 2 laser plasma

24. Laser-plasma Accelerates & Generates Synchrotron Radiation PIC after 2 mm propagation hω c /2  = 5 x 10 -24 γ 2 n e [cm -3 ] r 0 [μm] keV = 6 x 10 -5 N 0 K photons per 1% BW at hω c /2  ion core 20 μm 100 MeV, n e =10 19 cm -3, r 0 =2 µm Matching of laser duration, spot and plasma wave creates cavity regime keV x-rays with 100 MeV electrons nC charge 10 6 photons/eV 3 keV Faure et. al. Nature 431:541 2004 synchrotron radiation radius of curvature ~mm laser plasma

25. Laser-based Synchrotron Radiation: Experimental Setup 50 cm magnet X-ray camera/phosphor electrons x-rays He laser f=1 m 30fs, 30 TW, 10 Hz laser I=3x10 18 W/cm 2 (30 μm focus) n e ~10 19 cm -3 laser plasma

26. Laser-based Synchrotron Radiation: Experimental Setup laser plasma 10 shot average Non-exponential Plateau near 100 MeV

27. Laser-based Synchrotron Radiation: Experimental Setup laser plasma X-ray beam 20 mrad E X >3 keV Narrow (1-2° beam) 10 9 photons/shot over keV

28. Broad X-ray Spectrum Measured with Crystal and Filters ~200 μm 30 cm x-ray spot after diffraction UPTO ~20% collection (here 1%) Large spectrum from crystal & filters Simple model of transverse force and linear acceleration calculates x-rays from electrons (limited specificity) laser plasma

29. Experiment PIC Electron spectrum X-ray footprint (CCD) 150 MeV X-ray Variation with Density Matches Simulation energy divergence resonance consistent with mechanism simulation (Pukhov group) matches trend other processes (harmonics/ bremsstrahlung too weak) laser plasma

30. fringes mechanistic detail x-rays edge Spatial Coherence Studies X-ray Source & Electron Acceleration Laser-based-synchrotron oscillations around central axis, radiation at cusps no measure of electrons in accelerator Synchrotrons: Transverse beam monitoring coherence effects direct imaging Thomson scattering laser plasma

31. Single Fringe of Edge Diffraction Observed laser x-ray magnet (horizontal & vertical GaAs (100) edges Be filtered x-ray camera electrons 2 m 0.15 m Δx ~100 µm (20 µm pixels) Single shot image; vertically averaged Laser poynting causes peak position to fluctuate Δx ~ (Fresnel) (~λD Fraunhoffer) laser plasma

32. Broad Spectrum Contributes to Diffraction POWER SPECTRUM Power spectrum = source spectrum x Be x CCD camera response Be FRESNEL CALCULATION Large bandwidth washes out higher oscillations Neg. difference between spectral limits laser plasma

33. Use Gaussian radial distribution of oscillation amplitudes; Synchrotron radiation emission integrated to determine linear source profile Sharp curvature – Strong emission weak curvature low emission 100 MeV elec. 25 MeV elec. electron beam 3 keV radiation PIC self injection suggests full range of oscillation amplitudes X-rays Measure Transverse Dimension of Electrons in Plasma laser plasma

34. PIC self injection suggests full range of oscillation amplitudes X-rays measure upper limit of electrons Calculations from simple modeling of radiation indicate >100 MeV electrons dominate Sharp curvature – Hard x-rays weak curvature Soft x-rays electron beam electron profile x-ray profiles energetic electrons weak electrons X-rays Measure Transverse Dimension of Electrons in Plasma laser plasma

35. Bandwidth and pixel size limits resolution Agrees with simulation and simple modeling of radiation 4 µm laser plasma Experimentally < 5 μm Transverse Dimension; Simulation Shows 4 μm

36. Laser Based Synchrotron Radiation Shah et. al. PRE 74, 045401(R) 2006 Rousse, TaPhuoc, Shah et. al. PRL 93:13005, 2004 Plasma electrostatic field causes transverse oscillations and synchrotron radiation Broadband keV spectrum, directional femtosecond Fresnel diffraction gives < 5 μm FWHM x-ray/ electron source diameter (6x smaller than vacuum laser-focus). laser plasma

37. X-ray Generation from Laser Accelerated Electrons Direct relativistic scattering provides VUV-XUV at current intensities; copropagating electrons brighten source Oscillations of electrons in plasma electrostatic field generate synchrotron radiation More stable electron beams will lead to counterpropagating geometry for hard bright x-rays and eventually FELs for coherent, compact sources laser plasma

38. Acknowledgements LOA: Davidé Boschetto, Fréderic Burgy, Jean-Philippe Rousseau Budker Institute of Nuclear Physics: Oleg Shevchenko Nebraska: Donald Umstadter, Sudeep Banerjee Heinrich-Heine Universitat: Alexander Pukhov and Sergei Kiselev Funding National Science Foundation (International Fellowship) Centre Nationale de Recherche Scientifique (CNRS)

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40. laser plasma Relativistic Light Scattering

41. laser plasma Relativistic Light Scattering

42. Far-field Radiation Distribution and Source Size laser plasma Strictly sinusoidal motion would produce ~5 mrad x- ray beam Measured 40 mrad x- ray beam from combination of sinusoidal and helical trajectories.