- Email: [email protected]
Repeatability in radiative shock tube experiments
High Energy Density Physics 6 (2010) 157–161
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Repeatability in radiative shock tube experiments F.W. Doss*, R.P. Drake, C.C. Kuranz University of Michigan, Department of Atmospheric, Oceanic, and Space Sciences, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 December 2009 Accepted 12 December 2009 Available online 28 December 2009
We report here data gathered regarding radiative shock experiments carried out on October 23, 2008. This day featured a number of nominally identical experimental shots. We discuss the degree to which the shots qualitatively differed from one to another and to what degree quantitative measurements, such as shock position, proved to have repeatably obtainable values. In particular, we call attention to the use of radiative precursor-launched wall shocks as a diagnostic feature. Ó 2010 Elsevier B.V. All rights reserved.
Keywords: Hydrodynamics Radiative shocks X-ray radiography
1. Introduction The radiative shock experiment has been of interest for some time [1–6] as a system which strongly couples radiation and hydrodynamic fields, in which the dynamics are substantially altered from the radiation-free case. As post-shock temperature increases with shock speed, one finds that for fast ((10 km/s) shocks, thermal photon flux from the shock strongly heats the upstream gas, which can noticeably change the shock structure [7,8]. Because of the high pressures and temperatures to which terrestrial matter must be brought before the radiation and material energy fluxes become comparable, experiments of this type are currently carried out only in large scientific facilities. It is also in the nature of experiments at these pressures and temperatures that most of the laser targets and related structures do not survive from one shock experiment to the next. The experiments described in this paper took place at the Omega Laser Facility at Laboratory for Laser Energetics [9], and were intended to assess the degree of repeatability of initial conditions and experimental parameters for radiative shock experiments. To this purpose, after some initial shots which served to center the timing of the shock, the experiments were designed to be nominally identical, as described below. 2. Experimental design The experiment is designed to launch strongly radiating shock waves down a xenon-filled tube to a viewing volume, where they
* Corresponding author. E-mail address: [email protected] (F.W. Doss). 1574-1818/$ – see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.hedp.2009.12.007
are imaged by x-ray radiography. Due to the high density increase (a ratio of approximately 20, as discussed below) over the shock, a result of the radiation transport [6,10], we can image with great clarity the difference between the unshocked and shocked xenon. The experimental dimensions are a 21 mm thick beryllium drive disc, and a polyimide tube 625 mm outer diameter with 25 mm thick walls, filled with xenon at 1.1 atm pressure. The shocks are launched by illuminating the drive disc with 3.8 kJ of laser energy delivered by 10 drive beams in a 1 ns square pulse over an approximately 840 mm diameter circular spot. Detailed initial conditions showing the variation from shot-to-shot are shown in Table 1. Approximately 14 ns later, the set of backlighter beams deliver five beams of 70 J each to each of two sites on the orthogonal backlighter target. Each site contains a 300 mm V foil, illuminated by drive beams with 800 mm spot size for 200 ps. The backlighter emission then projects a cone of x-rays through the 50-mm-to-20-mm tapered pinhole. These x-rays pass through the target and into the film stack (Agfa D7 film backed with Fujifilm image plates). The film is ungated (Fig. 1). 3. Measured quantities The primary output of the experiment was a set of x-ray radiographs. Optimally, each shot could produce two orthogonal radiographs, either simultaneously or displaced in time by 1–2 ns. Experimental hazards caused many of the targets to fall short of this ideal, but thirteen usable radiographs were produced. From the radiographs, we may extract directly, through reference to the spatial fiducial provided by the gold grid, the distances of the shock front from the drive surface (see Fig. 4). For those shocks with complicated spatial profiles, the shock position is the average distance of the shock front. This shock position may be
158
F.W. Doss et al. / High Energy Density Physics 6 (2010) 157–161
Table 1 Detailed initial conditions for the experimental campaign. Beryllium thickness is measured in mm and is accurate to within 0.5 mm. Laser energy is measured in J accurate to 2% standard deviation. Pre-shot gas pressure is measured in atm to an accuracy of 0.005 atm. Shot number
Be disc
Laser energy
Pressure
52661 52663 52664a 52665 52667 52668 52669 52670 52671
21 21 22 21 21 21 21 21 21
3889.6 3882 3820.1 3892.4 3880.2 3859.8 3846 3841.5 3867.4
1.13 1.17 1.09 1.13 1.2 1.11 1.17 1.17 1.17
a The shot was known previous to the experiment to have an abnormality in its shock tube tilt.
used, with the view timing, to calculate the mean speed of the shock. We may also read off the width of the dense xenon layer, the dark layer downstream of the shock front, as averaged by eye. By comparing the dense layer width to the shock position, we learn the volumes occupied by the same quantity of xenon before and after being shocked, the ratio of which is the shock compression ratio. The gold grid fiducial is used with pre-shot metrology to infer a target coordinate system over the experimental image. We use
observed inconsistency with a known feature to infer the range of worst-case validity of the coordinate system used. In this paper, the location of the center of the shock tube, which should be 0 mm vertically displaced, is used as the reference feature. For example, Fig. 2(a) has an accurate tube center, while (b) shows some displacement. The absolute distances from the drive tube are therefore known to be correct to within this range of discrepancy. Depending on what processes contributed to the discrepancy (e.g. tube tilt, grid shifting, grid square size variability, etc.), the location may in fact be more accurately measured in the tube length direction than the range for that shot. We report in this paper the maximum range of discrepancy as measured for each experimental image, and for the time being make no further assumptions. We note that in the preparation for experiments, the degree of discrepancy was to some extent able to be anticipated; targets shot earlier in the shot campaign were accordingly prioritized, and it is only the last several shots which suffer from large fiducial error. In the case where we have two images of the same shot displaced by 1 ns, relatively free of complex structure, we may extract the local (to within the shutter speed of 0.2 ns) shock velocity. From the shock images shown in Fig. 2, we extract a characteristic velocity of 110 km/s for shock at this time. It has been recently reported [11] that radiographic data of highenergy-density shock tube experiments may contain information embedded in the physics of a shock–shock interaction stemming from the wall shocks. In high-energy-density systems, and
Fig. 1. Schematic of experimental targets and x-ray paths in the Omega chamber. X-ray images shown are simultaneous images from shot 52667. (For interpretation of the references to colour in this figure legend, the reader is refered to the webversion of this article).
F.W. Doss et al. / High Energy Density Physics 6 (2010) 157–161
159
200 µm
150
100
50
0
2
4
6
8
12 °
10
Fig. 3. Approximate effects of angle with respect to the line of view (horizontal axis, in degrees) on apparent width of the dense xenon layer (vertical axis, in mm). The solid diagonal lines show the trend of angles to produce a dense layer of greater apparent thickness. The dashed lines show data from Table 2, with shot 52664 omitted. Additionally, the histogram shows approximate angles observed of the dense layer over different views, with a mean of 5.3 .
4. Repeatability 4.1. Primary shock data Table 2 contains the key data parameters discussed above, as measured for each shot. From Table 2 we may also extract derived quantities, such as the approximate compression ratio of the shock. Table 3 shows the results of the calculation, resulting in an average compression ratio of 17 for the experiments. We would like to discuss briefly the possible errors in such a compression ratio. Because we image through an integrated path of chords across the shock tube, any angle by which the shock is misaligned with respect to the plane of tube will appear as an increase in xenon dense layer width. We incorporate this error source approximately as
61
13 ns data 14 ns data
particularly in the radiating shock case, the energy transport ahead of the shock may be great enough to drive ablation away from the tube walls ahead of the primary shock in the system. The tube material then expands radially into the tube, driving a secondary converging shock known as a wall shock. The point at which the wall shock interacts with the primary shock of the system is often visible in radiographs. The distance of the wall shock interaction point from the wall (the wall shock amplitude) may be readily measured, as may, in some cases, the angles of both the wall shock and primary shock deflections in the vicinity of the point. From the former measurement, we obtain a length for which there has been derived [11] a scaling relation relating the wall shock amplitude with the velocity of the primary shock and the material properties of the wall. From the measurement of angles, we may extract the Mach number of the primary shock relative to its immediate upstream environment.
65
Sh o t N u m b e r
Fig. 2. Two orthogonal images from Shot 52665, at a) 13 ns and b) 14 ns. The grid squares are 63.5 mm. (For interpretation of the references to colour in this figure legend, the reader is refered to the webversion of this article).
63
67 68 69 70 71 1500
1700
1900
2100
2300
2500
Shock Position Fig. 4. Positions of shocks measured experimentally in each shot, measured in distance from drive disc in mm. Error bars shown are worst-case estimates for each piece of data, based on displacement of a known feature (tube center) in target coordinates to a different relative location in radiography coordinates. Shot 52667 contains two points of simultaneous, overlapping, and agreeing data. Not shown: one piece of 16 ns data from shot 52661. (For interpretation of the references to colour in this figure legend, the reader is refered to the webversion of this article).
160
F.W. Doss et al. / High Energy Density Physics 6 (2010) 157–161
Table 2 Radiographic key data summary for the experiments of October 23, 2008. Spatial data are given in mm. Position refers to the location of the shock front from the initial location of the laser-irradiated surface of the drive disc. Xenon dense layer widths have a resolution limit of 9 mm. The range of possible positional error varies with metrology for each view. Timing data are given in ns and have a typical overall uncertainty of 0.250 ns (except for shots 52663–5, which have 0.500 ns). Where two images are taken, the error in relative timing is 0.010 ns. Shot number
Position in view 1
Position in view 2
Range in view 1
52661 52663 52664* 52665 52667 52668 52669 52670 52671
2308 2030 1748 2042 2085 2098 1940 2038 1943
2485
100 50 100 25 25 65 75 275 300
*
1798 2178 2077 2310
Range in view 2 70 75 75 25 75
Time of view 1
Time of view 2
Xe width in view 1
Xe width in view 2
14.03 13.00 12.95 13.05 13.06 13.15 13.09 14.15 13.06
16.03
125 122 90 135 167 103 150 137 121
117
12.95 14.05 13.06 14.15
91 115 136 137
Shot 52664 was unique in that it was a known out-of-spec target, with a drive disc resting at an angle >5 with respect to the shock tube which generated unusual data.
emeasured ¼
p d 1 q w w
(1)
where e is the compression ratio, p is the shock position, w is the dense layer width, d is the shock tube inner diameter, and q is the angle in radians of the shock with respect to the tube perpendicular. The values of p and w are readily obtainable from Table 2, and d is 575 mm. We see that for a typical shock of 3true ¼ p/ w ¼ 20, an angle of 1 would be sufficient to lower the measured ratio to 18. We suggest accordingly that the mean of compression ratios for this experiment likely lies between 17 and 20. In either case, this is consistent with the high density increases one expects from a system with significant radiative losses [10, p. 323]. Fig. 3 shows the effect of angular variation on the layer widths obtained in this experiment. To find the actual layer thickness, knowing the measured value (the dashed line) and the angle, one starts from the dashed line at that angle and follows the slope of the diagonal lines leftward to find the intersection with the vertical axis. In most cases here, the angle is not precisely known as the two views are not simultaneous. Also shown in Fig. 3 is a histogram of observed angles of the dense layer with respect to the plane of the tube (as measured by a chord following the center of the dense layer, measured against the perpendicular to the tube wall). The effect we are describing, which creates apparent layer broadening, is accurate only for small angles. For large angles, integration of opacities through the edges of the layer will begin to fall off and the broadening effect will be diminished. For moderate angles ((9 ) we expect the effect to be accurate, and it is possible that a layer of apparent thickness 150 mm might be closer to 100 mm in actuality. Fig. 4 contains the shock position data from shocks in the 13–14 ns range, together with estimated maximum possible error for each shot
Table 3 Derived compression ratios from data in Table 2. Typical experimental uncertainty in this inference is þ6/1 (þ5/0 from the effect of tilt, þ1/1 from the effect of position uncertainty). Shot number
Compression
Ratio
52661 52663 52664 52665 52667 52668 52669 52670 52671
18.5 16.6 19.4 15.1 12.5 20.4 12.9 14.9 16.1
21.2 19.8 18.9 15.3 16.9
in the measurement. The shots show approximately a 5% variation in shock position. While parameters such as the drive energy were uniform from shot-to-shot to within much better accuracy than this, the thickness of the drive disc was verified to only within 1 mm. For the 20 mm drive disc, this is a 5% variation, which might plausibly have this effect on the speed and overall distance traveled of the shock. In addition, we have recently discovered that the photolithographically produced grids are not identical to one another. A study to assess their range of variability is in progress. This also could plausibly account for much of the shot-to-shot range of possible variability.
4.2. Wall shock data Tables 4 and 5 contain data extracted from the wall shocks, as discussed above. We see in Table 4 the wall shock amplitude is relatively variable from shot-to-shot and, furthermore, image to image within a shot. This likely reflects a dependence of the physics on higher-dimensional structure, particularly radiation transport away from the shock in potentially complex geometries. A strong dependence on the quantity of radiation expelled from the shock will also result in a complex reading. From the data in Table 4, a characteristic amplitude of 67 mm is suggested. Table 5 shows us that the Mach number diagnostic is relatively robust over the set of repeated experiments. The average Mach number suggested is 3.0. Combined with the shock velocity measurement of 110 km/s arrived at above, which corresponds to a mean local Mach number of 3.1, we obtain a range of velocities for the observed shocks from 96.9 to 119.6 km/s. For comparison, the overall Mach number of the shock, relative to the initial xenon state far upstream of the shock, is approximately 600. The value is much smaller at the density jump because of the preheating of the upstream material by the radiation.
Table 4 Wall shock amplitudes, measured in mm. Estimated error is on the order of a resolution element, 9 mm. Shot number
Side 1
Side 2
Side 3
Side 4
52661 52663 52664 52665 52667 52668 52669 52670 52671
59.9 75 37.8 85.3 72.5a 97.0 67.8 57.6 59.6
73.9a 79.6
45.4
60.2
73.4 63.8
63.7 60.9a
82.2 60.9 75.1
a
72.2 49.0
The entries have unusual, three-dimensional structure evident in the image, and are almost certainly not representative of simple scaling laws.
F.W. Doss et al. / High Energy Density Physics 6 (2010) 157–161 Table 5 Primary shock Mach numbers inferred from wall shock characteristics. The orthogonal imaging allows up to four wall shock interactions to be inferred per shot. There may, however, be insufficient signal in a given image to identify both angles necessary for the wall shock analysis. The error in this inference is on the order of 0.1. Shot number
Side 1
52661 52663 52664 52665 52667 52668 52669 52670 52671
2.97
Side 2
Side 3
Side 4
2.94
3.10
3.02 2.92
3.21 2.90
3.13 2.95
3.15
3.01
2.93 2.73 2.92 3.37 3.03 3.01 3.25
Acknowledgements The authors would like to thank the University of Michigan target fabrication team, including Mike Grosskopf, Donna Marion, Robb Gillespie, and Marissa Mantey. The authors would also like to thank the technical staff at the Omega Laser Facility. This research was supported by the DOE NNSA under the Predictive Science Academic Alliance Program by grantDE-FC5208NA28616, under the Stewardship Sciences Academic Alliances program by grant DE-FG52-04NA00064, under the National Laser User Facility by grant DE-FG03?00SF22021, and by the Stewardship Science Graduate Fellowship program.
161
References [1] J.C. Bozier, G. Thiell, J.P. Le Breton, S. Azra, M. Decroisette, D. Schirmann, Experimental observation of a radiative wave generated in xenon by a laserdriven supercritical shock. Phys. Rev. Lett. 57 (11) (1986) 1304–1307. [2] X. Fleury, S. Bouquet, C. Stehle´, M. Koenig, D. Batani, A. Benuzzi-Mounaix, J.-P. Chie`ze, N. Grandjouan, J. Greiner, T. Hall, E. Henry, J.-P. Lafon, Leygnac, V. Malka, B. Marchet, H. Merdji, C. Michaut, F. Thais, A laser experiment for studying radiative shocks in astrophysics. Laser Part. Beams 20 (2002) 263. [3] P.A. Keiter, R.P. Drake, T.S. Perry, H. Robey, B.A. Remington, C.A. Iglesias, R.J. Wallace, J. Knauer, Observation of a hydrodynamically driven, radiativeprecursor shock. Phys. Rev. Lett. 89 (16) (2002) 165003. [4] S. Bouquet, C. Stehle´, M. Koenig, J.-P. Chie`ze, A. Benuzzi-Mounaix, D. Batani, S. Leygnac, X. Fleury, H. Merdji, C. Michaut, F. Thais, N. Grandjouan, T. Hall, E. Henry, V. Malka, J.-P.J. Lafon, Observation of laser driven supercritical radiative shock precursors. Phys. Rev. Lett. 92 (22) (2004) 225001. [5] M. Koenig, T. Vinci, A. Bennuzi-Mounaix, N. Ozaki, A. Ravasio, L. Boireau, C. Michaut, S. Bouquet, S. Atzeni, A. Schiavi, O. Peyrusse, D. Batani, Phys. Plasmas 13 (2006) 056504. [6] A.B. Reighard, R.P. Drake, K.K. Dannenberg, D.J. Kremer, M. Grosskopf, E.C. Harding, D.R. Leibrandt, S.G. Glendinning, T.S. Perry, B.A. Remington, J. Greenough, J. Knauer, T. Boehly, S. Bouqet, L. Boireau, M. Koenig, T. Vinci, Observation of collapsing radiative shocks in laboratory experiments. Phys. Plasmas 13 (2006) 082901. [7] Y.B. Zeldovich, Y.P. Razier, Physics of Shock Waves and High-temperature Hydrodynamic Phenomena. Academic Press, 1967. [8] F.H. Shu, The Physics of Astrophysics: Gas Dynamics. University Science Books, 1992. [9] T.R. Boehly, D.L. Brown, R.S. Craxton, R.L. Keck, J.P. Knauer, J.H. Kelly, T.J. Kessler, S.A. Kumpman, S. Loucks, S.A. Letzring, F.J. Marshall, R.L. McCrory, S.F.B. Morse, W. Seka, J.M. Soures, C.P. Verdon, Opt. Commun. 133 (1994) 495. [10] R.P. Drake, High-Energy-Density Physics. Springer, 2006. [11] F.W. Doss, H.F. Robey, R.P. Drake, C.C. Kuranz, Wall shocks in high-energydensity shock tube experiments. Phys. Plasmas 16 (2009) 112705.
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Repeatability in radiative shock tube experiments F.W. Doss*, R.P. Drake, C.C. Kuranz University of Michigan, Department of Atmospheric, Oceanic, and Space Sciences, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 December 2009 Accepted 12 December 2009 Available online 28 December 2009
We report here data gathered regarding radiative shock experiments carried out on October 23, 2008. This day featured a number of nominally identical experimental shots. We discuss the degree to which the shots qualitatively differed from one to another and to what degree quantitative measurements, such as shock position, proved to have repeatably obtainable values. In particular, we call attention to the use of radiative precursor-launched wall shocks as a diagnostic feature. Ó 2010 Elsevier B.V. All rights reserved.
Keywords: Hydrodynamics Radiative shocks X-ray radiography
1. Introduction The radiative shock experiment has been of interest for some time [1–6] as a system which strongly couples radiation and hydrodynamic fields, in which the dynamics are substantially altered from the radiation-free case. As post-shock temperature increases with shock speed, one finds that for fast ((10 km/s) shocks, thermal photon flux from the shock strongly heats the upstream gas, which can noticeably change the shock structure [7,8]. Because of the high pressures and temperatures to which terrestrial matter must be brought before the radiation and material energy fluxes become comparable, experiments of this type are currently carried out only in large scientific facilities. It is also in the nature of experiments at these pressures and temperatures that most of the laser targets and related structures do not survive from one shock experiment to the next. The experiments described in this paper took place at the Omega Laser Facility at Laboratory for Laser Energetics [9], and were intended to assess the degree of repeatability of initial conditions and experimental parameters for radiative shock experiments. To this purpose, after some initial shots which served to center the timing of the shock, the experiments were designed to be nominally identical, as described below. 2. Experimental design The experiment is designed to launch strongly radiating shock waves down a xenon-filled tube to a viewing volume, where they
* Corresponding author. E-mail address: [email protected] (F.W. Doss). 1574-1818/$ – see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.hedp.2009.12.007
are imaged by x-ray radiography. Due to the high density increase (a ratio of approximately 20, as discussed below) over the shock, a result of the radiation transport [6,10], we can image with great clarity the difference between the unshocked and shocked xenon. The experimental dimensions are a 21 mm thick beryllium drive disc, and a polyimide tube 625 mm outer diameter with 25 mm thick walls, filled with xenon at 1.1 atm pressure. The shocks are launched by illuminating the drive disc with 3.8 kJ of laser energy delivered by 10 drive beams in a 1 ns square pulse over an approximately 840 mm diameter circular spot. Detailed initial conditions showing the variation from shot-to-shot are shown in Table 1. Approximately 14 ns later, the set of backlighter beams deliver five beams of 70 J each to each of two sites on the orthogonal backlighter target. Each site contains a 300 mm V foil, illuminated by drive beams with 800 mm spot size for 200 ps. The backlighter emission then projects a cone of x-rays through the 50-mm-to-20-mm tapered pinhole. These x-rays pass through the target and into the film stack (Agfa D7 film backed with Fujifilm image plates). The film is ungated (Fig. 1). 3. Measured quantities The primary output of the experiment was a set of x-ray radiographs. Optimally, each shot could produce two orthogonal radiographs, either simultaneously or displaced in time by 1–2 ns. Experimental hazards caused many of the targets to fall short of this ideal, but thirteen usable radiographs were produced. From the radiographs, we may extract directly, through reference to the spatial fiducial provided by the gold grid, the distances of the shock front from the drive surface (see Fig. 4). For those shocks with complicated spatial profiles, the shock position is the average distance of the shock front. This shock position may be
158
F.W. Doss et al. / High Energy Density Physics 6 (2010) 157–161
Table 1 Detailed initial conditions for the experimental campaign. Beryllium thickness is measured in mm and is accurate to within 0.5 mm. Laser energy is measured in J accurate to 2% standard deviation. Pre-shot gas pressure is measured in atm to an accuracy of 0.005 atm. Shot number
Be disc
Laser energy
Pressure
52661 52663 52664a 52665 52667 52668 52669 52670 52671
21 21 22 21 21 21 21 21 21
3889.6 3882 3820.1 3892.4 3880.2 3859.8 3846 3841.5 3867.4
1.13 1.17 1.09 1.13 1.2 1.11 1.17 1.17 1.17
a The shot was known previous to the experiment to have an abnormality in its shock tube tilt.
used, with the view timing, to calculate the mean speed of the shock. We may also read off the width of the dense xenon layer, the dark layer downstream of the shock front, as averaged by eye. By comparing the dense layer width to the shock position, we learn the volumes occupied by the same quantity of xenon before and after being shocked, the ratio of which is the shock compression ratio. The gold grid fiducial is used with pre-shot metrology to infer a target coordinate system over the experimental image. We use
observed inconsistency with a known feature to infer the range of worst-case validity of the coordinate system used. In this paper, the location of the center of the shock tube, which should be 0 mm vertically displaced, is used as the reference feature. For example, Fig. 2(a) has an accurate tube center, while (b) shows some displacement. The absolute distances from the drive tube are therefore known to be correct to within this range of discrepancy. Depending on what processes contributed to the discrepancy (e.g. tube tilt, grid shifting, grid square size variability, etc.), the location may in fact be more accurately measured in the tube length direction than the range for that shot. We report in this paper the maximum range of discrepancy as measured for each experimental image, and for the time being make no further assumptions. We note that in the preparation for experiments, the degree of discrepancy was to some extent able to be anticipated; targets shot earlier in the shot campaign were accordingly prioritized, and it is only the last several shots which suffer from large fiducial error. In the case where we have two images of the same shot displaced by 1 ns, relatively free of complex structure, we may extract the local (to within the shutter speed of 0.2 ns) shock velocity. From the shock images shown in Fig. 2, we extract a characteristic velocity of 110 km/s for shock at this time. It has been recently reported [11] that radiographic data of highenergy-density shock tube experiments may contain information embedded in the physics of a shock–shock interaction stemming from the wall shocks. In high-energy-density systems, and
Fig. 1. Schematic of experimental targets and x-ray paths in the Omega chamber. X-ray images shown are simultaneous images from shot 52667. (For interpretation of the references to colour in this figure legend, the reader is refered to the webversion of this article).
F.W. Doss et al. / High Energy Density Physics 6 (2010) 157–161
159
200 µm
150
100
50
0
2
4
6
8
12 °
10
Fig. 3. Approximate effects of angle with respect to the line of view (horizontal axis, in degrees) on apparent width of the dense xenon layer (vertical axis, in mm). The solid diagonal lines show the trend of angles to produce a dense layer of greater apparent thickness. The dashed lines show data from Table 2, with shot 52664 omitted. Additionally, the histogram shows approximate angles observed of the dense layer over different views, with a mean of 5.3 .
4. Repeatability 4.1. Primary shock data Table 2 contains the key data parameters discussed above, as measured for each shot. From Table 2 we may also extract derived quantities, such as the approximate compression ratio of the shock. Table 3 shows the results of the calculation, resulting in an average compression ratio of 17 for the experiments. We would like to discuss briefly the possible errors in such a compression ratio. Because we image through an integrated path of chords across the shock tube, any angle by which the shock is misaligned with respect to the plane of tube will appear as an increase in xenon dense layer width. We incorporate this error source approximately as
61
13 ns data 14 ns data
particularly in the radiating shock case, the energy transport ahead of the shock may be great enough to drive ablation away from the tube walls ahead of the primary shock in the system. The tube material then expands radially into the tube, driving a secondary converging shock known as a wall shock. The point at which the wall shock interacts with the primary shock of the system is often visible in radiographs. The distance of the wall shock interaction point from the wall (the wall shock amplitude) may be readily measured, as may, in some cases, the angles of both the wall shock and primary shock deflections in the vicinity of the point. From the former measurement, we obtain a length for which there has been derived [11] a scaling relation relating the wall shock amplitude with the velocity of the primary shock and the material properties of the wall. From the measurement of angles, we may extract the Mach number of the primary shock relative to its immediate upstream environment.
65
Sh o t N u m b e r
Fig. 2. Two orthogonal images from Shot 52665, at a) 13 ns and b) 14 ns. The grid squares are 63.5 mm. (For interpretation of the references to colour in this figure legend, the reader is refered to the webversion of this article).
63
67 68 69 70 71 1500
1700
1900
2100
2300
2500
Shock Position Fig. 4. Positions of shocks measured experimentally in each shot, measured in distance from drive disc in mm. Error bars shown are worst-case estimates for each piece of data, based on displacement of a known feature (tube center) in target coordinates to a different relative location in radiography coordinates. Shot 52667 contains two points of simultaneous, overlapping, and agreeing data. Not shown: one piece of 16 ns data from shot 52661. (For interpretation of the references to colour in this figure legend, the reader is refered to the webversion of this article).
160
F.W. Doss et al. / High Energy Density Physics 6 (2010) 157–161
Table 2 Radiographic key data summary for the experiments of October 23, 2008. Spatial data are given in mm. Position refers to the location of the shock front from the initial location of the laser-irradiated surface of the drive disc. Xenon dense layer widths have a resolution limit of 9 mm. The range of possible positional error varies with metrology for each view. Timing data are given in ns and have a typical overall uncertainty of 0.250 ns (except for shots 52663–5, which have 0.500 ns). Where two images are taken, the error in relative timing is 0.010 ns. Shot number
Position in view 1
Position in view 2
Range in view 1
52661 52663 52664* 52665 52667 52668 52669 52670 52671
2308 2030 1748 2042 2085 2098 1940 2038 1943
2485
100 50 100 25 25 65 75 275 300
*
1798 2178 2077 2310
Range in view 2 70 75 75 25 75
Time of view 1
Time of view 2
Xe width in view 1
Xe width in view 2
14.03 13.00 12.95 13.05 13.06 13.15 13.09 14.15 13.06
16.03
125 122 90 135 167 103 150 137 121
117
12.95 14.05 13.06 14.15
91 115 136 137
Shot 52664 was unique in that it was a known out-of-spec target, with a drive disc resting at an angle >5 with respect to the shock tube which generated unusual data.
emeasured ¼
p d 1 q w w
(1)
where e is the compression ratio, p is the shock position, w is the dense layer width, d is the shock tube inner diameter, and q is the angle in radians of the shock with respect to the tube perpendicular. The values of p and w are readily obtainable from Table 2, and d is 575 mm. We see that for a typical shock of 3true ¼ p/ w ¼ 20, an angle of 1 would be sufficient to lower the measured ratio to 18. We suggest accordingly that the mean of compression ratios for this experiment likely lies between 17 and 20. In either case, this is consistent with the high density increases one expects from a system with significant radiative losses [10, p. 323]. Fig. 3 shows the effect of angular variation on the layer widths obtained in this experiment. To find the actual layer thickness, knowing the measured value (the dashed line) and the angle, one starts from the dashed line at that angle and follows the slope of the diagonal lines leftward to find the intersection with the vertical axis. In most cases here, the angle is not precisely known as the two views are not simultaneous. Also shown in Fig. 3 is a histogram of observed angles of the dense layer with respect to the plane of the tube (as measured by a chord following the center of the dense layer, measured against the perpendicular to the tube wall). The effect we are describing, which creates apparent layer broadening, is accurate only for small angles. For large angles, integration of opacities through the edges of the layer will begin to fall off and the broadening effect will be diminished. For moderate angles ((9 ) we expect the effect to be accurate, and it is possible that a layer of apparent thickness 150 mm might be closer to 100 mm in actuality. Fig. 4 contains the shock position data from shocks in the 13–14 ns range, together with estimated maximum possible error for each shot
Table 3 Derived compression ratios from data in Table 2. Typical experimental uncertainty in this inference is þ6/1 (þ5/0 from the effect of tilt, þ1/1 from the effect of position uncertainty). Shot number
Compression
Ratio
52661 52663 52664 52665 52667 52668 52669 52670 52671
18.5 16.6 19.4 15.1 12.5 20.4 12.9 14.9 16.1
21.2 19.8 18.9 15.3 16.9
in the measurement. The shots show approximately a 5% variation in shock position. While parameters such as the drive energy were uniform from shot-to-shot to within much better accuracy than this, the thickness of the drive disc was verified to only within 1 mm. For the 20 mm drive disc, this is a 5% variation, which might plausibly have this effect on the speed and overall distance traveled of the shock. In addition, we have recently discovered that the photolithographically produced grids are not identical to one another. A study to assess their range of variability is in progress. This also could plausibly account for much of the shot-to-shot range of possible variability.
4.2. Wall shock data Tables 4 and 5 contain data extracted from the wall shocks, as discussed above. We see in Table 4 the wall shock amplitude is relatively variable from shot-to-shot and, furthermore, image to image within a shot. This likely reflects a dependence of the physics on higher-dimensional structure, particularly radiation transport away from the shock in potentially complex geometries. A strong dependence on the quantity of radiation expelled from the shock will also result in a complex reading. From the data in Table 4, a characteristic amplitude of 67 mm is suggested. Table 5 shows us that the Mach number diagnostic is relatively robust over the set of repeated experiments. The average Mach number suggested is 3.0. Combined with the shock velocity measurement of 110 km/s arrived at above, which corresponds to a mean local Mach number of 3.1, we obtain a range of velocities for the observed shocks from 96.9 to 119.6 km/s. For comparison, the overall Mach number of the shock, relative to the initial xenon state far upstream of the shock, is approximately 600. The value is much smaller at the density jump because of the preheating of the upstream material by the radiation.
Table 4 Wall shock amplitudes, measured in mm. Estimated error is on the order of a resolution element, 9 mm. Shot number
Side 1
Side 2
Side 3
Side 4
52661 52663 52664 52665 52667 52668 52669 52670 52671
59.9 75 37.8 85.3 72.5a 97.0 67.8 57.6 59.6
73.9a 79.6
45.4
60.2
73.4 63.8
63.7 60.9a
82.2 60.9 75.1
a
72.2 49.0
The entries have unusual, three-dimensional structure evident in the image, and are almost certainly not representative of simple scaling laws.
F.W. Doss et al. / High Energy Density Physics 6 (2010) 157–161 Table 5 Primary shock Mach numbers inferred from wall shock characteristics. The orthogonal imaging allows up to four wall shock interactions to be inferred per shot. There may, however, be insufficient signal in a given image to identify both angles necessary for the wall shock analysis. The error in this inference is on the order of 0.1. Shot number
Side 1
52661 52663 52664 52665 52667 52668 52669 52670 52671
2.97
Side 2
Side 3
Side 4
2.94
3.10
3.02 2.92
3.21 2.90
3.13 2.95
3.15
3.01
2.93 2.73 2.92 3.37 3.03 3.01 3.25
Acknowledgements The authors would like to thank the University of Michigan target fabrication team, including Mike Grosskopf, Donna Marion, Robb Gillespie, and Marissa Mantey. The authors would also like to thank the technical staff at the Omega Laser Facility. This research was supported by the DOE NNSA under the Predictive Science Academic Alliance Program by grantDE-FC5208NA28616, under the Stewardship Sciences Academic Alliances program by grant DE-FG52-04NA00064, under the National Laser User Facility by grant DE-FG03?00SF22021, and by the Stewardship Science Graduate Fellowship program.
161
References [1] J.C. Bozier, G. Thiell, J.P. Le Breton, S. Azra, M. Decroisette, D. Schirmann, Experimental observation of a radiative wave generated in xenon by a laserdriven supercritical shock. Phys. Rev. Lett. 57 (11) (1986) 1304–1307. [2] X. Fleury, S. Bouquet, C. Stehle´, M. Koenig, D. Batani, A. Benuzzi-Mounaix, J.-P. Chie`ze, N. Grandjouan, J. Greiner, T. Hall, E. Henry, J.-P. Lafon, Leygnac, V. Malka, B. Marchet, H. Merdji, C. Michaut, F. Thais, A laser experiment for studying radiative shocks in astrophysics. Laser Part. Beams 20 (2002) 263. [3] P.A. Keiter, R.P. Drake, T.S. Perry, H. Robey, B.A. Remington, C.A. Iglesias, R.J. Wallace, J. Knauer, Observation of a hydrodynamically driven, radiativeprecursor shock. Phys. Rev. Lett. 89 (16) (2002) 165003. [4] S. Bouquet, C. Stehle´, M. Koenig, J.-P. Chie`ze, A. Benuzzi-Mounaix, D. Batani, S. Leygnac, X. Fleury, H. Merdji, C. Michaut, F. Thais, N. Grandjouan, T. Hall, E. Henry, V. Malka, J.-P.J. Lafon, Observation of laser driven supercritical radiative shock precursors. Phys. Rev. Lett. 92 (22) (2004) 225001. [5] M. Koenig, T. Vinci, A. Bennuzi-Mounaix, N. Ozaki, A. Ravasio, L. Boireau, C. Michaut, S. Bouquet, S. Atzeni, A. Schiavi, O. Peyrusse, D. Batani, Phys. Plasmas 13 (2006) 056504. [6] A.B. Reighard, R.P. Drake, K.K. Dannenberg, D.J. Kremer, M. Grosskopf, E.C. Harding, D.R. Leibrandt, S.G. Glendinning, T.S. Perry, B.A. Remington, J. Greenough, J. Knauer, T. Boehly, S. Bouqet, L. Boireau, M. Koenig, T. Vinci, Observation of collapsing radiative shocks in laboratory experiments. Phys. Plasmas 13 (2006) 082901. [7] Y.B. Zeldovich, Y.P. Razier, Physics of Shock Waves and High-temperature Hydrodynamic Phenomena. Academic Press, 1967. [8] F.H. Shu, The Physics of Astrophysics: Gas Dynamics. University Science Books, 1992. [9] T.R. Boehly, D.L. Brown, R.S. Craxton, R.L. Keck, J.P. Knauer, J.H. Kelly, T.J. Kessler, S.A. Kumpman, S. Loucks, S.A. Letzring, F.J. Marshall, R.L. McCrory, S.F.B. Morse, W. Seka, J.M. Soures, C.P. Verdon, Opt. Commun. 133 (1994) 495. [10] R.P. Drake, High-Energy-Density Physics. Springer, 2006. [11] F.W. Doss, H.F. Robey, R.P. Drake, C.C. Kuranz, Wall shocks in high-energydensity shock tube experiments. Phys. Plasmas 16 (2009) 112705.