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Radius scaling effects in nickel wire array Z-pinches
J. Quant. Spectrosc. Radiat. Transfer Vol. 44, No. 5/6, pp. 457--469, 1990 Printed in Great Britain. All rights reserved
0022-4073/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press pie
RADIUS SCALING EFFECTS IN NICKEL WIRE ARRAY Z-PINCHES C. DEENEY, T. NASH, P. D. LEPELL, K. CHILDERS, AND M. KRISHNANt Physics International Company 2700 Merced Street San Leandro, CA 94577 K. G. WHITNEY AND J. W. THORNHILL Naval Research Laboratory 4555 Overlook Avenue, SW Washington, DC 20375
Abstract - Nickel wire arrays of different masses and initial diameters have been imploded on the DNA/Double-EAGLE generator. Array masses and diameters were chosen to cause an implosion 10 to 20 ns before the peak current of 4 MA. The nickel L-shell radiated yield around 1 keV was found to be maximized at 35 kJ for a'n initial array diameter of 15 mm and a mass loading of 86 I.tg/cm. X-ray diagnostic data indicate that the 1-keV L-shell yield is maximized when the array diameter and mass are such that the implosion energy is just sufficient to thermalize on axis to a 3-ram diameter bulk plasma. This plasma is predominantly ionized into the L-shell with an ion density of 1019 cm-3 and an electron temperature of 450 eV. Initial diameters larger than optimum result in hotter lower density plasmas. The reduced density causes a reduction in the:yield. By contrast, for diameters less than optimum, the bulk thermalized plasma is too massive and too cold for efficient radiation from the L-shell. Localized "hot spots" do emit L-shell radiation, and consequently the total L-shell yield does not fall as precipitously with decreasing array radius as might be expected from the change in the bulk plasma parameters. 1. INTRODUCTION The advent of pulsed power generators for relativistic electron beam experiments made an impact on the Z-pinch community by providing multi-megampere, ~ 100 ns rise-time current generators. With such machines, research could be performed on moderate-atomic-number (that is, Z > 9) plasmas with temperatures of 0.2 to 1.5 keV and electron densities between 1020 and 1021 cm -3. This field has recently been reviewed by Pereira and Davis. 1 Much of the impetus for this research has been to maximize the X-ray radiation output from single wire and wire array loads. Single wires 2-4 have produced spectra from highly ionized states of elements with atomic numbers from 13 to 29. Although these spectra are consistent with plasmas that have electron densities and temperatures greater than 1021 cm -3 and 1 keV respectively, the total kilovolt radiation yields were low. It has been speculated that this was due to poor electrical coupling5 between a single wire and a magnetically insulated transmission line(MITL) or possibly because single wires become unstable early in the current rise. Kilovolt yields are much higher when wire arrays5 are imploded onto the axis from a centimeter or so radius. The array implosion's spectra6, 7 are consistent with plasmas having electron densities around 1020 cm-3 and electron temperatures of less than 800 eV. The differences in the kilovolt radiation yield between these two types of load could be due to the fact that single wires radiate in the form of multiple plasma spots with characteristic dimensions of a few hundred micrometers, compared to the wire arrays where the bulk of the plasma, with dimensions of a few millimeters diameter and a few centimeters long, had the properties outlined above. Therefore, the radiation output of single wires is thought to be due primarily to instabilities, whereas wire arrays are considered to produce a more uniform plasma due to the radial implosion. The initial radius(diameter) of the wire array is the particular implosion parameter that is the focus of this paper. It is critical in determining the radiation properties of array Z-pinches because of its effect on the temperature and density of the assembled plasma. ~ Presentaddress: ScienceResearchLaboratory,Suite 100, 1150BallenaBvd., Alameda,California, 95401. a~7
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Simple zero dimensional analysis of an imploding shell of mass per unit length, m/L, predicts that for a constant current, the following relationship holds between m, initial radius, R, of the array, the implosion time, t, and the current, I: mR2 - constant LI2t2
(1)
Assuming that, for a given generator, the peak current and the implosion time are fixed, with the implosion time being equal to the time of the peak current for optimal coupling, then the plasma parameters are adjusted by changing m and R with m being proportional to R -2. Intuitively, it is obvious that increasing m by decreasing R would tend to produce dense, cool plasmas, whereas small m and larger R implosions would tend to produce lower density, higher temperature plasmas. Specifically, if it is assumed that all the mass assembles into a constant plasma volume, then the plasma density should scale as m or R -2 and the implosion kinetic energy-per-ion should scale as 1/m or R 2 , for a fixed plasma kinetic energy coupled from the generator to the imploding load. Since the implosion energy, when thermalized, is distributed between ionization energy, radiation losses and electron thermal energy, the plasma temperature may not necessarily scale as R 2. Previous experiments to study this behavior have been performed by a group at the Naval Research Laboratory (NRL) and a group at Maxwell Laboratories (MLI). Stephanakis et al.8 imploded neon gas puffs produced by nozzles in the diameter range of 0.85 to 1.5 cm, at currents of around 1.2 MA. They found that as the initial nozzle diameter was decreased, the 1-keV radiation yield increased. Gersten et al. 9 found a similar result with K-shell radiation from aluminum wire array implosions at 4 MA on the Blackjack-5 generator at MLI. The MLI experiments were performed over an initial diameter range of 15 to 30 ram, keeping the implosion time constant. Both groups determined that the decreased array diameter produces a more dense but cooler pinched plasma. Since the radiation yield scales as the density squared, the increased density causes an increased K-shell radiation yield. Conversely, as the array diameter is increased, the higher assembled plasma temperatures are insufficient to compensate for the decreased plasma densities. It can be conjectured that for a given generator and load material, that as the load diameter is decreased, if the temperature falls below a given threshold, then the plasma would be too cold to give efficient excitation in the 1 to 1.5 keV photon energy region. Remember, that in the limit of a zero radius (on-axis) load, the dynamics of the pinch are different and the kilovolt radiation efficiencies are low. Hence, it seems likely that the kilovolt yield would be a double valued function of initial radius, and that there would be a specific initial radius that would optimize the kilovolt radiation for a given element on a given generator. The experiment described in this paper had the aim of experimentally determining the initial radius that produced the maximum yield of 0.85 to 1.3 keV emissions from the nickel L-shell, using wire arrays on the DNA/Double-EAGLE generator. The experiment is described in Section 2. The L-shell yield results and other associated X-ray data are presented in Section 3 and discussed in Section 4. The conclusions of this paper are presented in Section 5. 2. EXPERIMENTAL ARRANGEMENT The Double-EAGLE 10 generator is composed of two triplate waterline modules feeding a common vacuum diode. When wire arrays or gas-puffs are used to bridge the anode-cathode gap, a 4-MA, 90-ns risetime current pulse is delivered to the diode and these hollow loads implode, giving copious X-ray emission. The chosen element for wire array experiments in this paper is nickel, for which the n = 2 to 3 line emissions from the L-shell ionization stages fall in the range of 0.85 to 1.3 keV. 11 The cylindrical wire arrays were composed of twelve equally spaced (in azimuth) wires with cylinder diameters ranging from 6 mm to 20 mm. Individual wire diameters were adjusted to keep the product mR 2 fixed at 50 I.tg-cm where m and R are defined as before. The actual load parameters tested in this pulsing series are listed in Table 1. The implosion time for all the arrays was measured to be between 70 and 80 ns, as illustrated in Figure 1, where a filtered X-ray diode signal is shown with the corresponding current trace. Due to the small prepulse on Double-EAGLE, the implosion time is defined as shown in Figure 1. A comprehensive suite of X-ray diagnostics 12 was employed to measure the X-ray emission The total X-ray emission around 1 keV was determined using 2.5 Ixm Kimfol plus 1.8 Ixm aluminum filtered, tantalum foil calorimeters. In addition, aluminum cathode, X-my diodes 13 (XRD) with identical filters were used to measure the radiation power at 1 keV, following Young et al. 14 The XRD emission power signals were also numerically integrated in time to give the kilovolt L-shell yield. An unfiltered calorimeter measured the total radiated yield and this could be compared to the energy coupled into the diode as calculated from the electrical voltage and current measurements.
459
Radius scaling effects in nickel wire array Z-pinches Table I. Shot Parameters
ax.rax.l/~lmtl~
N o of W i r e s
Wire Thickness ~tm
mm
12 12 12 12 12
17 25 12.5 10 8
6 9 12.5 15 20
6
I
I
I
I
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m R2
L
x ns
53.6 48.6 52.7 48.4 48.5
75 72 82 80 80
I
5 4
1.0 n
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21O
,
0
l
100 1"
200
300
TIME
ns
F i g u r e 1. A D o u b l e - E A G L E current trace and X-ray diode trace (shaded) are s h o w n on a c o m m o n t i m e base for a l $ - m m nickel w i r e array implosion: shot 1869. The X - r a y diode is filtered with 2.5 Ixm Kimfol plus 1.8-~tm a l u m i n u m so as only to detect X-rays around 1 keV, that is f r o m the n = 3 - 2 transitions in nickel L-shell ionization states. The i m p l o s i o n time, x, relative to the current start is d e f i n e d as s h o w n .
The spatial and temporal behavior of different photon energy emitting regions was studied using filtered pinhole cameras. The filters were chosen to transmit photons with energies greater than 100 eV, 1000 eV and 7000 eV respectively . Time-resolution was incorporated into the pinhole cameras by using microchannel plates (MCP) with gating strips. Every strip had a factor-of-4 demagnified image of the plasma produced on it by a 504tin diameter pinhole. Seven or twelve strips were used per camera and each strip was gated with a 5-ns long, -1-kV pulse. Moreover, each strip was pulsed 5 ns after the preceding strip; thus, 35 to 60 ns of uninterrupted plasma emission could be studied. The strips derived their gating pulse from a common Krytron pulser which allowed for accurate time-correlation. A space-resolved 5 cmcurved lithium fluoride (LiF) crystal spectrometer gave spectral information on the nickel K-sheU radiation with a spatial resolution of 5 ram. Additionally, a second 5 cm-curved LiF crystal spectrometer, fitted with a five-strip-gated MCP, was used to time-resolve the nickel K-shell emission between 7.5 and 8.3 keV. The time-correlation of the time-gated diagnostics was accurately determined, since these diagnostics derive their gating signals from a common Krytron pulser unit. One of the gating pulses was sent to the digital data acquisition system to permit time correlation of the XRD signals with the gated MCP detectors.
460
C, DEENEYet al 3. RESULTS
Experimentally, the variation of kilovolt X-ray yield with the initial wire array diameter has been determined, as shown in Figure 2. The error bars on the experimental points account for both shot-to-shot scatter and differences between the integrated XRD and calorimeter measurements. These random errors are greater than the 20% possible error due to the variation in detector sensitivities and filter transmissions, over the range of 0.85 to 1.3 keV of the L-shell radiation. A curve is drawn through the average of the data points to highlight the trends as the diameter varies. From Figure 2, it is apparent that the optimum initial wire array diameter to produce kilovolt radiation is 15 ram. On the other hand, the total radiation, plotted as
40
30
20
10
O 0
I
!
10
20
30
DIAMETER mm Figure 2. The kilovolt, nickel L-shell yield as a function of initial wire array diameter. The error bars shown encompass the shot-to-shot reproducibility, as well as the variation between the filtered X-ray diodes and the similarly filtered tantalum foil/ nickel wire calorimeters. The solid line drawn through the data points is to show the trends as the diameter varies.
a function of the initial wire array diameter in Figure 3, was maximized when arrays of 9-mm diameter were imploded. Since the total radiated energy was between 40 and 50% of the electrical energy coupled into the diode, the kilovolt X-ray emission was not simply maximized because of more energy being coupled into the load due to better electrical impedance matching of the imploding load and the 0.3-f~ generator. Now, the challenge is to explain the behavior exhibited in Figure 2 using plasma parameters derived from the data obtained by the X-ray diagnostics. The logical course is first to identify which plasma parameters affect the radiation yield. Typically, the radiated yield, Y, from a plasma 15 is given by: Y (n i, Te) = K (Te) n2 AVAt
(2)
where ni is the ion density, Te is the electron temperature, AV is the plasma volume emitting the radiation and At is the emission time. The function K(Te) is determined by the photon range being studied and the atomic excitation and ionization physics of the element. K(Te) is a function of Te only in the optically thin limit. Consequently, the plasma temperature, density, volume and time history must be measured if the variation in yield is to be explained.
Radius scaling effects in nickel wire array Z-pinches
461
200
100
0 0
I
i
10
20
30
DIAMETER mm
Figure 3. Total radiated yield from nickel wire a r r a y implosions versus initial wire a r r a y diameter. The total radiated yields are measured using an unfiltered, tantalum foil/nickel wire calorimeter placed 5 meters from the source. The error bar shows the typical shot-to-shot variation. Figure 4 illustrates the spatial behavior of the X-ray emission for a 6-mm-diameter and a 15-mmdiameter implosion. The images that are filtered for hv > 100 eV are similar for both cases. There is a marked contrast, however, between the images that are filtered to see hv > 1000 eV. In the 6 mm case, as the array dynamics approach those of a single wire, the kilovolt L-shell emission comes from multiple localized regions, about 500 ktm in diameter, whereas 15-mm implosions result in the kilovolt emission originating from almost the entire plasma volume. Instabilities disrupt the pinch around 20 to 25 ns after the plasma first pinches. Therefore, taking the average volumes for the bulk and L-shell emitting plasmas during the first 15 ns of emission, the variation in volume of the kilovolt emitting plasma with initial array hv>
1000eV
hv > lOOeV 0--5 5 --10
2 cm
2 cm
SHOT 1868 6-mm a r r a y
10 N
15
15 --
20
20 --
25
25 --
30
30 --
35
TIME ns
2 cm
cm
SHOT 1869 15-mm a r r a y
Figure 4. Examples of the time-resolved, dual filter pinhole images of two different diameter implosions. These are a) a 6-mm a r r a y and b) a 15-mm array. The frame times shown are relative. The plasma lengths are 2 cm and the radial dimension scale is illustrated. The filters are such that one set transmits Xrays of energies greater than 100 eV, the other set transmits X-rays with energies greater than 1000 eV. Notice that the kilovolt images in the 6-mm case are very different from the images for the optimum 15-mm case. The 6m m arrays produce hot spots whereas the 15-mm arrays produce bulk plasmas that radiate kilovolt X-ray emission. This translates to differences in the kilovolt X-ray yield, that is; 10 kJ for the 6-mm a r r a y but 35 kJ for the 15-mm array.
462
C. DEENEYet al
diameter is apparent in Table 2. For diameters less than 15 mm, the L-shell emission is only emitted from localized regions and the L-shell emitting volume is only - 2% of the total plasma volume. Initial diameters of 15 mm and greater, on the other hand, produce plasmas that emit L-shell radiation from 90% of the bulk volume. The total plasma volume was, however, not sensitive to the variation in the wire array diameters. These localized L-shell sources also influence the characteristics of the X-ray diode signals shown in Figure 5. The L-shell emission for the 6- and 9-mm cases is the same 40 ns or so duration, but is composed of multiple 10-ns full-width half-maximum (FWHM) bursts. Twenty and fifteen millimeter diameter implosions produce a single pulse, with a 25 to 30 ns FWHM. Table II. Kilovolt and Bulk Plasma Emission Volumes A££g.Y..]~gll)g1~ mm
~
Bulk Plasma Volume cm 3
cm 3
6
0.01
0.16
9
0.01
0.16
12.5
0.02
0.16
15
0.15
0.16
20
0.15
0.16
ARRAY
DIAMETER
mm
D.
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u,I r~
.5 6 V
0
I
50
J///./2~
100
i,,,/ u
150
I
I
I
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I
i
TIME ns
Figure 5. Nickel L-shell emissions, around 1 keV, power versus time for various array diameters. The emission powers are measured using the 1.8-~tm aluminium plus 2-~tm Kimfol filtered X-ray diodes and assume the published calibrations for the photocathodes and filter transmissions. As the array diameter increases, the kilovolt X-ray emission transitions to a single pulse from the bulk plasma, as opposed to the multiple spikes caused by multiple hot spots, seen in the 6-and 9-mm cases.
Radius scaling effects in nickel wire array Z-pinches
463
To estimate the temperature of the plasma, the K-shell spectra are used. Evidently, the hydrogen-like and helium-like line radiation comes from hotspots 16-18 whose temperatures, ~ 2 keV, are not characteristic of the bulk plasma temperatures. Nevertheless, the innershell satellites and the Kct line are probably electron beaml6,19 excited within the bulk plasma and the relative ratio of these lines will depend on the ionization state distribution, hence temperature of the bulk plasma. A collisional radiative equilibrium (CRE) code was used to calculate the ionization state populations as functions of electron temperature for different ion densities. Two examples of the population curves are shown in Figure 6. Now, for the 6 through 12.5 mm arrays, the K-shell spectra (see Figure 7) indicated that the nickel Kct line comes from the entire length of the plasma. Moreover, the time-resolved K-shell spectra show that his line is emitted for the whole duration of the X-ray pulse. The Ktx line is produced in nickel ions in the neon-like and lower ionization states. Consequently, assuming that the IQt line is emitted from the bulk plasma, then the bulk plasma must only be ionized up to the neon-like stage. This behavior confirms what was already learned from the pinhole pictures; namely, that the L-shell emission comes from hotspots in these smaller diameter cases. Within the ion density range of 1019 - 1020cm -3, this puts a ceiling on the bulk electron temperature of 200250 eV for the small diameters. Fifteen and twenty millimeter implosions exhibit different K-shell spectra. These spectra indicate that the ion stage populations are peaked in the carbon- and beryllium-like states. I
~
f, I.i.
~.
I
I
N.-N~.__
I
I
Ni =
I
1019
I
cm-3
F 0.1 -
He-
0.01 -3 tO O
E
1.1..
0.1
co
0.01 101
200 300 400 500
600 7 0 0
800 900
1000
TO_ eV Figure 6. Nickel Ne-like through He-like ion stage fractions versus electron temperature, Te, for ion densities of (a) 1019 cm -3 and (b) 1018 c m "3. These are calculated using a collisional radiative model. Such distributions are consistent, assuming a CRE model, with electron temperatures between 600 and 800 eV. Plasma densities can be estimated by two methods. In method 1, by assuming that all the mass in the wire array assembles on-axis, uniformly in the plasma emission volume, the ion densities can be estimated. The assumption on which these estimates are based can be questioned. Previous experiments 7 on Blackjack-3 at MLI have suggested the possibility that not all the mass is imploded when massive wires are used in arrays. However, the nickel array experiments were performed at three times the current, with smaller diameter wires than the experiment repo~cl on Blackjack-3.
464
C. D~NEY et al
Hea i/~
~ ~ CATHODE//
I R
_ __z=o
K~
U):~I]u)-'~>"
0
UM B
~
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7
8
I
ENERGY keV
9
Figure 7. Examples spatially resolved, nickel K-shell spectra recorded from a 9-ram diameter implosion. The spatial resolution was in the axial dimension of the Zpinch. The insert shows the relative location, at the source, of the two densitometer scans through the data. Spectrum A, the one nearest the anode, shows a strong K(x characteristic line and innershell satellites; the distribution of the satellites give an approximate electron temperature of the bulk plasma of 200 eV. Spectrum B encompassed the bright hot spots seen on the X-ray pinhole images near the cathode; this spectrum shows bright hydrogen- and helium-like transitions as well as the non-thermal K s and innershell lines. The presence of hydrogen-like lines implies that the electron temperature was approximately 2 keV in the hot spots.
The emission powers from a plasma of a given volume depend on the ion density and electron temperature. Providing one knows the functional dependency of the emission rates with temperature and density, one can calculate the expected emission power from the known density and temperature. Conversely, by measuring the plasma electron temperature and plasma emission power, the ion density can be derived from these quantities. This is method 2. Figure 8 displays examples of the kilovolt n = 3 to 2 nickel L-shell emission rates, as functions of temperature, for different densities of a 3-mm-diameter plasma. These emission rates were calculated using an atomic model for nickel whose construction is described in Reference 21. The model consists of a complete set of excited states in each ionization stage that are discriminated only by their principal quantum number. The degeneracy factors of these states depend on the ionization stage in which they occur. The escape probability radiation transport that was employed to obtain the optically thick emission powers used only these fully degenerate states, and hence overemphasized the effects of plasma opacity.21 Both the optically thin and opacity corrected emission powers are shown in Figure 8, where the effects of plasma opacity are shown to be small. This method was employed to derive the densities for the 15 mm and 20 mm cases. The estimated ion densities and plasma electron temperatures are also shown in Figure 9. The densities calculated using method 2 agree with the density estimates using the method 1 for the 15 and 20 mm cases. This is taken as an indication that the density estimates using method 1 are probably also accurate for the smaller diameters. The electron temperature estimates have at worst a + 25% error, but they do show good agreement with a onedimensional self-similiar dynamics code that incorporates a Bennett equilibrium for the post assembly phase, developed by Mosher. 22 Taking the bulk plasma parameters for the 12.5-, 15- and 20-mm implosions and the measured FWHM of the L-shell X-ray emissions, then the estimated yields can be calculated from the curves in Figure 8. Comparing the estimated yields with the actual measured yields, as illustrated in Figure 10, it is observed that the 15- and 20-mm measured and calculated yields agree, whereas the 12.5-mm implosions do not predict the measured yields. This analysis confirms the interpretation of the pinhole images that the hot spots were responsible for the nickel L-shell emission in the 6 to 12.5 mm implosions
Radius scaling effects in nickel wire array Z-pinches
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465
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Te (keV) 10
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Te (keV) Figure 8. Nickel L-shell emission powers calculated using a scalable hydrogenic ionization model described in Reference 21. The emission curves, in T W cm -1, are shown as functions of electron temperature, keV, for two ion densities: a) 1019 cm -3 and b) 5 x 1018 cm-3. The powers are for the emissions which give rise to radiation in the range of 0.85 to 1.3 keV. Moreover, the radiation transport calculations assume the plasma is 3 mm in diameter and that the ion density is uniform. For ion densities less than 1019 cm "3, the effects of opacity are small.
QSRT 44-5/6~C
466
C. DEENEYet al 40
""l
HOT SPOT L-SHELL EMISSION
BULK PLASMA
30
I
20
I
10 ¸ I
[] Measured
1i • Calculated from ne, Te of bulk plasma J I
I
0
10
I
1
20
I
30
DIAMETER mm Figure 9. Plasma p a r a m e t e r s for the different initial wire a r r a y diameters. The plasma electron temperatures are calculated from the inner shell distributions in the Kshell spectra. The ion densities are calculated by two methods: 1) assuming all the mass is assembled uniformly in the plasma volume, 2) by estimating the required density to give the X-ray diode measured emission power using similar curves to those presented in Figure 8. Method 2 also requires that the electron t e m p e r a t u r e be known. 700
©
..=
600 -
500
-3
-
400 -
P 300
-
200 -
100 -
~ - Te --ni (Method 2) o . ni (Method 1)
--1
I
i
10
2O
30
Figure 10. The measured nickel L-shell yield, as presented in Figure 2, compared to the calculated Nickel L-shell yield based on the bulk plasma electron t e m p e r a t u r e and ion density (method 1) given in Figure 9 and the duration of the X-ray emission taken from Figure 5. Clearly, the calculated bulk plasma kilovolt X-ray emission for the 15- and 20-ram cases agree with the measured values: the same yields for the 12.5.mm case do not. This is a confirmation that hot spots are responsible for the majority of the nickel L-shell emission in the 12.5-mm a r r a y implosion.
Radius scaling effects in nickel wire array Z-pinches
467
4. DISCUSSION A systematic scan of initial wire array diameters has revealed that for an 80-ns implosion time, the nickel L-shell yield is maximized for a 15 mm diameter. This identification of an optimum diameter has extended the database on radius sealing obtained from the NRL and MLI experiments. Indeed, the results for the optimum 15 mm diameter and the larger 20-mm-diameter implosions agree with the conclusions from the previous radius scaling experiments; that is, decreasing diameters give higher density, lower temperature plasmas which produce more radiation. Furthermore, the data presented in this paper show that as the diameter decreases further, the assembled plasma density is not sufficient to compensate for the decreasing electron temperature and the bulk plasma yield drops. This point is illustrated in Figure 11 where the nickel L-shell emission powers as functions of temperature are shown for different densities; 1 x 1018, 5 x 1018, 1 x 1019, 1 x 1020 and 1 x 1021 cm -3. In the temperature range of 600 to 1200 eV, the emission power is relatively insensitive to the electron temperature, whereas at lower temperatures the emission powers depend more strongly on the electron temperature, especially between 100 and 400 eV.
10 2 I
101
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Figure 11. Nickel L-shell emission powers versus plasma electron temperature for different ion densities: A) 1 x 1018 cm -3, B) 5 x 1018 cm "3, C) 1 x 1019 cm -3 and D) 1 x 1020 cm -3. These emission powers assume a 3-mm diameter plasma and are calculated using a scalable hydrogenic ionization model discussed in Reference 21. This illustrates the smaller variation in emission rates between 400 and 1000 eV as compared to the more dramatic changes between 100 and 400 eV. The rapid fall-off with temperature in the latter temperature range explains the sudden transition from bulk kilovolt emission to hot spots, when the array diameter is adjusted from 15 mm to 12.5 mm.
468
C. DEENEYet al
Obviously, the measured yields do not fall as precipitously as predicted by the bulk plasma parameters for the 12.5-ram cases and the reason is the presence of the localized hot spot sources. Intense localized X-ray sources have been observed in many different types of Z-pinch; gas puff Z-pinch, 16,17 vacuum sparks 18 and exploding wires.3, 4 The explanations for their presence include radiative collapse,23 m = 0 instabilities 24 and electron beam heating.18, 25 Usually, the localized hot spots are the source of the small amounts of K-sheU emission in high Z elements used in the Z-pinches listed above and indeed, in this nickel wire array experiment, hot spots produce some 20-100 J of nickel hydrogen- and helium-like line radiation. However, in this experiment, localized sources are evident in the L-shell also, and these sources emit significant amounts of radiation--10 kJ or so. Further explanation of these localized hot spots will require experiments devoted to diagnosing their origin. 5. CONCLUSIONS The initial wire array diameter in Z-pinch implosions is critical to determining the radiation output of the final assembled plasma. As the diameter is decreased, the plasma temperature decreases and the density increases. In nickel, this has been shown to increase the kilovolt radiation until the diameter is less than 15 mm where the bulk plasma temperature becomes insufficient to excite the L-shell and the radiation from the bulk plasma decreases dramatically. However, localized X-ray sources, hot spots, are found to give copious L-shell X-ray emission, albeit less than the optimum, bulk L-sheU emission from 15-mm arrays. This work was sponsored by the Defense Nuclear Agency (DNA). The authors would like to acknowledge useful discussions with J. Davis, J. Apruzese, J. Giuliani, D. Mosher and R. Terry of the Naval Research Laboratory. The encouragement of Capt J. Fisher, DNA, is appreciated.
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3.
L.E. Aranchuk, S.L. Bogolyubski, G.S. Volkov, V.D. Korolev, Yu.V. Koba, V.I. Liksonov, A.A. Lukin, L.B. Nikandrov, O.V. TerKovskaya, M.V. Tulupov, A.S. Cherenko, V.Ya. Tsarfin & V.V. Yan'kov, Soy. J. Plasma Phys. 12(11), p 765, (1986).
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7.
J.C. Riordan, J.S. Pearlman, M. Gersten & J.E. Rauch, "Low Energy X-ray Diagnostics.", ed. D.T. Attwood & B. Henke, AIP Conf. Proc. 75, p 35, (1981).
8.
S.J. Stephanakis et al, "Radius Scaling for Neon Gas Puff Experiments.", NRL Plasma Technology Tech-Note 85-51, Washington DC 20375, December (1985).
9.
M. Gersten, W. Clark, J.E. Ranch, G.M. Wilkinson, J. Katzenstein, R.D. Richardson, J. Davis, D. Duston & J.P. Apruzese, Phys. Rev. A 33(1), p 477, (1986).
10.
P. Sincerny, D. Strachan, G. Frazier, C. Gilman, H. Halava, S. Wong, J. Bannister, T. DaSilva, S.K. Lam, P.D. LePell, J. Levine, R. Rodenburg & T. Sheridan, Proc. IEEE Fifth Conf. on Pulsed Power, p 151, (1985).
11.
R.L. Kelly, "Atomic and Ionic Spectra Lines Below 2000 Angstroms.". J. Phys. Chem. Reference Data, Vol 16 Suppl. 1, (1987).
12.
T. Nash, C. Deeney & M. Krishnan, "Application of Spectroscopy to Diagnosing Z-pinches.", Second Intl. Conf. on Dense Z-pinches, Laguna Beach, April (1989).
13.
R.H. Day, P. Lee, E.B. Saloman & D.J. Nagel, J. Appl. Phys. 52, p 6965, (1981).
Radius scaling effectsin nickel wire array Z-pinches
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14. F.C. Young, S.J. Stephanakis & V.E. Scherrer, Rev. Sci. Instrm. 57(8), p 2714, (1986). 15. C. De Michelis & M. Mattioli, Nuc. Fus 21(6), p 677, (1981). 16. J.D. Hares, R.E. Marts & R.J. Former, J. Phys D. 18, p 627, (1985). 17. P. Choi, A.E. Dangor, C. Deeney & C.D. Challis, Rev. Sci. lnstrm. 57(8), p 2178, (1986). 18. C.R. Negus & N.J. Peacock, J. Phys D. 12, p 91, (1979). 19. D.R. Kania & L.A. Jones, Phys. Rev. Len. 53(2), p 166, (1984). 20.
C. Deeney, T. Nash & M. Krishnan, "Observation of High Temperature Plasmas in Nickel Wire Implosions.", All ) Conf. l)roc. 195, p 62, (1989).
21. K.G. Whitney & M.C. Coulter, IEEE Trans. Plasma Science 16(5), p 552, (1988). 22. D. Mosher, All) Conf. l)roc. 195, p 191, (1989). 23. V.V. Vikhrev, JETl) Lett. 27(2), p 95, (1978). 24. K.H. Schoenbach, L. Michel & H. Fischer, Appl. Phys. Lett. 25(10), p 547, (1974). 25. T.N. Lee, Annals New YorkAcad. Sci. vol. 251, p 112, (1975).
0022-4073/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press pie
RADIUS SCALING EFFECTS IN NICKEL WIRE ARRAY Z-PINCHES C. DEENEY, T. NASH, P. D. LEPELL, K. CHILDERS, AND M. KRISHNANt Physics International Company 2700 Merced Street San Leandro, CA 94577 K. G. WHITNEY AND J. W. THORNHILL Naval Research Laboratory 4555 Overlook Avenue, SW Washington, DC 20375
Abstract - Nickel wire arrays of different masses and initial diameters have been imploded on the DNA/Double-EAGLE generator. Array masses and diameters were chosen to cause an implosion 10 to 20 ns before the peak current of 4 MA. The nickel L-shell radiated yield around 1 keV was found to be maximized at 35 kJ for a'n initial array diameter of 15 mm and a mass loading of 86 I.tg/cm. X-ray diagnostic data indicate that the 1-keV L-shell yield is maximized when the array diameter and mass are such that the implosion energy is just sufficient to thermalize on axis to a 3-ram diameter bulk plasma. This plasma is predominantly ionized into the L-shell with an ion density of 1019 cm-3 and an electron temperature of 450 eV. Initial diameters larger than optimum result in hotter lower density plasmas. The reduced density causes a reduction in the:yield. By contrast, for diameters less than optimum, the bulk thermalized plasma is too massive and too cold for efficient radiation from the L-shell. Localized "hot spots" do emit L-shell radiation, and consequently the total L-shell yield does not fall as precipitously with decreasing array radius as might be expected from the change in the bulk plasma parameters. 1. INTRODUCTION The advent of pulsed power generators for relativistic electron beam experiments made an impact on the Z-pinch community by providing multi-megampere, ~ 100 ns rise-time current generators. With such machines, research could be performed on moderate-atomic-number (that is, Z > 9) plasmas with temperatures of 0.2 to 1.5 keV and electron densities between 1020 and 1021 cm -3. This field has recently been reviewed by Pereira and Davis. 1 Much of the impetus for this research has been to maximize the X-ray radiation output from single wire and wire array loads. Single wires 2-4 have produced spectra from highly ionized states of elements with atomic numbers from 13 to 29. Although these spectra are consistent with plasmas that have electron densities and temperatures greater than 1021 cm -3 and 1 keV respectively, the total kilovolt radiation yields were low. It has been speculated that this was due to poor electrical coupling5 between a single wire and a magnetically insulated transmission line(MITL) or possibly because single wires become unstable early in the current rise. Kilovolt yields are much higher when wire arrays5 are imploded onto the axis from a centimeter or so radius. The array implosion's spectra6, 7 are consistent with plasmas having electron densities around 1020 cm-3 and electron temperatures of less than 800 eV. The differences in the kilovolt radiation yield between these two types of load could be due to the fact that single wires radiate in the form of multiple plasma spots with characteristic dimensions of a few hundred micrometers, compared to the wire arrays where the bulk of the plasma, with dimensions of a few millimeters diameter and a few centimeters long, had the properties outlined above. Therefore, the radiation output of single wires is thought to be due primarily to instabilities, whereas wire arrays are considered to produce a more uniform plasma due to the radial implosion. The initial radius(diameter) of the wire array is the particular implosion parameter that is the focus of this paper. It is critical in determining the radiation properties of array Z-pinches because of its effect on the temperature and density of the assembled plasma. ~ Presentaddress: ScienceResearchLaboratory,Suite 100, 1150BallenaBvd., Alameda,California, 95401. a~7
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Simple zero dimensional analysis of an imploding shell of mass per unit length, m/L, predicts that for a constant current, the following relationship holds between m, initial radius, R, of the array, the implosion time, t, and the current, I: mR2 - constant LI2t2
(1)
Assuming that, for a given generator, the peak current and the implosion time are fixed, with the implosion time being equal to the time of the peak current for optimal coupling, then the plasma parameters are adjusted by changing m and R with m being proportional to R -2. Intuitively, it is obvious that increasing m by decreasing R would tend to produce dense, cool plasmas, whereas small m and larger R implosions would tend to produce lower density, higher temperature plasmas. Specifically, if it is assumed that all the mass assembles into a constant plasma volume, then the plasma density should scale as m or R -2 and the implosion kinetic energy-per-ion should scale as 1/m or R 2 , for a fixed plasma kinetic energy coupled from the generator to the imploding load. Since the implosion energy, when thermalized, is distributed between ionization energy, radiation losses and electron thermal energy, the plasma temperature may not necessarily scale as R 2. Previous experiments to study this behavior have been performed by a group at the Naval Research Laboratory (NRL) and a group at Maxwell Laboratories (MLI). Stephanakis et al.8 imploded neon gas puffs produced by nozzles in the diameter range of 0.85 to 1.5 cm, at currents of around 1.2 MA. They found that as the initial nozzle diameter was decreased, the 1-keV radiation yield increased. Gersten et al. 9 found a similar result with K-shell radiation from aluminum wire array implosions at 4 MA on the Blackjack-5 generator at MLI. The MLI experiments were performed over an initial diameter range of 15 to 30 ram, keeping the implosion time constant. Both groups determined that the decreased array diameter produces a more dense but cooler pinched plasma. Since the radiation yield scales as the density squared, the increased density causes an increased K-shell radiation yield. Conversely, as the array diameter is increased, the higher assembled plasma temperatures are insufficient to compensate for the decreased plasma densities. It can be conjectured that for a given generator and load material, that as the load diameter is decreased, if the temperature falls below a given threshold, then the plasma would be too cold to give efficient excitation in the 1 to 1.5 keV photon energy region. Remember, that in the limit of a zero radius (on-axis) load, the dynamics of the pinch are different and the kilovolt radiation efficiencies are low. Hence, it seems likely that the kilovolt yield would be a double valued function of initial radius, and that there would be a specific initial radius that would optimize the kilovolt radiation for a given element on a given generator. The experiment described in this paper had the aim of experimentally determining the initial radius that produced the maximum yield of 0.85 to 1.3 keV emissions from the nickel L-shell, using wire arrays on the DNA/Double-EAGLE generator. The experiment is described in Section 2. The L-shell yield results and other associated X-ray data are presented in Section 3 and discussed in Section 4. The conclusions of this paper are presented in Section 5. 2. EXPERIMENTAL ARRANGEMENT The Double-EAGLE 10 generator is composed of two triplate waterline modules feeding a common vacuum diode. When wire arrays or gas-puffs are used to bridge the anode-cathode gap, a 4-MA, 90-ns risetime current pulse is delivered to the diode and these hollow loads implode, giving copious X-ray emission. The chosen element for wire array experiments in this paper is nickel, for which the n = 2 to 3 line emissions from the L-shell ionization stages fall in the range of 0.85 to 1.3 keV. 11 The cylindrical wire arrays were composed of twelve equally spaced (in azimuth) wires with cylinder diameters ranging from 6 mm to 20 mm. Individual wire diameters were adjusted to keep the product mR 2 fixed at 50 I.tg-cm where m and R are defined as before. The actual load parameters tested in this pulsing series are listed in Table 1. The implosion time for all the arrays was measured to be between 70 and 80 ns, as illustrated in Figure 1, where a filtered X-ray diode signal is shown with the corresponding current trace. Due to the small prepulse on Double-EAGLE, the implosion time is defined as shown in Figure 1. A comprehensive suite of X-ray diagnostics 12 was employed to measure the X-ray emission The total X-ray emission around 1 keV was determined using 2.5 Ixm Kimfol plus 1.8 Ixm aluminum filtered, tantalum foil calorimeters. In addition, aluminum cathode, X-my diodes 13 (XRD) with identical filters were used to measure the radiation power at 1 keV, following Young et al. 14 The XRD emission power signals were also numerically integrated in time to give the kilovolt L-shell yield. An unfiltered calorimeter measured the total radiated yield and this could be compared to the energy coupled into the diode as calculated from the electrical voltage and current measurements.
459
Radius scaling effects in nickel wire array Z-pinches Table I. Shot Parameters
ax.rax.l/~lmtl~
N o of W i r e s
Wire Thickness ~tm
mm
12 12 12 12 12
17 25 12.5 10 8
6 9 12.5 15 20
6
I
I
I
I
I
m R2
L
x ns
53.6 48.6 52.7 48.4 48.5
75 72 82 80 80
I
5 4
1.0 n
w -I .J ul -!-
21O
,
0
l
100 1"
200
300
TIME
ns
F i g u r e 1. A D o u b l e - E A G L E current trace and X-ray diode trace (shaded) are s h o w n on a c o m m o n t i m e base for a l $ - m m nickel w i r e array implosion: shot 1869. The X - r a y diode is filtered with 2.5 Ixm Kimfol plus 1.8-~tm a l u m i n u m so as only to detect X-rays around 1 keV, that is f r o m the n = 3 - 2 transitions in nickel L-shell ionization states. The i m p l o s i o n time, x, relative to the current start is d e f i n e d as s h o w n .
The spatial and temporal behavior of different photon energy emitting regions was studied using filtered pinhole cameras. The filters were chosen to transmit photons with energies greater than 100 eV, 1000 eV and 7000 eV respectively . Time-resolution was incorporated into the pinhole cameras by using microchannel plates (MCP) with gating strips. Every strip had a factor-of-4 demagnified image of the plasma produced on it by a 504tin diameter pinhole. Seven or twelve strips were used per camera and each strip was gated with a 5-ns long, -1-kV pulse. Moreover, each strip was pulsed 5 ns after the preceding strip; thus, 35 to 60 ns of uninterrupted plasma emission could be studied. The strips derived their gating pulse from a common Krytron pulser which allowed for accurate time-correlation. A space-resolved 5 cmcurved lithium fluoride (LiF) crystal spectrometer gave spectral information on the nickel K-sheU radiation with a spatial resolution of 5 ram. Additionally, a second 5 cm-curved LiF crystal spectrometer, fitted with a five-strip-gated MCP, was used to time-resolve the nickel K-shell emission between 7.5 and 8.3 keV. The time-correlation of the time-gated diagnostics was accurately determined, since these diagnostics derive their gating signals from a common Krytron pulser unit. One of the gating pulses was sent to the digital data acquisition system to permit time correlation of the XRD signals with the gated MCP detectors.
460
C, DEENEYet al 3. RESULTS
Experimentally, the variation of kilovolt X-ray yield with the initial wire array diameter has been determined, as shown in Figure 2. The error bars on the experimental points account for both shot-to-shot scatter and differences between the integrated XRD and calorimeter measurements. These random errors are greater than the 20% possible error due to the variation in detector sensitivities and filter transmissions, over the range of 0.85 to 1.3 keV of the L-shell radiation. A curve is drawn through the average of the data points to highlight the trends as the diameter varies. From Figure 2, it is apparent that the optimum initial wire array diameter to produce kilovolt radiation is 15 ram. On the other hand, the total radiation, plotted as
40
30
20
10
O 0
I
!
10
20
30
DIAMETER mm Figure 2. The kilovolt, nickel L-shell yield as a function of initial wire array diameter. The error bars shown encompass the shot-to-shot reproducibility, as well as the variation between the filtered X-ray diodes and the similarly filtered tantalum foil/ nickel wire calorimeters. The solid line drawn through the data points is to show the trends as the diameter varies.
a function of the initial wire array diameter in Figure 3, was maximized when arrays of 9-mm diameter were imploded. Since the total radiated energy was between 40 and 50% of the electrical energy coupled into the diode, the kilovolt X-ray emission was not simply maximized because of more energy being coupled into the load due to better electrical impedance matching of the imploding load and the 0.3-f~ generator. Now, the challenge is to explain the behavior exhibited in Figure 2 using plasma parameters derived from the data obtained by the X-ray diagnostics. The logical course is first to identify which plasma parameters affect the radiation yield. Typically, the radiated yield, Y, from a plasma 15 is given by: Y (n i, Te) = K (Te) n2 AVAt
(2)
where ni is the ion density, Te is the electron temperature, AV is the plasma volume emitting the radiation and At is the emission time. The function K(Te) is determined by the photon range being studied and the atomic excitation and ionization physics of the element. K(Te) is a function of Te only in the optically thin limit. Consequently, the plasma temperature, density, volume and time history must be measured if the variation in yield is to be explained.
Radius scaling effects in nickel wire array Z-pinches
461
200
100
0 0
I
i
10
20
30
DIAMETER mm
Figure 3. Total radiated yield from nickel wire a r r a y implosions versus initial wire a r r a y diameter. The total radiated yields are measured using an unfiltered, tantalum foil/nickel wire calorimeter placed 5 meters from the source. The error bar shows the typical shot-to-shot variation. Figure 4 illustrates the spatial behavior of the X-ray emission for a 6-mm-diameter and a 15-mmdiameter implosion. The images that are filtered for hv > 100 eV are similar for both cases. There is a marked contrast, however, between the images that are filtered to see hv > 1000 eV. In the 6 mm case, as the array dynamics approach those of a single wire, the kilovolt L-shell emission comes from multiple localized regions, about 500 ktm in diameter, whereas 15-mm implosions result in the kilovolt emission originating from almost the entire plasma volume. Instabilities disrupt the pinch around 20 to 25 ns after the plasma first pinches. Therefore, taking the average volumes for the bulk and L-shell emitting plasmas during the first 15 ns of emission, the variation in volume of the kilovolt emitting plasma with initial array hv>
1000eV
hv > lOOeV 0--5 5 --10
2 cm
2 cm
SHOT 1868 6-mm a r r a y
10 N
15
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35
TIME ns
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Figure 4. Examples of the time-resolved, dual filter pinhole images of two different diameter implosions. These are a) a 6-mm a r r a y and b) a 15-mm array. The frame times shown are relative. The plasma lengths are 2 cm and the radial dimension scale is illustrated. The filters are such that one set transmits Xrays of energies greater than 100 eV, the other set transmits X-rays with energies greater than 1000 eV. Notice that the kilovolt images in the 6-mm case are very different from the images for the optimum 15-mm case. The 6m m arrays produce hot spots whereas the 15-mm arrays produce bulk plasmas that radiate kilovolt X-ray emission. This translates to differences in the kilovolt X-ray yield, that is; 10 kJ for the 6-mm a r r a y but 35 kJ for the 15-mm array.
462
C. DEENEYet al
diameter is apparent in Table 2. For diameters less than 15 mm, the L-shell emission is only emitted from localized regions and the L-shell emitting volume is only - 2% of the total plasma volume. Initial diameters of 15 mm and greater, on the other hand, produce plasmas that emit L-shell radiation from 90% of the bulk volume. The total plasma volume was, however, not sensitive to the variation in the wire array diameters. These localized L-shell sources also influence the characteristics of the X-ray diode signals shown in Figure 5. The L-shell emission for the 6- and 9-mm cases is the same 40 ns or so duration, but is composed of multiple 10-ns full-width half-maximum (FWHM) bursts. Twenty and fifteen millimeter diameter implosions produce a single pulse, with a 25 to 30 ns FWHM. Table II. Kilovolt and Bulk Plasma Emission Volumes A££g.Y..]~gll)g1~ mm
~
Bulk Plasma Volume cm 3
cm 3
6
0.01
0.16
9
0.01
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i
TIME ns
Figure 5. Nickel L-shell emissions, around 1 keV, power versus time for various array diameters. The emission powers are measured using the 1.8-~tm aluminium plus 2-~tm Kimfol filtered X-ray diodes and assume the published calibrations for the photocathodes and filter transmissions. As the array diameter increases, the kilovolt X-ray emission transitions to a single pulse from the bulk plasma, as opposed to the multiple spikes caused by multiple hot spots, seen in the 6-and 9-mm cases.
Radius scaling effects in nickel wire array Z-pinches
463
To estimate the temperature of the plasma, the K-shell spectra are used. Evidently, the hydrogen-like and helium-like line radiation comes from hotspots 16-18 whose temperatures, ~ 2 keV, are not characteristic of the bulk plasma temperatures. Nevertheless, the innershell satellites and the Kct line are probably electron beaml6,19 excited within the bulk plasma and the relative ratio of these lines will depend on the ionization state distribution, hence temperature of the bulk plasma. A collisional radiative equilibrium (CRE) code was used to calculate the ionization state populations as functions of electron temperature for different ion densities. Two examples of the population curves are shown in Figure 6. Now, for the 6 through 12.5 mm arrays, the K-shell spectra (see Figure 7) indicated that the nickel Kct line comes from the entire length of the plasma. Moreover, the time-resolved K-shell spectra show that his line is emitted for the whole duration of the X-ray pulse. The Ktx line is produced in nickel ions in the neon-like and lower ionization states. Consequently, assuming that the IQt line is emitted from the bulk plasma, then the bulk plasma must only be ionized up to the neon-like stage. This behavior confirms what was already learned from the pinhole pictures; namely, that the L-shell emission comes from hotspots in these smaller diameter cases. Within the ion density range of 1019 - 1020cm -3, this puts a ceiling on the bulk electron temperature of 200250 eV for the small diameters. Fifteen and twenty millimeter implosions exhibit different K-shell spectra. These spectra indicate that the ion stage populations are peaked in the carbon- and beryllium-like states. I
~
f, I.i.
~.
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I
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200 300 400 500
600 7 0 0
800 900
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464
C. D~NEY et al
Hea i/~
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Figure 7. Examples spatially resolved, nickel K-shell spectra recorded from a 9-ram diameter implosion. The spatial resolution was in the axial dimension of the Zpinch. The insert shows the relative location, at the source, of the two densitometer scans through the data. Spectrum A, the one nearest the anode, shows a strong K(x characteristic line and innershell satellites; the distribution of the satellites give an approximate electron temperature of the bulk plasma of 200 eV. Spectrum B encompassed the bright hot spots seen on the X-ray pinhole images near the cathode; this spectrum shows bright hydrogen- and helium-like transitions as well as the non-thermal K s and innershell lines. The presence of hydrogen-like lines implies that the electron temperature was approximately 2 keV in the hot spots.
The emission powers from a plasma of a given volume depend on the ion density and electron temperature. Providing one knows the functional dependency of the emission rates with temperature and density, one can calculate the expected emission power from the known density and temperature. Conversely, by measuring the plasma electron temperature and plasma emission power, the ion density can be derived from these quantities. This is method 2. Figure 8 displays examples of the kilovolt n = 3 to 2 nickel L-shell emission rates, as functions of temperature, for different densities of a 3-mm-diameter plasma. These emission rates were calculated using an atomic model for nickel whose construction is described in Reference 21. The model consists of a complete set of excited states in each ionization stage that are discriminated only by their principal quantum number. The degeneracy factors of these states depend on the ionization stage in which they occur. The escape probability radiation transport that was employed to obtain the optically thick emission powers used only these fully degenerate states, and hence overemphasized the effects of plasma opacity.21 Both the optically thin and opacity corrected emission powers are shown in Figure 8, where the effects of plasma opacity are shown to be small. This method was employed to derive the densities for the 15 mm and 20 mm cases. The estimated ion densities and plasma electron temperatures are also shown in Figure 9. The densities calculated using method 2 agree with the density estimates using the method 1 for the 15 and 20 mm cases. This is taken as an indication that the density estimates using method 1 are probably also accurate for the smaller diameters. The electron temperature estimates have at worst a + 25% error, but they do show good agreement with a onedimensional self-similiar dynamics code that incorporates a Bennett equilibrium for the post assembly phase, developed by Mosher. 22 Taking the bulk plasma parameters for the 12.5-, 15- and 20-mm implosions and the measured FWHM of the L-shell X-ray emissions, then the estimated yields can be calculated from the curves in Figure 8. Comparing the estimated yields with the actual measured yields, as illustrated in Figure 10, it is observed that the 15- and 20-mm measured and calculated yields agree, whereas the 12.5-mm implosions do not predict the measured yields. This analysis confirms the interpretation of the pinhole images that the hot spots were responsible for the nickel L-shell emission in the 6 to 12.5 mm implosions
Radius scaling effects in nickel wire array Z-pinches
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Te (keV) Figure 8. Nickel L-shell emission powers calculated using a scalable hydrogenic ionization model described in Reference 21. The emission curves, in T W cm -1, are shown as functions of electron temperature, keV, for two ion densities: a) 1019 cm -3 and b) 5 x 1018 cm-3. The powers are for the emissions which give rise to radiation in the range of 0.85 to 1.3 keV. Moreover, the radiation transport calculations assume the plasma is 3 mm in diameter and that the ion density is uniform. For ion densities less than 1019 cm "3, the effects of opacity are small.
QSRT 44-5/6~C
466
C. DEENEYet al 40
""l
HOT SPOT L-SHELL EMISSION
BULK PLASMA
30
I
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1i • Calculated from ne, Te of bulk plasma J I
I
0
10
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1
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30
DIAMETER mm Figure 9. Plasma p a r a m e t e r s for the different initial wire a r r a y diameters. The plasma electron temperatures are calculated from the inner shell distributions in the Kshell spectra. The ion densities are calculated by two methods: 1) assuming all the mass is assembled uniformly in the plasma volume, 2) by estimating the required density to give the X-ray diode measured emission power using similar curves to those presented in Figure 8. Method 2 also requires that the electron t e m p e r a t u r e be known. 700
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100 -
~ - Te --ni (Method 2) o . ni (Method 1)
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Figure 10. The measured nickel L-shell yield, as presented in Figure 2, compared to the calculated Nickel L-shell yield based on the bulk plasma electron t e m p e r a t u r e and ion density (method 1) given in Figure 9 and the duration of the X-ray emission taken from Figure 5. Clearly, the calculated bulk plasma kilovolt X-ray emission for the 15- and 20-ram cases agree with the measured values: the same yields for the 12.5.mm case do not. This is a confirmation that hot spots are responsible for the majority of the nickel L-shell emission in the 12.5-mm a r r a y implosion.
Radius scaling effects in nickel wire array Z-pinches
467
4. DISCUSSION A systematic scan of initial wire array diameters has revealed that for an 80-ns implosion time, the nickel L-shell yield is maximized for a 15 mm diameter. This identification of an optimum diameter has extended the database on radius sealing obtained from the NRL and MLI experiments. Indeed, the results for the optimum 15 mm diameter and the larger 20-mm-diameter implosions agree with the conclusions from the previous radius scaling experiments; that is, decreasing diameters give higher density, lower temperature plasmas which produce more radiation. Furthermore, the data presented in this paper show that as the diameter decreases further, the assembled plasma density is not sufficient to compensate for the decreasing electron temperature and the bulk plasma yield drops. This point is illustrated in Figure 11 where the nickel L-shell emission powers as functions of temperature are shown for different densities; 1 x 1018, 5 x 1018, 1 x 1019, 1 x 1020 and 1 x 1021 cm -3. In the temperature range of 600 to 1200 eV, the emission power is relatively insensitive to the electron temperature, whereas at lower temperatures the emission powers depend more strongly on the electron temperature, especially between 100 and 400 eV.
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Figure 11. Nickel L-shell emission powers versus plasma electron temperature for different ion densities: A) 1 x 1018 cm -3, B) 5 x 1018 cm "3, C) 1 x 1019 cm -3 and D) 1 x 1020 cm -3. These emission powers assume a 3-mm diameter plasma and are calculated using a scalable hydrogenic ionization model discussed in Reference 21. This illustrates the smaller variation in emission rates between 400 and 1000 eV as compared to the more dramatic changes between 100 and 400 eV. The rapid fall-off with temperature in the latter temperature range explains the sudden transition from bulk kilovolt emission to hot spots, when the array diameter is adjusted from 15 mm to 12.5 mm.
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C. DEENEYet al
Obviously, the measured yields do not fall as precipitously as predicted by the bulk plasma parameters for the 12.5-ram cases and the reason is the presence of the localized hot spot sources. Intense localized X-ray sources have been observed in many different types of Z-pinch; gas puff Z-pinch, 16,17 vacuum sparks 18 and exploding wires.3, 4 The explanations for their presence include radiative collapse,23 m = 0 instabilities 24 and electron beam heating.18, 25 Usually, the localized hot spots are the source of the small amounts of K-sheU emission in high Z elements used in the Z-pinches listed above and indeed, in this nickel wire array experiment, hot spots produce some 20-100 J of nickel hydrogen- and helium-like line radiation. However, in this experiment, localized sources are evident in the L-shell also, and these sources emit significant amounts of radiation--10 kJ or so. Further explanation of these localized hot spots will require experiments devoted to diagnosing their origin. 5. CONCLUSIONS The initial wire array diameter in Z-pinch implosions is critical to determining the radiation output of the final assembled plasma. As the diameter is decreased, the plasma temperature decreases and the density increases. In nickel, this has been shown to increase the kilovolt radiation until the diameter is less than 15 mm where the bulk plasma temperature becomes insufficient to excite the L-shell and the radiation from the bulk plasma decreases dramatically. However, localized X-ray sources, hot spots, are found to give copious L-shell X-ray emission, albeit less than the optimum, bulk L-sheU emission from 15-mm arrays. This work was sponsored by the Defense Nuclear Agency (DNA). The authors would like to acknowledge useful discussions with J. Davis, J. Apruzese, J. Giuliani, D. Mosher and R. Terry of the Naval Research Laboratory. The encouragement of Capt J. Fisher, DNA, is appreciated.
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