Diagram of the laser beams and the diagnostics layout. 

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... a laser propagates through an underdense plasma, electromagnetic coupling of the laser light with the plasma affects its propagation. One important effect on the laser’s propagation is filamentation, where the interaction laser beam modifies the plasma density changing the index of refraction either ponderomotively or thermally. In either case, the gradient in the refractive index focuses the laser to higher intensities that further modifies the plasma density and causes the beam to breakup into filaments. Beam breakup due to filamentation modifies the laser plasma coupling properties. Understanding laser filamentation is important for de- signing high energy density physics experiments involving lasers at high intensities ͑ Ͼ 10 14 W / cm 2 ͒ . Changes in the laser properties affects coupling of the laser energy to the target. In this manuscript, we report on a novel technique for determining the onset of filamentation for a random phase plate ͑ RPP ͒ smoothed laser beam. Using a short-pulse diffraction-limited probe laser beam, images of the transmitted near-field intensity pattern are used to detect density fluctuations driven by the long-pulse interaction beam. As the RPP smoothed beam propagates through the plasma, the pon- deromotive or thermal pressure in the long, narrow, cigar- shaped speckles creates ellipsoidal perturbations in the plasma. As the short-pulse probe beam propagates perpendicularly through these ellipsoidal perturbations, the modi- fied index of refraction of the plasma changes the phase front of the probe beam, leading to fluctuations in the transmitted near-field intensity. When the longitudinal length of the interaction beam speckles is much greater than the transverse size of the probe beam, the transmitted intensity fluctuations show a preferential direction and extend completely across the measured transmitted beam intensity profiles. As the plasma density increases, the preferentially oriented intensity pattern begins to break up into smaller spatial scales signify- ing filamentation of the interaction beam. Preliminary simulations using the wave propagation code PF3D ͑ Refs. 1 and 2 ͒ qualitatively confirm that the preferential transmitted near- field intensity profiles are induced by the density fluctuations driven in the plasma by the interaction beam. Experiments measuring the filamentation of a smoothed interaction beam using a short-pulse probe beam were car- 3 ried out at the Trident laser facility. A single 527 nm Trident laser beam with up to 200 J is used to generate a plasma ͑ Fig. 1 ͒ . This beam, which we call the interaction beam, is focused through either a 2 or 6 mm hexagonal RPP using an f / 6 lens with a 120 cm focal length and has a 1.2 ns flattop pulse shape. The interaction beam is focused 0.7 mm above the gas-jet nozzle. The resulting intensity of the interaction beam on the gas-jet target is ϳ 1.4 ϫ 10 14 or ϳ 1.0 ϫ 10 15 W / cm 2 with the 2 or 6 mm RPP, respectively. The plasma is generated with helium gas producing electron densities and temperatures ranging between n ϳ 2 ϫ 10 19 – 2 ϫ 10 20 cm −3 ͑ n / n c ϳ 0.005– 0.05 where n c is the critical density for 527 nm light ͒ and T e ϳ 180– 350 eV. The plasma parameters are determined via Thomson scattering. The ϳ 2 ps probe laser beam is generated by a separate short-pulse oscillator that is synchronized to the long-pulse oscillator. The beam propagates down the beam line and en- ters a set of gold compressor gratings setup in the target area. After compression, the beam then passes through a potas- sium dihydrogen phosphate ͑ KDP ͒ crystal to convert the 1054 nm laser light to 527 nm with a pulse energy in the range of 7 – 50 mJ. The beam propagates though an f 4.5 lens and is focused into the plasma perpendicularly with respect to the interaction beam. The probe beam passes through the plasma and terminates on a bead blasted glass diffuser plate inside the vacuum chamber. A digital single lens reflex ͑ SLR ͒ Canon camera records the images of the transmitted near field for the probe beam from outside the vacuum chamber through a viewport. The image provides a measurement of the intensity pattern of the transmitted near- field beam profile. The probe beam is initially timed to fire ϳ 100 ps before the end of the interaction beam pulse, but can be shifted in time with respect to the interaction beam. Although the probe and interaction beam wavelengths are identical, background light due to scattering of the interaction beam in the gas jet did not cause a problem for measuring the transmitted probe beam intensity over the parameters of these experiments. However, at higher gas-jet densities or for higher Z gases, the background scattered light from the interaction beam could potentially increase. In which case, a different wavelength probe lasers or light shielding around the bead blasted glass plate could be used to reduce the effect of the background levels. Data from the transmitted beam diagnostic are shown in Fig. 2. Figure 2 ͑ a ͒ shows a measurement of the probe beam profile without the gas jet to serve as a reference. The near- field intensity pattern at low plasma densities, ϳ 0.01 n / n c , shows the asymmetric intensity pattern where the elongated striations are oriented along the direction of the interaction beam propagation Fig. 2 b . As the plasma density increases, Figs 2 ͑ c ͒ and 2 ͑ d ͒ , the transmitted pattern in the direction of the elongated striations breaks up into smaller scale lengths, potentially indicating filamentation of the interaction beam. Initial simulations using the wave propagation code 1,2 PF3D , that includes hydrodynamic laser plasma interactions, illustrate that an elongated near-field intensity pattern occurs when a nearly diffraction-limited short-pulse probe propagates perpendicularly through a plasma being driven by a RPP smoothed laser beam. For the simulation, a RPP smoothed beam is propagated through a plasma with the experimental parameters. At the desired time, the interaction beam simulation including hydrodynamic modification to the plasma is stopped. The simulation box is rotated by 90° and the short-pulse probe laser is propagated through the per- turbed plasma. An image of the simulated near-field intensity pattern is generated, as shown in Fig. 2 ͑ e ͒ . The near-field transmitted beam intensity shows a preferential orientation in the pattern, qualitatively consistent with experimental measurements. Figure 2 ͑ f ͒ demonstrates that the asymmetric near-field intensity pattern is only observed using the short pulses. The image shows a measurement of the transmitted probe beam from a previous experiment that used the same experimental setup described here but with a ϳ 200 ps laser pulse instead of the ϳ 2 ps laser pulse. The time-integrated measurement with the 200 ps pulse smears out details observed with the short-pulse laser probe. In addition, the 200 ps probe beam itself appears to filament and to spray the transmitted laser light outside the f / 4.5 beam cone as compared to the reference in Fig. 2 ͑ a ͒ . Thus, the 200 ps probe itself filaments. This does not occur for the short-pulse laser probe because for most of the plasma conditions reported here the pulse length is shorter than the growth time for filamentation. To provide more evidence that the preferential near-field intensity profiles are due to the interaction beam driven plasma perturbations, the relative timing between the short- pulse laser probe and the end of the interaction beam pulse was varied. The driven perturbations are expected to damp out after the interaction beam shuts off. As the relative time between the interaction and probe beams increases the plasma should become more uniform. Figure 3 shows the transmitted probe beam intensity profile at three different times, coincident with the end of the interaction beam pulse ͓ Fig. 3 ͑ a ͔͒ ϳ 100 ps after the end of the interaction beam pulse ͓ Fig. 3 ͑ b ͔͒ and ϳ 300 ps after the end of the interaction beam pulse ͓ Fig. 3 ͑ c ͔͒ . As the relative time between the probe and interaction beam increases, evidence of the preferential elongated striations subsides. The lack of preferential modulations in the probe beam’s near-field intensity profile as time increases between the probe and the end of the interaction beam pulse confirms that the probe beam is detecting driven plasma perturbations by the RPP smoothed interaction beam. The asymmetric beam breakup of the transmitted short- pulse laser probe intensity profile appears to be a direct measurement of plasma perturbations driven by the interaction beam, and PF3D simulations of the experiment support this conclusion. The breakup of these elongated intensity fluctuations in the near-field profile into short scale lengths as the plasma density is raised appears to correspond with filamentation of the interaction beam. Efforts are underway to dem- onstrate and to quantify that in fact this is a result of the interaction beam filamentation. In which case, it would be possible to use a short-pulse laser probe beam to measure filamentation of RPP smoothed beams. Future work will also examine the possibility of determining the fluctuation ampli- tudes and wavelengths from such data. The authors would like to express thanks for the hard work of the Trident laser crew: F. Archuleta, D. M. Esquibel, R. Gonzales, T. Hurry, and S. L. Reid. We would also like to thank Sandrine Gaillard for useful comments on the manuscript. This work was performed at Los Alamos National Laboratory under the auspices of Los Alamos National Se- curity, LLC, for the Department of Energy under Contract No. ...