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We used time-resolved shadowgraphy to characterize the pre-plasma formation in solid-target interaction experiments with micrometer-scale accuracy. We performed quantitative measurements of the plasma density for amplified spontaneous emission (ASE) levels ranging from 2·10−7 to 10−10 backed with 2-dimensional hydrodynamic simulations. We find that ASE levels above 10−9 are able to create a significant pre-plasma plume that features a plasma canal driving a self-focusing of the laser beam. For ASE levels of 10−10, no ASE pre-plasma could be detected.
© 2014 Optical Society of America
1. Introduction
Lasers reaching peak powers in the petawatt range and intensities above 1021 W/cm2 are nowadays available for a wide range of experiments in laboratories around the world. For many experiments, the interaction with solid and mostly undisturbed targets is a prerequisite [1, 2]. However, the temporal shape of highly intense short laser pulses often exhibits complicated structures including pre-pulses, an incoherent nanosecond pedestal and wings, which pre-ionize the target and thereby strongly influence the laser-matter interaction. The temporal structure of these light pulses is far from the Gaussian or “top hat” pulses used in simulations and this feature makes experimental results hard to interpret: first, a precise measurement of the laser pulse over 120 dB and many nanoseconds would be necessary to perfectly characterize the experimental conditions, and second, simulation tools capable of handling the many physical processes happening over intensities ranging from the ionization threshold at 109 W/cm2 up to maximum intensities exceeding 1021 W/cm2 would be required. Still, both experiment and simulation fail to deliver such tools.
There is a general agreement that pre-ionization strongly influences experimental data. In a limited number of cases, a certain pre-plasma can improve the outcome of the experiment. For instance in laser-ion acceleration with micrometer-thick targets, the enhanced absorption and self-focusing in the pre-plasma leads to higher maximum ion energies [3]. However, in order to exploit this effect, a precise control of the pre-plasma is essential. In contrast to these cases, there are also applications that cannot tolerate pre-ionization [1, 2]. For this reason, several techniques have been proposed and implemented to improve the temporal contrast of short-pulse lasers either in the front-end of those [4,5] or shortly before the interaction point [6]. As a consequence, a qualitative improvement has been reported for those experiments requiring high temporal contrast. However, these techniques also create different temporal pulse-profiles that complicate the comparison between experimental results. Therefore a systematic characterization of the pre-plasma plume for different contrast levels is desirable.
In this paper, we exploit a standard time-resolved shadowgraphy method to make an in situ characterization of the pre-plasma created by a short-pulse laser whose temporal contrast can be adjusted over up to 5 orders of magnitude. We use three pulse profiles which we consider representative of what can be found in short-pulse lasers around the world, with temporal contrast levels ranging from standard to ultra-high. The measured pre-plasma shadow shows a complicated spatial structure, which is analyzed and explained with the help of the RALEF-2D hydrodynamic simulation code [7]. In particular, the pre-plasma geometry can yield a significant self-focusing of the beam for the standard temporal contrast case.
2. Experimental setup
The experimental data was gathered at the PHELIX high-energy laser facility [8] in Darmstadt, Germany, where a high-contrast front-end based on the ultrafast Optical Parametric Amplification (uOPA) concept [5] was recently commissioned [9]. As shown in Fig. 1, the short oscillator pulses (100 fs) are directly amplified at the output of the short pulse laser oscillator using a time-gated parametric amplifier leading to short pulses of 100 microjoules without any degradation of its picosecond and nanosecond temporal-contrast properties. Parametric amplification imposes serious requirements on the pump beam used in the process such that a dedicated laser-diode-pumped pump laser had to be developed to fulfill the tight timing, pulse-duration and energy requirements. Thanks to this design [10], 5-mJ pulses at 520 nm with a pulse duration of about 1 ps enable reaching amplification gains of up to 2·105, which linearly translates into a reduction of the final nanosecond ASE of the laser. Depending on the amplification factor of the uOPA, the pumping-laser energy delivered to the first regenerative amplifier is accordingly reduced such that the regenerative amplifier still reaches saturation and delivers about the same output energy. In all cases, the amplification factor of uOPA and regenerative amplifiers remains constant at about 108.
For the experiment three gain levels of the uOPA were used: 1, 200 and 4·104, yielding the three temporal curves shown in Fig. 2, exhibiting a temporal ASE pedestal at 2·10−7, 4·10−9 and 10−10 with respect to the maximum intensity of the pulse, respectively. The temporal profiles where recorded at the output of the front-end, using an auxiliary compressor and a scanning high-dynamic-range third-order cross-correlator (Sequoia, Amplitude Technologies). As was already documented and discussed before [9], this measurement is a true representation of the final pulse profile that undergoes little distortion in the rest of the amplifier. Because the cross-correlator only delivers an information in the vicinity of the pulse maximum over a temporal window of roughly 500 ps, the temporal profile of the laser pulse is additionally recorded at full energy at the output of the compressor with sub-nanosecond accuracy using a fast photodiode (Thorlabs D400FC) and a 2.5 GHz oscilloscope (Tektronix TDS7254), as shown in the insert of Fig. 2. The measurement is truncated at 1 because of the scale used with the oscilloscope. Since the photodiode had to be highly saturated at the maximum intensity in order to attain a detectable ASE level, this measurement does not provide proper results for times which are closer to the maximum than 100 ps. For the highest ASE level, a pre-pulse at −115 ps can be noticed, which we attribute to beats between the oscillator and the first regenerative amplifier (multiple pulse injection). The amplitude of this pre-pulse is anti-proportional to the gain of the uOPA since only one pulse of the 72 MHz oscillator is amplified. This is confirmed by the intermediate and high-contrast traces where this pre-pulse is significantly reduced. For these two other curves, a pre-pulse coming from the interplay between an etalon effect in a Pockels cell and the temporal Kerr effect [11] is present at −210 ps. No other significant pre-pulses could be diagnosed within the −300 ps to 0 ps window of the cross-correlator. In addition to the constant nanosecond ASE pedestal, the pulse profile exhibits a slow rise of the pulse intensity with a slope factor of 5 per 10 ps between −100 ps and 0 ps, a feature which is typical for high-energy short-pulse laser systems. After amplification and compression, the short pulses are sent to the experiment chamber using the setup depicted in Fig. 1. The first dielectric mirror is a leaky mirror that transmits about 1% of the beam used for the shadowgraphy. This beam is first down-collimated to about 1-cm diameter with the help of an off-axis 90° copper parabolic mirror and a diverging lens. A set of reflective filters allows for controlling the pulse energy in the diagnostic beam-line during the alignment phase and the full-energy shot. We use frequency doubling with the help of a 1-mm BBO crystal to reduce the detection background due to scattering of the main pulse on the target. After a 50-mm delay-line the beam is sent to the target, whose interaction plane is image-relayed outside the chamber using a magnifying telescope. The F number of this imaging system is 7.5, a good trade-off between spatial resolution and sensitivity of the shadowgraphy setup. Indeed as explained below, a high F number is required in order to probe thin plasma clouds using shadowgraphy, while the small dimension of the pre-plasma requires an optical system with a reasonably small F number for spatial resolution purpose.
Fig. 2 Temporal profile of the PHELIX laser pulse for various adjustments of the contrast boosting module from standard (green) to intermediate (red) and high (blue) contrast levels. In the insert, a photodiode measurement of the nanosecond pedestal.
After entering the chamber, the main beam is reflected off a first turning mirror and finally focused with an f = 400-mm 45-degree off-axis parabolic mirror onto the target. Micrometer-thin copper targets were shot at an average energy of 47 J in 600 fs focused to a 4-μm spot (FWHM). Based on these values and a calibration of the focal spot image at low power the peak intensity was estimated at 2( ± 1)·1020 W/cm2 at the peak of the pulse. Flat 1-mm wide foils were used as targets for the interaction. The target thickness equal to 10 μm was chosen as a compromise to get the thinnest shadow on the shadowgraphy camera. Thinner targets did not give satisfactory results as they warped during mounting, increasing the effective thickness seen by the camera. During the shots, radiochromic films located in forward direction, perpendicular to the target, recorded the proton beam accelerated from the rear surface of the target. This additional diagnostic ensured that the expected intensities were reached. We measured maximum proton energies near 25 MeV, which is consistent with data reported in the literature for such an arrangement [12].
The timing of the diagnostic and main beams is crucial in this experiment. We used a fast photodiode (New Focus model 1454) together with a 8 GHz oscilloscope (Tektronix DPO70804) to simultaneously observe both main and diagnostic pulses, using the 10-Hz front-end beam. By making several measurements for various time delays, a +/−10 ps accuracy in the relative timing could be achieved.
3. Experimental results
In the experimental campaign we took about 40 shots to characterize the pre-plasma formation for the three different ASE levels described above. For these shots the time delay of the probe beam with respect to the main beam was varied between −233 ps (before the impact of the main pulse at 0 ps) and + 100 ps. Each shot was preceded by a low-energy reference shot where the main beam was blocked and only the probe beam was used to illuminate the target. A selection of images which were obtained from shots with the highest ASE level is presented in Fig. 3. The upper row shows the reference images and the lower row the images with the main beam on target. The laser beam comes from the right. On these images, one clearly sees a shadow developing on the front side of the target which is due to the pre-plasma expansion. As the light pulse interacts with the target, ionization occurs at the target surface as soon as the intensity exceeds a certain threshold and the resulting plasma expands hydrodynamically into the vacuum. In such a case, the plasma density gradient is very high close to the target surface and decreases away from it. This plasma gradient deflects the rays of the probe beam crossing the plasma in a similar way to a diverging lens. When the gradient is strong enough, the rays exit the plasma at an angle higher than the opening angle of the imaging telescope and are not recorded by the camera. This non-illuminated area appears then as a shadow on the picture. It must be noticed that the plasma gradient does not allow measuring the position of the plasma critical density but rather plasma densities orders of magnitude lower.
Fig. 3 Shadow images: reference image before the shot (upper row) and on-shot shadowgraphy images at various instants before the main shot for the highest ASE level.
On the images, one also notices a bright spot due to frequency-doubled light of the main beam. This is a known complication of shadowgraphy measurement at 2ω, but it did not affect the precision of the measurement. Here, we could reduce the magnitude of the spot by using perpendicular polarizations between main and probe beams, and a polarizer in front of the camera. The pre-plasma appears similar in shape and size for all time-delays between probe and main beams. At −227 ps the pre-plasma shadow is already well established with an extension perpendicular to the target plane of 38 μm, and stays rather constant up to −100 ps before the maximum of the pulse. For the other two time delays, the pre-plasma is slightly larger at 50 μm. The shape of the plasma shadow is also interesting because of its rather rectangular shape, indicating that the plasma expansion is stronger parallel to the target surface than perpendicular to it.
We repeated the analysis made above for all three ASE levels and at time delays before and after the peak of the pulse. The results are shown in Fig. 4. For the few hundreds of picoseconds ahead of the pulse, the pre-plasma shadow remains nearly constant. For the higher ASE level, the pre-pulse at −115 ps could be responsible for the slightly larger shadow at instants −66 ps, −33 ps and 0 ps. For the intermediate contrast level, the plasma shadow remains constant at about 20 μm. For the highest contrast level, no pre-plasma shadow could be measured. After the main peak of the pulse has been reached, the plasma expansion accelerates and the plasma shadow expands at a much faster rate. The vertical error bars in the measurement come mostly from the effective target thickness that creates an uncertainty on the interaction point, while the position reached by the shadow could be identified within a few microns. The targets exhibited various shadow thicknesses not correlated with their actual thicknesses because all targets warped somehow on their holders. A best +/− 5 micrometer accuracy of the measurement could be reached while other targets limited this accuracy to 30 μm. More sophisticated laser-cut targets and holders would be necessary to reduce this uncertainty to the micrometer level.
Fig. 4 Shadow size as a function of time. The zero delay corresponds to the maximum of the pulse intensity.
4. Interpretation and discussion
The images can be directly used to gain a qualitative understanding of the pre-plasma conditions. However in order to quantitatively explain this experiment, the plasma shadow must be interpreted in terms of plasma parameters, like position of the critical density and plasma temperature. Yet, the plasma shadow does not indicate the position of the plasma critical density but rather the location of a plasma density gradient characteristic of the numerical aperture of the measurement system. We used the 2-dimensional radiation hydrodynamics code RALEF-2D (Radiation Arbitrary Lagrangian-Eulerian Fluid dynamics) [7] to simulate our experiment. The code uses a second-order Godunov-like scheme on a structured quadrilateral grid and employs the arbitrary Lagrangian-Eulerian technique. Heat conduction and radiation transport in the plasma are taken into account, and the energy deposition by the laser is described by means of the inverse bremsstrahlung absorption, the dominant absorption mechanism for intensities below 1015 W/cm2 [13]. The simulations were performed assuming a cylindrical symmetry. The equation of state necessary for the simulations is described in [14] and the thermal conduction coefficient and spectral opacities have been generated by the THERMOS code [15].
The three ASE levels used in the experiment correspond to ASE intensities of 5·1013 W/cm2, 1012 W/cm2 and 2.5·1010 W/cm2. The two-dimensional electron-density distribution obtained for the three ASE levels is shown in Fig. 5, where the simulated target is 5 micrometer thick and located between x = 2 and x = 7 μm. In the simulation, the laser comes from the right and illuminates the target with a linearly growing intensity for 1 ns and a constant plateau for the following 1.5 ns, to fit the experimental conditions as shown Fig. 2. The plasma cloud expands into the vacuum at different velocities and its shape changes with growing intensity. For the highest ASE level, one can see a plasma channel developing along the laser axis. This occurs because of the particular conditions of the laser-matter interaction, happening after the plasma has expanded during the initial irradiation phase, due to the fact that the ablated plasma expands perpendicular to the ablation front inside a crater. Our hydrodynamic simulations show that the radial component of the plasma velocity which is directed towards the channel axis in the vicinity of the crater is transformed into an axial plasma flow away from the target by interaction with the surrounding plasma. This leads to a well-defined plasma channel with a purely axial velocity. Due to the high velocity in the channel the density is lower than in the surrounding plasma plume.
Fig. 5 Simulated electron density profiles for 3 ASE levels at 2.5·1010 W/cm2, 1012 W/cm2 and 5·1013 W/cm2 (left to right).
The electron density in the plasma is responsible for the index of refraction seen by the probe beam. Rays propagate along the target surface and accumulate a phase that depends on their distance to the target surface. For electron densities small compared to the critical density, the absorption in the plasma can be neglected and the plasma can be approximated by a purely refractive medium. The total phase accumulated by the probe beam can be written in the form:
Where L is a distance large compared to the plasma extension, and n the spatially dependent index of refraction. For the rays propagating near the surface, the gradient of ϕ(x) along x becomes steeper and the rays exit the plasma at a large angle given by the gradient of the accumulated phase. For a certain value of , these rays are not collected by the imaging system and the area appears dark on the camera. In this approach, we used the thin-object approximation which is only valid for small gradients. This approximation is valid because the F number of the imaging system corresponds to a half collection angle of 3.8 degrees, well within the paraxial approximation.We computed the ray positions corresponding to this maximum allowed deviation and reported them in Table 1, which shows the simulated plasma extensions together with the experimental data as plotted in Fig. 4. For the simulated data, the shadow size depends on the F number of the imaging system where an uncertainty given by alignment inaccuracies (mostly centering on folding mirrors) has to be taken into account. The simulated and experimental values are in very good agreement. The simulation predicts a significant plasma extension of many 10’s of micrometers for the highest ASE level. This was detected and measured at the same level by our setup. For the lowest ASE level, a pre-plasma in the micrometer range is predicted but its extension is smaller than the detection accuracy of the setup. For the intermediate level, the experimental values exceed slightly the predicted values.
Table 1. Comparison of simulated plasma shadow sizes and measured ones.
The simulation also shows a plasma that deviates from the half-sphere geometry usually described in textbooks [13]. Here the shape is showing a lower electron density on axis when the ASE level is high, that can be explained by the geometry of the laser-matter interaction that takes place during the nanosecond-long interaction. In order to further compare the simulated and measured shapes of the plasma plume, we calculated the wavefront gradient at various Y positions along the target surface by rotating the electron densities given in Fig. 5. This gives the shadow positions for all Y locations. This curve superimposed to the shadow image is presented in Fig. 6. We find again a very good agreement between the hydrodynamic simulation and the experimental measurement, not only in the X direction as reported above but also in the Y direction. This confirms the simulated plasma shape and the existence of a plasma canal created by ASE, only due to hydrodynamic effects.
Fig. 6 Experimental (picture) and simulated (yellow line) plasma shadow extension for an ASE intensity of 5·1013 W/cm2. The dotted line shows the target position and the laser comes from the right.
The existence of a pre-plasma changes the index of refraction in the vicinity of the target and when this pre-plasma extends over many 10’s of micrometers, it can in turn influence the propagation of the main beam. In order to test this hypothesis, we simulated in a first approximation the propagation of a Gaussian beam by numerically solving the Helmholtz equation in cylindrical coordinates for the radially varying index of refraction:
The result is shown in Fig. 7, where a perfect Gaussian beam is focused with a 3.4 μm waist (5 μm full width at half maximum) at the target surface. As can be seen in the figure, the plasma acts like a focusing lens which induces a focusing of the beam. According to this simulation, an increase of the intensity by a factor of 2 is reached at the target surface. This effect can significantly influence the outcome of an experiment, as the main part of the pulse undergoes self-focusing by the same amount. A rigorous simulation should for each time-step include the heating enhancement due to the self-focusing, which in turn creates more self-focusing. However, this laser-propagation effect is not presently included in RALEF-2D.Fig. 7 Self-focusing of the ASE beam. The laser comes from the right and the background describes the index of refraction of the pre-plasma. Without plasma (yellow line), the beam focuses to a 3.4 μm waist, which is being reduced to 2.6 μm when the pre-plasma is considered.
5. Conclusion and outlook
In conclusion, we presented an analysis of pre-plasma generation during the interaction of ultra-intense laser pulses with solid targets for three different contrast levels ranging from standard (ASE intensity of 5·1013 W/cm2) to high contrast (ASE intensity of 2.5·1010 W/cm2). The used temporal pulse profiles are considered representative for common high-power laser systems, hence we believe our findings can be utilized for the interpretation of experimental results obtained at any laser facility. Using time-resolved shadowgraphy we can identify an extended pre-plasma for the lowest contrast which stays constant on the 100 ps timescale. With the help of 2-dimensional radiation hydrodynamic simulations, the measured shadow boundary whose distance perpendicular to the target surface is on the order of 30-40 microns, can be linked to an electron density around 1020 cm−3. When changing over to the higher contrast levels, this shadow can be significantly reduced. For the highest contrast the pre-plasma is below the detection limit of our setup while the simulation reveals a minor plasma with a corresponding shadow dimension on the order of 5 microns. In addition, the 2-dimensional electron density distribution shows a remarkable feature: while for the higher contrast levels it is close to the half-sphere geometry which is typically described in literature, for low contrast shots it strongly deviates from such a shape. In fact, the lower electron density along the laser axis acts on the laser beam like a convex lens leading to an increase of intensity by a factor of two.
The pre-plasma defines the initial conditions for any experiment exploring the interaction of ultra-intense lasers with matter. Hence our results could contribute to a deeper understanding of physical processes happening in laser-generated plasmas. In particular, the plasma density distribution provided by this paper could be used as an initial distribution for numerical simulations of laser-plasma interactions. Starting with such a realistic configuration, instead of the steep density gradients which are commonly utilized could lead to much more realistic simulation results which could help to interpret experimental findings.
Acknowledgments
The authors want to thank the PHELIX team at GSI for their support and advice in the planning and realization of the experiment. This work was supported by the BMBF 05P12RDFA1 and the Helmholtz-Institute Jena. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
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