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PRODUCTION OF CUMULATIVE JETS GENERATED BY LASER-DRIVEN COLLAPSING HOLLOW CONES S. P. Nikitin1, J. Grun 2, Y. Aglitskiy3, C. Manka1, D. Zabetakis4, A.L. Velikovich2 and C. Miller1

1Research Support Instruments, Lanham, MD 20706 USA 2Plasma Physics Division, Naval Research Laboratory, Washington DC 20375 USA 3SAIC Inc. San Diego, CA 92121 USA 4 Center for Bio/Molecular Science and Engineering, Naval Research Laboratory, Washington DC 20375 USA Abstract: We observe cumulative plasma jets formed by hollow cones imploded via laser ablation of their outer surfaces. The velocity, shape, and density of the jets are measured with monochromatic 0.65 keV x-ray imaging. Depending on cone geometry, cumulative jets with ion density ~2×1020 cm-3 and propagation velocities >10 km/sec are formed. Similar results are observed when jets are formed by imploding wedges. Such jets can be used to simulate hydrodynamics of astrophysical jets interacting with stellar or interstellar matter.

Motivation.

The unprecedented imaging capabilities of the Hubble Space Telescope and Chandra X-Ray Observatory have revealed jet-like structures in a diverse array of astrophysical environments. Besides the well known jets from supermassive black holes in active galactic nuclei [1], jets are more or less ubiquitously associated with accretion. Examples are found in young stellar objects [2], proto-planetary nebulae [3], and stellar mass black holes [4]. The emerging connection between long duration gamma-ray bursts and Type I b/c supernovae [5] also suggests that jets may be generated during the core-collapse explosion of a massive star, and indications of such are also seen in the remnants of such events [6].

The phenomena associated with astrophysical jets, aside from mechanisms of their initial formation, include the morphology of the jet as it bores through an ambient medium, the nature of instabilities that could disrupt the jet’s coherence, the mechanisms preserving the jet collimation, the efficiency with which the ambient gas is entrained in the jet, and the behavior of a jet in a magnetized environment [7].

Jets may also have a role in Inertial Confinement Fusion (ICF), where laser-driven implosion of a deuterium-containing hollow pellet followed by heating of the pellet core results in ignition [8]. A number of authors have proposed that the energy of ICF lasers could be reduced if the heating of the pellet core is accomplished independently of the method used to implode the pellet. The first such suggestion [9] was to use an auxiliary intense picosecond laser pulse to ignite the pellet. A subsequent concept was to use energetic ions for the same purpose [10]. A recent suggestion [11] has been to use fast plasma jets that would penetrate the compressed pellet mantle and ignite the pellet core by deposition of kinetic energy. This concept is just beginning to be investigated.

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A number of these issues can be explored in the laboratory if suitably scaled jets can be produced. To simulate astrophysical jets, it is desirable that the scaled jets have a high Mach number, density equal to or lower than the ambient medium, and an internal energy density much higher than that of the ambient medium.

The authors of [12] appear to be the first to suggest that fast plasma jets can be achieved using laser ablation to implode cones. This method of jet formation is similar to the one used in explosively-driven shaped charges developed during World War II to penetrate armor plates [13]. Such shaped charges are made from a concave metallic liner backed by an explosive charge which, when initiated, collapses the liner onto its axis of symmetry where it forms a liquid-metal jet, often called a “cumulation jet”. The first experimental efforts to produce laser-ablative jets [14] did not produce reliable and well diagnosed results.

In this paper we report creation of laboratory jets from hollow cones and wedges collapsed onto their axes by pressure generated via laser ablation of their outer surfaces.

For incompressible fluids, jet velocity Vjet and mass Mjet and cone wall velocity Vcone and mass Mcone are related to the cone apex half-angle α through [13, 15]

cot2

jet

cone

VV

α⎛ ⎞≅ ⎜ ⎟⎝ ⎠

2sin2

jet

cone

MM

α⎛ ⎞≅ ⎜ ⎟⎝ ⎠

(1)

If the fluid is compressible, a jet is formed only if 1sin (1/ )effα γ−≥ . Here, effγ describes the fluid shock compressibility ([15] and references therein). For 5 / 3effγ = the corresponding cone apex angle 2α is 74º.

We chose conical geometry rather than cylindrical [16] anticipating that conical geometry, through variation of the cone angle, provides better control over the mass and the velocity of the jet. Having the drive laser and the expanding jet on opposite sides of the cone targets [17], unlike in [18], greatly simplifies studies of jet-ambient interactions.

Experimental setup. Our experimental setup is shown in Fig. 1. The hollow targets (cones and wedges)

for these experiments were manufactured by electroforming. Molds were machined from aluminum stock on a Haas Minimill, using custom carbide bits having the correct base angle for each specific cone geometry. The finished mold consisted of a flat surface with a series of protruding cones. Electroforming was accomplished with a nickel sulfamate solution, a nickel anode and a current density of 10-40 mA/cm2. After an appropriate time for the required metal thickness, the current was stopped, the mold rinsed with water and dried. The mold was then heated to 100º C to encourage separation between the aluminum and nickel and the cones removed from the mold. Both cones and wedges had 500 µm base size. Target wall thickness (5-10 μm) was determined by weighing a known area of the foil taken from a region between the preformed cones.

The targets are irradiated on the external side by a 4 ns, 100-200 J, 1.05 µm wavelength pulse from the PHAROS laser at the Naval Research Laboratory. The resulting irradiances of 1-2×1013 W/cm2 create ~1 Mbar ablative pressure [19] which causes the cone or wedge to implode toward its axis where under certain circumstances collapsing target material forms a cumulative jet. Although such an implosion scheme can be potentially susceptible to the Rayleigh-Taylor instability [20], this is not the case in our experiments,

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since the jets described here are consistently formed with high-adiabat targets characterized by a fast expansion rate

To maintain high material density during implosion, the rise time of laser intensity should be small compared to the time required for the shock wave to propagate through the wall of the target. Approximating the Hugoniot adiabat of Ni by

24.501 1.627 0.2064D U U= + − , where D and U are shock and mass velocity, respectively, both in km/s [21], and using the known expression 0p DUρ= for the shock pressure, we find that for ablative pressure ranging from 1 to 2 Mbar the corresponding shock velocity D varies from 7 to 8.6 km/s, and the shock transit time through 8 μm thick foil – from 1.14 to 0.9 ns. This implies that a sub-nanosecond rise time of the drive laser pulse is highly desirable to avoid complicated processes at an early phase of laser-target interaction (spallation, distortion of cone shape etc.).

Fig. 1. Experimental setup.

The required sub-nanosecond rise time of the laser drive pulse was achieved by

slicing the output of the Nd:glass oscillator with two 50-Ohm Pockels cells, connected to the advanced generator of kV pulses, capable of operating at switch times faster than 100 ps. Placing the second Pockels cell after the pre-amplifier reduces amount of amplified spontaneous emission from the laser and improves optical contrast at the output of the laser system. In the process of amplification to 100-200 J energies the sliced laser pulse changes its originally rectangular pulse shape, however its rise-time remains sub-nanosecond, as monitored by a fast photodiode connected to 2.5GHz bandwidth oscilloscope. A flat intensity profile over the 0.5 mm focused laser spot size is achieved by placing a random phase plate into the beam, employing the technique of induced spatial incoherence [22].

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The collapsing hollow target and the jet it produces are side lit with an x-ray pulse generated by a second laser beam focused onto a thin piece of alumina ceramic (Al2O3). This second laser pulse is delayed with respect to the drive laser pulse, electro-optically sliced to sub-nanosecond duration and amplified to 70-100 J energy. The emitted x-ray pulse side-lights the imploding target and reflects from a spherically bent mica crystal [23] onto a 2D Radicon detector which records the resulting time-resolved x-ray shadowgram. The angle of incidence on the mica crystal, its radius of curvature and relative positions of the side-lighter, crystal and image detector are chosen so that only x-rays at the 0.65-keV line of H-like Oxygen are reflected by the crystal, resulting in acquisition of a monochromatic image.

Soft sub-keV x-rays were chosen in order to reliably detect any low-density precursors to the cumulative jet that could be generated by such processes as spallation from the inner target surface. We have not observed any substantial pre-cursors to the jets. Therefore, hydrodynamic implosion of the hollow target is the major process leading to jet formation in our experiments.

The spatial resolution of the diagnostic is limited by significant astigmatism of the imager resulting from the required large angle of incidence at the mica surface. Optimization of the imager geometry to achieve adequate spatial resolution was done by numerical ray-tracing of the imager. The results of the raytracing were confirmed experimentally by obtaining an image of a square grid made of 160 μm thick wires placed in the object plane. Resulting resolution of the optimized imager was found to be better than 100 μm both in vertical and horizontal planes. Details of the monochromatic x-ray diagnostic used in our experiments are shown in Fig. 2.

Fig 2. Schematic of soft X-ray imager (left), raytraced image of a mesh (right top) and an experimental image of the same mesh (right bottom) demonstrates a sub-100 μm resolution.

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We have imploded a number of Ni cones with 2α ranging from 90º to 130º and wedges with 2α = 110º. All targets were side lit at delays ranging from 0 to 80 ns after rise of the drive laser pulse. For cones with 2α = 90º a cumulative jet formation was never observed. However, for the cones with 2α = 110o and 130o jets form consistently. These observations indicate that the critical angle required for jet formation for Ni cones is close to 2α ~ 100º. Similar results were obtained by imploding planar wedges.

Fig. 3 shows a sequence of jet images corrected for astigmatism and taken at different time delays after the laser pulse implodes Ni cones with 2α =110º, 2α = 130º and wedges with 2α =110º. Jet propagation velocities calculated from these images are 10±2 km/sec.

Fig. 3. Side lit x-ray images resulting from acceleration of 5µm Ni plane foils and implosion of 110º Ni cones, 130º Ni cones, and 110º Ni wedges made of the same foil at different delays after drive laser pulse. A formed jet propagates along the axis of the cone and it was observed that minor

(5-10o) deviations of the cone axis from the direction of the drive laser beam did not substantially affect the jet formation. This circumstance suggests that the jet formation is mainly related to the geometry of the cone rather than to the position of the laser spot on the target.

The planar jet from an imploded wedge is viewed side on. Mass density in the planar jet is calculated assuming 0.5 mm thick slab density distribution. For the case of axially symmetric jets generated from cones, the mass density distribution ( , )n r z only depends on the radial distance r and position z along the cone axis and can be calculated using discrete Abel transformation [24].

The on-axis jet density reaches ~ 2×1020 ions/cm-3 and the mass of the jet calculated by integrating ( , )n r z is found to be about ~ 10% of the cone mass, reasonably consistent with the expression (1). Collimation of the jet is characterized by an m-factor, describing

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mass angular distribution: 2( ) ~ (cos ) mjetM Mθ θ . Most of obtained jet images show

collimation factors m ~ 10. An example of Abel-inverted jet image is shown in Fig.4.

Fig. 4. Abel inverted images of jet at 60 ns after laser drive pulse implodes 130o Ni cone

To estimate the temperature of the jet material, thin planar foils were accelerated

and sidelit under the same experimental conditions as the cones and wedges (Fig. 3 (left)). The resulting images, such as the example shown in Fig. 3 (left), allow the determination of the expansion rate of the accelerated foil. From the rate of the foils’ two-dimensional expansion we estimate the thermal energy deposited in the foil. For this purpose we use the analytical self-similar solutions describing a homogeneous expansion of ideal gas ellipsoids [25], During laser ablation, thermal energy is rapidly delivered to the foil through shock heating, thermal conduction and x-ray radiation from the corona. Initially, the pressure gradient length is the shortest – of the order of the initial foil thickness, 4 to 10 μm, in the direction normal to the foil. Thus the foil starts to expand mostly in this direction [25]. The time that it takes for the expanding plasma to reach a quasi-spherical shape, as in Fig. 3 (left), indicates the initial peak pressure and the amount of thermal energy initially deposited in the plasma. The observed expansion time of 40 ns thereby corresponds to a peak pressure of 1-2 Mbar and deposited thermal energy of 0.5-0.6 J, which translate into an initial dense plasma temperature of 7-8 eV and an average ion charge Z = 2 to 3.

At this ablative pressure the target is accelerated at 3-4 km/s per nanosecond, so that a ~4 ns laser pulse results in final directed velocity ~12-15 km/sec. These estimates for foil velocity and peak pressure are in good agreement with direct velocity measurement from our x-ray images and pressure estimates based on laser intensity and pulse duration [19].

Conclusions. We have demonstrated that ablative implosion of cones and wedges is a reliable and

reproducible mechanism to produce fast high-density cumulative plasma jets. Both planar and axial jets can be formed using this method. Monochromatic x-ray side-lighting of the jets determined that the jet mass is ~ 10% of the cone mass, jet velocity is 8-12 km/sec and jet ion density ~ 2×1020 ions/cm3. Life time of the jets exceeds 80 ns.

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Analysis of the hydrodynamic expansion of a thin planar foil of material used for cone manufacturing indicates a jet material temperature of ~7-8 eV and a pressure of ~1-2 Mbar, consistent with ablative pressures generated at laser intensities of 10-20 TW/cm2 used in our experiments. The jets produced by the method described here can be used to investigate jet propagation into ambient media relevant to laboratory astrophysics, plasma hydrodynamics and for certain fast ignition approaches.

The authors thank J. Laming and J. P. Apruzese from NRL for helpful discussion. This work is performed under the auspices of the U.S. Department of Energy.

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