GRK1203 workshop, Oelde, Febr 2008 GRK1203 workshop on laser plasma physics and magnetic plasma confinement Laser Matter Interaction Processes

GRK1203 workshop, Oelde, Febr 2008 GRK1203 workshop on laser plasma physics and magnetic plasma confinement Absorption of sub-10 fs Laser Pulses by Solid Matter - Overview on Different Interaction Processes - Mirela Cerchez Institut für Laser und Plasmaphysik, Heinrich Heine Universität, Düsseldorf

GRK1203 workshop, Oelde, Febr 2008 Outline Motivation - physical processes involved in moderate laser intensity regime - novel interaction regime in ILPP experiment Experimental set-up, data evaluations and significant dependences Absorption mechanisms and their validity in ILPP experiment Conclusions

GRK1203 workshop, Oelde, Febr 2008

GRK1203 workshop, Oelde, Febr

GRK1203 workshop, Oelde, Febr Atoms/molecules “fixed” in solid structure Low temperature T ~ 0.05 eV

GRK1203 workshop, Oelde, Febr Atoms/molecules “fixed” in solid structure Low temperature T ~ 0.05 eV Ions, excited atoms and electrons “independently” moving Temperature of the constituents > 1eV

GRK1203 workshop, Oelde, Febr Solid Laser pulsePlasma

GRK1203 workshop, Oelde, Febr Solid Laser pulsePlasma Physical processes which accompanied the laser energy transfer Laser parameters for an optimum energy transfer (accordingly with research and application needs and/or interests); Conditions for the maximum efficiency of the energy transfer;

GRK1203 workshop, Oelde, Febr 2008 Interaction initial conditions – main influences Laser pulse parameters Matter initial conditions Solid target time I/I 0 Spatial coordinate nene TeTe

GRK1203 workshop, Oelde, Febr 2008 Interaction initial conditions – main influences Laser pulse parameters Matter initial conditions Solid target energy fraction carried by main, pre- or postpulses time scales of the pulse structure wavelength polarization angle of incidence … time I/I 0 Spatial coordinate nene TeTe

GRK1203 workshop, Oelde, Febr 2008 Interaction initial conditions – main influences Laser pulse parameters Matter initial conditions Solid target energy fraction carried by main, pre- or postpulses time scales of the pulse structure wavelength polarization angle of incidence … time I/I 0 Spatial coordinate nene TeTe conductor, semiconductor, insulator (electrical and heat conduction properties); target spatial and temporal parameters ( ρ, n e, T e,i, etc); preexistence of a preformed plasma; …

GRK1203 workshop, Oelde, Febr I [W/cm 2 ] After P. Gibbon and E. Förster, Plasma Phys. Control Fusion 38 (1996) Outgassing Melting Evaporation Large zoo of physical processes involved in the energy transfer

GRK1203 workshop, Oelde, Febr I [W/cm 2 ] After P. Gibbon and E. Förster, Plasma Phys. Control Fusion 38 (1996) Ionization Photoionization Electron impact ionization Multiphoton ionization Above threshold ionization Outgassing Melting Evaporation Large zoo of physical processes involved in the energy transfer

GRK1203 workshop, Oelde, Febr I [W/cm 2 ] After P. Gibbon and E. Förster, Plasma Phys. Control Fusion 38 (1996) Ionization Photoionization Electron impact ionization Multiphoton ionization Collisional absorption Above threshold ionization Outgassing Melting Evaporation Linear optics (Fresnel) Inverse Bremsstrahlung Large zoo of physical processes involved in the energy transfer

GRK1203 workshop, Oelde, Febr I [W/cm 2 ] After P. Gibbon and E. Förster, Plasma Phys. Control Fusion 38 (1996) Ionization Photoionization Electron impact ionization Multiphoton ionization Collisional absorption Above threshold ionization Outgassing Melting Evaporation Linear optics (Fresnel) Inverse Bremsstrahlung Resonance absorption Nonlinear RA regime Collisionless absorption … Anomalous skin effect Vacuum heating Large zoo of physical processes involved in the energy transfer

GRK1203 workshop, Oelde, Febr I [W/cm 2 ] After P. Gibbon and E. Förster, Plasma Phys. Control Fusion 38 (1996) Ionization Photoionization Electron impact ionization Multiphoton ionization Collisional absorption Above threshold ionization Outgassing Melting Evaporation Linear optics (Fresnel) Inverse Bremsstrahlung Resonance absorption Nonlinear RA regime Collisionless absorption … Anomalous skin effect Vacuum heating Large zoo of physical processes involved in the energy transfer

GRK1203 workshop, Oelde, Febr I [W/cm 2 ] After P. Gibbon and E. Förster, Plasma Phys. Control Fusion 38 (1996) Ionization Photoionization Electron impact ionization Multiphoton ionization Collisional absorption Above threshold ionization Outgassing Melting Evaporation Linear optics (Fresnel) Profile steepening Inverse Bremsstrahlung Resonance absorption Nonlinear RA regime Collisionless absorption … Anomalous skin effect Vacuum heating Large zoo of physical processes involved in the energy transfer

GRK1203 workshop, Oelde, Febr 2008 Plasma profile – an important parameter plasma expansion and electron density spatial distribution is controlled by the laser pulse parameters (intensity, duration, amount of energy content in the prepulse(s)) plasma expansion is described by a parameter, plasma scale length: Normalized plasma profile L/ λ, is a scaling parameter for different absorption mechanisms (collisional absorption, resonance absorption, vacuum heating, etc). Bulk target Preformed plasma Solid density Overcritical density Undercritical density x n c, critical density Electron density, n e In most of the previous experimental works, preplasma formation couldn’t be avoided either due to long pulses duration ( τ L >100 fs) or significant amount of energy content in the prepulses (ionizing processes before the main pulse)

GRK1203 workshop, Oelde, Febr 2008 High-contrast laser pulse, sub-10 fs, I laser = (1-5)*10 16 W/cm 2 Solid target Novel interaction regime

GRK1203 workshop, Oelde, Febr 2008 High-contrast laser pulse, sub-10 fs, I laser = (1-5)*10 16 W/cm 2 Solid target Novel interaction regime High contrast laser pulses better than 10 8 on ps time scale

GRK1203 workshop, Oelde, Febr 2008 High-contrast laser pulse, sub-10 fs, I laser = (1-5)*10 16 W/cm 2 Solid target Novel interaction regime High contrast laser pulses better than 10 8 on ps time scale No significant preplasma formation

GRK1203 workshop, Oelde, Febr 2008 High-contrast laser pulse, sub-10 fs, I laser = (1-5)*10 16 W/cm 2 Solid target Novel interaction regime High contrast laser pulses better than 10 8 on ps time scale No significant preplasma formation Ultra short laser pulses

GRK1203 workshop, Oelde, Febr 2008 High-contrast laser pulse, sub-10 fs, I laser = (1-5)*10 16 W/cm 2 Solid target Novel interaction regime High contrast laser pulses better than 10 8 on ps time scale No significant preplasma formation Ultra short laser pulses No hydrodynamic expansion

GRK1203 workshop, Oelde, Febr 2008 High-contrast laser pulse, sub-10 fs, I laser = (1-5)*10 16 W/cm 2 Solid target Novel interaction regime High contrast laser pulses better than 10 8 on ps time scale No significant preplasma formation Ultra short laser pulses No hydrodynamic expansion The laser pulse parameters allowed to study the absorption under conditions where the pulse energy is basically directly transferred to the solid matter during the laser interaction.

GRK1203 workshop, Oelde, Febr 2008 Experimental set-up Oscilloscope Retro-focus diagnostic Ulbricht sphere 800nm /22.5° mirror OA parabola f/3 800nm /45° mirror ~ 100 nm, 8 fs laser pulses Al target Optic bundle photodiode filtered Z

GRK1203 workshop, Oelde, Febr 2008 Experimental set-up Laser pulses: µJ in the target chamber Sub-10 fs pulse duration Diameter focal spot ~3 µm (FWHM) Average intensity : (4 - 5)۰10 16 W/cm 2 p and s – polarization Energy fluctuations less than 5% Target : mirror-flat aluminium layers deposited on planar silicon substrates. Oscilloscope Retro-focus diagnostic Ulbricht sphere 800nm /22.5° mirror OA parabola f/3 800nm /45° mirror ~ 100 nm, 8 fs laser pulses Al target Optic bundle photodiode filtered Z

GRK1203 workshop, Oelde, Febr 2008 Experimental set-up Laser pulses: µJ in the target chamber Sub-10 fs pulse duration Diameter focal spot ~3 µm (FWHM) Average intensity : (4 - 5)۰10 16 W/cm 2 p and s – polarization Energy fluctuations less than 5% Target : mirror-flat aluminium layers deposited on planar silicon substrates. Oscilloscope Retro-focus diagnostic Ulbricht sphere 800nm /22.5° mirror OA parabola f/3 800nm /45° mirror ~ 100 nm, 8 fs laser pulses Al target Optic bundle photodiode filtered Z ~ E reflected A= 1 - R = 1 - E reflected /E incident

GRK1203 workshop, Oelde, Febr 2008 Experimental tasks Laser pulses energy absorption and its significant dependences laser polarization angular dependence laser intensity dependence angle of the optimum laser absorption absorption dependence on the plasma profile,

GRK1203 workshop, Oelde, Febr 2008 Experimental results Experimental investigations of the angular dependence of the laser energy absorption for both p- and s- polarization; over wide range of incidence angles.

GRK1203 workshop, Oelde, Febr 2008 Experimental results Experimental investigations of the angular dependence of the laser energy absorption for both p- and s- polarization; over wide range of incidence angles. large preponderance of p- absorption on s- absorption maximum absorption value : ~ 77% at 80° angle of the maximum absorption: ≥ 80°

GRK1203 workshop, Oelde, Febr 2008 Experimental results Experimental investigations of the laser energy absorption as a function of laser intensity for both p- and s- polarization; over 4 orders of magnitude of the laser intensity (5x10 12 W/cm 2 – 5x10 16 W/cm 2 ).

GRK1203 workshop, Oelde, Febr 2008 Experimental results Experimental investigations of the laser energy absorption as a function of laser intensity for both p- and s- polarization over 4 orders of magnitude of the laser intensity (5x10 12 W/cm 2 – 5x10 16 W/cm 2 )

GRK1203 workshop, Oelde, Febr 2008 Experimental results Experimental investigations of the laser energy absorption as a function of laser intensity for both p- and s- polarization over 4 orders of magnitude of the laser intensity (5x10 12 W/cm 2 – 5x10 16 W/cm 2 )

GRK1203 workshop, Oelde, Febr 2008 Simulation results and remarks The computation and experimental results at average intensity of 2۰10 16 W/cm 2 are in well agreement for steeper profiles in the range of L ~ 10 nm. The computational results of PIC Plasma Simulation Code (PSC, *) are in very good agreement with the experiment assuming a profile of L/λ ~ 1%; The simulations confirm the absorption of p-polarization up to 80° and indicate that the interaction of the ultrashort laser pulses with the target takes place close to the solid density state of matter; The simulations results indicates that the extra-absorption of p-pol on s-pol involved an absorption mechanism of collisionless nature. (*) H. Ruhl, in Introduction to Computational Methods in Many Particle Body Physics (Rinton Press, Paramus, New Jersey, 2006)

GRK1203 workshop, Oelde, Febr 2008 Absorption mechanisms of ultrashort laser pulses in overdense plasmas … available for moderated laser intensities ~ I = W/cm 2 Collisional absorption: electrons gain their energy from the laser while colliding another particle (inverse bremsstrahlung):  applying the Fresnel equations for a step profile, L → 0  solving the wave equation (Helmholtz) for a certain plasma profile, L Collisionaless absorption: Resonance absorption (linear and non-linear regime) Vacuum heating (Brunel effect) Anomalous skin effect Sheath inverse bremsstrahlung

GRK1203 workshop, Oelde, Febr 2008 Collisional regime – Linear optics Low intensity, step target profile (mirror flat surface) Fresnel formulae determine the reflected and transmitted fraction of the incident radiation; Account for the conductivity proprieties of the metals at room temperature and depending on the radiation wavelength and polarization; describe the metallic surface by a complex index n=η+i*k L → 0

GRK1203 workshop, Oelde, Febr 2008 Collisional regime Inverse bremsstrahlung – Helmholtz solution The laser radiation is interacting with an inhomogeneous plasma characterized by a profile, L; electrons gain their energy from the laser while colliding another particle (inverse bremsstrahlung); The absorpted fraction is calculated accounting for the plasma response (in terms of permittivity ε) solving the wave equation: Therefore, absorption process depend on:  plasma frequency ω pe (x) → plasma profile L(x),  electron-ion collision frequency ν e-i (ex: approximation for hot plasmas, Spitzer formula) n c, critical density Bulk target Solid density x Electron density, n e A = f (I L, T e, L)

GRK1203 workshop, Oelde, Febr 2008 In Price et al. (PRL, 75, (1995)) have been reported important experimental results of absorption process in collisional regime: Experimental conditions normal incidence and λ = 800 nm;  short pulse (120 fs) and high contrast (10 7 )  over a large intensity range (I = W/cm 2 ). Main results  in the range I = W/cm 2 are dominant material proprieties (heat conduction and conductivity);  above I = W/cm 2, all materials present similar reflectivity and temperature dependence → universal plasma mirror “Universal plasma mirror” Some important previous experimental works…

GRK1203 workshop, Oelde, Febr 2008 For laser intensities larger than W/cm 2, the quiver energy of the electrons in the laser field becomes comparable with their thermal energy. One can discuss about an effective electron velocity: Accordingly, the effective collision frequency is reduced and introduces a dependence on the laser intensity of the absorption coefficient: Collisional regime in ILPP experiment

GRK1203 workshop, Oelde, Febr 2008 Collisional regime in ILPP experiment Within the assumption that the calculations results are in agreement with the s-polarization amount of absorption, they are not able to explain the large absorption detected in p-polarization case.

GRK1203 workshop, Oelde, Febr 2008 Resonance absorption :  the most efficient collisionless absorption process;  in the limit of the linear theory (available for long plasma profile):  the p-polarized laser field drives resonantly a plasma wave at the critical density (n e =n c → ω L = ω p );  the process is considered efficient in profiles of L/ λ > 0.08;  one recovers ~ 50% laser energy absorption at an optimum absorption angle which scales as θ opt ~ sin -1 [0.8(2 πL/λ ) -1/3 ]; Collisionless absorption regime Pictures from Plasma Physics Lectures, O. Willi

GRK1203 workshop, Oelde, Febr 2008 Resonance absorption :  the most efficient collisionless absorption process;  in the limit of the linear theory (available for long plasma profile):  the p-polarized laser field drives resonantly a plasma wave at the critical density (n e =n c → ω L = ω p );  the process is considered efficient in profiles of L/ λ > 0.08;  one recovers ~ 50% laser energy absorption at an optimum absorption angle which scales as θ opt ~ sin -1 [0.8(2 πL/λ ) -1/3 ]; Collisionless absorption regime n c cos 2 θ ncnc n e (x) From P. Gibbon et al., PRL, 68, (1992) Average electric field component normal onto the target, L/ λ=2, θ = 20°, n e /n c =2 Electron space phase, L/ λ=2, θ = 23°, n e /n c =2

GRK1203 workshop, Oelde, Febr 2008 Resonance absorption hypothesis and ILPP experiment (*) J. Osterholz et al., Phys. Rev Lett. 96, (2006) (**) R. Jung et al. submitted for publication For the present experiment, simulation results and independent previous investigations (*,**) indicates that an overdense preplasma is formed with a profile of few nm (~ nm); The absorption process in overdense plasmas (where ω p >>ω L ) with steep profile (case of present experiment) cannot be explained by the linear theory of the resonance absorption

GRK1203 workshop, Oelde, Febr 2008 Collisionless absorption regime Vacuum heating  originally proposed by Brunel and later on developed theoretical (Gibbon and Bell,1992; Andreev 1994) and experimentally reported by different groups (Grimes et al,1999; Dong et al, 2001, etc );  Considered to be effective when the electron oscillation amplitude x osc =v osc /ω L is larger than plasma profile, L;  In a simple physical scenario, thermal electrons are dragged out into the vacuum by the component of the normal electric field and part of them are accelerated back to the target within one cycle of the laser oscillation ; Electron orbits in the space-time coordinate. Laser-induced longitudinal Ex a) and the electron phase space b) Simulation results from Q.L. Dong et al., PRA, 64, (2001)

GRK1203 workshop, Oelde, Febr 2008 Vacuum heating hypothesis and ILPP experiment Vacuum heating  Previous simulations and experimental investigations identified a number of particular characteristics of this effect in our intensity range ( I L ~ W/cm 2, L/λ = 0.01 ):  the angular absorption tends to peak near θ opt = 45°;  maximum absorption fraction ~ 10%;  the absorption fraction scales with the laser irradiance as A VH ~ (I L* λ 2 ) 0.5 ; Simulation results from P. Gibbon and A.R. Bell, Phys. Rev. Lett.,68, 1535 (1992)

GRK1203 workshop, Oelde, Febr 2008 Vacuum heating hypothesis and ILPP experiment Vacuum heating  From our experimental conditions and observations ( x osc ~ 10 nm ):  optimum absorption angle θ opt > 80°;  maximum absorption fraction is ~ 80%;  A collisionless ~ (I L* λ 2 ) 0.10+/-0.05 Simulation results from P. Gibbon and A.R. Bell, Phys. Rev. Lett.,68, 1535 (1992)

GRK1203 workshop, Oelde, Febr 2008 Collisionless absorption regime Anharmonic resonance absorption (ARA) [P. Mulser et al. ”Anharmonic resonance absorption of the high-power laser beams”, submitted for publication in PRL (*)]  The anharmonic resonance absorption aims to describe the collisionless absorption process of high intensity laser pulses by overdense plasmas characterized by a plasma frequency ω p much larger the driving laser frequency, ω L. The absorption mechanism is effective when the laser intensity is high enough to induce nonlinear effects onto the plasma oscillations  The absorbing region is divided into a high number of layers of thickness d. Each of them represents an oscillator in which the electrons oscillate against the attracting immobile ion background;  For low excitation (linear domain, small amplitude of displacement ξ), the eigenfrequency of the oscillator ω 0 = ω p corresponding to the solid electron density;  In the nonlinear domain of excitation the eigenfrequency of the oscillator decreases according to:  Anharmonic resonance occurs when ω 0a equals the laser frequency ω L ; k y Ey α Overdense target ξ d electrons ions

GRK1203 workshop, Oelde, Febr 2008 Collisionless absorption regime Anharmonic resonance absorption (ARA) [P. Mulser et al. ”Anharmonic resonance absorption of the high-power laser beams”, submitted for publication in PRL (*)]  We come to the finding that the model of anharmonic resonance absorption is a favorable candidate with which is possible to explain the experimental observation:  address resonant collisionaless mechanism in overdense targets  the model predicts a threshold of the absorption onset  PIC simulations indicates electron trajectories identical with those presented in (*). k y Ey α Overdense target ξ d electrons ions

GRK1203 workshop, Oelde, Febr 2008 Physical processes and important parameters in laser plasma interaction in moderate intensity regime; Experimental investigations of the novel regime of ultra short laser pulses with overdense plasmas. The computational results are in very good agreement with the experiment assuming a profile of L/λ ~ 1%; Collisional and collisionaless processes and the validity/contribution on the IPLL experiment; In non-linear regime of RA, the new model of anharmonic resonance absorption aim to explain aims to describe the collisionless absorption process of high intensity laser pulses Conclusions

GRK1203 workshop, Oelde, Febr 2008 Thank you !