Apr 10, 2000 - an ionization precursor is observed ahead of the shock front. This suggests ... thin, dense shell (Cioffi, McKee, & Bertschinger 1988). This.
The Astrophysical Journal, 533:L159–L162, 2000 April 20 q 2000. The American Astronomical Society. All rights reserved. Printed in U.S.A.
DEVELOPING A RADIATIVE SHOCK EXPERIMENT RELEVANT TO ASTROPHYSICS K. Shigemori,1,2 T. Ditmire,1 B. A. Remington,1 V. Yanovsky,1 D. Ryutov,1 K. G. Estabrook,1 M. J. Edwards,1 A. J. MacKinnon,1 A. M. Rubenchik,3 K. A. Keilty,4 and E. Liang4 Received 2000 February 25; accepted 2000 March 8; published 2000 April 10
ABSTRACT We report on the initial results of experiments being developed on the Falcon laser to simulate radiative astrophysical shocks. Cylindrically diverging blast waves were produced in low-density (∼1018 cm23 ), high-Z gas by laser-irradiating Xe gas jets containing atomic clusters. The blast-wave trajectory was measured by Michelson interferometry. The velocity for the blast wave is slightly less than the adiabatic Sedov-Taylor prediction, and an ionization precursor is observed ahead of the shock front. This suggests energy loss through radiative cooling and reduced compression due to preheat deposited ahead of the shock, both consistent with one-dimensional radiation hydrodynamics simulations. Subject headings: conduction — hydrodynamics — ISM: kinematics and dynamics — radiative transfer — shock waves — supernova remnants
Astrophysical shocks are one of the fundamental energy sources in interstellar space (McKee & Draine 1991), heating the interstellar medium (ISM) and triggering a variety of dynamics in structures that they encounter (Klein & Woods 1998). Supernovae are one of the sources of astrophysical shocks; they are massive stars that explode, launching high-speed ejecta that sweep into the ISM. As a supernova evolves into a remnant, the ejecta-ISM interaction launches a strong “forward” shock into the ISM, and a stagnation (“reverse”) shock develops in the ejecta. Depending on the ejecta and ISM densities and on the shock velocities, the shocks may be radiative or purely hydrodynamic (adiabatic). The asymptotic trajectory for a blast wave is often approximated as a power law, R = bt a, where a is called the deceleration parameter. Sedov-Taylor (ST) blast waves correspond to adiabatic hydrodynamics (Sedov 1959), and the corresponding shock trajectory is derived from conservation of mass, momentum, and energy and the Rankin-Hugoniot jump relationships for the shock wave (Zeldovich & Raizer 1966; Chernyi 1957). In spherical geometry, the trajectory for ST blast waves is given by a power-law index of a = 25 . In the pressuredriven snowplow (PDS) regime, radiative losses lead to a very thin, dense shell (Cioffi, McKee, & Bertschinger 1988). This implies an effective adiabatic index g ≈ 1 since r 2 /r1 ≈ (g 1 1)/(g 2 1) for a strong shock. Behind the shell, the density is assumed to be negligible, but the pressure remains high, which leads to a = 27 in spherical geometry. When the radiative losses from the low-density gas behind the shock are sufficiently large that both its pressure and its density are negligible, one enters the momentum-conserving snowplow (MCS) regime, with a = 14 in spherical geometry. In cylindrical geometry, the trajectory for the adiabatic ST blast wave can be written as (Liang
& Keilty 2000; Keilty et al. 2000) R=
[
4 (g 1 1)(g 2 1) 2 p 3g 2 1
1/4
1/4
] ( ) E0 r0l
t 1/2,
(1)
where R is the radius, g is the adiabatic index, E 0 is the initial deposited energy, r 0 is the initial gas mass density, and l is the length of the cylindrical plasma. For the strongly radiative MCS regime, the blast front conserves mass and momentum, but not energy, giving, for cylindrical geometry, R=
(
18E 0 d 02 pr 0 l
1/6
)
t 1/3,
(2)
where d 0 is the initial position of the shock front. Note that in both spherical and cylindrical geometry, the radiative blast waves move more slowly than the adiabatic (ST) blast waves because of the loss of energy and the drop in pressure in the radiative regime. Note also that the cylindrical blast waves move faster than their spherical counterparts because of a slower decrease in pressure with time behind the shock from divergence. It has recently been pointed out that scaled, dynamically evolving astrophysics experiments could be conducted on intense laser facilities (Remington et al. 1999; Ryutov et al. 1999). There have been previous experimental observations of adiabatic ST blast waves in cylindrical geometry in low-Z gases that have revealed R ∼ t 1/2 trajectories (Dune et al. 1994; Clark & Milchberg 1997; Borghesi et al. 1998), and there have been experiments revealing indirect evidence of radiative blast waves by optical (Bozier et al. 1986) and UV emission (Grun et al. 1991). However, there has been little effort to generate experimentally a scaled astrophysical radiative blast wave in the laboratory. We hope that the experiment that we are developing will lead to useful benchmark data for newly emerging, multidimensional, radiative hydrodynamics astrophysics codes (Blondin et al. 1998; Stone & Norman 1992) and radiative shock theories (Bouquet et al. 2000; Cioffi et al. 1988). Our experiment was performed on the Falcon laser at Lawrence Livermore National Laboratory. A schematic view of the experimental setup is shown in Figure 1. We used a Ti:
1 Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551-9900. 2 Institute of Laser Engineering, Osaka University, Suita, Osaka, 565-0871, Japan. 3 University of California at Davis, Department of Physics, 1 Shields Avenue, Davis, CA 95616-8677. 4 Rice University, Department of Space Physics and Astronomy, MS 108, 6100 South Main, Houston, TX 77005-1892.
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Fig. 1.—Schematic view of the experimental setup. The blast-wave propagation was measured by the Michelson interferometry. The energy deposition was measured by a calorimeter with an f/2 collective lens.
sapphire laser with a wavelength of 820 nm to irradiate an Xe gas jet target. The pulse duration of the laser was approximately 30 fs at an output energy of 10–12 mJ. The laser light was focused with an f/15 lens into the gas target in order to generate an ∼1.8 mm–long cylindrical plasma. The spot diameter, and hence the initial plasma diameter, was about 50 mm. Recent studies have shown that several gases form large atomic clusters, which exhibit a very high laser absorption rate (Ditmire et al. 1997a, 1997b, 1998; Hutchinson et al. 1998). We employed a gas jet injection system to create atomic clusters. The gas that we used was Xe, and the backing pressure of the gas jet was around 200 pounds per square inch. The number density of the gas target was estimated to be ∼1 # 10 18 cm23. The mass density in the cluster is locally at near solid density, and the clusters of 5000–10,000 atoms form clumps of order ˚ size with large voids in between. This cluster con50–100 A figuration absorbs laser irradiation very strongly, and temperatures of a few keV plasmas have been generated in previous experiments (Shao et al. 1996). Therefore, this experimental technique is useful for creating high-temperature and relatively low density plasmas. We measured the temporal evolution of the electron density distribution by Michelson interferometry. The cylindrical plasma was probed with a small amount of laser light that was extracted from the main pulse using a 4% beam splitter. The probe beam traveled along a delay leg whose length was flexible (0–16 ns), and then it passed through the cylindrical plasma. The probed plasma was imaged with a telescope of magnification 7 onto a charge-coupled device (CCD) camera with a bandpass filter of 820 mm wavelength. The spatial resolution was 8 mm, as determined by the size of the CCD chip. Since we used the short-pulse laser as a probe beam, the temporal resolution was excellent (≈30 fs). We obtained data in 1 ns steps by changing the length of the delay leg. We measured separately the initial energy deposition into the gas jet by measuring the laser absorption fraction as the
laser passes through the gas jet. An f/2 lens was located opposite the incident laser in order to collect the light passing through the gas jet. We measured the energy of the collected light with a calorimeter. The measured absorption fraction of Xe is relatively high (∼50%) because it nucleates into clusters, in good agreement with previous experimental work (Ditmire et al. 1997a, 1997b, 1998). An example of an interferogram image of a cylindrical blast wave is shown in Figure 2a at 10 ns after laser irradiation. The edge marking the abrupt kink in the fringes indicates the front of the blast wave. The data clearly show that a cylindrical shelllike blast wave propagates radially outward in the gas. The laser is incident from the right in this interference image. The length of the cylindrical blast wave was measured to be 1.8 mm. We calculated the phase shift of the interferograms by a fast Fourier transform along the direction of the axis of the cylindrical plasma, and we deduced electron density by Abel inversion, assuming cylindrical symmetry. The resulting electron density profiles at 5, 10, and 15 ns after laser irradiation are shown in Figure 2b. The density profiles show both steep shock fronts and significant preionization ahead of the shock front. This ionization precursor moves radially outward with the shock front, suggesting that the preheat from the hot plasma behind the shock heats the cold ambient gas upstream prior to the arrival of the blast wave. We defined the position of the shock front as the half-maximum of the peak electron density, and we show the shock position versus time in Figure 3a. The experimental trajectory for t 1 5 ns is fitted by x 2 minimization to the expression R = bt a, giving a = 0.45 5 0.02. Our experimental result for a is intermediate between the adiabatic a = 12 in equation (1) and the fully radiative a = 13 in equation (2). The experimental results were compared with simulations using the radiation hydrodynamics code HYADES (Larsen &
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Fig. 2.—(a) Interferogram raw image at backing pressure of 200 pounds per square inch and at 10 ns after laser irradiation. (b) Electron density profiles at 5, 10, and 15 ns.
Fig. 3.—(a) Shock trajectory measurements and simulations. The plotting symbols correspond to the data. The thick solid line is the trajectory from the HYADES simulation, and the gray solid line is the corresponding electron temperature just behind the shock front. The dotted curve shows the trajectory from a simulation without radiation. (b) Pressure profiles at 1, 10, and 20 ns from the HYADES simulations with both electron heat conduction and radiation turned off (solid curves), with radiation turned off but including electron heat conduction (dotted curves), and with both electron heat conduction and radiation included (dashed curves).
Lane 1994), a one-dimensional Lagrangian code with a multigroup radiation transport and a tabular equation of state. We initiated the calculations with a temperature source at t = 0. The initial temperature was estimated from the measured laser absorption fraction to be 70 eV, assuming an initial ionization state of AZ S ≈ 20. The simulation also shows the ionization precursor (not shown), with the source of the long-range precursor being the radiation coming from the shock. The thick solid line in Figure 3a shows the trajectory from the HYADES simulation. In this calculation, R 0 = 25 mm, and we adjusted the initial parameters to be r 0 = 3.5 # 1024 g cm23 and T0 = 70 eV in order to reproduce the data optimally, implying an absorbed energy of ∼9 mJ. The dotted curvee in Figure 3a is the trajectory from the calculation without radiation, which approaches R ∝ t 1/2, as expected from adiabatic Sedov-Taylor theory. This calculation, however, slightly overpredicts the data. The gray line shows the electron temperature at the shock front from the simulation. To quantify the mechanisms behind heat transport, we calculated the Peclet number (convection/conduction), Pe = hn/x e, where h is a characteristic length, n is the velocity, and x e is the electron diffusivity (Braginski 1965; Ryutov et al. 1999) given by x e (cm2 s21) = (2 # 10 21)T(eV)5/2/[LZ(Z 1 1)ni(cm23)]. For Pe k 1, hydrodynamic convection dominates, whereas for Pe ≈ 1, electron heat conduction is important. We defined h to be half the shock radius (h = R/2 ) and n to be the shock velocity (n = ns). This gives Pe ≈ 0.5 at early times (t ≈ 1 ns) and Pe ≈ 3 at later times (t ≥ 10 ns). The effect of electron heat conduction decreases with time but never becomes negligible. Figure 3b shows pressure profiles from the HYADES simulations for three conditions at 1, 10, and 20 ns. The solid curves are “pure hydrodynamics” calculations with both the electron heat conduction and the radiation turned off. A steep shock front is apparent already at 1 ns, and the shock trajectory is consistent with adiabatic ST theory. The dotted curves are calculations with electron heat conduction included but no radiation. At early times, electron heat conduction transports the initial laser-deposited heat outward, which delays the formation of the shock until ∼5 ns. Late in time, however, this shock is nearly identical with the pure hydrodynamic shock since there are no radiative losses. The dashed curves are calculations with
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both the electron heat conduction and the radiation turned on. The shock looses strength because of the radiative energy losses, and it lags considerably behind the other two calculations. The pressure at the center drops because of the heat loss from radiation and conduction. Only when both the electron heat transport and the radiation are included do the calculations agree with the data. Early in time (t ! 5 ns), electron heat transport spreads the initial thermal energy out from R 0 = 25 mm to R1 = 100 mm (where R0 represents the initial radius for laser energy deposition and R1 represents the initial radius for shock formation), and the radiation removes ∼50% of the initial energy (radiative cooling). Later in time (t ≥ 5 ns), electron heat conduction transports heat from the hot central gas out to the dense shock front, where it is radiated away. We quantify this by the ratio of the pressure at the center (Pc) to that at the shock, Pc /Pshock, which takes values of 0.20–0.13 over the interval of 5–20 ns, compared with Pc /Pshock = 0.3–0.5 for ST blast waves. Another useful ratio is the fractional energy lost because of radiation, DE lost /E 0, which covers 0.58–0.75 over the interval 5–20 ns. We compare our results (from the simulation) with those from a simulated astrophysical shock in spherical geometry (Blondin et al. 1998). In the astrophysical simulation, the initial number density was 0.84 cm23, the initial shock energy was 1051 ergs, and the transition time to a radiative shock was ttr = 31,000 yr. The typical shock velocity in our experiment at 10 ns is 4.8 # 10 5 cm s21, and the sound speed of the (unpreheated) ambient medium is c s ≈ 3 # 10 4 cm s21, giving a hypothetical Mach number of M ≈ 16. However, the ionization precursor signals the presence of preheat due to electron heat conduction (with a range ≤50 mm) and radiation (with a range greater than 50 mm). Using cs for the preheated region just in front of the shock gives M = 3.3 at 10 ns. The density ratio (h = rshock /rambient = (g 1 1) M 2/ [(g 2 1) M 2 1 2]) of our experiment is 3–4, which corresponds to an adiabatic index of g = 1.7–1.4. (In the absence of preheat generated by the shock,
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h = 10, which implies an effective adiabatic index of g = 1.2.) The simulated astrophysical shock has h ≥ 4. The radiative effect is determined by the radiative cooling parameter x = trad /thydro, where trad is the radiative cooling time and thydro is the characteristic hydrodynamic time. In our experiment, the radiative cooling time was calculated from trad = 3k(ni Ti 1 ne Te)DR/2qrad, where ne is the electron density, DR is the shell thickness, and qrad is the radiative thermal heat flux. The hydrodynamic time is determined from thydro = DR/ns, which gives trad ≈ thydro ≈ 2 ns. This leads to x ≈ 1 at 10 ns, which implies that our experiment is in the coupled regime. Radiation and electron heat conduction are coupled to the hydrodynamics in front of the shock, creating the ionization precursor and decreasing the Mach number by nearly a factor of 5. The cooling parameter x for the simulated astrophysical shock is defined in a similar manner; i.e., x is defined as the postshock radiative cooling length, L cool ≈ vstrad, divided by the blast-wave radius (x = L cool /R). In the simulated astrophysical shock (Blondin et al. 1998) for t ! ttr, x is a monotonically decreasing function of time, with typical values ranging from 10 to 0.1. For t 1 ttr, the shock is strongly radiative, and x = 1023 to 1022. The pressure ratio (at the center vs. at the shock) for the simulated astrophysical shock is Pc /Pshock = 0.17 at t/ttr = 2.3, which is quite similar to the values in our experiment. For the astrophysical simulation, a is near the adiabatic result for spherical geometry before the transition time (a ≈ 25 ), shows large variability during the transition, and moves asymptotically toward a ≈ 13 after 105 yr, which is slightly larger than the a = 27 expected theoretically for a PDS regime. We are grateful to R. P. Drake for a very thorough critique of this manuscript. This work was performed under the auspices of US Department of Energy contract W-7405-Eng-48 and was supported in part by LLNL LDRD grant 98-ERD-022 and JSPS Fellowship 0733.
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