Vacuum heating of solid target irradiated by femtosecond laser pulses

Transcription

1 Vol. 46 No. SCIENCE IN CHINA (Series G) February 2003 Vacuum heating of solid target irradiated by femtosecond laser pulses DONG Quanli ( ) &ZHANGJie( ) Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 00080, China Received April, 2, 2002 Abstract The interaction of femtosecond laser pulses with solid targets was studied through experiments and particle-in-cell (PIC) simulations. It is proved that the vacuum heating and the inverse bremsstralung process are the main mechanisms of the laser pulse absorption under such conditions. The distribution of hot electrons and that of X-ray are found to have double-temperature structure, which is confirmed by PIC simulations. While the lower temperature is attributed to the resonant absorption, the higher one, however, is caused by the laser-induced electric field in the target normal direction. The time-integrated spectra of the reflected laser pulse shows that the mechanism of electron acceleration is determined by the plasma density profile. Keywords: vacuum heating, electron acceleration, harmonics. The availability of the ultra-short laser pulse with relativistic intensity [] stimulated the study of the laser-plasma interaction. It is well known that the interaction between laser pulses and plasmas depends greatly on the plasma density scale length. In experiments with long laser pulses, the plasma density scale length evolves during the interaction, making it too complex to diagnose the interaction process. In the femtosecond or sub-picosecond laser pulse experiment, however, the plasma expands so little that the fs laser pulse interacts with solid density plasmas. Similarly, by introducing an appropriate pre-pulse, a plasma with well-determined conditions can be created. The interaction between fs laser pulses and such plasmas provides a good test bed to study the interaction of ultra-intense, ultra-short laser pulses with plasmas. In this paper, we report our experimental investigations of the fs laser pulse interaction with solid density plasmas, which are confirmed by PIC simulations. In our experiments, we monitored the expansion of the plasma by using the interferometry technique [2]. The average laser pulse intensity ranged from to where λ 0 is the wavelength of the laser pulse in the vacuum W/cm. The plasma density scale length L < 0. λ0, Femtosecond laser pulse absorption at the surface of the solid target Nowadays, most of the published experimental research works on the interaction of fs laser pulses with solid targets are limited to the laser normal incidence. The normal skin effect (NSE), the abnormal skin effect (ASE) [3] and the sheath inverse bremsstralung (SIB) [4] absorption are considered to play an important role in the interaction under such conditions. The interaction process is different when a p-polarized laser pulse is incident obliquely on the target such that the

2 72 SCIENCE IN CHINA (Series G) Vol electric field can pull electrons out of the steep plasmas. If L r 0 = ee /mω, the oscillating electron driven by the laser electric field will bring away and convert the energy of the laser pulse to the kinetic energy of the plasma when they penetrate into the over-dense plasma. Such an absorption process was first described by Brunel as the vacuum heating (VH) [5], and later analyzed by Gibbon [6] and Kato [7]. However, there are no systematic experimental studies on VH yet [8].We demonstrate experimentally that VH is one of the main heating mechanisms of the plasma, as is confirmed by PIC simulations. Experiments were conducted on the Ti:sapphire lasers at Laboratory of Optical Physics, Institute of Physics, CAS. This laser system operates at around 800 nm at a repetition rate of 0 Hz delivering 5mJ energy in 50 fs with a peak-to-pedestal contrast ratio of 0 5 at ps. According to the adiabatic model of the plasma expansion, the temperature is estimated to be about 30 ev [9]. The laser absorption ratio can be determined from the measured scattered and reflected laser pulse. Fig. gives the determined absorption (hollow-circle-line) in experiments, which shows that the absorption increases as the laser intensity increases. As a comparison, we also plotted the measured absorption by the inverse bremsstralung process in the plasma (solid line) given by Price [0]. The great discrepancy between the two groups of data is not surprising. It is obvious that there is some other absorption mechanism in our experiments. In order to investigate the physical mechanism during the interaction, we did some PIC simulations using the electron scale length measured by the technique of the frequency domain interferometry and the temperature deduced above. The absorption curve of the simulation is shown as the solid-square-line in the figure. The PIC simulations also show that, at lower temperature, the laser absorption ratio is determined by the density scale length of the plasma, and that at lower laser intensity, the absorption ratio is more sensitive to the density scale length than that at higher laser intensity. We note that our PIC code does not include the collision effect between particles. As shown by the electron distribution in the phase space, the main absorption mechanism in the PIC simulation is the vacuum heating. Fig.. Absorption ratio versus laser intensities., Our experimental value: hollow-circle line; 2, the sum of VH and IB; 3, the VH absorption; 4, the IB absorption [0]. In PIC simulations, the L are applied: L= λ 0 when I<0 4 W/cm 2 ; L=0.04 B0.0λ 0 for I between 0 4 and 0 5 W/cm 2 ; L=0.07B0.0λ 0 when I >0 5 W/cm 2. After we added the experimental data of the IB absorption to the values from the PIC simulations and compared the sum (solid-circle-line) with our experimental results, we found a good agreement. This im-

3 No. VACUUM HEATING OF SOLID TARGET IRRADIATED BY FEMTOSECOND LASER PULSES 73 plies that the vacuum heating does exist in the experiments under our conditions. We noticed the discrepancy at the low and high intensity end. The reasons are different and can be explained as follows. At lower intensities, the laser intensity is just over the ionization threshold. The ionization process and the intra-atomic absorption play an important role in the interaction []. The behavior of such plasma cannot be simulated with the PIC method. At higher intensities, an over-dense plasma is formed. However, because the plasma surface is disturbed by the laser electric component dragging electrons out of and pushing them back into the plasma, it cannot be regarded as a plasma mirror as in the experiments conducted by Price. Given that the IB absorption is increased due to the plasma surface disturbance, we believe that the sum of absorption due to VH and IB will show a better agreement with our experiments at higher intensity. 2 Electron acceleration in VH process We also measured the energy spectrum of electrons ejected out from the front of the target and that of X-rays behind the target [2]. The X-ray behind the target is emitted from the energetic electrons through the inverse bremsstralung process when being decelerated by the solid target. Simple theoretical analysis [3] and experiments with mono-energy electrons proved that the X-ray emission is correlated to the energy of the electrons by jsol( E, hν ) ( E hν ),wheree and hν are the energy of electron and X-ray photo, respectively. So, the spectrum of the measured X-ray emission behind the target shows the distribution of the high energetic electrons penetrating into the remaining solid target [3 5]. Both of the spectrum of the measured X-ray in our experiments and that of the high energetic electron penetrating into the target in the PIC simulation show a double-temperature structure [4]. The lower one of the two temperatures is about several kev and can be attributed to the resonant absorption. The other temperature, however, can reach about 40 kev. This temperature cannot be simply attributed to the laser drive. The linear absorption mechanisms such as the resonance absorption cannot produce so high energetic electrons at the intensity we used. The parameter instabilities, which can accelerate electrons to high energy in plasmas with smoother density profiles, cannot take place under our experimental conditions. From the electron phase space, we found that these energetic electrons are produced by the combination of the laser electric field and the laser-induced electric field in the normal direction of the target. The PIC simulation results show that a group of electrons are pulled out of the plasma target every laser cycle. Fig. 2(a) gives the trajectories of electrons in the time-space coordinate. Some of these electrons can be sent back to the plasma at the same laser cycle, and others can stay out of the target for a long time, forming a cloud of electrons. The electron cloud and the ions in the plasma target form a static electric field before the target. At the target surface, an oscillating electric field formed due to the periodic action of the laser electric field pulling the electrons out of and sending them back into the target. The laser-induced electric field is shown in fig. 2(b). We also recorded the electron density before the target and the laser absorption versus time. It is found that when a group of electrons are sent back to the target, there is one absorption peak accordingly.

4 74 SCIENCE IN CHINA (Series G) Vol. 46 This is the characteristic of the vacuum heating described by Brunel. Fig. 2. Electron trajectories from the PIC simulation (a) and the laser induced longitudinal electric field (b). Now we introduce one simple model to describe the effects of the static electric field on the electron acceleration. The longitudinal motion of one electron in the electron cloud before the target is md dt e E x t E x t and the laser electric field, respectively. can be filled by the measured data in the PIC simulations. υ / = ( x (, ) + L (, )). Here, Ex and EL Ex EL can be approximated as follows: L are the laser-induced electric field E = 2( η) E cos( ω t + k x+ Φ) when x < 0.3λ0 and E L = 0 when x > 0.3λ0. Φ is the initial phase at the beginning of electron acceleration, η = 40% as deduced from the experiments and PIC simulations. The results show that only the laser-induced electric field can accelerate the electron to the momentum of 0.4 mc. When the electron passes through the sheath of the plasma, it will be accelerated or decelerated by the oscillating part of the laser-induced electric field. The maximum momentum an electron can obtain is 0.5 mc. 3 Laser harmonics in VH process The high harmonics of the laser pulse produced in the interaction between ultrashort laser pulses and solid targets is considered to be one method for obtaining X-ray at the range of water windows [7,8]. In experiments, the harmonics emitted in the interaction between laser and plasmas are often used to judge the physical mechanisms. Fig. 3(a) shows the time-integrated spectra of the reflected laser pulse from the steep surface of the plasma target (solid line). When L < λ0, the spectrum is dominated by the integral harmonics of the laser pulse. Such a spectrum is due to the oscillation of the plasma surface driven by the electric field of the laser pulse with the frequency of ω [9,20] 0. When the ions are immobile, the time-integrated spectra (dotted line) are much narrower than that obtained when ions are mobile. Under the simulation conditions of mobile ions, the plasma surface was somewhat irregular, causing its oscillating frequency to spread a little, which is in turn shown by the spectrum of the harmonics. The effect of the ion motion is more

5 No. VACUUM HEATING OF SOLID TARGET IRRADIATED BY FEMTOSECOND LASER PULSES 75 obvious when the laser intensity is stronger or the pulse duration is longer [2]. Such high harmonics produced at the surface of the plasma, if its frequency is high enough, can pass through the over-dense plasma and be measured behind the target. The lower energy cutoff will give out the quantitative estimate of the maximum plasma density [22]. Fig. 3(b) shows the time-integrated spectra of the reflected laser pulse when the plasma density profile is smoother ( L = 2λ0 ). Under such conditions, the spectrum is dominated by the harmonics of ω 0. The difference in the components of the spectra under the two conditions indi- 2 cates that the absorption mechanism is different. The evolution of the electron distribution in the phase space reveals that with the smoother density profile, the laser pulse was absorbed through the two plasmon decays. At the position of n 4 c, the laser pulse stimulates the plasma wave with frequency of ω 0, which will interact with the following part of the laser pulse, producing the 2 harmonics of 0 2 ω. Fig. 3. The time-integrated spectra of the reflected laser pulse from step plasma (a) and smoother plasma (b). Another characteristic of the spectra of the reflected laser pulse from the surface of the plasma target with a steep density profile is the line emission ( ω 5.9ω0 ) of the over-dense plasma (fig. 3(a)). Such a line emission is much more intense than the fourth and fifth harmonics of the laser pulse, indicating that its producing mechanism is different from that of the harmonics. By varying the electron density applied in PIC simulations, the frequency of such a line emission is correlated with the plasma electron density as ω/ ω 0 = ne / n c. This relation reveals that this line emission is the characteristic radiation of the plasma wave [23]. Such a plasma wave is stimulated and amplified by the electrons penetrating from the surface into the over-dense plasma. Our PIC simulation results show that the angle of the laser pulse incidence determines the static electric field in front of the target, and therefore determines the number of the energetic electrons. Theoretical analysis shows that the electron flux determines the plasma wave and therefore deter-

6 76 SCIENCE IN CHINA (Series G) Vol. 46 mines the intensity of the line emission [24]. Using the analysis above, we can explain the phenomena observed in experiments of ref. [23]. In the experiments, when the incidence angle changes from 45 to 5, the measured plasma line emission becomes weaker and weaker, indicating qualitatively that the energetic electrons decreases in number as the incidence angle decreases. 4 Conclusion In summary, we reported our investigation of the interaction between fs laser pulses and plasmas. Under conditions of the steep plasma, the vacuum heating and the IB absorption are the main absorption mechanisms of the fs laser pulse. It is found that the two parts of the laser-induced electric field are responsible for the acceleration of the out-going and in-going energetic electron. The spectrum from the PIC simulations was also studied. The characteristic line emission of the plasma we found can be used for diagnosis of the density of the over-dense plasma. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos and ) and the National High-Tech ICF Program and the National Key Basic Research Special Foundation (NKBRSF) under Grant No. G References. Perry, M. D., Mourou, G., Terawatt to Petawatt subpicosecond lasers, Science, 994, 264: Blanc, P., Audebert, P., Fallies, F. et al., Phase dynamics of reflected probe pulses from sub-00fs laser-produced plasmas, J. Opt. Soc. Am. B, 996, 3: Andreev, K. A.A., Platonov, Y., Gauthier, J. -C., Skin effect in strongly inhomogeneous laser plasmas with weakly anisotropic temperature distribution, Phys. Rev. E, 998, 58: Yang, T. Y. B., Kruer, W. L., More, R. M. et al., Absorption of laser light in overdense plasmas by sheath inverse bremsstrahlung, Phys. Plasmas, 995, 2: Brunel, F., Not so resonant, resonance absorption, Phys. Rev. Lett., 987, 59: Gibbon, P., Bell, A. R., Collisionless absorption in sharp-edged plasmas, Phys. Rev. Lett., 992, 68: Kato, S., Bhattacharyya, B., Nishiguchi, A. et al., Wave breaking and absorption efficiency for short pulse p-polarized laser light in a very steep density gradient, Phys. Fluids B, 993, 5: Grimes, M. K., Rundquist, A. R., Lee, Y. -S., et al., Experimental identification of vacuum heating at femtosecond-laser-irradiated metal surfaces, Phys. Rev. Lett., 999, 82: Kruer, W. L., The Physics of Laser Plasmas Interaction, New York: Addison-Wesley, 988, Price, D. F., More, R. M., Walling R. S. et al., Absorption of ultrashort laser pulses by solid targets heated rapidly to temperatures 000 ev, Phys. Rev. Lett., 995, 75: Rozmus, W., Tikhonchuk, V. T., Cauble, R., A model of ultrashort laser pulse absorption in solid targets, Phys. Plasmas, 996, 3: Kruer, W. L., The Physics of Laser Plasmas Interaction, New York: Addison-Wesley, 988, Chen, L. M., Zhang, J., Dong, Q. L. et al., Hot electron generation via vacuum heating process in femtosecond laser-solid interactions, Phys. Plasmas, 200, 8: Hokin, S., An X-ray target probe for superthermal electron and field line pitch measurements, Rev. Sci. Instrum., 992, 63:

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