Femtosecond laser energy deposition in strongly absorbing cluster gases diagnosed by blast wave trajectory analysis

Transcription

1 PHYSICS OF PLASMAS VOLUME 8, NUMBER 10 OCTOBER 2001 Femtosecond laser energy deposition in strongly absorbing cluster gases diagnosed by blast wave trajectory analysis J. Zweiback a) and T. Ditmire b) Laser Program, L-477, Lawrence Livermore National Laboratory, Livermore, California Received 23 February 2001; accepted 8 June 2001 An intense ultrafast laser pulse can be very strongly absorbed in a moderate density gas composed of van der Waals bonded clusters. In this paper, the deposition of the energy of intense 30 fs light pulses in a gas of deuterium clusters has been diagnosed using a technique based on analysis of the trajectories of the resulting cylindrically symmetric blast waves. Using the well-known relation between blast wave velocity and energy deposition in gas, the laser energy deposited per unit length as a function of distance in gas jet plume was measured. These measurements were conducted in jets containing either deuterium clusters or simple deuterium molecules American Institute of Physics. DOI: / I. INTRODUCTION Recent experiments have explored many aspects of intense picosecond and femtosecond laser interactions with gases of atomic and molecular clusters. These studies have been motivated by the possibility of using a cluster gas jet target to produce strong x-ray or neutron bursts. Short pulse lasers focused into gas jets of noble gas clusters have been shown to be very strongly absorbed by the gas 1,2 and to emit substantial x rays. 3 5 A number of groups are examining the possibility of exploiting this strong absorption to make an efficient, debris-free source of soft x rays for next generation lithography. 6 This strong absorption has also been exploited to perform D D fusion experiments in gases containing deuterium clusters. 7,8 The hot plasmas produced by this absorption may also represent an interesting test bed for other high temperature plasma experiments. For example, the high absorption of a clustering gas has been used to examine nonlocal electron heat transport in low density plasma, 9 and the absorption of femtosecond laser pulses in Xe gases has been used to create radiative blast waves. 10 All of these studies have utilized the fact that clusters will form when a gas jet is pulsed into vacuum under appropriate pressure and temperature conditions. An ultrafast laser, whose duration is comparable to or faster than the 100 fs to 1 ps disassembly time of the clusters 5,11 will exhibit greatly enhanced absorption in this jet over that of an unclustering gas. This is a consequence of the local high density in the cluster, aiding collisional and other absorption mechanisms. These heated clusters release the absorbed laser energy in an explosion. 12,13 In brief, the cluster s electrons absorb the laser energy by collisional processes and subsequently escape the cluster. Larger clusters confine the electrons by spacecharge forces, leading to a hydrodynamic-type explosion, smaller clusters permit a complete escape of electrons leading to a Coulomb explosion. In either case, a large fraction of a Present address: Phaethon Communications, 5005 Brandin Ct., Fremont, CA b Present address: Department of Physics, University of Texas, Austin, TX the laser energy absorbed is released in ion kinetic energy. To exploit this effect in applications, however, it is desirable to know how the laser deposits energy in the jet as it enters the jet plume. Energy depletion and refraction of the laser pulse will have important effects on the energy deposition in the cylindrical filament produced by the interaction. In this paper, we present measurements of the deposition of energy as a function of propagation distance when a 30 fs laser pulse is focused to a peak intensity of W/cm 2 into a plume of deuterium. We have studied deposition both when clusters are present and when they are absent from the jet. We perform these measurements by examining the time evolution of the blast wave that results from the laser heating of the filament, exploiting the fact that the blast wave trajectory can be directly related to the energy deposition per unit length in the gas. We perform these measurements using time resolved interferometry. II. DESCRIPTION OF THE TECHNIQUE When laser energy is deposited in a gas in a localized region, the high pressure associated with the elevated temperature can drive a shock wave. This occurs if the resulting heated gas pressure is larger than a few kbar. When the shock wave evolves over a time scale much longer than the initial energy deposition time and over a spatial scale much larger than the initial volume of energy deposition, the shock decays and evolves as a blast wave. In the case in which electron and radiative energy transport is not important i.e., when the temperature of the plasma behind the shock is not too high, or less than a few tens of ev at the density of our experiment, the blast wave evolution will approach that of the self-similar case, in which the wave trajectory is largely independent of the conditions of the initial energy deposition. 14 The blast wave trajectory as a function of time can be easily derived from the well-known jump relations given by the Rankine Hugoniot equations. For a cylindrically symmetric blast wave, the radius of the wave, in the late time limit, evolves as X/2001/8(10)/4545/6/$ American Institute of Physics

2 4546 Phys. Plasmas, Vol. 8, No. 10, October 2001 J. Zweiback and T. Ditmire FIG. 1. Schematic of the experimental apparatus. r t f E 1/4 l 0 t 1/2, where E l is the initial energy deposited per unit length in the cylinder, 0 is the initial gas density, and f ( ) is a function of the adiabatic constant of the gas ratio of specific heats given by f ( ) ((4/ )( 1)( 1) 2 (3 1) 1 ) 1/4. Thus, a measurement of r(t) can yield E l if is known. Futhermore, the clear test of whether the blast wave has approached the self-similar limit is that the trajectory evolves as t 1/2. Experimentally, when a plasma filament is heated, we can use Eq. 1 provided that the resulting blast wave evolves as a cylindrically symmetric wave. This will be generally true if the radius of the blast wave is significantly smaller than the longitudinal extent of the initial plasma filament. More rigorously, the regime in which the use of Eq. 1 is accurate in interpreting blast wave data can be derived by examination of the hydrodynamic equations. For example, the conservation of mass equation / t "( v) 0 implies that the blast wave will evolve as a cylindrical wave if z z r r r r. 2 This is roughly equivalent to requiring that the radius of curvature of the shock front, R, in the z propagation direction satisfy at all times R r t. 3 Similar conclusions can be derived by examination of the other hydrodynamic equations. In the data analysis that follows, we ensure that R is less than 15% of r(t) in all data used. Only at the very latest times do we find that Eq. 3 is not satisfied with 15% accuracy and these data are discarded from the analysis. III. EXPERIMENTAL RESULTS Our experiments were conducted with the apparatus illustrated in Fig. 1. In all experiments, we examined the deposition of laser energy in a gas jet composed of deuterium. 1 FIG. 2. Raw interferometric data of a blast wave in deuterium clusters at three different times, 0, 1, and 7 ns. These experiments were conducted in support of DD fusion experiments from exploding deuterium clusters. 8 We focused a 30 fs, 800 nm pulse into the plume of deuterium gas from a high pressure, pulsed gas jet. The laser pulse contained 120 mj of energy and was focused with an f /15 lens into the vacuum chamber, yielding an intensity in vacuum of roughly W/cm 2. The focal spot was roughly 50 m and the resulting plasma filament length was 2 3 mm, a length determined by the spatial extent of the gas jet plume. The gas jet could produce clusters or monomolecular gas depending on the stagnation conditions. A plume of unclustered deuterium molecules would be produced when the jet was operated at a backing pressure of 70 atm and a gas reservoir temperature near room temperature 293 K. When the jet was cryogenically cooled with liquid nitrogen it produced a deuterium gas plume of clusters 16 whose average size as measured by Rayleigh scattering was 5 nm. 7 We measured laser energy absorption in these two jet conditions, finding that, while absorption is very small when clusters are absent, the formation of deuterium clusters by cooling the jet results in absorption approaching 100%. 8

3 Phys. Plasmas, Vol. 8, No. 10, October 2001 Femtosecond laser energy deposition in strongly FIG. 4. Electron density as a function of z in the cooled gas jet with clusters. FIG. 3. Radially deconvolved electron density profiles blast waves at the center of the images in Fig. 2. We diagnosed this plasma by splitting a small portion of the main laser pulse with a pellical beam splitter and crossing this probe pulse orthogonal to the main laser ionization axis. This beam backlit the plasma filament which was then imaged into a Michelson interferometer. This technique has been successfully applied to the diagnosis of refraction during intense laser propagation in plasmas. 17 A charge coupled device camera yielded an interferometric image of the plasma filament with 5 m resolution. The time evolution of the filament was measured by taking multiple shots and varying the time delay between ionizing pump and probe pulses. The interferograms yield a phase map of the cigarshaped plasma as a function of time. The radial distribution of electron density was derived by assuming cylindrical symmetry a very good assumption for our data and applying an Abel inversion to the observed radial phase shift. Since the shock waves generated were of high Mach number, the gas after passage through the shock front was ionized and, therefore, the trajectory of the shock wave could be mapped. With these interferograms, we were able to determine the location of the blast wave front to within 5 m. Raw interferometric data of a blast wave in deuterium clusters at three different times, 0, 1, and 7 ns, are illustrated in Fig. 2. The laser enters the image from the left. The location of the laser focus in vacuum is roughly 1 mm before the jet center (z 1.0 mm 0.25 mm). The laser was focused about 2 mm below the nozzle output, though it was slightly closer in the data taken with the warm jet. The location of the center of the gas jet nozzle is set at z 0 in these images. The image at 7 ns also illustrates that Eq. 3 is satisfied since R 3 mm while the maximum blast wave radius is less than 0.5 mm. The radially deconvolved electron density profiles of these images at the center of the images are shown in Fig. 3. From these data, we see the development of the blast wave. At early time the electron density exhibits a radial profile peaked on axis, indicative of the optical ionization of the cluster medium by the Gaussian radial profile focused pulse. By 1 ns, the hot filament has begun to expand and a sharp shock begins to develop. At 7 ns, the blast wave is well formed and the gas density profile exhibits the classic shelllike structure of a late time blast wave. To ascertain the energy deposition from the blast wave velocity, accurate knowledge of the gas jet density is required. This is determined through a measurement of the electron density shortly after ionization by the laser. Since the deuterium will be fully ionized by the laser pulse, measurement of electron density on axis yields atom density at that point in z. An interferogram of the plasma produced in the cooled, cluster containing gas jet is shown in Fig. 2 and annotated as at t 0 ns. This image is taken within 20 ps of the initial laser ionization, a time well before any hydrodynamic motion of the heated gas has taken place. The electron density as a function of z determined from deconvolution of this image is illustrated in Fig. 4. These data indicate that the laser propagates through a rising density profile with a peak density of cm 3. The scale length of this density profile is roughly 1 mm. Similar data for the warm gas jet are illustrated in Fig. 5. The average density in the warm jet is comparable to that seen in the cooled jet. This results from the fact that the experiment with the warm jet was conducted with the laser focus slightly closer to the nozzle 1.5 mm than in the cold jet case 2 mm. This proximity change

4 4548 Phys. Plasmas, Vol. 8, No. 10, October 2001 J. Zweiback and T. Ditmire FIG. 5. Electron density as a function of z in the warm gas jet no cluster formation. offsets the increased density from cooling the jet. It also results in a somewhat faster density ramp in the case of the warm jet data which can be seen from comparison of Figs. 4 and 5. To make use of Eq. 1 in determining energy deposition, the blast wave trajectory at various points along the propagation axis must be measured. Figure 6 shows the trajectory of the ionization front for two different points along the laser propagation axis in the cooled, clustering jet, a point 1.5 mm before the focus in vacuum 2.0 mm before the center of the FIG. 7. Trajectory of the ionization front for two different points along the laser propagation axis in the warm, nonclustering jet. Solid lines represent best fits of Eq. 4. jet plume and a trajectory closer to the gas plume center, 0.7 mm before the center of the jet near best focus in vacuum. Data at similar points in the laser propagation in the warm, nonclustering gas jet are shown in Fig. 7. As these data indicate, the trajectory, after an initial blast wave formation phase of about 3 ns, follows the expected t 1/2 trajectory predicted by Eq. 1. It is striking to note that the blast wave produced in the clustering gas jet manifests a much faster trajectory Fig. 6 than the nonclustering case Fig. 7, betraying the much greater energy deposited in the deuterium plasma in the case in which the gas clusters. IV. DATA ANALYSIS FIG. 6. Trajectory of the ionization front for two different points along the laser propagation axis in the cooled, clustering jet. Solid lines represent best fitsofeq. 4. To derive the energy deposition we fit an equation similar to Eq. 1. Equation 1 is good only for very late times, however, a more accurate representation is one in which the initial radius of the energy deposition is included. Taking account of the initial plasma radius, the blast wave trajectory can be written as 18 r t 1 2 1/2 r 0 f 2 E l / 0 t 1/2 f E 1/4 l 0 t 1/2. This equation is fit to all measured blast wave trajectories using r 0 and E l as free parameters. This fitting also requires knowledge of the deuterium equation of state, manifested in Eq. 4 through the adiabaticity index,. This parameter will likely be slightly below the value of 5/3 expected for an ideal gas of dissociated D 2, since some degrees of freedom i.e., sink of energy are introduced by the ionization of the deuterium atoms and the shock is strong enough that no D 2 survives. 4

5 Phys. Plasmas, Vol. 8, No. 10, October 2001 Femtosecond laser energy deposition in strongly FIG. 8. Calculated eff for two different deuteron densities as a function of shock Mach number. To derive this parameter in the conditions of interest for us, we have utilized a simple model. In our experiments the blast wave velocity is well above the deuterium sound speed with Mach numbers of 20 to 60 characteristic of most of the data i.e., shock velocities of 1.5 to m/s. In this regime, the postshock temperature is a few ev, a temperature in which the deuterium is nearly completely ionized consistent with our data which measure the presence of electrons behind the shock front. If we ignore the energy of D 2 dissociation, we can estimate the adiabatic parameter by using the fact that the internal energy of the gas behind the shock is E 3 2 n e n D kt n 1 I p, 5 where n e and n D are the electron and deuterium densities, n 1 is the density of ionized deuterium ions, and I p is the deuterium ionization potential. n 1 can be found from the Saha equation n e n 1 n 0 2 m ekt 2 3/2 e I p /kt 2 if we ignore electron population in excited states of the neutral deuterium a reasonable approximation for temperatures of a few ev. Here n 0 is the density of unionized deuterium. Since we consider ionized deuterium plasma, we can use the fact that n e n 1 and the fact that E p/( 1) where the plasma pressure is p (n e n D )kt to derive an effective, 2 eff 1 3 g T,n D, 7 where g T,n D 4I p 1 3kT 1 2n 1/2 D 2 2 /m e kt 3/4 e I /2kT. 8 p In the absence of ionization, when kt 0, g 0 and we retrieve the ideal gas value for of 5/3. This simple model ignores the energy of dissociation and is therefore only accurate for temperatures in which the deuterium is strongly ionized 2 ev whereas the approximation made in Eq. 6 6 FIG. 9. a Measured energy deposited per unit length in the cooled cluster forming jet. b Integrated energy deposited along the propagation path in the jet, calculated from the data of a. is accurate for temperatures of less than about 5 ev. Nonetheless, this temperature window rests in the range in which the strong blast waves in our experiments likely heat the deuterium; we, therefore expect that this simple model will give a reasonable estimate for. We can then use the Hugoniot relations for a shock wave in gas to derive a relation between the shock Mach number and eff. The Hugoniot relations can be manipulated to yield for the Mach number M T/T 0, where T 0 is the initial gas temperature. Using Eqs. 7 9 we have calculated eff for a variety of different Mach numbers relevant to our experiment at densities observed in the gas jet. Figure 8 shows the calculated eff for two different deuteron densities and cm 3. This illustrates that at the high Mach numbers observed, the deuterium eff rests around 1.4 to 1.5. This holds over a wide range of density. For this reason, we use eff 1.45 in the following analysis. We have found that variation of eff between 1.4 and 1.5 in the data analysis yields only minor variations in the deposited energy measured 18%. As we describe in the following, this eff also yields total energy absorption values consistent with absorption measurements. Armed with this gamma value, the z dependence of the gas density, and fits to the data by Eq. 4, we can derive the energy deposition. The energy deposited per unit length in the cooled cluster forming jet is illustrated in Fig. 9 a. We find that as much as 100 mj/mm of energy is deposited. We also note that the deposition rate falls off prior to the laser pulse reaching the center of the gas jet plume, where the gas

6 4550 Phys. Plasmas, Vol. 8, No. 10, October 2001 J. Zweiback and T. Ditmire FIG. 10. Measured energy deposited per unit length in the warm, nonclustering gas jet. density is highest and energy deposition should be largest. The reason for this can be seen in Fig. 9 b where the integrated energy deposited is plotted. From this, it can be seen that the laser energy, which is initially 120 mj, is nearly depleted by the gas prior to its reaching the center of the jet. The deconvolved data appear to overestimate slightly the total integrated energy deposited in the jet. This may be a consequence of a small error in the estimate for. The drop in intensity from energy depletion prevents the maximum deposition of energy occurring at the center of the jet plume, where the density is greatest. This fact has important consequences for driving fusion in this experiment. 19 We also note that if one assumes a focal radius near that seen from the initial ionization profile, we can estimate the deposited energy per atom in the plasma. The data of Fig. 9 a indicate that roughly 5 kev per atom is deposited in the plasma. While this technique does not yield the partition of energy between electrons and ions, if we assume that the majority of the deposited energy resides in the ions, which acquire energy from the Coulomb explosion of the clusters, we find that the average ion energy is consistent with other estimates of the ion energy from previous fusion experiments. 8 The energy deposited as a function of distance in the warm gas jet i.e., the jet without clusters is shown in Fig. 10. The energy deposited is over two orders of magnitude less, even though the initial gas density is comparable to the density of the cooled jet experiments. This result is consistent with the drop in absorption seen when clusters are not present in the gas jet. In this case, there is no energy depletion of the laser pulse as it passes through the jet. From these data, we have calculated the approximate energy deposited per atom in the plasma. We find that the deposition is remarkably independent of density, indicating that the energy deposition mechanism is largely a single molecule effect. Once again, assuming a focal diameter of 100 m we estimate that roughly 20 ev of energy is deposited per atom. The deposited energy is roughly consistent with the few ev of energy expected from above threshold ionization of the deuterium molecules followed by a simple Coulomb explosion of a few ev. 20 V. CONCLUSION These data confirm the dramatic difference in absorption efficiency of femtosecond laser pulses at high intensity seen between a gas of clusters and a gas of single molecules at similar densities. In particular the energy depletion of the laser pulse seen in the case of the clustering jet is very evident; an effect which can have an important effect on the yield of DD fusion in these experiments. These results also illustrate that the use of blast wave trajectory analysis can be a useful method for determining how an intense laser propagates through an absorbing gas. Through an understanding of the details of the laser propagation in these experimental circumstances, applications such as x-ray production and fusion neutron production can be optimized. ACKNOWLEDGMENTS We would like to acknowledge useful conversations with Steve Moon, John Edwards, John Crane, and Howard Powell. We also acknowledge the important technical assistance of Greg Hays, Vince Tsai, Rich Shuttlesworth, and Gerry Anderson. This work was carried out at the Lawrence Livermore National Laboratory under the auspices of the U.S. Department of Energy Contract No. W-7405-Eng T. Ditmire, R. A. Smith, J. W. G. Tisch, and M. H. R. Hutchinson, Phys. Rev. Lett. 78, K. Kondo, A. B. Borisov, C. Jordan, A. McPherson, W. A. Schroeder, K. Boyer, and C. K. Rhodes, J. Phys. B 30, A. McPherson, B. D. Thompson, A. B. Borisov, K. Boyer, and C. K. Rhodes, Nature London 370, T. Ditmire, T. Donnelly, R. W. Falcone, and M. D. Perry, Phys. Rev. Lett. 75, E. Parra, I. Alexeev, J. Fan, K. Y. Kim, S. J. McNaught, and H. M. Milchberg, Phys. Rev. E 62, R G. D. Kubiak, L. J. Bernardez, K. D. Krenz, D. J. O Connell, R. Gutowski, and A. M. Todd, Debris-free EUVL sources based on gas jets, OSA Trends Opt. Photonics Ser. on Extreme Ultraviolet Lithography 4, T. Ditmire, J. Zweiback, V. P. Yanovsky, T. E. Cowan, G. Hays, and K. B. Wharton, Nature London 398, J. Zweiback, R. A. Smith, T. E. Cowan, G. Hays, K. B. Wharton, V. P. Yanovsky, and T. Ditmire, Phys. Rev. Lett. 84, T. Ditmire, E. T. Gumbrell, R. A. Smith, A. Djaoui, and M. H. R. Hutchinson, Phys. Rev. Lett. 80, K. Shigemori, T. Ditmire, B. A. Remington, V. Yanovsky, D. Ryutov, K. G. Estabrook, M. J. Edwards, A. J. MacKinnon, A. M. Rubenchik, K. A. Keilty, and E. Liang, Astrophys. J. Lett. 533, L J. Zweiback, T. Ditmire, and M. D. Perry, Femtosecond time resolved studies of the dynamics of noble gas cluster explosions, Phys. Rev. Lett. submitted. 12 T. Ditmire, J. W. G. Tisch, E. Springate, M. B. Mason, N. Hay, R. A. Smith, J. Marangos, and M. H. R. Hutchinson, Nature London 386, M. Lezius, S. Dobosz, D. Normand, and M. Schmidt, Phys. Rev. Lett. 80, Y. B. Zel dovich and Y. P. Raizer, Physics of Shock Waves and High- Temperature Hydrodynamic Phenomena Academic, New York, A. Cavaliere and A. Messina, Astrophys. J. 209, R. A. Smith, T. Ditmire, and J. W. G. Tisch, Rev. Sci. Instrum. 69, A. J. Mackinnon, M. Borghesi, A. Iwase, M. W. Jones, G. J. Pert, S. Rae, K. Burnett, and O. Willi, Phys. Rev. Lett. 76, M. J. Edwards unpublished. 19 J. Zweiback, R. A. Smith, V. P. Yanovsky, T. E. Cowan, G. Hays, K. B. Wharton, and T. Ditmire, Nuclear fusion from Coulomb explosions of D 2 clusters ionized by a femtosecond laser, in Multi-photon Processes, edited by L. DiMauro, R. Freeman, and K. Kulander American Institute of Physics, New York, 2000, p K. Codling and L. J. Frasinski, Contemp. Phys. 35,