Investigation of Parametric Instabilities in Femtosecond Laser-Produced Plasmas Dissertation zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) vorgelegt dem Rat der Physikalisch-Astronomischen Fakulta¨t der Friedrich–Schiller–Universita¨t Jena von Diplom-Physiker L´aszl´o Veisz geboren am 20. Ma¨rz 1974 in Budapest, Ungarn Gutachter 1. Prof. Dr. Roland Sauerbrey 2. Prof. Dr. Peter Mulser 3. Prof. Dr. Georg Pretzler Tag der letzten Rigorosumspru¨fung : 1.8.2003 Tag der o¨ffentlichen Verteidigung : 28.8.2003 Contents 1 Introduction 1 2 Theoretical background 4 2.1 Plasma characterization and description................................................................4 2.1.1 The phase space distribution ......................................................................5 2.1.2 The two-fluid description of the plasma ....................................................7 2.2 Waves in plasmas ...................................................................................................8 2.2.1 Electron plasma waves ..................................................................................... 9 2.2.2 Ion-acoustic waves .................................................................................................. 9 2.2.3 Electromagnetic waves ......................................................................................... 10 2.3 Effects in laser plasma physics ................................................................................. 13 2.3.1 Effects of ionization ...................................................................................... 13 2.3.2 Ponderomotive force ..................................................................................... 15 2.3.3 Absorption of laser light in plasmas ........................................................16 2.3.4 Damping of plasma waves .................................................................................. 19 3 Parametric instabilities and 3 ω0/2 generation 21 3.1 General considerations .........................................................................................21 3.2 Two-plasmon decay .................................................................................................. 26 3.3 Stimulated Raman scattering ...............................................................................32 3.4 Other parametric instabilities ...............................................................................34 3.5 3 ω0/2 generation ..................................................................................................... 36 3.6 Application to experiments ..................................................................................37 i CONTENTS ii 4 Validation of the linear theory 43 4.1 Experimental setup ...............................................................................................44 4.2 Results ....................................................................................................................... 46 4.3 Discussion ................................................................................................................. 49 5 Angular distribution measurements 55 5.1 Experimental setup ...............................................................................................56 5.2 3 ω0/2 signal dependence on the scale length ....................................................... 57 5.3 3 ω0/2 angular distribution .................................................................................... 60 5.3.1 Experimental results .................................................................................60 5.3.2 Angular distribution as a function of the intensity ................................. 62 5.3.3 Angular distribution for various scale lengths ........................................63 5.4 Discussion of the angular distribution ................................................................. 64 5.5 Spectral measurements .........................................................................................71 5.5.1 Experimental results .................................................................................71 5.5.2 Discussion ..................................................................................................... 73 6 Polarization and growth rate of 3 ω0/2 78 6.1 Setup and plasma reflectivity ...............................................................................79 6.2 Intensity dependence of the three-halves harmonic radiation ............................80 6.3 Autocorrelation measurements on 3 ω0/2 ............................................................. 84 7 Summary 91 Bibliography 93 Chapter 1 Introduction Ultrahigh-intensity lasers are fundamental tools in modern physics. Their fast evolution over the last 15 years [1] started with the invention of chirped pulse amplification (CPA) [2]. This technique opened a new window to the investigation of light-matter interactions. The CPA technique made it possible to generate much shorter laser pulses down to the femtosecond regime with laser peak powers reaching the 1–1000 terawatt level. Nowadays the most of the ultrahigh intensity lasers in the world are applying this method. One of these lasers is the Jena 12 TW laser [3]. These lasers can be focussed down to a few micrometers and enormous intensities up to 1021 W/cm2 can be reached. At these intensities the electric field exceeds many times the binding energy of electrons in an atom. After a plasma is formed, the electrons oscillate at relativistic velocities in these fields [4]. The interaction of ultrahigh-intensity laser pulses with plasmas became a central point of the investigations [5]. There is a great variety of applications of these plasmas from particle acceleration, generation of electromagnetic waves to inertial confinement fusion. There is a large body of work about laser-plasma based electron acceleration [6]. It was suggested originally in underdense plasmas by Tajima and Dawson [7]. One type of these accelerators, the laser wakefield accelerator, is based on the generation of electron plasma waves and the electrostatic fields of these waves accelerates the electrons [7]. The other type is the direct laser acceleration, which is similar to inverse free electron laser. The electrons are transversally oscillating in the self-generated electric and magnetic fields of a plasma channel generated by the self-focused laser pulse. When this betatron oscillation frequency coincides with the Doppler shifted laser frequency, a resonant energy transfer occurs and the electrons gain energy from the laser [8]. The advantage of these accelerators is the small size due to the large static electric fields in plasmas (about 100 GV/m) compared to the rf accelerator fields (less than 100 MV/m). The highest 1 2 electron energy observed from plasma electron accelerator is 200 MeV [9]. Hot electrons produced by lasers in dense plasmas on solid targets are also investigated in detail [5, 10]. The plasma waves generated by resonance absorption or the ponderomotive force of the laser can increase the electron energy. The electron acceleration mechanisms are studied in detail, because most of the appli- cations involve these fast electrons. For example as the fast electrons leave the plasma, large longitudinal static electric fields are generated due to charge separation. Ions can be accelerated in laser produced plasmas by these fields [11, 12, 13]. Another challenging field is the generation of electromagnetic emission in plasmas such as high order harmon- ics [5, 14] for example from steep plasma surface, EUV radiation from atomic transitions [15, 16] or incoherent x-ray generation [17, 18]. The fast electrons generate bremsstrahlung in material and this can trigger nuclear reactions for example (γ,n) reactions [10, 19] and photo-fission of actinides [20]. An important topic of laser produced plasmas involves inertial confinenement fusion (ICF) [21]. A small capsule including the fuel is irradiated with a short laser, x-ray or ion beam pulse, which ablates the outer layer of the capsule and implodes the inner part generating shock waves. The compression of the target ignites the fuel. A fast ignitor concept was suggested to reduce the energy requirements of ICF [22, 23]. The precompressed fuel is ignited by an additional high power laser. Some new alternative concepts were also proposed such as coronal ignition [24]. Parametric instabilities have an important impact on ICF, laser absorption, hot elec- tron generation and propagation of light in plasmas, therefore, they were investigated in detail [25, 26] in the long pulse regime (> 100 ps). Relevant instabilities involving the decay of the incident laser radiation, are stimulated Raman and Brillouin scattering (SRS and SBS) and two-plasmon decay (TPD). SRS (SBS) in plasmas is the decay of the laser electromagnetic wave into an electron plasma wave (ion acoustic wave) and another elec- tromagnetic wave. TPD is the decay of an electromagnetic wave into two electron plasma waves and takes place in the vicinity of the quarter critical density. These plasma waves can couple with the incident laser light to generate 3 ω0/2 radiation, which was studied experimentally [27, 28, 29] and theoretically [30]–[31]. After the introduction of CPA the laser based fusion and especially the fast ignitor con- cept led to a reinvestigation of some of the instabilities at higher intensities and shorter pulses [32, 33]. Particular attention was paid to SRS of ultrashort laser