Apruzese, J. P.

Coverdale, Christine A.

Davis, J.

Deeney, Christopher

Douglas, Melissa R.

Thornhill, J. W.

Whitney, K. G.

UNT Digital Library

The Observation of an Optimal Wire Number Range in Long ImplosionTime Aluminum Z-pinchesC.A. Coverdale,C. Deeney, and M.R. DouglasSandia National LaboratoriesJ.P. Apruzese, K.G. Whitney, J.W. Thornhill, and J. DavisNaval Research LabAbstractExperiments performed on the 8 MA Saturn Accelerator to investigate the effects ofinterwire gap spacing on long implosion time aluminum Z-pinches have resulted in theobservation of a regime of optimal wire number. The experimental series utilized 40 mmdiameter arrays and varied the wire number from 32 wires to 282 wires, corresponding tointerwire gaps of 3.9 mm to 0.4 mm, with all other parameters held fixed. Additionalshots with 32 mm diameter loads performed corresponded to interwire gaps of 0.91 mmto 0.36 mm. Aluminum K-shell yields of> 60 kJ were consistently measured, and thepulsewidths and risetimes of the x-ray pulses showed trends of long, slow rising pulsesfor interwire gaps> 3 mm and short, fast rising pulses for interwire gaps greater than 0.7mm, but less than 3 mm, results consistent with theory. For the smallest interwire gapsstudied (< 0.7 mm), the trend again appeared to be towards longer, slower rising x-raypulses. These results suggest a regime of wire number in which Z-pinch performance isoptimized.The study of Z-pinches has been a rich field the last several years with the advent of highcurrent pulsed power generators such as Saturn [1] and Z [2]. Moreover, advances in thetheoretical understanding of Z-pinch physics and in computational modeling capabilitieshave led to the application of Z-pinches to many problems, including astrophysicsmeasurements, radiation effects material studies, and inertial confinement fusion. [3-5]1DISCLAIMERThis report was prepared as an account of work sponsoredby an agency bf the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orimplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or reflect those of the United StatesGovernment or any agency thereof.DISCLAIMERPortions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument..Key to these applications was the development of high output power, fast x-ray pulsesthrough the use of high wire number arrays and nested wire arrays. [6-12]In a wire array Z-pinch, a large fast-rising current is passed through a cylindrical array offine wires. The wires vaporize into a plasma that is accelerated to the axis by a growingLorentz force (JxB). The imploding plasma gains kinetic energy, which rapidlytherrnalizes when the material stagnates on axis. This process produces compressedplasmas with high temperatures and densities that radiate up to 250 TW of x-ray power.Traditionally, most wire array Z-pinch work has occurred with short pulse drivers (<1 00ns current risetime). The reduced cost and complexity of long pulse drivers (> 100 nscurrent risetime) have made them a desirable option for the future generators, includingthe 8 MA, 300 ns implosion time Decade Quad. [13] In order for the potential benefits tobe realized, however, the physical phenomena, including instability growth, which differbetween short and long pulse Z-pinches need to be studied and understood, especially forwire arrays.One of the first theoretical models of wire array dynamics, developed by Haines [14],defines a critical wire number, nC,it,representing the minimum number of wires necessaryto ensure that the individual wire plasmas sufficiently expand and merge prior toimplosion on the axis. Such merging is believed to be beneficial since it smoothes theinitial perturbations resulting from discrete wire initiation and magnetic field effects thatcan lead to unstable z-pinch implosions. Specifically, nC~it= nr~vtP, where r. is the initialradius of the wire array, v is the expansion velocity of the wires, and tp is the implosiontime. For low wire number arrays, i.e., n < nCtit,the interwire gap (IWG) betweenadjacent wires is large. In this case, the wires, which explode and become plasma (orpartially plasma), cannot expand far enough to fill the gaps prior to the stagnation on theaxis. The array implodes as a set of discrete individual wires with azimuthalasymmetries. For smaller IWG, i.e., n > nC~it,the wires merge early compared to theimplosion time and the array implodes as an annular plasma shell. Experimentally, it hasbeen observed in the short pulse mode at the Saturn and Z facilities that the output powerincreases as the interwire gap decreases [6-8], a result consistent with this model. BasedRECEIVED2on Haines’ model, and others [15], it is apparent that the dynamics of the wire explosionand plasma implosion can differ for short and long implosion time experiments.Specifically, the timescales available for wire explosion and expansion, and the influenceof implosion velocity on the stagnation and thermalization, could have substantial effects.The Haines model, for example, would predict a decrease in the critical wire number forlonger implosion times, assuming all other parameters are unchanged.The first long pulse Z-pinch experiments with wire arrays were carried out at Saturnusing tungsten wires with implosion times up to 250 ns. [16] The measured x-ray powers(> 20 TW) were comparable to those achieved with short implosion times, anencouraging result consistent with post-experiment calculations [17] and with Haines’wire array model. [14] These observations suggested that for longer implosion times, thewires have a longer time in which to merge prior to acceleration and stagnation. Aninference from these results and subsequent modeling was that larger interwire gaps(spacing between adjacent wires) are feasible. To demonstrate conclusively that longimplosion times could positively impact the performance of wire arrays and to test someof the wire array models, a systematic scan of wire number using aluminum wire arrayswas performed. Aluminum was chosen for several reasons, including the need forinformation relevant to K-shell scaling laws, the ability to diagnose plasma conditions viaspectroscopy, and the availability of good short pulse data for comparison. [18]Aluminum radiates in the K-shell at approximately 1.8 keV. The results presented hereconfirm the previous implication of improved wire merger for longer implosion times,with an observed critical interwire gap of- 3 mm for a 165 ns implosions. Previous shortpulse (60 ns) experiments also utilizing Al wire arrays had shown a critical interwire gapof 1 mm. [18] In addition, for the first time, it was observed that the pulsewidth andrisetime increased if too many wires were employed. These results identify a range ofwire numbers in which Z-pinch performance is optimized. The experimentalobservations, and comparisons to a wire array model and simulations, are presented inthis paper.The8-MA Sa~generator stores 5MJofelectricd energy in36Mmbtis. Whendelivered downline in its typical short pulse mode (50 ns current risetime), a 20 TW, 50ns pulse is measured at the water-vacuum interface. An adjustment in pulse formingswitching produces a long pulse mode for Saturn, which gives a 5 TW, 230 ns electricalpulse at the water-vacuum interface, with 11.5 MA measured in a short circuit load.The x-ray output of the wire array implosions is studied using several x-ray diagnostics.Aluminum K-shell yields (-1.8 keV) are measured using four filtered photoconductingdetectors (PCDS) and a filtered gold bolometer with near intrinsic resistivity. [19] Ameasurement of the total radiated yield is obtained with a bare nickel bolometer. Time-resolved power estimates for 0.18 -1.5 keV x-rays are obtained from an array of filteredcarbon cathode x-ray diodes (XRDS). [20] Spectral information is gathered using severalspectrometers, both time-integrated and time-resolved. Spatial properties of the Z-pinchare measured with an x-ray pinhole camera.Initial experiments using 40 mm diameter Al wire arrays had shown a peak K-shell yieldof- 65 kJ with a load mass per unit length of 620 pg/cm, which corresponded to animplosion time near 165 ns. [21,22] Using this optimal mass, a set of experiments wasdesigned that varied the wire number from 32 wires to 282 wires, corresponding tointerwire gaps of 3.9 mm to 0.45 mm, as shown in Table 1. Note that the individual wirediameter also decreased with decreasing interwire gap, a consequence of keeping allother parameters fixed. Decreasing the IWG below 0.45 mm was not possible with 40mm diameter arrays due to limitations on the wire sizes available, so in order to pursuecontinued reductions in IWG, experiments were also performed using 32 mrn diameterarrays. For these experiments, the implosion time was still held fixed at -165 ns,corresponding to an initial load mass per unit length of-960 ~g/cm, and the wire numberwas varied from 110 to 280 (IWG of 0.9 mm to 0.36 mm).Shown in figure 1 are the current waveforms, and resulting K-shell power waveforms forthree of the arrays used in this experiment. The load currents were all near 7.5 MA forthe wire arrays, but the K-shell power waveforms show distinct differences with4increasing wire number. As observed in experiments with short implosion times, the K-shell and total powers increased with increased wire number (decreased IWG). Variationsof greater than a factor of 2 were observed in the K-shell power (and total power) overthe range of interwire gaps studied. The measured K-shell energy, however, remainedconstant at 60-70 kJ. The powers and yields are at levels similar to those observed in theshort pulse mode. Interestingly, a decrease in both the K-shell and total powers isobserved at the smallest interwire gaps. The yields and powers are detailed in Table 1.Two-dimensional radiation magnetohydrodynamic (MHD) modeling and analyses ofpinhole images have indicated that the risetime of the x-ray pulse is a good metric of thepinch quality. Risetimes for this experiment are plotted in figure 2. The risetimes areshort for IWG <2 mm (-5 ns), then show a slight increase for IWG >2 mm, and asubstantial increase, to 15 ns for the K-shell and 24 ns for the total x-rays, for IWG >3mm. The risetimes for IWG <0.7 mm also show an increase, up to 9 ns, which correlateswith a power decrease. The pinch diameters, as measured from the time-integratedpinhole images, are summarized in Table 1 and are consistent with the trends in therisetimes seen in Figure 2, including an increase in diameter for the smallest IWG. The32 mm diameter data, also plotted in Figure 2, confirms the increase in risetime at thesmall IWG seen with the 40 mm diameter data. It should be noted that the small IWG(high wire number) risetime increase observed in the long pulse experiments has not beenpreviously seen in any other previous short or long pulse experiment. [6-8,16,18]Trends in the implosion dynamics are reflected in the measured x-ray spectra.Temperatures and densities extracted fi-om this data suggest electron temperatures of 600-1100 eV and ion densities of >1019 cm-3, levels similar to those obtained in the shortpulse mode. As plotted in Figure 3, the temperatures decrease and the densities increaseas the IWG decreases. The density increase is associated with a decrease in pinchdiameter and the temperature decrease is associated with higher opacities and possiblyradiative cooling. It is known that gradients exist in the imploded plasmas and moredetailed spectral analyses will be performed. [23] As observed with other parameters inthis experiment, the trends in temperature and density reversed for the higher wirenumber arrays.A comparison of the short pulse and long pulse data clearly demonstrates that the longerwire initiation process has improved the pinch performance for the longer implosion timeloads. Haines’ heuristic wire merger model [14] predicts a critical interwire gap of 1.5mm for the short pulse mode and 4.5 mm for the long pulse model. While the .experiments show somewhat smaller critical IWG for both the short and long pulse cases,the ratio of the critical IWG is the same (approximately a factor of 3), and theexperimental observations imply improved wire merger for longer implosion times.However, the heuristic model provides no explanation for the effect observed at smallIWG (< 0,7 mm).To better understand the results of the experiments and the effects of wire merger,detailed lD ALE and 2D r-z MHD calculations were performed.[24] The calculationsshow a trend where conventional 2D r-z modeling is appropriate, and this trend is directlyrelated to the merger of the wires. Table 2 summarizes some of the calculations. For the126 and 180 wire number cases (small IWG), the current per wire was low, but the wiresexpanded quickly and merged well before acceleration toward the axis. For these cases,the 2D r-z modeling required low perturbation levels in order to reproduce the measuredrisetimes. (Note: the wire array is approximated by a thin shell, which is seeded with aninitial perturbation meant to represent the true 3-D nature of the array initiation process.This perturbation produces instabilities which are believed to grow during the implosionphase.) For IWG -2 mm, the wires merged immediately after the start of theacceleration, and a slightly higher perturbation level was necessary. For the largest IWG,the wires did not merge, and the 2D r-z modeling was not appropriate. These results areconsistent with the trends observed in the experimental data, including the IWG at whichchanges are observed in the output., However, the computational model cannot explainthe experimentally observed degradation of pinch parameters at the smallest IWGS (< 0.7mm). Speculations for this degradation at small IWG include non-uniform current paths,6low current per wire effects, and wire initiation effects. Continuing theoretical andcomputational efforts are needed to explain why an optimal wire number exists,In summary, long pulse implosions on Saturn have shown an increase in x-ray power anddecrease in pulsewidth and risetime for IWG >0.7 mm when the intenvire gap spacingwas decreased, a result consistent with previous short pulse wire number studies, Adecrease in x-ray power and increase in pulsewidth and risetime were observed for thehighest wire number loads, defining a range of optimal interwire gap (optimal wirenumber) of 0.7 mm to 3 mm. The changes in x-ray power and temporal characterobserved for O.7 mm < IWG <3 mm are consistent with wire merger models andcalculations. This IWG spacing was a factor of three larger for the long pulseexperiments: a clear indicator of improved wire merger with a longer implosion time.These observations confirm the speculations made in Reference 16. The additionalobservation of a degradation of Z-pinch output for IWG <0.7 mm challenges thepreviously held beliefs that continued improvements would be observed with continueddecreases in IWG.The authors would like to gratefully acknowledge the contributions of the diagnostictechnicians (Pat Ryan, John McGurn, Dan Nielson, Ruth Smelser, Steve Lazier, and DanJobe) and the Saturn crew, Thanks also go to Ralph Schneider and Maj. David Bell ofthe Defense Threat Reduction Agency for their input and the continued support of theseexperiments. *This work was supported by DTRA and DOE. Sandia is a multiprograrnlaboratory operated by Sandia Corporation, a Lockheed Martin Company, for the UnitedStates Department of Energy under Contract DE-AC04-94AL85000.References1. R.B. Spielman, et. al., “Dense Z-Pinches, Second International Conference,” editedby N.R. Pereira, et. al., AIP Conf. Proc. 195,3 (AIP, Woodbury, NY, 1989).2. R.B. Spielman, et. al., Physics of Plasmas, 6,2081 (1998).3. P.T. Springer, et. al., J. Quant. Spectrosc. Radiat. Transfer 58, 927(1997).4. C. Deeney, et. al., Phys. Plasmas 6,2081 (1999).75. M.K. Matzen, et. al., Phys. Plasmas 4,1519 (1997).6. T.W.L. Sanford, et. al., Phys. Rev. Lett., 77,5063 (1996).7. C. Deeney, et. al., Phys. Plasmas, 5,2431 (1998).8. T.W. L. Sardiord, et. al., IEEE Trans. on Plasma Sci., 26, 1086 (1998).9. C. Deeney, et. al., Phys. Rev. Lett., 81,4883 (1998).10. C. Deeney, et. al., Phys. Plasmas, 5,2605 (1998).11. K.G. Whitney, et. al., Phys. Plasmas, 2,2590 (1995).12. C. Deeney, et. al., Phys. Rev. A, 44,6762 (1991).13. J,W. Thornhill, et. al., AIP Conference Proceedings, 409, 193 (1997),14. M.G. Haines, IEEE Trans. on Plasma Sci., 26, 1275 (1998).15. M.P. Desjarlais and B.M. Marder, Phys. Plasmas, 6,2057 (1999).16. C. Deeney, et. al., Phys. Plasmas, 6,3576 (1999).17. M.R. Douglas, et. al., Phys. Plasmas, 7,2945 (2000).18. T.W.L. Sanford, et. al., Phys. Plasmas, 6, 1270 (1999).19. R.B. Spielman, et. al., Rev. Sci. Instrum., 70,651 (1999).20. G.A. Chandler, et. al., Rev. Sci. Instrurn., 70,561 (1999).21. C.A. Coverdale, et. al., Bull. Am. Phys. Sot., 44,52 (1999).22. C.A. Coverdale, et. al., IEEE Conference Record, 2000 IEEE ICOPS, p. 92 (2000):23. J.P. Apruzese, et. al., submitted to Phys. Plasmas (2000).24. M.R. Douglas, et. al., IEEE Conference Record, 2000 IEEE ICOPS, p. 135 (2000).8,Figure CaptionsFigurel: Overlay of theload current wavefoms, mdK-shell power wavefoms forthe32 wire, 126 wire, and 180 wire arrays.Figure 2: The measured total and K-shell x-ray risetimes as a function of interwire gap.The open symbols represent the 32 mm diameter load data.Figure 3: Measured electron temperature and density as a fimction of interwire gap.9Table 1: Load parameters and measured output of the Aluminum wire arraysLoadradius(mm)404040404040323232WireIIWire Interwire K-shell K-shell K-shellnumber dia. gap Yield FWHM power(pm) (~) (kJ) (ns) (TW)32 30.5 3.9 60.6 29 1.356 22.9 2.2 66.1 10.5 2.570 20.3 1.8 48 11 1.7126 15.2 1.0 60.4 8.5 2.6180 12.7 0.7 62.9 7 3.4282 10.2 0.45 60.4 14.2 2.4110 20.3 0.9 50.8 1.9194 15.2 0.52 40 12.6m , , , ,280 I 12.7 I 0.36 1 61.6 I 15 I 1.8TotalFWHM(ns)27.613.613.89.49.612.91414Total I PinchIpower dia.(TW) (mm)is20 5.433 2.622 3.542 2.452 1.844 2.828 [ 3.8Table 2: Highlights of the computational results. Merger times are based on the IDALE simulations; perturbation levels are listed for cases where 2D r-z modeling wasappropriate. ** for this case, 2D r-(1modeling shows merger of the wires.ltik=L=$@wlo5*~Witenu-lixzdia.(g.nj) (nrrj (n-@180 40 0.70 0.35b2614011. mlo.5070 40 1.80 ().$x)56 40 224 1.12!32140! 3.9311.%Irm&rtinEprtlikdal(m) let’el(”?+-t+o.85rmlat75m I 3108765432101— 32 wires /’-- .““””-””-126 wires ft---- !80 wires ,f-50 0 50 100 150i3.532.521.510.50200 250 300time (ns)112520151050 1 I I I !0 1 2 3 4interwire gap (mm)12.1500 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1000f!~’i m ~i;14/\ ;;,,,:!I d,...-”’”-.-.J””’”””””””,,_ ,._......” ” . ”” ..”-,;~p, y“ 1i “’.,\”;,,/ +~ ; K.500 -i . . ...+ . .....+ ------.....=>“>.EEl ‘“ “*o I I I 1 t I I \o 0.5 1 1.5 2Interwire2.5 3 3.5 4Gap (mm)104_+.12013

The Observation of an Optimal Wire Number Range in Long Implosion Time Aluminum Z-Pinches

Abstract

Similar works

Full text

Available Versions

UNT Digital Library