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J. Meyer-ter-Vehn, Max-Planck-Institute for Quantum Optics, Garching, Germany April 16 – 21, 2007

International Max Planck Research School on Advanced Photonics Lectures on Relativistic Laser Plasma Interaction. J. Meyer-ter-Vehn, Max-Planck-Institute for Quantum Optics, Garching, Germany April 16 – 21, 2007. Lecture: Overview, Electron in strong laser field,

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J. Meyer-ter-Vehn, Max-Planck-Institute for Quantum Optics, Garching, Germany April 16 – 21, 2007

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  1. International Max Planck Research School on Advanced Photonics Lectures onRelativistic Laser Plasma Interaction J. Meyer-ter-Vehn, Max-Planck-Institute for Quantum Optics, Garching, Germany April 16 – 21, 2007 • Lecture: Overview, Electron in strong laser field, • Lecture: Basic plasma equations, self-focusing, direct laser acceleration • Lecture: Laser Wake Field Acceleration (LWFA) • 4. Lecture: Bubble acceleration • Lecture: High harmonics and attosecond pulses from • relativistic mirrors

  2. I (W/cm2) 1025 non-relativistic: a < 1 GeV protons laser GeV electrons electron 1020 1018 a = 1 CPA a > 1 relativistic: 1015 1960 2015 1985 2000 beam generation Relativistic Laser Electron Interaction and Particle Acceleration J. Meyer-ter-Vehn, MPQ Garching a = eA/mc2

  3. electronspectrum Relativistic plasma channels and electron beams at MPQ C. Gahn et al. Phys. Rev. Lett. 83, 4772 (1999) gas jet laser 6×1019W/cm2 plasma 1- 4 × 1020 cm-3 observed channel

  4. Laser-induced nuclear and particle physics 107 positrons/shot

  5. Neutrons From Deuterium Targets

  6. Graphik IOQ Jena 2004 Ewald Schwörer

  7. Experiments: Multi-10 MeV ion beams from thin foils observed Simulations: 1 kJ , 15 fs laser pulse focussed on 10 mm spot of 1022/cm3 plasma Relativistic protons: 5 GeV at 1023 W/cm2 D. Habs, G. Pretzler, A. Pukhov, J. Meyer-ter-Vehn, Prog. Part. Nucl. Physics 46, 375 (2001)

  8. few mg DT imploded core few mm 100 mm IPP Summer University, Garching 2006 Inertial Confinement Fusion (ICF)J. Meyer-ter-VehnMax-Planck-Institute for Quantum Optics, Garching

  9. 15 ps 5 ps 1000 g/cc DT seed (0.1 mg T) 20 mg D2 beam heated region 25 ps 35 ps bulk fuel 45 ps 55 ps yield 1.3 GJ D2 burn produces more tritium than in seed: breeding ratio: 1.37 5 kJ Simulation D2 burn fast-ignited from DT seed Atzeni, Ciampi, Nucl. Fus. 37, 1665 (1997)

  10. Nature Physics 2, 456 (2006) L=3.3 cm, f=312 mm Laser 1 GeV electrons Divergence(rms): 2.0 mrad Energy spread (rms): 2.5% Charge: > 30.0 pC Plasma filled capillary Density: 4x1018/cm3 1.5 J, 38 TW, 40 fs, a = 1.5

  11. Design considerations for table-top, laser-based VUV and X-ray free electron lasers F. Grüner, S. Becker, U. Schramm, T. Eichner, M. Fuchs, R. Weingartner, D. Habs, J. Meyer-ter-Vehn, M. Geissler, M. Ferrario, L. Serafini, B. van der Geer, H. Backe, W. Lauth, S. Reiche http://arxiv.org/abs/physics/0612125 (Dec 2006) See also from DESY: Arxiv:physics/0612077 (8 Dec 2006)

  12. w-5/2 Observation of high harmonics from plasma surfaces acting as relativistic mirrors B. Dromey, M. Zepf et al., Nature Physics 2, 698 (2006)

  13. circ. pol. (CP): lin. pol. (LP): for lin. (circ.) polarization Plane Laser Wave

  14. (non-relativistic v/c << 1) Average intensity: Power unit: Relativistic Intensity Threshold

  15. 1. Problem: Normalized light amplitude a0 = eA0/mc2 Show that the time averaged light intensity I0is related to the normalized light amplitude a0 by where l is the wavelength,z equals 1 (2) for linear (circular) polarization, and P0 is the natural power unit Confirm that the laser fields are Use that, in cgs units, the elementary charge is e = 4.8 1010 statC and 1 gauss = 1 statC/cm2.

  16. electrodynamics mechanics Lorentz: t´= g (t - vx/c2) x´= g ( x - vt ) g = (1- v2/c2) -1/2 Galilei: t´= t x´= x - vt   Relativistic Lagrange function: dA = dLdt = 0 L = - mc2 (1- v2/c2)1/2 - qF + (q/c) v•A L = gL = -mc2 - (q/c) pmAm Special relativity Einstein (1905): Also laws of mechanics have to follow Lorentz invariance

  17. 2. Problem: Relativistic equation of motion The Lagrange function of a relativistic electron is (c velocity of light, e and m electron charge and rest mass, f and A electric and magnetic potential) Use Euler-Lagrange equation to derive equation of motion with electric field , magnetic field , and electron momentum

  18. Symmetries and Invariants for planar propagating wave Relativistic Electron Lagrangian For electron initially at rest: (relativistically exact !)

  19. Relativistic side calculation

  20. Relativistic electrons from laser focus observedC,L.Moore, J.P.Knauer, D.D.Meyerhofer, Phys. Rev. Lett. 74, 2439 (1995) (follows from L(x-ct) symmetry) • >>1 electrons emerge in laser direction

  21. Relativistic equations of motion

  22. x Figure-8 motion in drifting frame (w=kc) Relativistic electron trajectories: linear polarization

  23. Relativistic electron trajectories: circular polarization x

  24. 3. Problem: Derive envelope equation Consider circularly polarized light beam Confirm that the squared amplitude depends only on the slowly varying envelope function a0(r,z,t), but not on the rapidly oscillating phase function Derive under these conditions the envelope equation for propagation in vacuum (use comoving coordinatez=z-ct, neglect second derivatives):

  25. 4. Problem: Verify Gaussian focus solution Show that the Gaussian envelope ansatz inserted into the envelope equation leads to Where is the Rayleigh length giving the length of the focal region.

  26. New physics described in these lectures At relativistic intensities, Il2 > 1018 W/cm2 mm2, laser light accelerates electrons to velocity of light in laser direction and generates very bright, collimated beams. The laser light converts cold target matter (gas jets, solid foils) almost instantaneously into plasma and drives huge currents. The relativistic interaction leads to selffocused magnetized plasma channels and direct laser acceleration of electrons (DLA). In underdense plasma, the laser pulse excites wakefields with huge electric fields in which electrons are accelerated (LWFA). For ultra-short pulses (<50 fs), wakefields occur as single bubbles which self-trap electrons and generate ultra-bright mono-energetic MeV-to-GeV electron beams. At overdense plasma surfaces, the electron fluid acts as a relativistic mirror, generating high laser harmonics in the reflected light. This opens a new route to intense attosecond light pulses.

  27. ICF target implosion

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