simon c. bott et al- quantitative measurements of wire ablation in tungsten x-pinches at 80 ka

8/3/2019 Simon C. Bott et al- Quantitative Measurements of Wire Ablation in Tungsten X-pinches at 80 kA

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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 5, OCTOBER 2008 2759

Quantitative Measurements of Wire Ablation inTungsten X -pinches at 80 kA

Simon C. Bott, Member, IEEE , David M. Haas, Yossof Eshaq, Utako Ueda, Sergey V. Lebedev, Member, IEEE ,Jeremy P. Chittenden, Member, IEEE , James B. A. Palmer, Simon N. Bland, Member, IEEE ,

Gareth N. Hall, Member, IEEE , David J. Ampleford, Member, IEEE , and Farhat N. Beg, Member, IEEE

Abstract—This paper investigates the ablation of wires intwo-wire tungsten X -pinches driven by an 80-kA current over50 ns. High-resolution imaging using a Nomarski interferometerallows measurements close to the X -pinch cross point, where theablation “flare” structure is observed to clearly develop duringthe drive-current rise time. Electron density profiles are recoveredas a function of both distance normal to the wire and of time.Results compare favorably to the rocket model of wire ablation.In addition, the density contrast over the ablation “stream” and“gap” structure is measured and compared to similar measure-

ments made using quantitative radiography on the 1-MA 250-nsMAGPIE generator at Imperial College London, London, U.K.

Index Terms—Precursor plasma, wire ablation, X -pinch.

I. INTRODUCTION

THE UNDERSTANDING of the ablation phase of explod-

ing wire experiments is of fundamental importance to their

continued development. In cylindrical wire arrays, this phase

comprises up to 80% of the experiment, and the mass redistrib-

ution resulting from wire ablation is crucial to the generation

of impressive X-ray powers measured from imploding wire-

array Z -pinches [1] and, hence, their application to inertial

confinement fusion research.When a fast-rising current is passed through fine wires, a

heterogeneous plasma structure is formed: A cold dense core

is surrounded by a low-density hot corona which carries much

of the drive current [2]–[4]. Where a global magnetic field is

Manuscript received September 30, 2007; revised November 9, 2007. Firstpublished October 24, 2008; current version published November 14, 2008.This work was supported by U.S. Department of Energy Junior Faculty GrantDE-FG02-05ER54842.

S. C. Bott is with the Center for Energy Research, University of California,San Diego, La Jolla, CA 92093 USA (e-mail: [email protected]).

D. M. Haas, Y. Eshaq, U. Ueda, and F. N. Beg are with the Departmentof Mechanical and Aerospace Engineering, University of California, San

Diego, La Jolla, CA 93093 USA (e-mail: [email protected]; [email protected];[email protected]; [email protected]).

S. V. Lebedev is with the Plasma Physics Group, Blackett Labora-tory, Imperial College London, London SW7 2AZ, U.K., and also withBudker Institute of Nuclear Physics, Novosibirsk 630090, Russia (e-mail:[email protected]).

J. P. Chittenden, S. N. Bland, and G. N. Hall are with the PlasmaPhysics Group, Blackett Laboratory, Imperial College London, London SW72AZ, U.K. (e-mail: [email protected]; [email protected];[email protected]).

J. B. A. Palmer is with the Plasma Physics Department, AWE Plc,Aldermaston RG7 4PR, U.K. (e-mail: [email protected]).

D. J. Ampleford is with Sandia National Laboratories, Albuquerque, NM87185-1194 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPS.2008.2003964

present, the low-density corona is swept to the system axis

by the J ×Bglobal force. The rate at which mass is ablated

from the wire cores to replenish the corona is, in general, well

approximated by a rocket model, assuming a fixed velocity of

the ablated material [5]

V abldm

dt=

μ0I 2

4πR0

(1)

where V abl is the fixed “ablation” velocity, dm/dt is the massablation rate per unit length, I is the drive current, and R0 is

the array radius. The acceleration of material from wires is not

axially uniform, however, and all systems with a global field

demonstrate a periodic radial flaring structure. This has been

observed by both laser imaging and radiography at different

current levels for many different experiments, including cylin-

drical [6], [7] and conical [8] wire arrays and X -pinches [9].

The cause of this structure is currently not clear. A modified

m = 0 magnetohydrodynamic (MHD) instability [10] and an

electrothermal instability [11] are two of the several possible

candidates, and experimental information is needed to define

both the underlying mechanism and its likely scaling withdriver current.

In an X -pinch, the global magnetic field changes along the

Z -axis as wire separation increases, and therefore offers an op-

portunity to study the variation of the ablation rate with this pa-

rameter and to determine whether the rocket model provides an

adequate description in this case. Measurements of the global

ablation rate and flare wavelength have been made for conical

wire arrays at larger diameters and higher drive currents [8],

but this paper is the first study of these phenomena for X -pinch

experiments. It should be noted that laser interferometry has

been used previously to study X -pinch evolution, notably in

[12], but this work focuses on the quantitative measurement of

the ablation structure close to the wire core. Mass ablation ratesof X -pinches at 80 kA are then compared to cylindrical wire ar-

rays at the 1-MA MAGPIE facility at Imperial College London.

II. EXPERIMENTAL SETUP

The X -pinch pulser at UCSD comprises a Marx bank (4 ×0.2-μF capacitors charged to 50 kV), a coaxial discharge line, a

water-filled pulse-forming line, and a self-breaking switch (SF6

at 18 lbf/in2). This typically delivers 80 kA to a load with a rise

time of 50 ns.

The load is formed from two wires of 7.5-μm tungsten.

These are hung initially parallel between two electrodes, which

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2762 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 5, OCTOBER 2008

Fig. 5. Comparison of X-pinch mass density profiles (assuming that Z = 10) for 31–49 ns, and indication of the measured and expected differences in positions“stream1” and “stream2” from the rocket model (V abl = 1.5 × 105 m · s−1).

Fig. 6. Plots showing the variation of stream/gap density ratio with (left) time (0.5 mm from wire core) and (right) distance from wire (time averaged) for 80-kAW X-pinches.

forming the flare structure. From the X -pinch experiments

described in the previous section, the electron density ratio

(ρe,stream/ρe,gap)can be measured. Again, assuming a fixed

Z ,

this is equivalent to mass density contrast ρ, and Fig. 6

shows the variation of the density ratio between stream po-

sitions and gap positions. The left plot shows that this ratio

changes with time, which is measured for ρStream1/ρGap2 and

ρStream2/ρGap2 at 0.5 mm from the wire core. As the mass

ablation rate is changing with position, the average of these two

values indicates how this ratio changes if the radial position

of the streams and gaps were the same (e.g., in a cylindrical

wire array), and this is shown as the line on the plot. The

ratios obtained vary between 1.2 and 2.0 over the time range

investigated, and shows a slow increase with time at 0.5 mm

from the wire core.

The plot on the right in Fig. 6 shows the time-averageddensity contrast as a function of distance from the wire core.

This shows a weak dependence on distance showing a slow

increase from ∼1.5 at 0.25 mm to ∼2.3 at 0.75 mm (error

bars are an indication of the error in the averaging process).

The stream/gap density contrast is relatively invariant with both

distance from the wire core and of time.

This work on X -pinches at UCSD can be compared to cylin-

drical wire-array experiments carried out at the MAGPIE fa-

cility in collaboration with Imperial College London (1 MA

and 250-ns rise time). The arrays are comprised of 16 wires of

13-μm tungsten on a 16-mm diameter, and X -pinch radiogra-

phy was used to image the arrays [6] with a temporal resolution

of 1 ns and a spatial resolution of ∼5 μm. A stepwedge de-

posited on the Ti radiation filter provides calibration for the film

exposure for areal densities in the 3× 10−4- to 3 × 10−3-kg ·

m−2 range. At the edge of the array, single edge wires can be

imaged, which again provides a measure of the mass ablationstructure of an individual wire. In Fig. 7, a radiograph of one




BOTT et al.: QUANTITATIVE MEASUREMENTS OF WIRE ABLATION IN TUNGSTEN X-PINCHES AT 80 kA 2763

Fig. 7. (Right) High-magnification radiograph of the edge wire, (top left)average stream and gap lineout, and (bottom left) variation of stream/gapdensity ratio with radius.

such wire is shown in high magnification, and the position

of “streams” and “gaps” is clearly visible. The calibration of

the radiograph allows quantitative lineouts to be taken, and

averages for the three “stream” positions (solid lineouts) and

“gap” positions (dashed lineouts) are given.

The contrast in density between stream and gap positions is

also measurable from these experiments, and this is given as a

function of the distance from the wire core [Fig. 7(b)]. The data

are somewhat noisy, and the dashed line on the plot indicates

how the average value is varying. The ratio of ρstream/ρgapagain changes by only a small amount ranging from 1.5 close to

the wire core to 2.3 at 1.5 mm toward the axis. Both the values

and trends are similar to those found for the previous X -pinchexperiments. For both experiments, we can calculate both the

magnetic field strength that is local to the wire (Blocal) and the

global field (Bglobal). For the X -pinch experiments, a current

radius of 100 μm around the wire core was assumed, with

40 kA/wire, and flares at 1-mm radius from the global

axis. These values give Blocal = 80 T, Bglobal = 16 T, and,

therefore, Blocal/Bglobal = 5. For the wire-array experiments,

Blocal = 125 T, Bglobal = 25 T, and, again, Blocal/Bglobal =5. This perhaps suggests that the similarity of the ablation struc-

ture is a result of this ratio of the fields and that this is the dom-

inant term in determining the quantitative ablation structure.

The fact that the density contrast shows relatively low valuesis very interesting. If the flaring structure is the result of a

perturbed m = 0 MHD instability, this contrast may provide

information as to what modifications occur in global magnetic

field. For a pure m = 0 mode (e.g., in a single wire), the

radial density profile outside the necked regions will be zero,

as plasma is well confined here, forcing entirely axial mass

transport. The flaring regions, which result from this transport

and subsequent acceleration to the global axis, will contain all

the mass ablated from the wire core, and hence, the density

contrast would be very large. This is clearly not the case

experimentally. Extended investigation of the density contrast

in the ablation structure should be carried out to provide insight

into these processes as a function of current and material, andthis will be the subject of future publications.

ACKNOWLEDGMENT

The authors would like to thank the Target Fabrication

Group, AWE Plc, Aldermaston, U.K., for the construction of

the W stepwedge used in the MAGPIE experiments.

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[2] I. K. Aivazov, V. D. Vikharev, G. S. Volkov, L. B. Nikandrov,V. P. Smirnov, and V. Y. Tsarfin, “Formation of a plasma precursor dueto the collapse of multiwire liners,” JETP Lett., vol. 45, p. 28, 1987.

[3] R. F. Benjamin, J. S. Pearlman, E. Y. Chu, and J. C. Riordan, “Mea-surements of the dynamics of imploding wire arrays,” Appl. Phys. Lett.,vol. 39, no. 10, pp. 848–850, Nov. 1981.

[4] S. V. Lebedev, I. H. Mitchell, R. Aliaga-Rossel, S. N. Bland,J. P. Chittenden, A. E. Dangor, and M. G. Haines, “Azimuthal structureand global instability in the implosion phase of wire array Z -pinch exper-iments,” Phys. Rev. Lett., vol. 81, no. 19, pp. 4152–4155, Nov. 1998.

[5] S. V. Lebedev, F. N. Beg, S. N. Bland, J. P. Chittenden, A. E. Dangor,M. G. Haines, K. H. Kwek, S. A. Pikuz, and T. A. Shelkovenko, “Effect

of discrete wires on the implosion dynamics of wire array Z pinches,”Phys. Plasmas, vol. 8, no. 8, pp. 3734–3747, Aug. 2001.

[6] S. V. Lebedev, F. N. Beg, S. N. Bland, J. P. Chittenden, A. E. Dangor,M. G. Haines, S. A. Pikuz, and T. A. Shelkovenko, “Effect of core-coronaplasmastructure on seeding of instabilities in wire arrayZ pinches,” Phys.

Rev. Lett., vol. 85, no. 1, pp. 98–101, Jul. 2000.[7] D. B. Sinars, M. E. Cuneo, B. Jones, C. A. Coverdale, T. J. Nash,

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[8] D. J. Ampleford, S. V. Lebedev, S. N. Bland, S. C. Bott,J. P. Chittenden, C. A. Jennings, V. L. Kantsyrev, A. S. Safronova,V. V. Ivanov, D. A. Fedin, P. J. Laca, M. F. Yilmaz, V. Nalajala,I. Shrestha, K. Williamson, G. Osborne, A. Haboub, and A. Ciardi,“Dynamics of conical wire array Z -pinch implosions,” Phys. Plasmas,

vol. 14, no. 10, p. 102 704, Oct. 2007.[9] S. M. Zakharov, G. V. Ivanenkov, A. A. Kolomenskii, S. A. Pikuz, andA. I. Samokhin, “Plasma of an exploding multiwire load in the diode of ahigh-current accelerator,” Sov. J. Plasma Phys., vol. 13, p. 115, 1987.

[10] C. J. Garasi, D. E. Bliss,T. A. Mehlhorn,B. V. Oliver, A. C. Robinson, andG. S. Sarkisov, “Multi-dimensional high energy density physics modelingand simulation of wire array Z -pinch physics,” Phys. Plasmas, vol. 11,no. 5, pp. 2729–2737, May 2004.

[11] M. G. Haines, “A three-dimensional model of wire array instability, abla-tion, and jetting,” IEEE Trans. Plasma Sci., vol. 30, no. 2, pp. 588–592,Apr. 2002.

[12] I. H. Mitchell, R. Aliaga-Rossel, R. Saavedra, H. Chuaqui, M. Favre,and E. S. Wyndham, “Investigation of the plasma jet formation in X-pinch plasmas using laser interferometry,” Phys. Plasmas, vol. 7, no. 12,pp. 5140–5147, Dec. 2000.

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Dec. 1979.

Simon C. Bott (M’07) received the M.Phys. degreein chemical physics and the Ph.D. degree from theUniversity of Sheffield, Sheffield, U.K.

He joined the Plasma Physics Group, BlackettLaboratory, Imperial College London, London, U.K.,in 2003, as a Postdoctoral Research Associate andsubsequently joined the Center for Energy Research,University of California, San Diego, in 2006. His

research interests include all aspects of wire-arrayZ -pinch evolution, X-pinches, laboratory astro-physics, and pulsed-power systems.




2764 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 5, OCTOBER 2008

David M. Haas is currently working toward the Ph.D. degree in pulsed-power-driven X-pinch plasmas with the Department of Mechanical and AerospaceEngineering, University of California, San Diego.

Yossof Eshaq is currently with the Department of Mechanical and AerospaceEngineering, University of California, San Diego, working on pulsed-power-driven X-pinches.

Utako Ueda is currently with the Department of Mechanical and AerospaceEngineering, University of California, San Diego, working on pulsed-power-driven X-pinches.

Sergey V. Lebedev (M’03) received the M.Sc.degree in physics from Novosibirsk University,Novosibirsk, Russia, in 1978 and the Ph.D. degreein physics from Budker Institute of Nuclear Physics,Novosibirsk, in 1987.

Since 1978, he has been with Budker Insti-tute of Nuclear Physics. From 1995 to 1996, hewas a Visiting Scientist with the University of Campinas, Campinas, Brazil. Since 1996, he hasbeen with the Plasma Physics Group, Blackett Labo-ratory, Imperial College of Science and Technology,

London, U.K., where he is currently a Professor of plasma physics. He hasauthored more than 100 papers published in international journals. His prior

research interests include the physics of high-current microsecond relativisticelectron beams and their interaction with plasma in pulsed-power technologyand in plasma-diagnostic techniques. His current research interests include thedynamics of wire array Z -pinch implosions, pulse shaping of X-ray radiationusing nested wire arrays, studies of different processes determining the effi-ciency of pinch radiation production, and laboratory astrophysics through theexperimental modeling of supersonic radiatively cooled plasma jets.

Dr. Lebedev is a Fellow of the American Physical Society. He has servedon the Executive Committee of the IEEE Plasma Science and ApplicationsCommittee.

Jeremy P. Chittenden (M’07) received the B.Sc.degree in physics from the University CollegeLondon, London, U.K., and the Ph.D. degree inplasma physics from the Imperial College of Sci-ence, Technology, and Medicine, London, in 1987and 1990, respectively.

In October 2003, he was a Senior Lecturer withthe Imperial College of Science, Technology, andMedicine and was promoted to Reader in plasmaphysics in October 2006. He is currently withthe Plasma Physics Group, Blackett Laboratory,

Imperial College London, London. He has published more than 60 journalpapers on Z -pinches, inertial confinement, fusion, X-pinch plasmas, X-raylasers, laboratory astrophysics, multidimensional magnetohydrodynamic mod-eling, and pulsed-power engineering. His research interests include the use of pulsed-power systems to produce plasmas of extremely high temperatures and

densities.Dr. Chittenden was the Chairperson of the 2005 Conference on DenseZ -Pinches held in Oxford, U.K.

James B. A. Palmer received the B.Sc. degree (with honors) in physics andoptical science from the University of Reading, Berkshire, U.K., in 1997. Heis currently working toward the Ph.D. degree in the Plasma Physics Group,Blackett Laboratory, Imperial College London, London, U.K.

Since 1998, he has been with AWE Plc, where he has been with the PlasmaPhysics Department since 2000. His research interests include the effects of wire arrays on on-axis targets and X-pinch radiography.

Simon N. Bland (M’08) was born in England onSeptember 16, 1974. He received the M.Sci. degreein physics and the Ph.D. degree from the ImperialCollege of Science, Technology, and Medicine,London, U.K., in 2001, with hisPh.D. dissertationonthe “Dynamics of Wire Array Z -Pinch Implosions.”

Since 2001, he has been a Research Associatewith the Plasma Physics Group, Blackett Laboratory,Imperial College London, London. Over the courseof his studies, he has won numerous awards, pre-sented work to the public at science festivals, and

coauthored 20 published journal papers.

Gareth N. Hall (M’08) received the Ph.D. degreefrom Imperial College London, London, U.K.

He is currently a Postdoctoral Researcher withthe Plasma Physics Group, Blackett Laboratory,Imperial College. His research interests includeX-ray spectroscopy of wire-array plasmas and allaspects of wire-array behavior, particularly the studyof novel array configurations such as spherical andcoiled arrays.

David J. Ampleford (M’06) received the M.Sci. and Ph.D. degrees fromImperial College London, London, U.K., in 2001 and 2005, respectively, withhis Ph.D. dissertation on investigating the use of conical wire-array Z -pinchesto model protostellar jets.

Since 2005, he has been a Postdoctoral Researcher with Sandia NationalLaboratories, Albuquerque, NM, where his research is centered around thephysics of wire-array Z -pinches, specifically the dynamics of conical wire-array implosions, and the use of nested wire arrays for X-ray pulse shaping.

Farhat N. Beg (M’97) received the Ph.D. degreein plasma physics from Imperial College London,London, U.K., in 1995.

From 1996 to 2003, he was a Research Associatewith Imperial College before moving to the De-partment of Mechanical and Aerospace Engineering,University of California, San Diego, as an AssistantProfessor in 2003. In 2007, he was appointed tohis current position as Associate Professor. He hasauthored more than 90 papers published in refereed

journals on plasma focus, Z -pinches, short-pulselaser-solid interactions, fast ignition, and X-ray sources.

Dr. Beg is the General Chair of International Conference on Plasma Science,which will be held in San Diego in 2009. He was the recipient of the 2008 IEEENuclear and Plasma Sciences Society Early Achievement Award.

simon c. bott et al- quantitative measurements of wire ablation in tungsten x-pinches at 80 ka

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