- Email: [email protected]
Magnetic acceleration of aluminum foils for shock wave experiments
High Energy Density Physics 6 (2010) 242–245
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Magnetic acceleration of aluminum foils for shock wave experiments Stephan Neff*, David Martinez, Christopher Plechaty, Sandra Stein, Radu Presura Nevada Terawatt Facility, University of Nevada, Reno, 5625 Fox Ave, Reno NV 89506, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 January 2010 Accepted 6 January 2010 Available online 18 January 2010
Scaled experiments studying the interaction of shock waves with inhomogeneous background media are essential for understanding many astrophysical phenomena, since they can be used to test analytical theories and simulation codes. We are currently developing such experiments at the Nevada Terawatt Facility. We are using a pulsed power generator (1 MA peak current) to accelerate thin aluminum flyer plates. By impacting these foils on low-density foam targets, we will be able to carry out scaled experiments. We have demonstrated velocities of up to 8 km/s for 50 mm thick aluminum flyers, and are planning to further increase the flyer velocities. We have also carried out first impact tests with transparent polycarbonate targets. Several improvements for our setup are currently in planning, and these improvements will enable us to design scaled experiments for our facility. Ó 2010 Elsevier B.V. All rights reserved.
Keywords: Magnetically accelerated flyers Shock waves Laboratory Astrophysics Pulsed power
1. Introduction
2. Theory
The interaction of shock waves with inhomogeneous background media is important in many astrophysical problems, such as the interaction of supernova remnants with interstellar gas clouds. Scaled experiments can be used to study these phenomena and such experiments have been proposed for the Z-machine in Sandia [1]. The shock wave in these experiments would be created by impacting a magnetically accelerated flyer plate upon a low-density foam target. Measuring the interaction of the shock wave with inhomogeneities in the foam could then be used to test predictions from analytical theory and to benchmark astrophysical simulation codes. While the flyer parameters achievable on the Z-machine are unparalleled (over 34 km/s for several hundred micrometer thick flyers), the high cost and limited availability of shots on Z make experiments on smaller pulsed power machines, such as the Zebra pulsed power generator at the Nevada Terawatt Facility (NTF), desirable. They also have a higher repetition rate than Z. In this paper, we report the results of flyer acceleration tests and first impact tests that we have carried out at NTF, building on previous experiments [2]. We start by discussing the underlying theory and estimating the shock parameters that can be reached at our facility; we then describe our experimental setup, give results of our acceleration experiments so far, and describe first impact tests with polycarbonate. We conclude our paper by giving an outlook on planned improvements and future experiments.
Flyer impact is a convenient method to launch shocks into solid targets and is a standard experimental technique in equation-ofstate measurements. In the following, we describe the impact in the laboratory frame, in which the target is initially at rest. We treat both the flyer and the target as fluids, an approximation which is admissible since the shock strengths in our experiments are much higher than the yield strengths of both materials.
* Corresponding author. E-mail address: [email protected] (S. Neff). 1574-1818/$ – see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.hedp.2010.01.003
2.1. Collision method Before the flyer impacts the target, the flyer is moving with a constant velocity to the right. For simplicity, we assume that the flyer is homogeneous and that the problem can be described in slab geometry. Upon impact, two shock waves are generated, as illustrated in Fig. 1. One shock wave moves to the right into the target, while a second shock wave, the reverse shock, moves to the left into the flyer. There are four distinct regions in the system: Region A, the unshocked target; Region B, the shocked target; Region C, the shocked flyer; and Region D, the unshocked flyer. These four regions are separated by three surfaces: two shock fronts (separating regions A and B and regions C and D, respectively) and a contact surface that separates the flyer from the target (regions B and C). The relations between the fluid parameters (density, pressure, fluid velocity) at the shock fronts are given by the Rankine– Hugoniot relations [3]. In contrast, the pressures and fluid velocities are identical at both sides of the contact interface; only the
S. Neff et al. / High Energy Density Physics 6 (2010) 242–245
243
p(u)das for the target material, which is initially at restdwe have to plot p(vfl u), where vfl is the initial flyer velocity. This graphical method to determine the shock parameters is illustrated in Fig. 2 for an aluminum flyer impacting a 400 mg/cm3 TMPTA (trimethylpropene-triacrlylate) foam target with a velocity 10 km/s. Once we know the shock pressure and fluid velocity, we can easily calculate the other shock parameters. For instance, the density of the shocked material (r) is given by (3)
rS ¼
densities are different at both sides of the interface. It is a contact discontinuity, so the pressure and fluid velocity must be identical on both sides [3]. Once the reverse shock waves reaches the left side of the flyer, a rarefaction wave is created that moves to the right through the shocked material. It moves faster than the shock front and thus eventually catches up with it, attenuating its amplitude and creating a blast wave moving through the target. This blast wave then continues to move through the target, losing energy during its propagation until it turns into a low-amplitude sound wave and finally dies out. 2.2. Calculation of the initial shock pressure The shock pressure that is created upon impact can be calculated from the Hugoniot curves for the flyer and the target. In the following calculation we assume that the front of the flyer (the side impacting the target) is still solid. Since we only calculate the initial shock pressure, the state of the back of the flyer does not enter the calculations. It does, however, influence the evolution of the shock wave later on. The analysis of shock wave propagation must thus take this non-ideal effect into account. For many materials, the shock velocity (D) is approximately a linear function of the fluid velocity (u) D [ A D Bu
(1)
where A and B are constants for a given material. The Hugoniot curve is therefore determined by these two parameters. This linearity usually only holds over a limited range of shock strengths, since phase transitions and other phenomena can break it. However, most D–u plots can be approximated by piecewise linear curves. From this relation and the conservation of mass and momentum it follows that the shock pressure (p) is given by pðuÞ [ r0 ½A$u D B$u2
(2)
where r0 is the initial density of the material. Since the shock pressure and fluid velocity are equal at both sides of the contact interface, we can use this relation to calculate the shock parameters for our impact experiment by simply plotting Eq. (2) in the laboratory reference frame for both the target and the flyer. The intersection of the two Hugoniot curves yields the shock parameters. When plotting the curves, we have to take into account that the flyer moves relative to the reference frame. So instead of plotting
(3)
To illustrate the range of shock parameters that we expect to reach in our facility, we have calculated them for three flyer velocitiesdall of our experiments use aluminum flyersdand a polycarbonate target which we have used in our first impact tests; we have also calculated the parameters for TMPTA foam targets at three different densities (20 mg/cm3, 100 mg/cm3, and 400 mg/ cm3) Table 1. The Hugoniot data (the parameters r0, A, and B in Eq. (2)) used in the calculations are from published literature [4–6]. These calculations show that even for low-density foam targets high pressures can be achieved, making the setup suitable for scaled experiments. 2.3. Non-ideal effects These simple calculations only estimate the parameters upon impact and do not model the propagation of the shock. For example, the attenuation caused by the rarefaction wave catching up with the shock wave is not taken into account. Another effect that influences the dynamics is Ohmic heating. During acceleration, the finite resistance of the flyers leads to Ohmic heating at their back, resulting in non-uniform density and pressure in the flyer. Modelling the shock dynamics will require a one-dimensional fluid code; calculating the flyer parameters after acceleration, an MHD code. If the shock wave travels for distances comparable with the original flyer diameter, the assumption of slab geometry is no longer valid and a two-dimensional code will be necessary. Experiments with inhomogeneities in the target will require either two-dimensional or three-dimensional simulations. Currently we are focusing our efforts on demonstrating the experimental capabilities necessary to carry out scaled experiments. However, once we are ready, we will use hydrodynamical simulations to design the experiments. 600 TMPTA foam (400 mg/cc) Aluminum flyer
500
Pressure (kbar)
Fig. 1. (Color online) The flyer impact launches two shock waves: one moving through the target and a second one moving through the flyer.
r0 D AþBu ¼ r0 : Du A þ ðB 1Þu
400
Conditions at contact interface between flyer and target
300 Hugoniot curve flyer plate (10 km/s)
200 Hugoniot curve foam target 100
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Fluid velocity (km/s) [Laboratory frame] Fig. 2. (Color online) The crossing-point of the Hugoniot curves for the flyer plate and the target determines the pressure and fluid velocity at the contact interface, since both quantities are continuous at the contact surface.
244
S. Neff et al. / High Energy Density Physics 6 (2010) 242–245
Table 1 Parameters calculated from Hugoniot curves. Given are the initial target density (r0), the flyer velocity (vfl), the fluid velocity (u), the shock pressure (p), the shock velocity (D), and the density of the shocked material (rS). Material
r0 (mg/cc)
Polycarbonate
vfl (km/s)
u (km/s)
p (kbar)
D (km/s)
rS (mg/cc)
1200
5 10 15
3.5 6.7 9.7
316 921 970
7.5 11.6 15.5
2263 2837 3203
TMPTA
20
5 10 15
4.9 9.8 14.7
9 29 60
9.3 14.8 20.4
42 59 72
TMPTA
100
5 10 15
4.8 9.4 13.8
33 118 251
8.8 14.3 19.6
221 293 340
TMPTA
400
5 10 15
4.4 8.3 12.1
110 373 771
6.2 11.2 16.0
1382 1551 1626
3. Experiment Our experiments use the Zebra pulsed power generator at the Nevada Terawatt Facility for accelerating the flyer plates. The Zebra generator was originally operated at Los Alamos as HDZP-II [7]; it can deliver a 1 MA current with a 90 ns rise time. The NTF also houses a 50 TW short-pulse laser system (Leopard), which we plan to use later on for backlighting our foam targets. First tests coupling Zebra with the laser for backlighting wire-array loads have been successful. 3.1. Electromagnetic flyer acceleration We use a stripline configuration for our Zebra load to accelerate aluminum flyer plates which are several millimeters in diameter and between 20 and 130 microns thick. Fig. 3 shows the load configuration. The load consists of a massive center electrode and a copper strip (around 1 cm wide and 1 mm thick) that carries the return current; a 1 mm gap is between them. The load is essentially a magnetic dipole, with a high magnetic pressure in the gap between the two conductors. To mount the aluminum flyer, a hole is punched in the copper strip and an aluminum foil is glued to the inside (facing the center conductor) with conducting epoxy. Due to the skin effect, the current flows predominantly on the inside
Fig. 4. (Color online) Results of a two-dimensional calculation for a setup assuming a harmonic frequency of using the finite-element code Comsol [8]. Shown are streamlines for the magnetic flux density and a contour plot of the current density.
surfaces of the gap. A 1 MA discharge current thus creates a 100 T magnetic field and 40 kbar of magnetic pressure in the gap. This magnetic pressure accelerates the flyer until the electric contact with the copper band breaks; at this point, the flyer continues to move with constant velocity. Upon impact on the target, a shock wave is launched into the target. The calculated current density and magnetic field of our setup is shown in Fig. 4. This calculation assumes a two-dimensional geometry and neglects end effects. The geometry has been optimized in comparison to a proof-of-principle setup used earlier [2], resulting in a more homogeneous magnetic pressure across the flyer. The description so far neglected Ohmic heating. This heating of the flyer has two effects: (i) a part of the flyer changes its state, and (ii) ablation from the back of the flyer increases the velocity of the remaining material (rocket effect). Besides effecting the flyer velocity, the state of the flyer is also important for the analysis of the impact experiments. This phase change complicates the analysis of the experiments and it is thus desirable to use flyers thick enough for the flyer front to remain solid. In our tests so far, we are not able determine the state of the flyer. To remedy this situation, we will use reflectometry in future experiments. This diagnostic method will enable us to check if the front of the flyer is still solid. In addition, we plan to carry out a magnetohydrodynamical simulation to determine the minimum thickness required for a solid front after the acceleration. 3.2. Flyer velocity measurements Measuring the flyer velocity is essential for carrying out successful experiments. We measure the flyer velocity by taking a shadowgraphic image 1 ms–2 ms after the current peak. The Table 2 Flyer velocities v achieved in three experimental campaigns. The flyer diameters were 2 mm (Campaign 1), 6.4 mm (Campaign 2), and 5.6 mm (Campaign 3). Campaign
Fig. 3. (Color online) Snapshot of our short-circuit load inside the chamber. Shown is a side-view of the central electrode, the copper band, and a transparent target for flyer impact experiments.
1
2
3
Thickness (mm)
v (km/s)
v (km/s)
v (km/s)
20 50 75 130
2.0–2.3 1.3–1.7
3.0–5.6 2.2–3.0
6.7–8.5 7.0–7.3
0.7–0.9
S. Neff et al. / High Energy Density Physics 6 (2010) 242–245
Fig. 5. Shock waves created by the impact of two aluminum flyers. Ablation from the back of the flyers is filling the gap between the copper band and the center electrode.
acceleration phase only lasts between 100 ns and 200 ns and the flyer is moving with a constant speed afterward. By measuring the distance the flyer has traveled by the time the image is taken, we can thus determine the flyer velocity. While this method is very easy for us to use d shadowgraphy is one of the core diagnostics available on Zebrad it has some major drawbacks. Its accuracy is limited to z10% by the uncertainty in the time of flyer release (the time the electrical contact breaks) and it cannot determine the state of the flyer front. To remedy these shortcomings, we are currently implementing a velocity interferometer (VISAR) which will give us an accurate and time-resolved measurement of the velocity. Table 2 lists the flyer velocities we have achieved in the three campaigns we have carried out so far. Besides varying the flyer thickness, we also improved our load design in successive campaigns. The original load design had a round center conductor [3], which led to a inhomogeneous magnetic field in the gap between the electrodes. In the second campaign, we started using the geometry depicted in Fig. 4. This geometry produces a more homogeneous field in the gap and is also more stable mechanically, allowing us to reuse the center electrode for many Zebra shots. In the third campaign we started using conducting epoxy to glue the flyer to the copper band, instead of the normal epoxy we had used in the first two campaigns. The improved electrical contact resulted in increased flyer velocities; another effect was that the risk of arcing in the gap was significantly reduced, resulting in more reproducible measurements. We have been able to accelerate 50 micron thick flyers to velocities above 8 km/s and 75 micron flyers to velocities above 7 km/s. The flyer velocities that we have achieved so far are already very promising. We expect a further improvement by using a current multiplier which has recently been tested on Zebra [9]. This current multiplier will increase the discharge current to 1.6 MA, so that we will be able to either accelerate thicker flyers or to achieve higher velocities for a given thickness. 3.3. First impact tests Our scaled experiments will use low-density foam targets with embedded high-density inhomogeneities (’clumps’). We will use
245
X-ray backlighting to image the shock in these targets. The backlighting will use our 50 TW Leopard laser and is currently being developed at NTF. As it is not yet available, we have carried out first impact experiments using polycarbonate targets to test if our flyers are able to drive shock waves. Since our targets are transparent, we used shadowgraphy to image the shock waves in them. Fig. 5 shows a shadowgraphic image taken in an experiment using two flyers impacting on polycarbonate. The image is rotated compared to Fig. 3, so the flyers are moving upwards in this image. Visible on the very bottom of the image is the edge of the center conductor. Above it, separated by a 1 mm wide gap, is the copper band, onto which the two flyers had been mounted. Above the copper band, separated by a 2 mm wide gap, is the edge of the polycarbonate target. Clearly visible are two sets of roughly hemispherical shock waves caused by the impact of the two flyers. Also visible is the ablation from the back of the two flyers. The straight feature above the two sets of shock waves is not caused by the flyers. We have observed it in a test that used the copper band without flyers. It might be caused be inductive heating of the polycarbonate prior to the flyer impact and we plan to conduct further tests to see if it might influence experiments with foam targets. These first impact tests have demonstrated that our flyers have enough energy to drive shock waves. Once backlighting is available, we will switch to foam targets to carry out scaled experiments. 4. Summary The experiments reported in this article have shown that it is feasible to carry out scaled experiments studying shock wave interactions on Zebra. We have demonstrated flyer velocities of up to 8 km/s and expect further improvements by using a current multiplier. Currently we are lacking some of the diagnostics necessary for the scaled experiments. Once X-ray backlighting and VISAR diagnostics are operational and we have verified our results with these diagnostics, we will be ready and start designing our experiments. Acknowledgment This work has been supported by DOE/NNSA under UNR grant DE-FC52-06NA27616. References [1] R.P. Drake, Phys. Plasma. 9 (2002) 3545. [2] S. Neff, J. Ford, S. Wright, D. Martinez, C. Plechaty, R. Presura, Astrophys. Space Sci. 322 (2009) 189. [3] Y.B. Zel’dovich, Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover, 2002. [4] M.D. Knudson, R.W. Lemke, D.B. Hayes, C.A. Hall, C. Deeney, J.R. Asay, J. Appl. Phys. 94 (2003) 4420. [5] L.F. Gudarenko, M.V. Zhernokletov, S.I. Kirshanov, A.E. Kovalev, V.G. Kudel’kin, T.S. Lebedeva, et al., Combustion, Explosion and Shock Waves 40 (2004) 344. [6] M. Koenig, A. Benuzzi, F. Philippe, D. Batani, T. Hall, Phys. Plasma. 6 (1999) 3296. [7] J.S. Shlachter, Plasma Phys. Controlled Fusion 32 (1990) 1073. [8] Comsol Multiphysics. Comsol, Inc., 2006. [9] A.S. Chuvatin, V.L. Kantsyrev, L.I. Rudakov, M.E. Cuneo, A.L. Astanovitskiy, R. Presura, et al., AIP Conf. Proc. 1088 (2009) 253.
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Magnetic acceleration of aluminum foils for shock wave experiments Stephan Neff*, David Martinez, Christopher Plechaty, Sandra Stein, Radu Presura Nevada Terawatt Facility, University of Nevada, Reno, 5625 Fox Ave, Reno NV 89506, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 January 2010 Accepted 6 January 2010 Available online 18 January 2010
Scaled experiments studying the interaction of shock waves with inhomogeneous background media are essential for understanding many astrophysical phenomena, since they can be used to test analytical theories and simulation codes. We are currently developing such experiments at the Nevada Terawatt Facility. We are using a pulsed power generator (1 MA peak current) to accelerate thin aluminum flyer plates. By impacting these foils on low-density foam targets, we will be able to carry out scaled experiments. We have demonstrated velocities of up to 8 km/s for 50 mm thick aluminum flyers, and are planning to further increase the flyer velocities. We have also carried out first impact tests with transparent polycarbonate targets. Several improvements for our setup are currently in planning, and these improvements will enable us to design scaled experiments for our facility. Ó 2010 Elsevier B.V. All rights reserved.
Keywords: Magnetically accelerated flyers Shock waves Laboratory Astrophysics Pulsed power
1. Introduction
2. Theory
The interaction of shock waves with inhomogeneous background media is important in many astrophysical problems, such as the interaction of supernova remnants with interstellar gas clouds. Scaled experiments can be used to study these phenomena and such experiments have been proposed for the Z-machine in Sandia [1]. The shock wave in these experiments would be created by impacting a magnetically accelerated flyer plate upon a low-density foam target. Measuring the interaction of the shock wave with inhomogeneities in the foam could then be used to test predictions from analytical theory and to benchmark astrophysical simulation codes. While the flyer parameters achievable on the Z-machine are unparalleled (over 34 km/s for several hundred micrometer thick flyers), the high cost and limited availability of shots on Z make experiments on smaller pulsed power machines, such as the Zebra pulsed power generator at the Nevada Terawatt Facility (NTF), desirable. They also have a higher repetition rate than Z. In this paper, we report the results of flyer acceleration tests and first impact tests that we have carried out at NTF, building on previous experiments [2]. We start by discussing the underlying theory and estimating the shock parameters that can be reached at our facility; we then describe our experimental setup, give results of our acceleration experiments so far, and describe first impact tests with polycarbonate. We conclude our paper by giving an outlook on planned improvements and future experiments.
Flyer impact is a convenient method to launch shocks into solid targets and is a standard experimental technique in equation-ofstate measurements. In the following, we describe the impact in the laboratory frame, in which the target is initially at rest. We treat both the flyer and the target as fluids, an approximation which is admissible since the shock strengths in our experiments are much higher than the yield strengths of both materials.
* Corresponding author. E-mail address: [email protected] (S. Neff). 1574-1818/$ – see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.hedp.2010.01.003
2.1. Collision method Before the flyer impacts the target, the flyer is moving with a constant velocity to the right. For simplicity, we assume that the flyer is homogeneous and that the problem can be described in slab geometry. Upon impact, two shock waves are generated, as illustrated in Fig. 1. One shock wave moves to the right into the target, while a second shock wave, the reverse shock, moves to the left into the flyer. There are four distinct regions in the system: Region A, the unshocked target; Region B, the shocked target; Region C, the shocked flyer; and Region D, the unshocked flyer. These four regions are separated by three surfaces: two shock fronts (separating regions A and B and regions C and D, respectively) and a contact surface that separates the flyer from the target (regions B and C). The relations between the fluid parameters (density, pressure, fluid velocity) at the shock fronts are given by the Rankine– Hugoniot relations [3]. In contrast, the pressures and fluid velocities are identical at both sides of the contact interface; only the
S. Neff et al. / High Energy Density Physics 6 (2010) 242–245
243
p(u)das for the target material, which is initially at restdwe have to plot p(vfl u), where vfl is the initial flyer velocity. This graphical method to determine the shock parameters is illustrated in Fig. 2 for an aluminum flyer impacting a 400 mg/cm3 TMPTA (trimethylpropene-triacrlylate) foam target with a velocity 10 km/s. Once we know the shock pressure and fluid velocity, we can easily calculate the other shock parameters. For instance, the density of the shocked material (r) is given by (3)
rS ¼
densities are different at both sides of the interface. It is a contact discontinuity, so the pressure and fluid velocity must be identical on both sides [3]. Once the reverse shock waves reaches the left side of the flyer, a rarefaction wave is created that moves to the right through the shocked material. It moves faster than the shock front and thus eventually catches up with it, attenuating its amplitude and creating a blast wave moving through the target. This blast wave then continues to move through the target, losing energy during its propagation until it turns into a low-amplitude sound wave and finally dies out. 2.2. Calculation of the initial shock pressure The shock pressure that is created upon impact can be calculated from the Hugoniot curves for the flyer and the target. In the following calculation we assume that the front of the flyer (the side impacting the target) is still solid. Since we only calculate the initial shock pressure, the state of the back of the flyer does not enter the calculations. It does, however, influence the evolution of the shock wave later on. The analysis of shock wave propagation must thus take this non-ideal effect into account. For many materials, the shock velocity (D) is approximately a linear function of the fluid velocity (u) D [ A D Bu
(1)
where A and B are constants for a given material. The Hugoniot curve is therefore determined by these two parameters. This linearity usually only holds over a limited range of shock strengths, since phase transitions and other phenomena can break it. However, most D–u plots can be approximated by piecewise linear curves. From this relation and the conservation of mass and momentum it follows that the shock pressure (p) is given by pðuÞ [ r0 ½A$u D B$u2
(2)
where r0 is the initial density of the material. Since the shock pressure and fluid velocity are equal at both sides of the contact interface, we can use this relation to calculate the shock parameters for our impact experiment by simply plotting Eq. (2) in the laboratory reference frame for both the target and the flyer. The intersection of the two Hugoniot curves yields the shock parameters. When plotting the curves, we have to take into account that the flyer moves relative to the reference frame. So instead of plotting
(3)
To illustrate the range of shock parameters that we expect to reach in our facility, we have calculated them for three flyer velocitiesdall of our experiments use aluminum flyersdand a polycarbonate target which we have used in our first impact tests; we have also calculated the parameters for TMPTA foam targets at three different densities (20 mg/cm3, 100 mg/cm3, and 400 mg/ cm3) Table 1. The Hugoniot data (the parameters r0, A, and B in Eq. (2)) used in the calculations are from published literature [4–6]. These calculations show that even for low-density foam targets high pressures can be achieved, making the setup suitable for scaled experiments. 2.3. Non-ideal effects These simple calculations only estimate the parameters upon impact and do not model the propagation of the shock. For example, the attenuation caused by the rarefaction wave catching up with the shock wave is not taken into account. Another effect that influences the dynamics is Ohmic heating. During acceleration, the finite resistance of the flyers leads to Ohmic heating at their back, resulting in non-uniform density and pressure in the flyer. Modelling the shock dynamics will require a one-dimensional fluid code; calculating the flyer parameters after acceleration, an MHD code. If the shock wave travels for distances comparable with the original flyer diameter, the assumption of slab geometry is no longer valid and a two-dimensional code will be necessary. Experiments with inhomogeneities in the target will require either two-dimensional or three-dimensional simulations. Currently we are focusing our efforts on demonstrating the experimental capabilities necessary to carry out scaled experiments. However, once we are ready, we will use hydrodynamical simulations to design the experiments. 600 TMPTA foam (400 mg/cc) Aluminum flyer
500
Pressure (kbar)
Fig. 1. (Color online) The flyer impact launches two shock waves: one moving through the target and a second one moving through the flyer.
r0 D AþBu ¼ r0 : Du A þ ðB 1Þu
400
Conditions at contact interface between flyer and target
300 Hugoniot curve flyer plate (10 km/s)
200 Hugoniot curve foam target 100
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Fluid velocity (km/s) [Laboratory frame] Fig. 2. (Color online) The crossing-point of the Hugoniot curves for the flyer plate and the target determines the pressure and fluid velocity at the contact interface, since both quantities are continuous at the contact surface.
244
S. Neff et al. / High Energy Density Physics 6 (2010) 242–245
Table 1 Parameters calculated from Hugoniot curves. Given are the initial target density (r0), the flyer velocity (vfl), the fluid velocity (u), the shock pressure (p), the shock velocity (D), and the density of the shocked material (rS). Material
r0 (mg/cc)
Polycarbonate
vfl (km/s)
u (km/s)
p (kbar)
D (km/s)
rS (mg/cc)
1200
5 10 15
3.5 6.7 9.7
316 921 970
7.5 11.6 15.5
2263 2837 3203
TMPTA
20
5 10 15
4.9 9.8 14.7
9 29 60
9.3 14.8 20.4
42 59 72
TMPTA
100
5 10 15
4.8 9.4 13.8
33 118 251
8.8 14.3 19.6
221 293 340
TMPTA
400
5 10 15
4.4 8.3 12.1
110 373 771
6.2 11.2 16.0
1382 1551 1626
3. Experiment Our experiments use the Zebra pulsed power generator at the Nevada Terawatt Facility for accelerating the flyer plates. The Zebra generator was originally operated at Los Alamos as HDZP-II [7]; it can deliver a 1 MA current with a 90 ns rise time. The NTF also houses a 50 TW short-pulse laser system (Leopard), which we plan to use later on for backlighting our foam targets. First tests coupling Zebra with the laser for backlighting wire-array loads have been successful. 3.1. Electromagnetic flyer acceleration We use a stripline configuration for our Zebra load to accelerate aluminum flyer plates which are several millimeters in diameter and between 20 and 130 microns thick. Fig. 3 shows the load configuration. The load consists of a massive center electrode and a copper strip (around 1 cm wide and 1 mm thick) that carries the return current; a 1 mm gap is between them. The load is essentially a magnetic dipole, with a high magnetic pressure in the gap between the two conductors. To mount the aluminum flyer, a hole is punched in the copper strip and an aluminum foil is glued to the inside (facing the center conductor) with conducting epoxy. Due to the skin effect, the current flows predominantly on the inside
Fig. 4. (Color online) Results of a two-dimensional calculation for a setup assuming a harmonic frequency of using the finite-element code Comsol [8]. Shown are streamlines for the magnetic flux density and a contour plot of the current density.
surfaces of the gap. A 1 MA discharge current thus creates a 100 T magnetic field and 40 kbar of magnetic pressure in the gap. This magnetic pressure accelerates the flyer until the electric contact with the copper band breaks; at this point, the flyer continues to move with constant velocity. Upon impact on the target, a shock wave is launched into the target. The calculated current density and magnetic field of our setup is shown in Fig. 4. This calculation assumes a two-dimensional geometry and neglects end effects. The geometry has been optimized in comparison to a proof-of-principle setup used earlier [2], resulting in a more homogeneous magnetic pressure across the flyer. The description so far neglected Ohmic heating. This heating of the flyer has two effects: (i) a part of the flyer changes its state, and (ii) ablation from the back of the flyer increases the velocity of the remaining material (rocket effect). Besides effecting the flyer velocity, the state of the flyer is also important for the analysis of the impact experiments. This phase change complicates the analysis of the experiments and it is thus desirable to use flyers thick enough for the flyer front to remain solid. In our tests so far, we are not able determine the state of the flyer. To remedy this situation, we will use reflectometry in future experiments. This diagnostic method will enable us to check if the front of the flyer is still solid. In addition, we plan to carry out a magnetohydrodynamical simulation to determine the minimum thickness required for a solid front after the acceleration. 3.2. Flyer velocity measurements Measuring the flyer velocity is essential for carrying out successful experiments. We measure the flyer velocity by taking a shadowgraphic image 1 ms–2 ms after the current peak. The Table 2 Flyer velocities v achieved in three experimental campaigns. The flyer diameters were 2 mm (Campaign 1), 6.4 mm (Campaign 2), and 5.6 mm (Campaign 3). Campaign
Fig. 3. (Color online) Snapshot of our short-circuit load inside the chamber. Shown is a side-view of the central electrode, the copper band, and a transparent target for flyer impact experiments.
1
2
3
Thickness (mm)
v (km/s)
v (km/s)
v (km/s)
20 50 75 130
2.0–2.3 1.3–1.7
3.0–5.6 2.2–3.0
6.7–8.5 7.0–7.3
0.7–0.9
S. Neff et al. / High Energy Density Physics 6 (2010) 242–245
Fig. 5. Shock waves created by the impact of two aluminum flyers. Ablation from the back of the flyers is filling the gap between the copper band and the center electrode.
acceleration phase only lasts between 100 ns and 200 ns and the flyer is moving with a constant speed afterward. By measuring the distance the flyer has traveled by the time the image is taken, we can thus determine the flyer velocity. While this method is very easy for us to use d shadowgraphy is one of the core diagnostics available on Zebrad it has some major drawbacks. Its accuracy is limited to z10% by the uncertainty in the time of flyer release (the time the electrical contact breaks) and it cannot determine the state of the flyer front. To remedy these shortcomings, we are currently implementing a velocity interferometer (VISAR) which will give us an accurate and time-resolved measurement of the velocity. Table 2 lists the flyer velocities we have achieved in the three campaigns we have carried out so far. Besides varying the flyer thickness, we also improved our load design in successive campaigns. The original load design had a round center conductor [3], which led to a inhomogeneous magnetic field in the gap between the electrodes. In the second campaign, we started using the geometry depicted in Fig. 4. This geometry produces a more homogeneous field in the gap and is also more stable mechanically, allowing us to reuse the center electrode for many Zebra shots. In the third campaign we started using conducting epoxy to glue the flyer to the copper band, instead of the normal epoxy we had used in the first two campaigns. The improved electrical contact resulted in increased flyer velocities; another effect was that the risk of arcing in the gap was significantly reduced, resulting in more reproducible measurements. We have been able to accelerate 50 micron thick flyers to velocities above 8 km/s and 75 micron flyers to velocities above 7 km/s. The flyer velocities that we have achieved so far are already very promising. We expect a further improvement by using a current multiplier which has recently been tested on Zebra [9]. This current multiplier will increase the discharge current to 1.6 MA, so that we will be able to either accelerate thicker flyers or to achieve higher velocities for a given thickness. 3.3. First impact tests Our scaled experiments will use low-density foam targets with embedded high-density inhomogeneities (’clumps’). We will use
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X-ray backlighting to image the shock in these targets. The backlighting will use our 50 TW Leopard laser and is currently being developed at NTF. As it is not yet available, we have carried out first impact experiments using polycarbonate targets to test if our flyers are able to drive shock waves. Since our targets are transparent, we used shadowgraphy to image the shock waves in them. Fig. 5 shows a shadowgraphic image taken in an experiment using two flyers impacting on polycarbonate. The image is rotated compared to Fig. 3, so the flyers are moving upwards in this image. Visible on the very bottom of the image is the edge of the center conductor. Above it, separated by a 1 mm wide gap, is the copper band, onto which the two flyers had been mounted. Above the copper band, separated by a 2 mm wide gap, is the edge of the polycarbonate target. Clearly visible are two sets of roughly hemispherical shock waves caused by the impact of the two flyers. Also visible is the ablation from the back of the two flyers. The straight feature above the two sets of shock waves is not caused by the flyers. We have observed it in a test that used the copper band without flyers. It might be caused be inductive heating of the polycarbonate prior to the flyer impact and we plan to conduct further tests to see if it might influence experiments with foam targets. These first impact tests have demonstrated that our flyers have enough energy to drive shock waves. Once backlighting is available, we will switch to foam targets to carry out scaled experiments. 4. Summary The experiments reported in this article have shown that it is feasible to carry out scaled experiments studying shock wave interactions on Zebra. We have demonstrated flyer velocities of up to 8 km/s and expect further improvements by using a current multiplier. Currently we are lacking some of the diagnostics necessary for the scaled experiments. Once X-ray backlighting and VISAR diagnostics are operational and we have verified our results with these diagnostics, we will be ready and start designing our experiments. Acknowledgment This work has been supported by DOE/NNSA under UNR grant DE-FC52-06NA27616. References [1] R.P. Drake, Phys. Plasma. 9 (2002) 3545. [2] S. Neff, J. Ford, S. Wright, D. Martinez, C. Plechaty, R. Presura, Astrophys. Space Sci. 322 (2009) 189. [3] Y.B. Zel’dovich, Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover, 2002. [4] M.D. Knudson, R.W. Lemke, D.B. Hayes, C.A. Hall, C. Deeney, J.R. Asay, J. Appl. Phys. 94 (2003) 4420. [5] L.F. Gudarenko, M.V. Zhernokletov, S.I. Kirshanov, A.E. Kovalev, V.G. Kudel’kin, T.S. Lebedeva, et al., Combustion, Explosion and Shock Waves 40 (2004) 344. [6] M. Koenig, A. Benuzzi, F. Philippe, D. Batani, T. Hall, Phys. Plasma. 6 (1999) 3296. [7] J.S. Shlachter, Plasma Phys. Controlled Fusion 32 (1990) 1073. [8] Comsol Multiphysics. Comsol, Inc., 2006. [9] A.S. Chuvatin, V.L. Kantsyrev, L.I. Rudakov, M.E. Cuneo, A.L. Astanovitskiy, R. Presura, et al., AIP Conf. Proc. 1088 (2009) 253.