Spectroscopic features of implosions of Mo single- and double-planar wire arrays produced on the 1 MA Z-pinch generator

ARTICLE IN PRESS Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 2877–2890

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Spectroscopic features of implosions of Mo single- and doubleplanar wire arrays produced on the 1 MA Z-pinch generator M.F. Yilmaz , A.S. Safronova, V.L. Kantsyrev, A.A. Esaulov, K.M. Williamson, G.C. Osborne, I. Shrestha, N.D. Ouart Physics Department, University of Nevada, Reno, NV 89557, USA

a r t i c l e in fo

abstract

Article history: Received 17 March 2008 Received in revised form 20 July 2008 Accepted 23 July 2008

The spectroscopic features of implosions of Mo single- and double-planar wire arrays are studied. The experiments were performed on the 1 MA Zebra generator at UNR. Implosions of Mo planar wire arrays radiate high peak powers and produce hightemperature L-shell plasmas. In particular, plasma electron temperature of single-planar wire arrays of Mo reached 1375 eV. To estimate and analyze the evolution of plasma parameters in space and time, spatially resolved, time-integrated L-shell Mo X-ray spectra as well as time-gated and time-integrated pinhole images were collected and analyzed. A non-LTE kinetic model was applied to study the spatial structures, temperatures and densities of different wire loads of Mo planar wire arrays. Effects of non-Maxwellian hot electrons on L-shell radiation of Mo are discussed. Furthermore, Mo planar wire arrays generate bright spots or clusters of bright spots along the axial directions. Temperature and density gradients inside these bright spots or its clusters are also investigated. The results are compared with results of previous experiments with X-pinches on UNR Zebra and nested wire arrays at SNL-Z. Radiation magnetohydrodynamics modeling was performed to analyze the mechanisms of Z-pinch plasma heating in the presence of strong density gradients. Published by Elsevier Ltd.

Keywords: Inertial confinement fusion Wire arrays Plasma spectroscopy Radiation magnetohydrodynamics L-shell radiation Opacity Electron beams Bright spots Z-pinch

1. Introduction Z-pinch generators have been used widely as sources of powerful X-ray radiation for inertial confinement fusion (ICF) and other applications. Sandia’s 20 MA 100-ns rise time Z-pinch generator (SNL-Z) produced hot and dense plasma that generated X-ray radiation yields (2 MJ) and powers (4250 TW) from implosions of wire arrays [1–4]. Plasma spectroscopic modeling plays a very important role in providing information on the plasma parameters: temperatures and densities of the Z-pinch plasmas and on implosion dynamics of Z-pinch wire array experiments [5,6]. Different wire array configurations such as single and nested cylindrical, single- (SPWA) and double- (DPWA) planar wire arrays were tested on the university-scale UNR-Zebra 1 MA 100-ns rise time Z-pinch generator [7]. Our preliminary experiments on planar wire arrays showed energy conversion enhancement from the Z-pinch magnetic energy to the radiation source [8] and the capability for radiation pulse shaping, which is also required for ICF capsule ignition [3]. In particular, the total radiation yield of Mo DPWA is ET423 kJ, which is higher than that of the Mo SPWA ET418 kJ [9,10]. However, our recent modeling of radiation from Mo SPWA showed the L-shell radiation plasma temperature, Te1400 eV,

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E-mail address: [email protected] (M.F. Yilmaz). 0022-4073/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.jqsrt.2008.07.011

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to be higher than DPWA, Te1200 eV [10,11]. The produced plasma parameters from SPWA and DPWA and X-pinches on the university-scale generators indicate that these configurations should be tested at the 20 MA level and above [4]. Earlier, the non-LTE collisional–radiative L-shell Mo model was developed and successfully used to model L-shell Mo spectra from different Z-pinch and X-pinch experiments. In particular, the L-shell radiation from symmetric and asymmetric Mo X-pinches and the influence of non-Maxwellian hot electron beams on the L-shell spectra were studied [12–14]. Properties of L-shell radiation from combined Mo X-pinches and planar wire arrays composed of different wire material also were analyzed [15]. Furthermore, plasma electron temperature and density gradients in time and in space from nested Mo wire arrays were investigated [16,17]. In the present work, L-shell radiative properties of the implosions of Mo SPWA and DPWA on the 1 MA Zebra at UNR have been studied. The effects of non-Maxwellian hot electrons on plasma temperature and density were analyzed and discussed. Axial temperature and density gradients inside clusters of bright spots are also investigated. Section 2 presents the experimental set-up and diagnostics. In Section 3, collected data are analyzed. In Section 4, the non-LTE L-shell model was used to diagnose the plasma parameters such as plasma electron temperature, density and fraction of hot electrons. Section 5 provides Radiation magnetohydrodynamics (MHD) modeling to analyze the Z-pinch plasma heating mechanism. Summary and conclusions are given in Sections 6 and 7, respectively. 2. Experiments and diagnostics 2.1. Z-pinch loads The experiments were performed on the 1-MA 100 ns rise time pulsed power generator Zebra at UNR. The current was measured with B-dot probes. Mo SPWA loads consisted of 9–15 wires in a single row with an inter-wire gap of 0.7 or 1.0 mm. Mo DPWA loads consisted of two parallel rows of wires with 8 or 10 wires per row (inter-row gap was 1.5 or 3 mm) with the inter-wire gap of 0.7–1.0 mm. Wire diameter was 7.9 mm for all loads. Previous experimental results illustrated that the rise time and radiation yields were similar for inter-wire gaps between 0.5 and 1.0 mm [15]. The wire lengths (anode–cathode gap) were 20 mm for both configurations (Table 1). 2.2. Diagnostics/set-up X-ray spectrometers and fast X-ray/EUV detectors were applied to analyze the spectral region from 10 eV to more than 10 keV. Photo-conducting detectors (PCDs) and X-ray diodes (XRDs) were used to measure the power and yields of the X-ray radiation and time history. The time resolution was 0.5 ns for PCDs and 0.7 ns for XRDs. A standard Ni bolometer without filter has been used in these experiments to measure the total radiation yields (from EUV to harder X-rays: 0.01–5 keV) [8]. The radiated power was measured by the XRDs. The XRD was filtered by a 5 mm kimfoil film. The kimfoil transmitted to two regions: the first region is 0.18 keVohno0.28 keV and the second region is hn40.7 keV. This spectral range hn40.18 was named ‘‘sub-keV’’ [8,18–21]. The PCD was filtered with an 8 mm Be foil. This filter transmitted radiation with photon energies harder than 0.75 keV. This spectral region was named ‘‘keV’’ [8,18–21]. Time-integrated pinhole X-ray images (with a spatial resolution of 220 mm) were recorded through two 70 mm diameter pinholes with three layers of the Kodak BIOMAX MS film [22]. The first pinhole was filtered with 8 mm kapton, 3 mm mylar and 0.3 Al, while the second had in addition a 110 mm mylar. The first film was registered on radiation with lo10.3 and lo4.4 A˚, the second film at lo3.7 and lo3.1 A˚ and the third film at lo2.9 and lo2.7 A˚ [8,18–21]. Time-gated X-ray pinhole images were registered by a microchannel plate (MCP) detector, which has six time frames with a duration of 3 ns and an inter-frame interval of 10 ns. Spatial resolution of this pinhole camera is 230 mm. The pinhole camera has two parallel identical rows of pinholes (six in each row) in a plate of Pt/Ir. Pinholes were filtered with aluminized mylar films with different thicknesses. These filters and pinholes are protected from debris by a 15 or 25 mm Be filter. The MCP output image was recorded on the Kodak Pan Film 2484 or P3200TMAX. The one row formed images for l1/2o10.0 A˚ and the other one for l1/2o3.5 A˚ (or l1/10o12.0 and l1/10o4.0 A˚) [8,18–21]. Axially resolved time-integrated L-shell spectra (with a resolution of 1.5 mm) were recorded by a spectrometer with a convex KAP crystal (2d ¼ 26.63 A˚ and the radius of curvature is 51 mm) through a 12.5 mm Be filter or an 8 mm Kapton+1 mm Mylar+0.3 mm Al filter. Spectra were registered with a Kodak BIOMAX MS film. K-Shell spectra were recorded by a Table 1 Configuration of single-planar wire arrays (SPWA) and double-planar wire array (DPWA), number of wires, wire material, wire diameters and masses of the loads Shot no. 596 795 816 1033

Type of load SPWA SPWA DPWA DPWA

Number of wires 9 15 16 20

Composition

Configuration

Wire (mm)

Mo Mo Mo Mo

jjjjjjjjj jjjjjjjjjjjjjjj jjjjjjjjjjjjjjjj jjjjjjjjjjjjjjjjjjjj

7.9 7.9 7.9 7.9

Mass (mg) 90 150 160 200

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spectrometer with a convex LiF crystal (2d ¼ 4.027 A˚ and the radius of curvature is 25.4 mm) through a 70 mm Be filter with 3 mm Mylar coating [8,18–21].

3. Interpretation of experimental data The shape and duration of the XRD and PCD signals in Fig. 1a and b show that the Mo SPWA and DPWA implosions resemble each other. However, DPWA’s total and sub-keV radiated energies from filtered XRD and PCD are higher than that of SPWA’s [8–10]. Figs. 2 and 3 present the time-gated pinhole images recorded with an MCP detector and PCD signal to see the evolution of plasma and the keV-radiated power with time. Images from hn41 keV (lo12.0 co) in Figs. 2(a) and 3(a) show that plasma columns are straight and include several bright spots or clusters of bright spots [15,23]. These formations are observed even during early times before the stagnation. No keV precursor-like radiation (before the stagnation for both shots in Figs. 2b and 3b) was seen as for single cylindrical array implosions [8]. In Fig. 4 time-integrated pinhole images of DPWA are presented. The image in Fig. 4(a) from lo10.3 A˚ as well as images at lower wavelengths show bright spot clusters inside the plasma column. The size of the column, the largest (few mm) for the softer X-rays (lo10.3 A˚), decreases as the wavelength decreases and becomes less than 1 mm for the hard X-rays (lo2.9 A˚). The part of the plasma column is brighter near the anode surface and is surrounded by the cloud that is caused by the electron beam bombardment of the anode surface. Instability breaks were seen along the plasma column and also near the cathode side in time-integrated pinhole images (lo4.4 A˚) of 16 wires of Mo DPWA of shot 816 (mass of 160 mg) and 20 wires of DPWA of shot 1033 (mass of 200 mg) (Figs. 4 and 5b). Fig. 5 shows the spatial correlation of bright spots between time-integrated L-shell spectra and the pinhole image recorded with lo4.4 A˚ (which also corresponds to the L-shell region of Mo) for 16 wires of Mo DPWA (shot 816) [15]. For such spectra, the size of the slit was 0.5 mm and geometrical magnification was 3, which give a spatial resolution of 1.5 mm in the axial direction; thus, we were able to resolve spectra at least at the edges of each cluster. The location of clusters of bright spots correlates well with time-integrated pinhole images recorded at lo4.4 A˚. It is possible that clusters are formed by the collection of much smaller-size spots but even the resolution of a pinhole camera of 220 mm is not enough to resolve them. Modeling of the different regions of bright spots in the time-integrated spectra from Mo DPWA (shot 816) indicates

1

80 Current

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Fig. 1. (a) Mo SPWA (shot 795) (b) Mo DPWA (shot 816). XRD (black line 5 mm kimfoil filter), PCD (dashed line: 6 mm kimfoil filter) and load current (gray line).

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2 0 -100

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Time (ns) Fig. 2. Mo SPWA (shot 795). (a) MCP X-ray time-gated images taken along axis a ¼ 301 to the array plane in hn43 keV (top row) and hn41 kev (bottom row). The duration of the frames is 3 ns. The interval between the frames is 10 ns. (b) PCD (8 mm Be) signals at the bottom and current and MCP frame timings are labeled 1, 2, 3, 4, 5, 6.

that these hotter plasmas are being radiated by the hottest core of bright spots or clusters of bright spots and is discussed in detail in Section 4. Figs. 6 and 7 present the lineouts of axially resolved X-ray spectra. Fig. 6b shows three 0.5-mm-thick (N1, N2 and N3) lineouts axially resolved X-ray spectra from nine wires of Mo SPWA of shot 596 (mass of 90 mg). Fig. 7b shows five 1.5-mm- thick (N1, N2, N3, N4 and N5) lineouts axially resolved spectra from 15 wires of Mo SPWA of shot 795 (mass of 150 mg). Lineouts from the heavier SPWA of shot 795 indicate that the intensity of Ne-like 3C (1s2 2s2 2p5 3d 1p11s2 2s2 2p6 1s0) and 3D (1s2 2s2 2p5 3d 3D1-1s2 2s2 2p6 1s0) transitions is decreased towards the cathode. However, intensities of Ne-like 3G (1s2 2s2 2p5 3d 3P1-1s2 2s2 2p6 1s0), Na1 and Mg1 lines increased. This might be due to opacity effects near the cathode side. Fig. 8b shows five 1.0-mm-thick (N1, N2, N3, N4 and N5) lineouts axially resolved spectra from 20 wires of Mo DPWA of shot 1033. The broadening of the lines is larger near the anode and cathode side. 4. Modeling of the L-shell Mo spectra from planar wire arrays The previously developed non-LTE collisional–radiative L-shell Mo model has been used in this work [11,12]. In particular, it was applied to diagnose the plasma electron density (ne), plasma electron temperature (Te) and the fraction of the hot electrons (f) for the collected spectra of L-shell Mo in the region of 4.0–5.5 A˚. Briefly, energy levels, spontaneous and collisional rates, collisional and photoionization cross-sections were taken from a relativistic multiconfiguration atomic structure code (HULLAC). The ground states of all ions from neutral to bare Mo configurations were considered. Detailed structure for O-like to Mg-like Mo ions included singly excited states up to n ¼ 7 for O-through Ne-like ions, both singly and doubly excited states up to n ¼ 7 and n ¼ 4 for Na- and Mg-like ions [12,13]. The model integrates collision cross-sections over electron distribution functions to obtain collisional rates. Electron distribution functions include both Maxwellian and non-Maxwellian contributions using the formula F(e) ¼ (1f)Fm(e)+ fFnm, Fm is the Maxwellian distribution, Fnm is the non-Maxwellian distribution (which in this paper is described

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λ < 10.3 Å

Cathode

λ < 4.4 Å

λ < 3.7 Å

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λ < 3.1 Å

λ < 2.9 Å

λ < 2.7 Å

Fig. 4. Mo DPWA (shot 816). X-ray time-integrated pinhole images in different spectral ranges with the 220 mm resolution.

by a Gaussian distribution) and f is the fraction of the hot electrons. Hot electrons usually indicate the presence of electron beams in the plasma. Hot electrons decrease the bulk temperature of the plasma and increase the charge state balance and spread the ionization stages [12,13]. In this work, Voigt profiles were used to fit line broadening of the experimental spectra. The resolution l/dl ¼ 350 used in modeling agrees well with the instrumental resolution.

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Fig. 5. Mo DPWA (shot 816). (a) Time-integrated X-ray images from the KAP spectrometer (12.5 mm Be filter). (b) Time-integrated pinhole image from spectral range lo4.4 A˚ with the 220 mm resolution.

Electron densities (ne) have been inferred from the relative line intensities of certain Ne-like lines (3A (3p–2s), 3B (3p–2s), 3F (3s–2p), 3G (3s–2p)). For example, it has been shown that the (3A+3B)/(3F+3G) ratio of Ne-like lines can be used for ne diagnostics. (This ratio is almost not sensitive to hot electrons and opacity influences in the range of 5  1019–5  1021 cm3 and is almost insensitive to Te changes in the range from 1018 to 1021 cm3 [12,13].) Electron density was derived by a comparison of the (3A+3B)/(3F+3G) ratio for experimental and synthetic spectra for all considered loads. The percentage difference of this ratio between experimental and synthetic spectra varied by 1–11% between all configurations [see Figs. 6(b), 7(b), 8(b) and 10(b)). However, in SPWA of shot 795 and DPWA of shots 1033 and 816, the (3A+3B)/(3F+3G) ratios from experimental spectra were almost 30% less near the cathode sides than near the anode side [see Figs. 7(b), 8(b) and 10(b)]. The electron temperatures have also been inferred from relative line intensities but from different charge states. The ratio of the Mg1/Na1 and F1/Mg1 can be used as a plasma electron temperature diagnostic [12,13]. For example, the Mg1/Na1 and F1/Mg1 ratios are sensitive to the Te in the range of 900 eVoTeo1375 eV at moderate densities (5  1018–1 1022 cm3). The ratio of Mg1/Na1 lines of synthetic spectra was in agreement with the experimental spectra for both SPWA and DPWA. The percent difference of the Mg1/Na1 ratio between experimental and synthetic spectra varied 0.1–20% from the anode to the cathode (Fig. 6b, 7b, 8b, and 10b). In addition for DPWA (shots 1033 and 816) (see Fig. 8b and 10b), the Mg1/Na1 ratio from the experimental spectra near the anode and the cathode side was less than in the center by almost 30% percent. The ratio of F1/Mg1 between synthetic spectra and experimental spectra was not in such good agreement as Mg1/Na1. This discrepancy may be explained by the presence of the non-Maxwellian electrons generated near the anode and the cathode sides. The intensity of the F1-like features in experimental spectra in most cases was higher than the modeled spectra. When temperatures were increased to improve the fit of intensities of F1-like features, the Mg1-like features would not fit. However, the addition of 2.5% hot electrons improved the intensities of the F-like and Mg1-like lines as well as of 3F and 3G Ne-like lines for the DPWA spectra (see Fig. 9). As a result of the addition of hot electrons, Te decreased from 1090 to 600 eV and the density from 3  1019 to 5  1018 cm3, which was as expected [12,13]. The modeling of Mo SPWAs indicates that nine wires (mass of 90 mg) radiate the densest L-shell plasma ne ¼ 4  1021 cm3 at Te ¼ 1050 eV [Fig. 6(b)] and 15 wires (mass of 150 mg) radiate the hottest L-shell plasma Te ¼ 1375 eV at ne1 1019 cm3 [Fig. 7(b)] for all considered SPWA and DPWA loads. The modeling of 16 wires DPWA (mass of 160 mg) indicates ne ¼ 5  1019 cm3 at Te ¼ 1100 eV. The parameters from the heaviest load, 20 wires in a DPWA (mass of 200 mg), indicate ne ¼ 1 1021 cm3 and Te ¼ 1070 eV. Therefore, higher peak densities were accessed in the radiated plasma from the DPWA with 20 wires, which was denser than with 16 wires [Fig. 8 (b) and 10(b)]. In Fig. 5, the time-integrated X-ray spectra and pinhole image from spectral range lo4.4 A˚ [Fig. 4(a)] were compared to identify the temperature and density gradients of the hot clusters following the method in [15]. Lineouts at different axial positions across individual bright regions in the time-integrated spectra from implosions of Mo DPWA were modeled (Fig. 10). Temperature and density values indicate that the plasma was hotter and denser at the centers of clusters, for example, Te ¼ 1090 eV, ne ¼ 3  1019 cm3 for N2 and Te ¼ 1180 eV, ne ¼ 4  1019 cm3 for N5. The axial gradients of electron densities and temperatures for four considered experiments are summarized in Figs. 11 and 12, respectively.

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Fig. 6. Mo SPWA (shot 596). (a) Images of axially resolved time-integrated spectra. (b) Lineouts of the spectra (N1 ¼ N2 ¼ N3 ¼ 0.5 mm). Modeling from N1 (gray lines) gives Te ¼ 900 eV, ne ¼ 1 1021 cm3, N2 gives Te ¼ 950 eV, ne ¼ 2  1021 cm3, N3 gives Te ¼ 1050 eV, ne ¼ 4  1021 cm3.

5. Radiation MHD modeling A rough estimation of the stagnating Z-pinch temperature can be performed, for example, by using the Bennett equilibrium condition for isothermal pinch (see Ref. [24]): ¯ ¼ T B ð1 þ ZÞ

m0 I2 AmA , 8p mL

(1)

where TB is the equilibrium (Bennett) temperature, Z¯ is the mean ion charge, I is the total current through the pinch, A is the atomic weight of the pinch material (for Mo A ¼ 95.94), mA is the atomic mass unit and mL is the pinch mass per unit length. It should also be mentioned here that the Bennett equilibrium is static, while the Z-pinch is likely a very dynamic object and may never be in equilibrium. It is possible that the temperature of the bulk of the plasma is close to the Bennett temperature TB, while the bright regions evolve dynamically and obtain higher temperatures. So, the spectroscopic analysis yields the temperature in the bright emitting regions and does not necessarily tell you the bulk temperature. The MHD simulations in this paper will mostly be related to these brightest emitting regions. For the same current I through the pinch, the Bennett temperature TB depends only on the pinch mass per unit length. For the SPWA of shot 596 we have mL ¼ 4.5 mg/mm. In this case at maximum current I ¼ 1 MA the LTE model provides the following estimations: TB ¼ 335eV at Z¯ ¼ 32. (Both values of TB and Z¯ are obtained through the iterative process to satisfy the Bennett equilibrium(1) for specific mL.) For the DPWA of Shot 1033 with a heavier load mL ¼ 10 mg/mm, the LTE model yields TB ¼ 184 eV and Z¯ ¼ 26. If we take the radius of the stagnating Z-pinch rp to be equal to 250 mm (we have taken as a very rough estimation from experimental data), the electron number density at the pinch center can be estimated as 1022 cm3. It should be noted here that the LTE approximation tends to overestimate the mean ion charge and, consequently, underestimate the Bennett temperature. This difference between the calculations of plasma temperature by the LTE and kinetic non-LTE models usually increases with the decrease in plasma density. The radiation MHD simulations performed for Al Z-pinch [24] have demonstrated that at the Bennett temperature and typical pinch densities, the radiation power is so high that it cannot be compensated either by the thermalization of the kinetic energy of imploding plasma or by the Ohmic plasma heating (in the Spitzer model). Thus, because of the strong radiative cooling of pinch plasma, the Bennett temperature cannot be reached. The latter effect triggers a radiative collapse of the pinch plasma, the theoretical study of which ascends to the early works of Pease [25] and Braginskii [26]. However, it was mentioned here that in some codes the radiative collapse tends to be mitigated even in 1D RMHD modeling of Z-pinches phenomenologically through enhanced transport coefficients tuned to produce final pinch radii matching

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Fig. 7. Mo SPWA (shot 795). (a) Images of axially resolved time-integrated spectra. (b) Lineouts of the spectra (N1 ¼ N2 ¼ N3 ¼ N4 ¼ N5 ¼ 1.5 mm). Modeling from N1 (gray lines) gives Te ¼ 1180 eV, ne ¼ 1 1018 cm3, N2 gives Te ¼ 1200 eV, ne ¼ 2  1018 cm3, N3 gives Te ¼ 1240 eV, ne ¼ 4  1018 cm3, N4 gives Te ¼ 1375 eV, ne ¼ 11019 cm3.

experimental observations or through the turbulence [27]. In another approach the radiative collapse of Z-pinch can be stopped by achieving the high ion temperatures [28]. Although the equilibrium conditions for highly radiating Z-pinches cannot be satisfied for the whole pinch plasma, they still can be fulfilled locally in the plasma regions; that density is only a fraction of the average density of the Z-pinch. The basic reason for the latter effect is that the volume radiation power losses in optically thin plasma are proportional to the plasma density. At the same time, plasma resistance is almost independent of plasma density. Thus, the Ohmic heating of plasma is only defined by the amount of electric current passing through it. In lower-density plasmas, Ohmic heating can compensate strong radiation power losses that create the equilibrium or quasi-equilibrium hot spot plasma regions. Although, the bulk of the Z-pinch has higher mass density, it likely radiates as a black body. Because the intensity of the black body radiation does not depend on the plasma density, the lower mass density but higher temperatures bright spots will still look the brightest part of the Z-pinch. Let us consider the model of the equilibrium diffuse Z-pinch with uniform distributions of temperature Ths and current density Jz. Hence, to balance the plasma pressure against the magnetic field pressure, the mass density profile should be " # AmA m0 I2hs r2 rðrÞ ¼ 1 2 ; rp T hs ð1 þ Z¯ hs Þ 4p2 r 2p

rpr p ,

(2)

where Z¯ hs ðT hs ; rÞ is mean ion charge in the hot spot plasma region, and Ihs is the total electric current through the hot spot. The radiation MHD simulations with the code POS [29] predicts the maximum pinch temperature that can be sustained solely by Ohmic heating to be Ths ¼ 500 eV. The simplified radiation MHD model used by the code POS accounts only for free–free and free–bound electron transitions in the simplified Zeldovich approximations [30]. The equilibrium density profile specified by Eq. (2) for Ths ¼ 500 eV and Ihs ¼ 250 kA (according to Eq. (2) current Ihs is only a function of the Z-pinch mass per unit length mL) is shown in Fig. 13(a). As we can see, the intensity of the magnetic field B peaks above the level of 200 T (2 MG). The electron magnetization factor xe ¼ oe/ve, which is the ratio of the electron cyclotron frequency oe to the frequency of the electron collisions Ve [31], rises toward the outer edge of the profile. Note that the kinetic transport effects, such as heat conduction, may be significantly damped in highly magnetized xeb1 plasma. The parameter B ¼ ve/vA, where ve ¼ jz/ene is the electron drift velocity and vA is the Alfven velocity, is less than unity throughout the profile. The latter feature predefines the relative weakness of the possible two-fluid effects (decoupled dynamics of the electron and ion plasma components) in the hot plasma regions at the discussed range of parameters. Strong two-fluid effects Bb1 may result in asymmetric plasma behavior near the cathode and the anode. These effects may also be responsible for the anomalous plasma heating due to strong Hall effect [32–34].

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Fig. 8. Mo DPWA (shot 1033). (a) Images of axially resolved time-integrated spectra. (b) Lineouts of the spectra (N1 ¼ N2 ¼ N3 ¼ N4 ¼ N5 ¼ 1.0 mm). Modeling from N2 (gray lines) gives Te ¼ 1030 eV, ne ¼ 5  1020 cm3, N3 gives Te ¼ 1050 eV, ne ¼ 6  1020 cm3, N4 gives Te ¼ 1070 eV, ne ¼ 7  1020 cm3.

If we increase the amount of electric current through the hot spot Ihs keeping the same value of equilibrium temperature Ths ¼ 500 eV, the plasma mass per unit length must also increase if we retain the equilibrium. As we can see in Fig. 13(b), because of Ohmic heating and radiation the calculated (by the POS code) value of the electron temperature departs from the equilibrium value of 500 eV. Such deviation is minimal in the lower-density shoulder of the radial profile and is more significant in the higher-density shoulder. Hence, if we consider the hot spot region with the higher fraction of Z-pinch mass (mLX0.6 mg/mm, or, in terms of electron number density, neX1021 cm3), the fast radiative cooling will drive plasma into a radiative collapse, just as in the case of the Al Z-pinch, considered in Ref. [24]. The regions with the fractional Z-pinch mass are likely to be formed as a result of the Rayleigh–Taylor (RT) instability, which forms strong density gradients along the z-axis. In this case we should expect that along the axial direction the hotter and lower-density plasma regions will alternate with cooler and higher-density plasma layers. In such Z-pinch configurations the Hall effect can be greatly increased [10]. Fig. 14 presents the results of two-dimensional radiation MHD modeling of plasma cooling due to heat transport in the axial direction. The plasma conditions are assumed to be uniform in the axial directions but with cold boundaries (fixed value of the plasma temperature at z ¼ 0 and 0.25 mm). As we can see, the cooling wave propagates in non-magnetized plasma (r ¼ 0) with the velocity 150 mm/ns. In highly magnetized plasma (r ¼ 0.15 mm), this rate is significantly lower: 15 mm/ns. Thus, if the hot spot region is filled with magnetized plasma, it can sustain its temperature for time periods of 10 ns even in the presence of cooler plasma layers at its boundaries.

6. Discussion Modeling of spatially resolved time-integrated spectra using the non-LTE kinetic model spectra from Section 4 has shown the following plasma parameters. In general, electron temperatures (Te) for SPWA varied from 900 to 1350 eV and for DPWA it varied from 1000 to 1180 eV. Electron densities (ne) for SPWA varied from 1 1018 to 4  1021 cm3 and for DPWA varied from 3  1019 to 7  1020 cm3. The simple analytical estimations, performed for the uniform Z-pinch in equilibrium with the magnetic field, suggest plasma temperatures to be in the range 180–350 eV. At the same time, the radiation MHD simulations demonstrate that the Z-pinch regions with fractional mass density (mLp0.6 mg/mm or nep1021 cm3), formed by the growing RT or m ¼ 0 instability modes, can be effectively heated up to 500 eV solely by Ohmic heating. Higher actual plasma temperatures in experiments can be explained by the concurrent action of other mechanisms of plasma heating, such as the thermalization of the kinetic energy. Although the latter mechanism has a

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3D

3G

3C Na1

Intensity (a.u)

Na2 Mg1

Mg1

3F L-α

F1 3A

4.2

3B

4.4

4.6

4.8

5

5.2

5.4

λ (Å) Fig. 9. Mo DPWA (shot 816). Black line is the axially resolved time-integrated spectra near the anode side [N1, Fig. 10(b)]. Dashed black line is modeling with the hot electrons, f ¼ 0.020, Te ¼ 600 eV, ne ¼ 4  1018 cm3. Gray line is modeling without hot electrons Te ¼ 1090 eV, ne ¼ 3  1019 cm3.

3D Anode

3A

3B F1

3C

3G 3F

L-α

N1

N1 N2

N2

N3

N3 N4

N4 20 mm

N7 N8

N5 Intensity (a.u)

N5 N6

N6

N7 N8

N9

N9 N10

N10 N11 N12

N11 N12

Cathode

4.2

4.4

4.6

4.8 λ(Å)

5

5.2

5.4

4.2

4.4

4.6

4.8

5

5.2

5.4

λ(Å)

Fig. 10. Mo DPWA (shot 816). Modeling of the radiation from bright clusters. Modeling from N1 (gray lines) gives Te ¼ 1070 eV, ne ¼ 2  1019 cm3, N2 gives Te ¼ 1090 eV, ne ¼ 3  1019 cm3, N3 gives Te ¼ 1070 eV, ne ¼ 2  1019 cm3, N4 gives Te ¼ 1060 eV, ne ¼ 2  1019 cm3, N5 gives Te ¼ 1180 eV, ne ¼ 4  1019 cm3, N6 gives Te ¼ 1060 eV, ne ¼ 1 1019 cm3, N7 gives Te ¼ 1090 eV, ne ¼ 1 1019 cm3, N8 gives Te ¼ 1110 eV, ne ¼ 4  1019 cm3.

transient nature and works on a much shorter time scale than the Ohmic heating, it still can influence the time-integrated spectroscopic measurements by increasing the ‘‘average’’ electron temperature, which is weighted by emissivity and tends to be closer to the peak temperature. Another important aspect worth mentioning here is that the MHD simulations

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1E+22

Electron density (cm-3)

1E+21

Shot 596 Shot 795

1E+20

Shot 816 Shot 1033

1E+19

1E+18

1E+17

0

5

10 15 Distance from cathode (mm)

20

Fig. 11. Density (ne) dependence from the anode to the cathode. The (3A+3B)/(3F+3G) ratio was used to estimate density values.

1500

Electron temperature (eV)

1400

1300 Shot 596 Shot 795

1200

Shot 816 Shot 1033

1100

1000

900

800

0

5

10

15

20

Distance from anode (mm) Fig. 12. Temperature (Te) dependence from the anode to the cathode. The ratios of the Mg1/Na1 and F1/Mg1 were used to estimate temperature values.

accounted for radiation using the LTE model and the consideration of only free–free and bound–free electron transitions. As a result, this radiation model may predict significantly lower temperatures, overestimating the average ion charge /ZS and radiative cooling rate, as compared to the calculations provided by the more accurate kinetic non-LTE line radiation model. The high intensity of 3F and 3G lines in comparison with 3D (or 3C) lines may manifest either influence of opacity or hot electrons. Experimental spectra in Figs. 7b, 8b and 10b show that the intensity of the 3G lines was higher than that of the 3D lines. Optical depth (t) determines that plasma is either thin or thick (opaque). For optically thin plasmas (to1) small amount of the photons is absorbed. However, in optically thick plasma, significant amounts of the photons are absorbed

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xe

102

ζ 0.3

1020

101

0.2

1019

100

0.1

ne

ζ

xe

B

B, kT

ne, cm-3

1021

1018

0

0.05

0.1

0.15

10-1 0.25

0.2

0

r, mm 600

Te, eV

500 fast radiative cooling

400 300 200 100 1018

I = 250 kA (mL = 0.15 μg/mm) I = 350 kA (mL = 0.3 μg/mm) I = 500 kA (mL = 0.6 μg/mm)

1019

1020 ne,

1021

1022

cm-3

Fig. 13. (a) Equilibrium Bennett profile, specified by Eq. (2) for Ths ¼ 500 eV and Ihs ¼ 250 kA (mass per unit length mL ¼ 0.15 mg/mm). Plots represent the electron number density ne, electron magnetization factor xe, two-fluid parameter B and the magnetic field intensity B versus the radius r. (b) Profile dependences of the electron temperature Te(r) versus the electron number density ne(r) for three different values of Ihs in Eq. (2). The equilibrium value of Te ¼ 500 eV is marked by the horizontal broken line. Dense plasma regions ne41021 cm3 are affected by the strong radiative cooling.

500

500 r = 0.15 mm t = 2 ns

400

400

Te, eV

r=0

300

300

t=0 t = 1 ns t = 2 ns

200

200

100 0

0.05

0.1

0.15

0.2

100 0.25

z, mm Fig. 14. Two-dimensional radiation MHD modeling of the cooling of the hot spot plasma region due to the presence of cold plasma layers along the z-axis. Initial radial profiles of plasma parameter correspond to the ones in Fig. 14a. The initial temperature profile in the axial direction is shown by the broken line. Temperature profiles are shown at different times at two radial positions r ¼ 0 and r ¼ 0.15 mm referring to Fig. 13a.

and the radiation transport equation has to be solved self-consistently with the set of collisional–radiative atomic kinetics equations [35]. We performed calculations of the optical depth (t) at Te ¼ 1000 eV and the plasma size of 100 mm different for values of ne. We found that ne less than or equal to 1020 cm3 the optical depth exceeds one for lines 3C and 3D and is much less than

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one for 3A, 3B, 3F and 3G lines. As ne increases, the optical depth of all lines increases and becomes more than 15 for lines 3C and 3D and about 1 for 3F and 3G lines within the considered range. So less optical depth of the 3F and 3G might increase the relative intensity of 3F and 3G lines with respect to 3C and 3D lines. Increasing wire numbers in the configurations, and therefore mass, might enhance the opacity. The generation of hot electrons might also be another reason for the high intensity of 3F and 3F lines [13]. Figs. 8b and 10b show that the line broadenings were larger near the anode and the cathode side and narrower at the center. Line shapes at axial positions near the anode and the cathode fit a Gaussian profile, whereas at the center of the Z-pinch the line shape is Lorentzian. Thermal distribution of ion velocities with high ion temperatures (Ti) and generation of hot electrons might cause broadening of lines near the anode and the cathode sides. For nested Mo wire arrays on Z facility at SNL, the electron density was higher near the anode side and the temperature was higher near the cathode [17]. For implosions of planar wire arrays, which are characterized by the formation of bright spots along the z-axis, the dependence of ne from distance depends mainly on the location of these bright spots. Then Fig. 11 does not show the increase of ne towards the anode. However, Fig. 12 shows that the plasma electron temperatures gradually increase towards the cathode, which is consistent with the result for implosions of nested Mo wire arrays at SNL-Z [17]. The radiation MHD simulations suggest high magnetization of the hot spot plasma with the estimated intensity of the magnetic field up to 200 T (2 MG). Highly magnetized plasma is characterized by a weak kinetic heat transport. Also, there is no evidence of the strong two-fluid effects in the hot spot plasma regions. Thus, the MHD simulations suggest that the observed asymmetry of plasma parameters with respect to the anode and cathode is likely to be explained by the non-symmetrical array implosion, or by the non-Maxwellian effects, such as the generation of the electron beam from the cathode or the generation of the ion beam from the anode. Another evidence of the presence of the electron beams is the observance of the cold characteristic line Mo L-a near the anode and cathode sides in almost all time-integrated spectra (Fig. 6b, 7b, 8b and 10b), which might be explained by the generation of the beams near the electrodes. The total radiating mass (mrad) in the L-shell Mo has been calculated for the SPWA of shots 596 and 795. For the SPWA of shot 596 (mass of 90 mg), the average ion charge /ZSE32 and mradE8.15 mg, which is about 9% of the total mass. For the Mo SPWA of shot 795 (mass of 150 mg), the ion charge /ZSE30.5 and mradE16.1 mg, which is about 11% of the total mass. The radiation MHD simulations suggest the value of the electric current through the highly radiating hot spot plasma regions to be in the range 0.25–0.35 MA. Assuming that these regions occupy a significant fraction of Z-pinch length, their total radiated mass according to the MHD modeling may be up to 10 mg (as it follows from the simplified static 1D and 2D radiation MHD models discussed in the previous sections), which is in good agreement with the above estimation by the spectroscopic modeling. 7. Conclusion The comprehensive spectroscopic study of implosions of Mo SPWA and DPWA has been accomplished for the first time. Spatially resolved plasma parameters for SPWA and DPWA implosions on Zebra have been determined. In particular, L-shell spectra of Mo from SPWA and DPWA have been analyzed and compared for all considered experiments. The applied nonLTE Mo model describes the experiments well for all lineouts except for the ones near the cathode side for the heavier loads of double planar arrays. This discrepancy might be caused by opacity or hot electron effects. The electron temperature (Te) gradually increases from the anode to the cathode. Temperature behavior is consistent with the results of the modeling of axially resolved L-shell Mo spectra from the SNL-Z nested arrays. The maximum Te ¼ 1375 eV was found for the heavier load of Mo SPWA (shot 795), which was larger than for X-pinches [14]. The electron density was found to be two orders of magnitude smaller for heavier SPWA and DPWA 1019 cm3 than for lighter single-planar arrays 3  10 21 cm3. The densest plasma estimated in this study was ne5  1021 cm3, which is half of that from the X-pinches (1022 cm3). Experimental spectra from SPWA and DPWA showed the presence of hot electron beams. Including a small fraction of hot electrons in the synthetic spectra improved the agreement with the experiment. Investigating the structure and parameters of bright spots by the plasma spectroscopic and radiational MHD model shows that hottest and densest plasma may exist in the center of bright spots or in clusters of bright spots.

Acknowledgements This work was supported by NNSA under DOE Cooperative Agreements DE-FC52-06NA27588, DE-FC52-06NA27586, and in part by DE-FC52-06NA27616. References [1] Spielman RB, Deeney C, Chandler GA, Douglas MR, Fehl DL, Matzen MK, et al. Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ2. Phys Plasmas 1998;5:2105–11. [2] Deeney C, Nash TJ, Spielman RB, Seaman JF, McGurn JS, Jobe DO, et al. Improved large diameter wire array implosions from increased wire array symmetry and on-axis mass participation. Phys Plasmas 1998;5:2431–41.

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