1 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, Lecture: Overview, Electron in strong laser field, 2.Lecture: Basic plasma equations, self-focusing, direct laser acceleration 3.Lecture: Laser Wake Field Acceleration (LWFA) 4. Lecture: Bubble acceleration 5.Lecture: High harmonics and attosecond pulses from relativistic mirrors

2 Relativistic Laser Electron Interaction and Particle Acceleration J. Meyer-ter-Vehn, MPQ Garching a = eA/mc I (W/cm 2 ) 2015 GeV electrons GeV protons CPA a = 1 non-relativistic: a < 1 laser electron a > 1 relativistic: beam generation

3 Relativistic plasma channels and electron beams at MPQ C. Gahn et al. Phys. Rev. Lett. 83, 4772 (1999) gas jet laser 6×10 19 W/cm 2 observed channel electron spectrum plasma 1- 4 × cm -3

4 Laser-induced nuclear and particle physics 10 7 positrons/shot

5 Neutrons From Deuterium Targets

6 Graphik IOQ Jena 2004 Ewald Schwörer

7 Relativistic protons: 5 GeV at W/cm 2 D. Habs, G. Pretzler, A. Pukhov, J. Meyer-ter-Vehn, Prog. Part. Nucl. Physics 46, 375 (2001) Experiments: Multi-10 MeV ion beams from thin foils observed 1 kJ, 15 fs laser pulse focussed on 10  m spot of /cm 3 plasma Simulations:

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

9 D 2 burn fast-ignited from DT seed Atzeni, Ciampi, Nucl. Fus. 37, 1665 (1997) bulk fuel DT seed (0.1 mg T) beam heated region 20 mg D 2 15 ps 25 ps 55 ps 35 ps 5 ps 45 ps 1000 g/cc 5 kJ yield 1.3 GJ D 2 burn produces more tritium than in seed: breeding ratio: 1.37 Simulation

10 Nature Physics 2, 456 (2006) L=3.3 cm,  =312  m Laser 1.5 J, 38 TW, 40 fs, a = 1.5 Plasma filled capillary Density: 4x10 18 /cm 3 Divergence(rms): 2.0 mrad Energy spread (rms): 2.5% Charge: > 30.0 pC 1 GeV electrons

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,F. GrünerS. BeckerU. SchrammT. EichnerM. FuchsR. Weingartner D. HabsD. Habs, J. Meyer-ter-Vehn, M. Geissler, M. Ferrario, L. Serafini,J. Meyer-ter-VehnM. GeisslerM. FerrarioL. Serafini B. van der GeerB. van der Geer, H. Backe, W. Lauth, S. ReicheH. BackeW. LauthS. Reiche (Dec 2006) See also from DESY: Arxiv:physics/ (8 Dec 2006)

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

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

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

15 1. Problem: Normalized light amplitude a 0 = eA 0 /mc 2 Show that the time averaged light intensity I 0 is related to the normalized light amplitude a 0 by where l is the wavelength,  equals 1 (2) for linear (circular) polarization, and P 0 is the natural power unit Confirm that the laser fields are Use that, in cgs units, the elementary charge is e = statC and 1 gauss = 1 statC/cm 2.

16 Special relativity Relativistic Lagrange function: L = - mc 2  v 2 /c 2 ) 1/2 - q  + (q/c) vA Galilei: t´= t x´= x - vt Lorentz: t´=  (t - vx/c 2 ) x´=  x - vt )   v 2 /c 2 ) -1/2 mechanics electrodynamics Einstein (1905): Also laws of mechanics have to follow Lorentz invariance  A =  L d    L =  L = -mc 2 - (q/c) p  A 

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 observed C,L.Moore, J.P.Knauer, D.D.Meyerhofer, Phys. Rev. Lett. 74, 2439 (1995)  >>1 electrons emerge in laser direction (follows from L(x-ct) symmetry)

21 Relativistic equations of motion

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

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 a 0 (r,z,t), but not on the rapidly oscillating phase function Derive under these conditions the envelope equation for propagation in vacuum (use comoving coordinate   =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, I 2 > W/cm 2  m 2, 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