X-ray Generation in Plasma Using Laser-Accelerated Electrons

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 Bound Atomic Optics Light magnetic field negligable Non-linearities arise from atomic potential - Z+ << a 1 Relativistic Optics Magnetic field causes electron moves in direction of light wave Non-linearities for free electrons Relativistics harmonics, Effective force manipulates plasma 0 transverse a ~1 0 both transverse and longitudinal >> a 1 0 longitudinal a0~E/ω

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

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

5. Bright and Short-Pulse X-rays for Diffraction, Imagery, and Diagnostic 1. Ultrafast studies (femtosecond) ~Å Be shell fuel layer x-ray (normal) phase-contrast x-ray 2. Phase Contrast X-rays of laser-fusion interaction simulation1 1 mm wave e- laser 3. Diagnostic of process (laser-wakefield acceleration) electron energy z trapped e- ~10 µm 1A. Pukhov and J. Meyer-ter-Vehn Appl. Phys. B,74, (2002)

6. Synchrotron RadiationBroad spectrum, narrow beam, 10-100 picoseconds EX-ray γ3/ρ GeV e- m keV hν Relativistic Electrons Provides Desirable X-ray Qualities Absent in Line-emission Sources x-rays solid Laser on solid targets/Kαfemtosecond but low-brightness electrons laser electron electron magnetic field ρ (radius of curvature)

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

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

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

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

12. plasma laser Relativistic Harmonics • Relativistic Intensity results in higher order radiation << a 1 0 transverse a ~1 0 both transverse and longitudinal >> a 1 0 longitudinal fundamental 6th harmonic 11th harmonic 16th harmonic a0=0.01 rest electron normalized intensity θ (deg)

13. plasma laser Relativistic Harmonics • Relativistic Intensity results in higher order radiation • Previously 2nd, 3rd reported << a 1 0 transverse a ~1 0 both transverse and longitudinal >> a 1 0 longitudinal fundamental 6th harmonic 11th harmonic 16th harmonic a0=2 rest electron normalized intensity θ (deg)

14. plasma laser Relativistic Harmonics • Relativistic Intensity results in higher order radiation • Energetic electrons result in forward peaking << a 1 0 transverse a ~1 0 both transverse and longitudinal >> a 1 0 longitudinal fundamental 6th harmonic 11th harmonic 16th harmonic a0=2 1 MeV electron copropagating normalized intensity θ (deg)

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

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

17. plasma laser Even Harmonics Consistent with Relativistic Process He at a~2, linear polarization ≈5x1018 e-/cm-3 source image 12 13th harmonic 11 wavelength Signal vs. Density • Relativistic harmonics • Linear ne scaling, even orders • Atomic harmonics • ne2 scaling, no even orders

18. plasma laser Relativistic Process Occurswith Circular Polarization I = 5x1017 W cm-2 n = 1018 cm-3 Linear Pol. I = 4x1018 W cm-2 n = 1019 cm-3 Circular Pol. • RELATIVISTIC • i. Even orders • ATOMIC • i. Odd orders only

19. plasma laser Relativistic Process Occurswith Circular Polarization I = 5x1017 W cm-2 n = 1018 cm-3 Linear Pol. I = 4x1018 W cm-2 n = 1019 cm-3 Circular Pol. • RELATIVISTIC • Even orders • Lin/Circ polarization • ATOMIC • Odd orders only • Lin pol. only

20. plasma laser 4 μm focal spot Relativistic Process Occurswith Circular Polarization I = 5x1017 W cm-2 n = 1018 cm-3 Linear Pol. I = 4x1018 W cm-2 n = 1019 cm-3 Circular Pol. • RELATIVISTIC • Even orders • Lin/Circ polarization • Generate only at focus • ATOMIC • Odd orders only • Lin. pol. Only • Large volume of generation

21. plasma laser Angular Profile Shows Role of Accelerated Electrons slit image source 12 11 grating detector wavelength • Take into account energetic electrons and divergence of laser and electrons • Using a0~6 (10x more power) • order 100 harmonic radiation observed. Angular profile similarly depended on 1 MeV electrons.

22. plasma laser Relativistic High Harmonics1,2 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 a0~10, and the higher harmonics have even broader angular distribution… Banerjee et. al. POP20:182, 2003 Taphuoc et al. PRL 91: 195001, 2003

23. plasma laser X-ray Generation from Electron Beam Propagation in a Plasma D. Whittum. Physics of Fluids B, 4:730, 1992 Beam coulomb field repels ambient electrons Electron beam self charge and magnetic force cancel plasma F=mωp2r/2 r0 Ion channel Synchrotron radiation1 50 GeV electrons, ne~1014/cm3, 5-30 keV x-rays Ex-rayγ2 ner0 amplitude 1Esarey et. al. PRE 65,056505, 2002 Joshi, et. al.Phys. Plas., 9:1845, 2002.

24. plasma laser Laser-plasma Accelerates & Generates Synchrotron Radiation synchrotron radiation 20 μm ion core radius of curvature ~mm Faure et. al. Nature 431:541 2004 PIC after 2 mm propagation Matching of laser duration, spot and plasma wave creates cavity regime keV x-rays with 100 MeV electrons nC charge 106 photons/eV 3 keV 100 MeV, ne=1019 cm-3,r0=2 µm hωc/2 = 5 x 10-24γ2 ne[cm-3] r0[μm] keV <N> = 6 x 10-5N0K photons per 1% BW at hωc/2

25. plasma laser Laser-based Synchrotron Radiation: Experimental Setup 30fs, 30 TW, 10 Hz laser I=3x1018 W/cm2(30 μm focus) ne~1019 cm-3 X-ray camera/phosphor x-rays magnet electrons He 50 cm laser f=1 m

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

27. plasma laser X-ray beam 20 mrad EX>3 keV Laser-based Synchrotron Radiation: Experimental Setup • Narrow (1-2° beam) • 109 photons/shot over keV

28. plasma laser 30 cm Broad X-ray Spectrum Measuredwith Crystal and Filters x-ray spot after diffraction ~200 μm • 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)

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

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

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

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

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

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

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

36. plasma laser Laser Based Synchrotron Radiation 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). Rousse, TaPhuoc, Shah et. al. PRL 93:13005, 2004 Shah et. al. PRE74, 045401(R) 2006

37. plasma laser 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

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. plasma laser Relativistic Light Scattering

41. plasma laser Relativistic Light Scattering

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