Spectroscopic analysis of Cu wire array implosions on the refurbished Z generator

High Energy Density Physics 8 (2012) 284e289

Contents lists available at SciVerse ScienceDirect

High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp

Spectroscopic analysis of Cu wire array implosions on the refurbished Z generator A. Dasgupta a, *, R.W. Clark b, N.D. Ouart c, J.L. Giuliani a, W. Thornhill a, J. Davis a, B. Jones d, D.J. Ampleford d, S.B. Hansen d, C.A. Coverdale d a

Plasma Physics Division, Naval Research Laboratory, Washington, DC, USA Berkeley Scholars Inc., Springfield, VA, USA c NRC/NRL Post Doc, Plasma Physics Division, Naval Research Laboratory, Washington, DC, USA d Sandia National Laboratories, Albuquerque, NM, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 March 2012 Accepted 8 March 2012 Available online 28 March 2012

Experimental investigations of pinches on the refurbished Z (ZR) generator using Cu arrays have been initiated and more are planned for the near future. Significant X-ray emissions in the K-shell from moderately high atomic number plasmas such as Cu generate extreme interest. However, the production of these hard photons from high Z materials comes with a price. There is substantial loss of radiative yield due to stripping through many electrons present in high Z materials to reach to the H- or He-like ionization stages. Production of hard X-rays for materials with atomic number higher than Cu such as Kr is very difficult and theoretical predictions are even more uncertain. Previous experimental efforts using Cu as a plasma pinch load are encouraging and promote further investigations of this element on the refurbished Z machine for achieving photon energies higher than 5 keV and obtaining sufficient radiative yield. We will analyze the ionization dynamics and generate Cu spectrum using the temperature and density conditions obtained from 1-D non-LTE radiation hydrodynamics simulations of Cu wire array implosions on ZR. These results will be compared with K- and L-shell experimental spectrum of shot Z 1975. Theoretical K- and L-shell spectroscopy provides validation of atomic and plasma modeling when compared to available experimental data and also provides useful diagnostics for the plasma parameters. Our self-consistently generated non-LTE collisionalradiative model employs an extensive atomic level structure and data for all dominant atomic processes that are necessary to model accurately the pinch dynamics and the spectroscopic details of the emitted radiation. Published by Elsevier B.V.

Keywords: Collisional radiative model Non-LTE Radiation transport Emission spectra

1. Introduction Interpretation and analysis of important parameters such as radiation output, charge state distributions, and X-ray emission from high-temperature, high-density laboratory plasmas such as Z pinches and laser produced plasmas lead to significant advancements in the knowledge of the production and evolution of these plasmas. Understanding of these parameters for plasmas in laboratory experiments using reliable theoretical modeling also provides insights into the knowledge of plasmas in astrophysical objects under similar conditions. X-ray emission spectra from the K- and particularly complex L-shell of high Z (atomic number) ions provide valuable information with which to assess plasma conditions and X-ray performance in a variety of laboratory plasmas such as Z-pinch plasmas. Experiments at the Z facility can be used to test complex theories and models of X-ray production. Cu wire arrays are investigated as an intensive X-ray radiation source at the Z machine in the US * Corresponding author. E-mail address: [email protected] (A. Dasgupta). 1574-1818/$ e see front matter Published by Elsevier B.V. doi:10.1016/j.hedp.2012.03.012

Sandia National Laboratories. The implosion dynamics of an array of Cu wires on the Z and/or ZR accelerator produces an abundance of radiation from the K- and L-shell ionization stages and provides reliable diagnostics capabilities [1]. These dynamic plasmas are inherently non-LTE, with opacity and other factors influencing the Xray output. We will analyze the ionization dynamics and generate Kand L-shell spectra using the conditions generated on Z and/or ZR, described by a 1-D non-LTE radiation hydrodynamics model [2]. Although K-shell radiation is of extreme interest and K-shell photons for Cu have energies > 5 keV, modeling L-shell spectra is more challenging due to the complex L-shell structure. The accuracy of predictions of K-shell energetics and diagnostics depend heavily on Lshell energetics. Analysis of L-shell spectra provides a wealth of information, as the x-ray spectra of these ions are rich in structure due to multiple overlapping satellite lines that accompany the resonance lines. Identification of these lines for diagnostic calculations poses challenges but diagnostic research involving L-shell ions, while not as extensive as that involving K-shell ions, provides potentially more rewards. Diagnostics of complex L-shell spectra open a new arena for validation of atomic and plasma models when compared with

A. Dasgupta et al. / High Energy Density Physics 8 (2012) 284e289

experiments. Our atomic model therefore includes the atomic data for all the relevant processes needed to accurately describe both L- as well as K-shell spectra. Modeling of radiation from high atomic number species such as Cu requires a detailed non-LTE kinetics model with accurate radiation transport. Plasmas created in Z pinches are far from LTE where the plasma properties such as internal energies and opacities depend only on the local temperature and density and the level populations are described by statistical distributions of the excited states. This is especially true for the K-shell region. It is true that for low photon energies where free-free opacity is large, the plasma will approach LTE conditions. However, LTE atomic populations result into overionizing the plasma due mainly to neglect of radiative and dielectronic recombination and producing excessive excited state populations due chiefly to the neglect of spontaneous decay. The resulting radiative emission will produce incorrect spectral characteristics. In pinch experiments, the dense plasma produced near stagnation is optically thick to line radiation and this radiation can significantly change the level populations by photoexcitation and photoionization. In the L- and K-shell photon energy range, a number of spectral lines will be optically thick with optical depth greater than unity, especially near stagnation. In the K-shell region, the He-a line is quite thick, and the other lines typically exhibit moderate opacities. Thus a full collisional radiative model coupled with a non-local radiation field is necessary to describe the ionization dynamics. The Cu nested wire arrays for Z 1975 shots included 4% Ni and additional radiation data from Fe and Cr were also observed in the spectra. The presence of Fe and Cr and additional Ni was due to the stainless-steel (SS) cathode. Our atomic model thus included multimaterial atomic data for a mixture of 93% Cu, 4% Ni, 2.4% Fe, and 0.6% Cr. X-ray emissions from high atomic number materials often exhibit substantial K-a. K-a emission is associated with the 2p / 1s innershell-electron radiative transitions in highly charged ions [3,4]. These lines have the appearance of satellite lines in the X-ray spectra of laboratory and astrophysical plasmas. Besides photoexcitation and photoionization from hard K-shell radiation, K-a emission can originate from collisional processes involving hot electrons in the final phase of pinching plasmas such as Z-pinches, X-pinches, and gaspuffs [5]. The small amount of hot electrons that may be produced in these plasmas can alter the diagnostics [6]. There is evidence of K-a features of Cu, Ni, Fe, and Cr from the Z 1975 data. As these K-a lines provide good diagnostics, we are investigating them in detail and the results of our findings will be reported in a future article. 2. Atomic model For an ion in ionization stage Z and level j, the non-LTE kinetic rate equation appropriate for collisional radiative equilibrium is

X X dnZ;j nZ;i CXZ;i[Z;j þ ne nZ;i CDZ;iYZ;j ¼ 0 ¼ þne dt ij X þ n2e nZþ1;0 CRZþ1;0YZ;j þ nZ;i AZ;iYZ;j þ

X

i>j

nZ;i PXZ;i[Z;j þ ne nZþ1;0 RRZþ1;0YZ;j

i
þ ne nZþ1;0 DRZþ1;0YZ;j  ne nZ;j  ne nZ;j

X

 nZ;j

i
CXZ;j[Z;i

i>j

CDZ;jYZ;i  ne nZ;j CIZ;j[Zþ1;0

i
X

X

AZ;jYZ;i  nZ;j

X i>j

PXZ;j[Z;i  nZ;j PIZ;j[Zþ1;0 ð1Þ

285

where the subscript arrow on the creation rates denote “from” and for the destruction rates it denotes “to”. The nomenclature for the rate coefficients is: collisional excitation (CX); collisional ionization (CI); photoionization (PI); radiative decay (A); and photoexcitation (PX). The inverse processes of collisional de-excitation (CD), 3-body or collisional recombination (CR), and radiative recombination (RR) are determined by detailed balance from CX, CI, and PI, respectively. Dielectronic recombination is denoted by DR. Photoexcitation and photoionization can be non-local in the sense that the rate coefficient depends on the local radiation field that is determined by photon transport from all regions of the plasma. A detailed description of the rates of all the atomic processes included in the above equation is given in Ref. [7]. We employ a full non-LTE (NLTE) collisional radiative equillibrium (CRE) method for the application of our atomic model [7]; a full time-dependent treatment of the atomic populations is also possible with our model. For high ion density regions of interest, 1018  ni  1022 cm3, the plasma ionization condition cannot be described by coronal equilibrium, in which radiative decay rates are much larger than collisional excitations and essentially all ions exist in the ground and Dn ¼ 0 levels. Neither can the plasma be described as being in LTE, where all states of a given configuration are statistically populated. For K- and L-shell ions of moderate Z elements, only at densities above this range do the excited levels begin to come into statistical equilibrium. Thus a full non-LTE kinetics model is needed to investigate the high electron density regimes found in laboratory plasmas. When the plasma ionization state responds to changes in hydrodynamic quantities, the plasma is in collisional radiative equilibrium and steady-state population densities are obtained by solving the equilibrium equations, dnz,j/ dt ¼ 0. Our atomic model has been constructed using a very detailed yet computationally efficient level structure for a large number of excited states and the processes coupling these levels. Collisional excitation makes a significant contribution to populating the excited levels and dielectronic recombination (DR) is the dominant recombination mechanism. DR is often the most important process in many laboratory and astrophysical plasmas [8e10]. Atomic structure data including energy levels and radiative transition probabilities as well as the collisional excitation and ionization rates and the collisional, radiative and dielectronic recombination rates were self-consistently generated using the Flexible Atomic Code (FAC) suite of codes [11,12]. In FAC, structure calculations are based on relativistic configuration interactions with independent particle basis functions and relativistic effects are included using a Dirac Coulomb Hamiltonian. All ground levels and excited levels with n  4 are kept at the fine-structure levels, while for 5  n  7, the configuration-averaged level structures are used for all K- and L-shell ions. A more limited level structure is embedded in a configuration state model for the remainder of the ionization stages. These detailed atomic models obtained using self-consistently generated atomic data including low lying finestructure Rydberg levels are crucial for proper spectroscopic diagnostics. Data for all the relevant radiative and collisional processes described in Eq. (1) are calculated. A detailed description of generation of data for all these processes is described in Ref. [7]. The electrons in the plasma are assumed to have a Maxwellian velocity distribution and are the dominant species in populating the levels for the K- and L-shell spectra. Thus the rate coefficients for all the processes are obtained by integrating the cross sections over a Maxwellian electron distribution. 3. Radiation transport and hydrodynamics simulation The experiment of interest is the doubly nested wire array pinch, Z 1975, performed on the refurbished Z (ZR) generator at

286

A. Dasgupta et al. / High Energy Density Physics 8 (2012) 284e289

Sandia National Laboratories. The arrays, composed of a coppernickel alloy wire, had a total mass of 2.57 mg and a 2:1 outer to inner mass and wire number ratio. The initial array radii were 65 and 32.5 mm and 20 mm in axial height. Emission lines of Fe and Cr were also observed in experimental spectra, and likely arise due to a scrape-off plasma from the feed electrode during the power flow. The simulation presented below is performed with the onedimensional DZAPP code. The radial extent of the plasma is resolved into 30 Lagrangian zones. The magnetohydrodynamics component solves the radial momentum, ion and electron thermal energy, and an induction equation for the azimuthal magnetic field. A radiative loss term is included in electron energy equation. The thermal conductivity for both ions and electrons and the resistivity for the diffusion of the magnetic field use the expressions of Braginskii with a mean charge state. The plasma dynamics is coupled to a transmission line circuit model for the ZR generator at the plasma-vacuum interface. The circuit model includes current losses, treated as shunts, in the convolute and in the final feed with a right angle turn. Total energy conservation and Poyntings theorem are used to check the numerical solution for accuracy and found to be satisfied to better than 1% (typically 0.1% or less) throughout the simulation. The code is very nearly a “first-principles” code; the only phenomenological “adjustable“ variable is an electron-ion thermal equilibration multiplier that artificially slows equilibration, lengthens the duration of stagnation, and prevents radiative collapse. A large fraction of the plasma energy is radiated away in a typical Z pinch. Thus, DZAPP treats the atomic and radiation physics in non-local thermodynamic equilibrium (non-LTE) in a coupled, self-consistent manner. This method predicts the ionization populations more accurately. As noted above, lines of Cu, Ni, Fe and Cr were observed in the experimental spectra. The calculations are performed with the mixture: 93.0% Cu, 4.0% Ni, 2.4% Fe, and 0.6% Cr. The Ni abundance was chosen because the copper wires employed in the experiment had a nominal 4% Ni component; the Fe and Cr abundances were selected to approximately match the respective He-a intensities of the experimental spectrum. The relative abundances are consistent with the Fe and Cr components coming from the stainless-steel cathode. Detailed atomic models for Cu, Ni, Fe and Cr are used in the simulations. The model for Cu includes 779 atomic levels and 1609 transported emission lines. The models for Ni, Fe and Cr have 778, 776 and 774 levels, respectively, and, since they are minor constituents, 450 lines are transported for each. The radiation transport includes the effects of photoionization and photoexcitation. Non-local radiation couplings from each zone to every other zone are computed for each bound-bound, bound-free and free-free process using a probabilistic approach [13e15] where an escape probability is derived, integrated over the line profile, as a function of line-center optical depth based on a frequency of maximum escape. Similarly, for bound-free continuum radiation arising from radiative recombination, an escape probability is derived, integrated over the bound-free profile, as a function of optical depth at the edge. The probabilistic method of transport of both line and continuum radiation is an economic and efficient way for simulation of most laboratory and astrophysical plasmas. Inner-shell opacities, which are important in the cool, dense plasma regions, are also included in our model. The positions of the ionization-dependent absorption edges are taken from the Hartree-Fock calculations of Clementi and Roetti. Since the local emissivities and opacities are functions of the atomic populations, and the populations depend on photon transport, such as the effects of photopumping by the radiation field, an iterative process is employed on each call to the non-LTE solver to obtain convergence in the level population and radiation field. Such calls are made approximately every 100 MHD steps, or more often if

the total internal energy changes by more than a fixed amount (typically 5%) in any zone. The total internal energy consists of the ion and electron thermal energy plus the ionization/excitation energy of the population levels. The radiative loss term from each zone for the electron energy equation is also computed during this call. In between these calls, the radiative loss and excitation/ionization energy per unit mass are kept constant. At the end of each MHD step the spectral energy distribution of the radiated energy escaping the whole plasma is constructed. Each bound-bound transition is taken to have a Voigt profile evaluated at the local ion temperature from which the emission arose and 21 photon energies are used to resolve the line. Hundreds of energies are used to cover free-bound recombination and free-free emissions are accumulated. Upon completion of the entire simulation the synthetic time-integrated spectrum is calculated from the accumulated totals of these spectral distributions. 4. Spectral line intensities Fig. 1 presents some overall properties of the simulation results for Z 1975. The load current is through the wire array and its peak value is about 5 MA less than the current before the convolute due to the shunts in the circuit model. The breakdown and ablation phases of the wires is not addressed in the present model. Instead we take the initial density distribution to be composed of two Gaussians, one centered at the outer and the other at the inner array radius. This profile represents an early radial expansion of each array as the rising current initiates heating of the wires. The denoted radius in Fig. 1 is the location of the plasmaevacuum interface, initially is at 4 cm. The fiducial time (t ¼ 0) is set at the peak of the K-shell radiation pulse, which comprises photons above 5 keV. The experiment provided a K-shell yield of 24 kJ while the integral of the simulated pulse has 27 kJ. The larger pulse contains the total radiation, which is predominantly from the L-shell like ions of Cu and Ni. In this domain the simulated yield is 477 kJ, notably above the measured value of 258 kJ. This difference arises from two limitations of the model. First the atomic model for the components does not contain a sufficient number of levels in the low ionization stages, because it emphasizes the level structure of the L- and K-shell ions. Hence the simulated pinch, which radiates its coupled energy, emits via Lshell ions rather than through lower ionization stages. Second, the 1D character of the simulation means that all the load material implodes together. In the experiment there is axial structure due

30 1 P>1 keV (TW) 2

20 Iload (MA)

10 PK-shell (TW)

r (cm)

0 -150

-100

-50 time (ns)

0

50

Fig. 1. Current profile, radius, and total radiative and K-shell powers as a function of time for Z 1975 data from the DZAPP simulation.

A. Dasgupta et al. / High Energy Density Physics 8 (2012) 284e289

to trailing mass, which radiates at a low temperature. Despite these limitations, the agreement of the simulated spectra with the data discussed below indicates that the temporal simulation accurately accounts for some aspects of the implosion physics. These findings are also in good agreement with the investigations of Hansen et al. for the same Z 1975 shot (see Ref [16]). Fig. 2 presents snapshots of the plasma dynamics before (t ¼ 4 ns), at (t ¼ 0 ns), and following (t ¼ 8 ns) peak power as a function of the radius r. The ion density ni of Fig. 2(a) shows the maintenance of a dense shell during the stagnation. Inside of this shell the plasma has a high electron temperature Te and ion temperature Ti shown in Fig. 2(c) and (d). At each time the dense shell is at the same location as the rapid falloff in Te, Ti, and the mean ionization state Z in Fig. 2(b). The primary character of the stagnation is a hot, low density core from which the K-shell emission arises, and an outer, high-density shell comprised of L-shell ions. The maximum in radiative emission occurs near the time of peak compression (minimum radius), as seen in this figure. At peak compression, the density reaches about 1020 cm3 and the ion temperature in this model reaches almost 500 keV. The average charge is about 27 near the peak compression. Time-integrated synthetic spectra were generated for K- and Lshell Cu, Ni, Fe and Cr ions from the simulation of shot Z 1975 and compared with data. We emphasize that the synthetic K- and Lshell spectra are time-integrals of the non-LTE emission (including photopumping and radiation transport) self-consistently calculated throughout the pinch. Thus, these spectra are not the result of a post-process, but represent the integral of the radiated power that cools the electrons throughout the simulation. In Fig. 3, we show a comparison of K-shell spectra with strong He-like and H-like lines of Cu and Ni, the components in the nested wire arrays and some

a

He-like lines for Fe and Cr that are coming from the cathode. Our 1D non-LTE collisional radiative simulation of the K-shell spectra is in good agreement with the experimental data, except for several strong satellite like features present in the data that are missing in our simulated spectra. Most of these strong overlapping lines may be due to K-a emissions from Cu, Ni, Fe, and Cr. The spectral feature of K-a emission lines from Cu ions in the energy range of 8.05e8.15 keV overlaps with the Ni Ly-a lines in this figure. There are also features around 6.3 and 7.6 keV that could correspond to inner-shell K-a emission from Fe and Ni ions, respectively. However, since we do not include any contributions due to K-a emission in our simulation, our spectrum does not show the these features. The K-shell spectrum contains the Rydberg series of lines from H-like and He-like Cu, resulting from the decay of np (n < 7) states to the 1s orbitals. The strongest line in the spectrum is the Cu Hea complex, consisting of the closely-spaced Cu He-like 1s2p 1P1 to 1s2 1S0 He-a line and the density-sensitive 1s2p 3P1 to 1s2 1S0 intercombination line. In time-dependent spectra, the He-a line can exhibit self-reversal; the optical depth at line-center becomes large near peak implosion, and peak power is radiated in the wings of the line. This does not normally occur with the intercombination line. It sometimes happens that the overlap of the self-reversed He-a and intercombination lines makes it appear that the latter line is larger. There is good agreement in the Cu He-like Rydberg lines out through n ¼ 6. The Ly-a Cu line consisting of contributions from 2p 2P1/2 and 2p 2P3/2 to 1s 2S1/2 also shows good agreement, whereas the higher-order lines do not. The He-a lines of Fe and Cr match the data reasonably well, as does the Ly-a line of Fe, but the Ni He-a line intensities are lower compared to the data.

c

1022

287

ni (1020 cm-3)

4.0

Te (keV) t=0

1021

3.0

t=+8 ns

t=0

2.0

1020

t=+8 ns

1.0

1019

t=-4 ns

t=-4 ns

1018

0.0

b

d 30.0

600.0

Ti (keV)

Z 500.0

t=+8 ns t=-4 ns

t=0

20.0

t=0

400.0 300.0 200.0 t=-4 ns

100.0 10.0 0.0

0.1

0.2

0.3

r (cm )

0.4

0.5

0.0 0.0

t=+8 ns

0.1

0.2

0.3

0.4

0.5

r (cm)

Fig. 2. Plasma properties as a function of radius at three different times centering around the time of peak K-shell emission power. (a), (b), (c), and (d) show the ion densities, average charge state, and the ion and electron temperatures.

288

A. Dasgupta et al. / High Energy Density Physics 8 (2012) 284e289

103 7

4.5

102

6

101 31 30

100

8 9

16 17

32 233

25 266

28 29

3.0 1

12

18 19

10

10-1

1.5

3

In Fig. 4, we compare part of our simulated L-shell spectra with the data of Cu Z 1975. At present, the model underpredicts the continuum emission seen in the data in this region, which could indicate that there is a greater quantity of cooler trailing material in the experiment than in the model. In order to compare modeled

Table 1 K-shell line identification for Cu, Ni, Fe and Cr. Index

Ion

Upper level 2p 2p 3p 3p 4p

2

P1/2 P3/2 2 P1/2 2 P3/2 2

Lower level 1s 1s 1s 1s 1s

2

S1/2 S1/2 2 S1/2 2 S1/2 2 S1/2 2

Ar (s1)

8.666 8.699 10.281 10.291 10.848

4.42Eþ14 4.47Eþ14 1.16Eþ14 1.20Eþ14 4.83Eþ13

1s2p 3P1 1s2p 1P1 1s3p 3P1 1s3p 1P1 1s4p 3P1 1s n ¼ 5 1s n ¼ 6 1s n ¼ 7

1s2 1s2 1s2 1s2 1s2 1s2 1s2 1s2

S0 1 S0 1 S0 1 S0 1 S0 1 S0 1 S0 1 S0

8.345 8.390 9.859 9.872 10.389 10.633 10.764 10.842

9.51Eþ13 7.05Eþ14 2.75Eþ13 1.91Eþ14 2.25Eþ13 1.37Eþ12 5.52Eþ11 2.58Eþ11

2p 2P1/2 2p 2P3/2

1s 2S1/2 1s 2S1/2

8.072 8.103

3.84Eþ14 3.88Eþ14

1s2 1s2 1s2 1s2 1s2

S0 S0 S0 1 S0 1 S0

7.764 7.805 9.171 9.182 9.663

7.38Eþ13 6.18Eþ14 2.15Eþ13 1.68Eþ14 9.04Eþ12

1s 2S1/2 1s 2S1/2

6.950 6.976

2.86Eþ14 2.88Eþ14

1s2p 1s2p 1s3p 1s3p 1s4p

3

P1 P1 3 P1 1 P1 1

2p 2P1/2 2p 2P3/2 3

1 1 1

2 1

S0 S0 1 S0 1 S0 1 S0

6.661 6.699 7.869 7.879 8.292

4.20Eþ13 4.68Eþ14 1.25Eþ13 1.27Eþ14 1.44Eþ13

2p 2P1/2 2p 2P1/2

1s 2S1/2 1s 2S1/2

5.914 5.931

2.08Eþ14 2.09Eþ14

1s2p 3P1 1s2p 1P1 1s3p 1P1

1s2 1S0 1s2 1S0 1s2 1S0

5.645 5.681 6.677

2.19Eþ13 3.44Eþ14 6.65Eþ12

1s2p 1s2p 1s3p 1s3p 1s4p

P1 P1 3 P1 1 P1

1

E (keV)

1

1s 1s2 1s2 1s2 1s2

1

21 3

24

26

23

22

20 19

1.4 1.45 Energy (keV)

1.35

12.0

Fig. 3. Time-integrated K-shell spectra of Cu, Ni, Fe, and Cr compared to Z 1975 data. The lines are idendified in Table 1.

H-like Cu 1 CuXXIX 2 CuXXIX 3 CuXXIX 4 CuXXIX 5 CuXXIX He-like Cu 6 CuXXVIII 7 CuXXVIII 8 CuXXVIII 9 CuXXVIII 10 CuXXVIII 11 CuXXVIII 12 CuXXVIII 13 CuXXVIII H-like Ni 14 NiXXVIII 15 NiXXVIII He-like Ni 16 NiXXVII 17 NiXXVII 18 NiXXVII 19 NiXXVII 20 NiXXVII H-like Fe 21 FeXXVI 22 FeXXVI He-like Fe 23 FeXXV 24 FeXXV 25 FeXXV 26 FeXXV 27 FeXXV H-like Cr 28 CrXXIV 29 CrXXIV He-like Cr 30 CrXXIII 31 CrXXIII 32 CrXXIII

17 2 25 9 16 10 11 18 15 14 8 13 12

0.0

10.0 8.0 Energy (keV)

6.0

4

5 11 13

12 5

10-2

6

7

1.50

Fig. 4. Time-integrated simulation of Cu L-shell spectra compared to Z 1975 data. The lines are identified in Table 2.

line emission with the data, we subtracted the continuum background from the data. This was accomplished by first calculating a local minimum for each frequency point in the spectrum (defined as the minimum value over the adjacent 30e50 spectral frequencies). Then this quantity was subtracted from the spectral intensity at that point, and the resulting spectrum was normalized. The strong lines in this figure are from n ¼ 3e2 transitions of Li-like and Be-like Cu lines in the energy range of 1.3e1.5 keV. Our simulated spectra are in good agreement with the data except for the central strong 1s23d2D5/21s22p2P3/2 Li-like line. This

Table 2 Cu L-shell line identification. Index Li-like 1 2 3 4 5 6 7 Be-like 8 9 10 11 12 13 B-like 14 15 16 C-like 17 N-like 18 O-like 19 20 21 F-like 22 23 24 Ne-like 25 26

Ion

Upper level

Lower level

E (keV)

Ar(s1)

CuXXVII CuXXVII CuXXVII CuXXVII CuXXVII CuXXVII CuXXVII

1s23s 2S1/2 1s23s 2S1/2 1s23p 2P1/2 1s23p 2P3/2 1s23d 2D3/2 1s23d 2D3/2 1s23d 2D5/2

1s22p 2P1/2 1s22p 2P3/2 1s22s 2S1/2 1s22s 2S1/2 1s22p 2P1/2 1s22p 2P3/2 1s22p 2P3/2

1.396 1.371 1.467 1.475 1.425 1.400 1.402

1.49Eþ12 3.16Eþ12 1.22Eþ13 1.18Eþ13 2.97Eþ13 5.80Eþ12 3.50Eþ13

CuXXVI CuXXVI CuXXVI CuXXVI CuXXVI CuXXVI

1s22s3d 3D2 1s22s3d 3D3 1s22s3d 1D2 1s22p3d 3P0 1s22p3d 3D3 1s22p3d 1F3

1s22s2p 3P1 1s22s2p 3P2 1s22s2p 1P1 1s22p2 3P1 1s22p2 3P2 1s22p2 1D2

1.390 1.373 1.343 1.382 1.371 1.358

2.77Eþ13 3.57Eþ13 2.65Eþ13 2.66Eþ13 3.33Eþ13 5.33Eþ13

CuXXV CuXXV CuXXV

1s22s23d 2D5/2 1s22s23d 4D7/2 1s22s2p3d 2F

1s22s22p 2P3/2 1s22s22p 4P5/2 1s22s2p2 2D5/2

1.331 1.334 1.332

3.05Eþ13 1.41Eþ13 2.10Eþ13

CuXXIV

1s22s2p23p

1s22s22p2 3P2

CuXXIII

2

3

1s 2s2p 3p 2

2

3

1.369

1.30Eþ12

2

2

3 4

1.325

5.77Eþ11

2

2

4 3

1s 2s 2p

S3/2

CuXXII CuXXII CuXXII

1s 2s 2p 4s 1s22s22p34d 1s22s22p34d

1s 2s 2p P0 1s22s22p4 1D2 1s22s22p4 1S0

1.491 1.494 1.467

3.51Eþ11 1.28Eþ12 2.60Eþ11

CuXXI CuXXI CuXXI

1s22s22p44d 1s22s22p44d 1s22s2p54d

1s22s22p5 2P1/2 1s22s22p5 2P3/2 1s22s2p6 2S1/2

1.410 1.431 1.409

7.75Eþ11 1.56Eþ12 9.39Eþ11

CuXX CuXX

1s22s22p54d 1s22s2p64p

1s22s22p6 1S0 1s22s22p6 1S0

1.344 1.478

1.05Eþ12 9.34Eþ11

A. Dasgupta et al. / High Energy Density Physics 8 (2012) 284e289

disagreement is somewhat disturbing given the fact that most of the other lines in the data of similar intensities are in excellent agreement. However, the strong Li-like line is most likely to be affected by opacity in the experimental data. Further, the timeintegrated L-shell spectra of single and nested Cu wire arrays shot Z 1268 by Coverdale et al. [17], show that this line is much stronger than the adjacent Li-like and Be-like lines as predicted by our modeling and has overall good agreement with our findings of the relative intensities of the Li-like 1s23d 2D5/21s22p 2P3/2 and 1s23d 2D5/21s22p 2P3/2 lines in Fig. 4. The electron temperature and density quoted in their analysis of highly ionized L-shell species were 1.1 keV and 7  1020 cm3 respectively [17]. This suggests that the spectral data were obtained from line outs near the axis and thus the electron temperature was higher in comparison to that of the Z 1975 data in Fig. 4. In the cooler region away from the axis, as the temperature becomes lower, the strong Li-like line becomes less intense in comparison to other strong lines. This is a possible explanation for the discrepancy between the spectral features of data and modeling of this line in Fig. 4. 5. Summary and conclusions We have calculated the synthetic time-integrated K- and L-shell radiation from a Cu Z pinch plasma using a 1D non-LTE collisional radiative model and compared with time-integrated Z 1975 data from the refurbished Z generator. Since the nested wire arrays contained some Ni and radiation from the SS cathode material was also observed in the data, our simulation included a detailed atomic model for Cu as well as Ni, Fe, and Cr. Calculating the X-ray spectra of hot plasmas requires knowledge of atomic data and structure to evaluate the precise ionization dynamics and it is imperative that the data needed for the CRE model be generated using state-of-the art computer codes. Due to the enormous quantity of the data involved for many atomic levels, especially for complex ions, simple approximations and crude atomic models are often employed for analysis. A major issue of this investigation is how to construct an atomic model containing a detailed yet manageable number of levels that will adequately describe the plasma (see also Ref. [18]). Self-consistent coupling of detailed radiation transport provides accurate photoionization and photoexcitation modifications to the local atomic populations. Although the Ni Lyea line overlaps with some of the Ne-like and F-like Kea lines, we believe that due to the relatively very small concentration (4%) of Ni in the wires, the strong line in the 8.05e8.15 keV are due to Cu Kea lines. More work needs to be done to validate this further. We note that time-integrated spectra from a Z pinch embody the history of the plasma dynamics throughout the stagnation period. The good agreement of

289

our simulated spectra, using the 1D MHD DZAPP code and selfconsistently generated data from state-of-the-art codes such as FAC for both K- and L-shell line emissions, with experimental Cu data of Z 1975 is very encouraging. We will continue to analyze Cu spectral data from new experiments that are planned in the near future on Z. Acknowledgment This work was supported by the US Department of Energy/ NNSA. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. References [1] C.A. Coverdale, B. Jones, D.J. Ampleford, J. Chittenden, C. Jennings, J.W. Thornhill, J.P. Apruzese, R.W. Clark, K.G. Whitney, A. Dasgupta, J. Davis, J. Guiliani, P.D. LePell, C. Deeney, D.B. Sinars, M.E. Cuneo, High Energy Density Phys. 6 (2010) 143. [2] J.W. Thornhill, A.L. Velikovich, R.W. Clark, J.P. Apruzese, J. Davis, K.G. Whitney, P.L. Coleman, C.A. Coverdale, C. Deeney, B.M. Jones, P.D. Lepell, IEEE Trans. Plasma Sci. 34 (5) (2006) 2377. [3] V.L. Jacobs, G.A. Doschek, J.F. Seely, R.D. Cowan, Phys. Rev. A 39 (1989) 2411. [4] P. Beiersdorfer, T. Phillips, V.L. Jacobs, K.W. Hill, M. Bitter, S. von Goeler, S.M. Kahn, Ap. J. 409 (1993) 846. [5] H. Gabriel, K.J.H. Philips, Mon. Not. R. Astron. Soc. 189 (1979) 319. [6] F.B. Rosmej, J. Phys. B, Mol. Opt. Phys. 30 (1997) L819eL828. [7] A. Dasgupta, J.G. Giuliani, J. Davis, R.W. Clark, C.A. Coverdale, B. Jones, D. Ampleford, IEEE Trans. Spec. Issue Z-Pinch Plasmas 38 (4) (2010) 598. [8] A. Dasgupta, K.G. Whitney, H.L. Zhang, D.H. Sampson, Phys. Rev. E 55 (1997) 3460. [9] A. Dasgupta, K.G. Whitney, M. Blaha, M. Buie, Phys. Rev. A 46 (1992) 5973. [10] A. Dasgupta, J. Davis, R.W. Clark, J.W. Thornhill, J.L. Giuliani, K.G. Whitney, Y.K. Chong, AIP Conf. Proc. 7th Int. Conference Dense Z-Pinches 1088 (2009) 37. [11] M.F. Gu, Astrophys. J. 590 (2003) 1131. [12] M.F. Gu, Can. J. Phys. 86 (2008) 675. [13] J.P. Apruzese, J. Quant. Spectrosc. Radiat. Transfer 34 (1985) 447. [14] J.P. Apruzese, J. Davis, K.G. Whitney, J.W. Thornhill, P.C. Kepple, R.W. Clark, C. Deeney, C.A. Coverdale, T.W.L. Sanford, Phys. Plasmas 9 (5) (2002) 2411. [15] R.W. Clark, J. Davis, J.P. Apruzese, J.L. Giuliani, J. Quant. Spectrosc. Radiat. Transfer 53 (3) (1995) 307. [16] S.B. Hansen, B. Jones, J.L. Giuliani, J.P. Apruzese, J.W. Thornhill, H.A. Scott, D.J. Ampleford, C.A. Jennings, C.A. Coverdale, M.E. Cuneo, G.A. Rochau, J.E. Bailey, A. Dasgupta, R.W. Clark, J. Davis, High Energy Density Phys. 7 (2011) 303. [17] C.A. Coverdale, B. Jones, P.D. LePell, C. Deeney, A.S. Safronova, V.L. Kantsyrev, D. Fedin, N. Ouart, V. Ivanov, J. Chittenden, V. Nalajala, S. Pokola, I. Shrestha, AIP Conference Proceedings of the 6th International Conference on Dense ZPinches 808 (2006) 45. [18] S.B. Hansen, J. Bauche, C. Bauche-Arnoult, M.F. Gu, High Energy Density Phys. 3 (2007) 109.