s. c. bott et al- study of the effect of current rise time on the formation of the precursor column...

8/3/2019 S. C. Bott et al- Study of the effect of current rise time on the formation of the precursor column in cylindrical wire

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Study of the effect of current rise time on the formation of the precursorcolumn in cylindrical wire array Z pinches at 1 MA

S. C. Bott,1 D. M. Haas,1 Y. Eshaq,1 U. Ueda,1 F. N. Beg,1 D. A. Hammer,2 B. Kusse,2

J. Greenly,2 T. A. Shelkovenko,2 S. A. Pikuz,2 I. C. Blesener,2 R. D. McBride,2

J. D. Douglass,2,a K. Bell,2 P. Knapp,2 J. P. Chittenden,3 S. V. Lebedev,3 S. N. Bland,3

G. N. Hall,3 F. A. Suzuki Vidal,3 A. Marocchino,3 A. Harvey-Thomson,3

M. G. Haines,3 J. B. A. Palmer,4 A. Esaulov,5 and D. J. Ampleford61

Center for Energy Research, University of California San Diego, California 92093-0417, USA2Laboratory of Plasma Studies, Cornell University, New York 14853, USA3Blackett Laboratory, Imperial College London, SW7 2BW, United Kingdom

4AWE Plc, Aldermaston, Berkshire RG7 4PR, United Kingdom

5Department of Physics, University of Nevada, Reno, Nevada 89557, USA

6Sandia National Laboratories, California 94551-0969, USA

Received 26 February 2009; accepted 8 June 2009; published online 1 July 2009

The limited understanding of the mechanisms driving the mass ablation rate of cylindrical wiresarrays is presently one of the major limitations in predicting array performance at the higher currentlevels required for inertial confinement fusion ICF ignition. Continued investigation of thisphenomenon is crucial to realize the considerable potential for wire arrays to drive both ICF andinertial fusion energy, by enabling a predictive capability in computational modeling. We present thefirst study to directly compare the mass ablation rates of wire arrays as a function of the current rise

rate. Formation of the precursor column is investigated on both the MAPGIE 1 MA, 250nsMitchell et al., Rev. Sci. Instrum. 67, 1533 1996 and COBRA 1 MA, 100ns Greenly et al.,Rev. Sci. Instrum. 79, 073501 2008 generators, and results are used to infer the change in theeffective ablation velocity induced by the rise rate of the drive current. Laser shadowography, gatedextreme ultraviolet XUV imaging, and x-ray diodes are used to compare the dynamical behavioron the two generators, and X-pinch radiography and XUV spectroscopy provide density evolutionand temperature measurements respectively. Results are compared to predictions from an analyticalscaling model developed previously from MAGPIE data, based on a fixed ablation velocity. ForCOBRA the column formation time occurs at 1165 ns and for Al arrays and 1465 ns for Warrays, with Al column temperature in the range of 70165 eV. These values lie close to modelpredictions, inferring only a small change in the ablation velocity is induced by the factor of 2.5change in current rise time. Estimations suggest the effective ablation velocities for MAGPIE andCOBRA experiments vary by a maximum of 30%. 2009 American Institute of Physics.DOI: 10.1063/1.3159864

I. INTRODUCTION

Wire array Z pinches13 represent the most powerfullaboratory x-ray sources,4,5 and have recently been employedas a drive for high energy density physics,6 laboratoryastrophysics,716 radiation science,1722 and shock2329 ex-periments. One of the most interesting of these applications,however, is as a possible driver for inertial confinementfusion3034 ICF and inertial fusion energy IFE.3539 Theperformance of a wire array is dominated by the ablationprocesses taking place at the wires, and while in general the

dynamical evolution is well understood, a comprehensive,quantitative model of the ablation process is not currentlyavailable. This results in uncertainties in the likely scaling ofx-ray power with driver current, and consequently under-standing of the prolonged ablation phase of wire array ex-periments is of fundamental importance to their continueddevelopment as both a high power x-ray source and a pos-sible driver for ICF.

Wire arrays comprise an annulus of fine wires, typicallya few tens of microns in diameters, arranged on a diameter ofseveral millimeters. When a fast-rising current is passed, aheterogeneous plasma structure is formed by each wire: acold dense core is surrounded by a low density hot coronawhich carries much of the drive current.4046 The azimuthalglobal magnetic field generated by the parallel current pathsin the wires accelerates the low density corona to the arrayaxis via the jBglobal force.

47 The rate at which mass isablated from the wire cores to replenish the corona is well

approximated by a Rocket model,

48

which assumes a fixedvelocity of the ablated material. The accepted value for thisablation velocity Vabl is 1.510

5 m s1, establishedfrom experiments on the MAGPIE generator at Imperial Col-lege London.49 Values of the fluid velocity determined bycomputational simulations typically converge to similar val-ues close to the array axis, and show reasonable agreementwith simple rocket model estimations of radial mass profilesduring the ablation phase.50

The complexity of recovering data from an environmentsuch as an exploding wire core subjected to current rise rates

aPresent address: Tri Alpha Energy Inc., Foothill Ranch, California 92610,USA.

PHYSICS OF PLASMAS 16, 072701 2009

1070-664X/2009/167 /072701/14/$25.00 2009 American Institute of Physic16, 072701-1

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://php.aip.org/php/copyright.jsp
http://dx.doi.org/10.1063/1.3159864http://dx.doi.org/10.1063/1.3159864http://dx.doi.org/10.1063/1.3159864http://dx.doi.org/10.1063/1.3159864http://dx.doi.org/10.1063/1.3159864http://dx.doi.org/10.1063/1.3159864


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of 1014 A /s make reliable measurements difficult, andtherefore subject to a number of uncertainties. Similarly, themodeling of initially solid wires which are rapidly driventhrough phase transitions into the plasma state in a fullythree-dimensional 3D geometry is beyond current compu-tational abilities, particularly since the spatial resolution re-quired is of the order of a few microns in a total system sizeof10 mm extent in three dimensions. However, the ap-pearance of the compact precursor column5155 at the axis incylindrical wire array experiments is a direct result of theextended ablation times resulting from the core-corona struc-ture. Mass ablated from the stationary wire cores collides atthe system axis, and both the formation time and increase indensity following formation are a direct reflection of themass ablation rate at the wire position. Therefore, investiga-tion of the properties of the precursor column properties canyield information about the mass ablation rate of such arrays.

At present, it is thought that an ICF ignition scale driverwill require currents 60 MA,30,35,38 and so there is a need

to establish how wire ablation processes scale with currentssignificantly beyond what is available at present. There hasbeen much work to address this using a range of pulsedpower generators, centering around the scaling of the x-raypower with the maximum current drive.56,57 However, therise time of the generator current drive may also be an im-portant factor, from both a physics and technical point ofview. A longer rise-time generator is more easily constructedusing current technology, and hence more cost effective, thana 100 ns rise-time generator. However, if the mass abla-tion rate varies with the current rise time this directly affectsthe load performance at a given mass, and will need to be

accounted for in the design of an ignition scale load.In this work, quantitative measurements of the formation

of the precursor column have been made on the COBRAfacility at Cornell University58 with a peak current of 1 MAin 100 ns. These results are compared to previous and recentdata from the MAGPIE generator59 at Imperial College Lon-don with the same maximum current, but a rise time of 250ns. Data are compared to predictions from an analytical scal-ing model for the precursor dynamics published previously55

in an attempt to determine specifically whether the currentrise time influences the ablation physics of wire arrays. Thisrepresents the first direct experimental comparison of the ef-

fect of current rise time on ablation physics in cylindricalwire arrays.

The remainder of the paper is structured as follows: Sec.II describes formation processes and a scaling model of theprecursor plasma column along with predictions for the ex-pected variation of these processes with rise time. In Sec. IIIthe experimental setup and diagnostics are described. SectionIV presents results on the formation and characterization ofthe precursor column on the COBRA generator along withcomparisons to those on MAGPIE. Section V provides asummary and discussion of the data, and conclusions arepresented in Sec. VI.

II. PRECURSOR COLUMN FORMATION PROCESSESAND SCALING

Previous studies investigated the formation processes ofthe precursor column on MAGPIE 1 MA, 250 ns and pre-sented the likely physical processes by which the columnforms.55 As the current drive begins, mass is ablated from thewires and is accelerated toward the array axis. The streams

from each wire converge and form a diffuse initial densityprofile. For streams with a short ion mean free path, such asfor Al on MAGPIE, stagnation occurs and generates a rela-tively compact object 23 mm across. For streams with meanfree paths comparable to the array radius at early times, amore diffuse object results. Typically, assuming Vion= Vabl=1.5105 m s1, this difference is observed as a function ofthe wire material, and as streams arrive at the axis aluminumstreams have a mean free path of1 mm, while tungstenstreams with much higher kinetic energy at the same ablationvelocity have mean free paths of7 mm. This collisionlessflow for higher atomic number materials delays the onset ofthe processes described below,60 and the formation of the

column is observed later in the experiment.As material continues to ablate and arrive at the axis, the

ion density at the axis continues to rise. Since the radiationloss rate is proportional to nion

2, the energy radiated from theaxis also continues to increase. At some point, the energyradiated from the column becomes greater than that deliv-ered through thermalization of the kinetic energy of thestreams. This allows the plasma to cool and contract. Thisfurther raises the density, and hence radiation loss rate,which allows a further contraction, and the result is a non-linear contraction of the initial density profile to form a com-pact high density objectthe compact precursor column.The point at which this process is triggered is defined experi-mentally by a peak in the radiation output signature, and thiscontraction process typically takes less than 10 ns once ini-tiated. The column reaches a minimum radius at the end ofthis process. This diameter shows a dependence on theatomic number of the array material, varying from 3 mmfor carbon to 0.25 mm for Au. This variation is well matchedby the assumption of a balance between the thermal pressureof the column at a temperature which is assumed to be ap-proximately the same for all materials 60 eV on MAG-PIE determined from extreme ultraviolet XUV spectros-copy for Al arrays54, and the kinetic pressure of theincoming ablated plasma streams which continue to impact

at the column perimeter. The column expands late in time asmass continues to accumulate, the rate of expansion againvarying inversely with atomic number.

The formation of the column at a given point in thecurrent rise for MAGPIE experiments led to the developmentof a scaling model for the formation time and temperaturevariation for a given column diameter. The model is based onthe accumulation of mass at the axis of a cylindrical wirearray consistent with the rocket model of wire ablation48 andthe concept of a critical line density at the axis whichallows the column to form.

The precursor column formation process is triggered bythe increasing mass density at axis which increases the ra-

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diation loss, allowing the plasma to cool. Since the radiationloss rate is proportional to the ion density this is equivalentto asserting that the advent of a certain ion density at the axistriggers the column formation. A volume density requiresprior knowledge of a column diameter and hence is not use-ful for prediction, and so a line density at the axis is taken asthe scaling quantity. The variation of the ion line density atthe axis can be determined from the rocket model,

Nionaxist =0

4VaR0mion

0

tR0/VaI2tdt. 1

To allow scaling of the formation time to other genera-tors, the density at column formation time is taken fromMAGPIE experiments, where the radiation peak denotingformation is observed at 155 ns into the current drive. At thispoint the drive current has reached 0.6 MA with a sin 2 wave-form, this defines the critical ion line density as 61018 m1, i.e., when the density at the array axis for agiven generator and array reaches this value, the precursorcolumn is expected to form. This approach assumes that ab-lation streams are collisional on arrival at the array axis andno counterstreaming occurs, and so applies directly to lowatomic number loads such as aluminum at the MA level.

This was previously applied to the Z machine at Sandia

National Laboratories.55

Here, the model is applied to CO-BRA to give predictions of the formation times of the pre-cursor column for Al and W arrays. This is shown is Fig. 1for both the MAGPIE 1 MA, 250 ns and COBRA 1 MA,100 ns generators. The prediction for Al precursor columnformation on COBRA is 107 ns. For W, the critical ion linedensity is reached at a later time in the current drive for agiven mass ablation rate due to its greater mass, and this isreached at 139 ns for COBRA. In addition, counterstreamingclose to the axis was inferred on MAGPIE for some 40 ns,55

delaying column formation further. Assuming a counterstreaming period reduced by the 2.5 factor increase in currentrise rate on COBRA we can estimate a formation time of 155

ns. Note that these values use the average experimental cur-rent pulse from the COBRA experimental series given below,and the model uses the average experimental current pulsefrom the present and previous studies on MAGPIE.

The pressure balance argument in Ref. 55 also allows anestimate of the precursor column temperature given a col-umn diameter. The thermal pressure of the column is bal-anced against the kinetic pressure of the ablated plasma

streams at column formation,

Z+ 1Tt = I2t R0/Va0

tR0/VaI2tdtVamionReq2 , 2

where Z is the average ionization state in the column, and Reqis the minimum column diameter. The precursor columntemperature at formation on COBRA can be estimated byassuming the precursor column diameter is the same as onMAGPIE and using the faster rise time of the generator inEq. 2 a comparison of the experimental column diameterson both MAPGIE and COBRA is given in Sec. V. At theexpected time of column formation, the COBRA currentwaveform is at a higher level, and so a higher kinetic pres-sure impinges on the column at this time. In order to main-tain the same column diameter, the thermal pressure, andhence column temperature, must be higher than the 60 eV onMAGPIE. Assuming a 1.6 mm column diameter for alumi-num, Z+1T 1400, which yields a temperature of140175 eV for Z=810. This model assumes that radia-tion loss rates are sufficiently high following column forma-tion that all stagnating kinetic energy is radiated away, withno further dependence on material atomic number, and so thesame temperature is predicted for all materials. It is assumedthat the stagnation of streams on the column contributes onlyto the kinetic pressure in Eq. 2 and not to the internal

energy of the column.

III. EXPERIMENTAL SETUP

The use of MAGPIE and COBRA for these experimentswas to allow as direct a comparison as possible of loads atdifferent rise times to the same maximum current. Arrayswere 16 mm in diameter and typically comprised 16 wires ofaluminum, tungsten, or copper. In addition the array heightswere comparable, being 23 mm for MAGPIE and 20 mm forCOBRA. The wire arrays were designed to be overmassed ineach case, and did not implode during the experiments. ForAl arrays 50 and 30 m wires were used on MAGPIE and

COBRA, respectively, and for W, 13 and 10 m. The use ofother wire sizes is indicated where appropriate. On both gen-erators the return current path is at large diameter comparedto the array, and is provided by four MAGPIE or five CO-BRA return rods, and this allows both the monitoring of theload current by Rogowski coil, and the mounting of Xpinches for radiography, as described below. The averageload currents were 1.08 MA in 110 ns on COBRA and 0.94MA in 250 ns on MAGPIE. Typical current pulses are givenin Fig. 2, along with the running integral of square of thecurrent as a function of time for both generators, which de-scribes the momentum delivered to the load for each currentdrive.

FIG. 1. Variation of the ion line density at the array axis with time forMAGPIE and COBRA. Horizontal line indicates critical ion line density forprecursor column formation, and vertical lines indicate precursor formationtimes for MAGPIE measured and COBRA predicted.

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The diagnostic arrangement on both generators also in-cluded similar diagnostics. Laser shadowography and inter-ferometry 532 nm, pulse length 0.5 ns on MAGPIE and 0.2ns on COBRA were used to examine the dynamic evolutionof arrays, along with gated XUV framing cameras, and opti-cal streak photography. Diamond photoconducting x-raydiodes61 PCDs were used to examine radiation output dur-ing column formation, and XUV spectroscopy allowed an

estimation of the column temperature. The XUV spectrom-eter used a 600 grooves/mm plane Au grating at a grazingincidence 4 to image spectra onto either a film packKodak 10101 for time-integrated measurements or a gatedXUV camera for time-resolved measurements. This setupgave a spectral range of 10240 . X-pinch radiography wasalso employed to measure the density of the precursor col-umn as a function of time. One or more return posts werereplaced by an X pinch which projects through the array andimages onto a film pack mounted inside the vacuum cham-ber. The radiation filter of 12.5 m Ti transmits in the rangeof 35 keV and images were recorded on Kodak M100 orDR-50 film. On both generators the radiography setup pro-

vided a full view of the array and was calibrated using a stepwedge of suitable thicknesses of the array material. Specificdetails are given in Sec. III. On MAGPIE, two images pershot are possible, while on COBRA a recent development62

allows up to five images per shot.

IV. RESULTS

The general formation dynamics of the precursor columnon COBRA were observed on imaging diagnostics for com-parison to predicted values and results on MAGPIE. A totalof six tungsten loads and nine aluminum loads were fired. Asequence of gated self-emission images 30 eV for W

loads, shown in Fig. 3, summarizes the observed processeson COBRA. Early in time, prior to column formation, abroad emission profile was observed with axial gated emis-sion imaging note that the small diameter circular emissionring is due to a hardware aperture machined into the cathode

wire mount. This is several millimeters in diameter for W,and 3 mm for Al, as demonstrated by plotting lineoutsacross the array for both materials at approximately 100 nsFig. 4. At this time the radiation output in the 100200 eVwindow is increasing and reaches a defined peak Fig. 5,and at the same time the precursor column is observed as astrongly emitting object on the optical streak images, shownin Fig. 5.

Correlation of the x-ray signal to the streak image showsthat column formation is approximately coincident with the

peak radiation output note that this is a nonimploding arrayand this peak is not a stagnation yield. This correlation pro-vides a clear indication of the formation time of the column,as described in Sec. II, and for comparison purposes the for-mation time is taken directly from the streak image in eachshot. Over a series of experiments, the onset of the formationprocesses is determined to occur at 1165 ns for Al arraysand 1467 ns for W arrays on COBRA.

The formation of the column as observed by axial emis-sion imaging allows the diameter of the emitting region to befollowed during the collapse process. This is shown for an Alload in Fig. 6. The collision of plasma can be seen betweenwire positions, and this again denotes the short mean free

path of Al streams. Corresponding features are not seen forW arrays due to the collisionless nature of the streams see,for example, Fig. 3 of Ref. 55.

The minimum diameters for Al and W columns immedi-ately after formation were averaged between laser imagingand axial emission images and are 1.550.3 and1.00.2 mm for Al and W, respectively. Late in time, laserimaging shows the column diameter increasing. This is alsoobserved on the streak images and an estimation of the ex-pansion rate can be made. For W this is 10 m /ns and forAl 40 m /ns. On MAGPIE similar measurements resultsin expansion rates of 2.5 and 10 m /ns for W and Al, re-spectively. It is interesting to note that the ratio of the rates

FIG. 2. Current pulses for MAGPIE and COBRA, along with running inte-gral of the square of the current pulse.

FIG. 3. Sequence of gated self-emission images for W loads in COBRAshowing formation dynamics of the precursor column.

FIG. 4. Lineouts across Al and W arrays at 100 and 104 ns, respectively,showing broad early time emission profiles.




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for Al and W is the same for both generators. The highervalues on COBRA are likely to be due to the greater massflux onto the column at this time since the current peaksshortly before this period providing the largest mass ablationrate. On MAGPIE the current is still below maximum de-spite the later column formation time and the mass flux iscorrespondingly lower, resulting in a lower postformationexpansion rate.

The formation dynamics on COBRA are directly compa-rable to those determined on MAGPIE generator in Ref. 55.The initial build-up followed by a peak in the soft x-rayoutput, and collapse to small radius are all easily identifiablein the above results. The timings of these events, however,

occur earlier in time on COBRA. The similarity of the twosystems is demonstrated by plotting the variation of diam-eters from gated XUV images for both aluminum and tung-sten on scales normalized to the minimum observed diam-eters and average time of formation of the precursor columnfor MAGPIE and COBRA data sets. This is shown in Fig. 7.The normalized plots show that indeed the systems evolve ina very similar fashion on the two generators. In addition,some interesting features are observed in the COBRA experi-ments. First, laser shadow imaging observed the formation ofthe precursor column at the anode prior to the cathode Fig.8, as was observed on the MAGPIE generator.55 The highquality of the streak images along with the observation of the

precursor column part way formed on the same shot gives a

value for the anode-to-cathode formation rate of106 m s1, again similar to MAGPIE experiments. It isstill not clear whether this is a result of a small linear varia-tion in the ablation rate with axial position, as discussed inRef. 55 or if other processes play a role. Note that the axialmodulations on the plasma flow from the wires on the laserimages in Fig. 8 is the universally ablation flare structure,which is observed in all exploding wire experiments inwhich magnetic field both local to the wire and global, re-sulting from the array as a whole, are dynamically signifi-cant. This structure is observed at all current levels,42,48,63,64

and has been investigated both analytically65 andcomputationally,66,67 and it was recently demonstrated that

3D magnetohydrodynamic MHD simulations can repro-duce this behavior.67 Quantitative experimental measure-ments of this structure from the present study are presentedbelow and discussed in Sec. VI.

The streak images also show complex structure aroundthe formation time of the precursor column Fig. 9. In ad-dition to features described above, a well defined emissionregion moving radially outward from the axis is observedimmediately following the formation. It is possible that thisstructure represents a shock, formed by the collapse of theprecursor column moving outward into the lower densityplasma. The approximate velocity is 104 m s1, which isslightly above the estimated local sound speed in the plasma

FIG. 5. Correlation of the peak in the radiation signature to the observationof the precursor column on the optical streak images for a W array onCOBRA.

FIG. 6. Variation of emission diameter during column formation for Al arrayon COBRA.




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streams assuming Te =10 eV, Z=8. If this is indeed ashock, which should be addressed specifically in future stud-ies, this system may have applications to systems such ascore-collapse supernovae.6870

The use of X-pinch radiography allowed recovery of themass density of the precursor column for a number of shotson both MAGPIE and COBRA. Calibration of the film ex-posure was achieved using a step wedge of various thick-nesses of the array material deposited on the Ti radiationfilter.71 For the W arrays thicknesses of 13.75, 27.5, 70.1,163, 316.3, 555, and 1079 nm were applied via radiofre-quency sputtering deposition. The lower usable limit of thecalibration is determined by the contrast of the recoveredimage, and typically for W the 13.75 nm step is not resolv-able, giving an areal density range of 5.3104 2.1102 kg m2. For the Al arrays, commercially availablefoils of 0.4, 0.8, 1.6, 3, 6, and 10 m were mounted manu-ally. All these steps are resolvable in the images obtained andgive an areal density range of 1.08103 2.7102 kg m2. These allowed conversion of the exposureto areal mass density. To calculate volumetric mass density,the precursor column is assumed to be a cylinder of uniform

density with the average column diameter taken as the ab-sorption path length in the direction of the diagnostic. Thediameter is taken as the average from radiography, XUVgated imaging, and laser images where available coincidentwith the radiograph time. Examples of radiographs from Wand Al arrays on COBRA are given in Fig. 10, along withareal density lineouts. These include, to the authors knowl-edge, the first quantitative radiographic measurements of analuminum precursor column in cylindrical wire arrays. Theplots in Fig. 11 compare the radiography data for Al and Warrays on both MAGPIE and COBRA to estimations of themass evolution of the precursor column estimated from therocket model of ablation. In general, data do not disagree if

the typical ablation velocity of 1.5105

m s1

is used, how-ever the errors on the experimental measurements are con-siderable. This is particularly true for Al results due to thelow contrast obtained using the present radiography detec-tion setup. To indicate the sensitivity of the comparison tothe value of the ablation velocity used, values of 1.0105

and 3.0105 m s1 are also presented. For tungsten arrays,a slightly lower value of the ablation velocity, may provide abetter fit to the data for both MAGPIE and COBRA. Foraluminum, either 1.5105 or 1.0 5105 m s1 representsthe data equally well. A larger data set with significantlyimproved errors would be needed to facilitate a more de-tailed analysis, and this will be pursued in future studies.

FIG. 7. Plot of diameter variation of precursor column during formation forleft Al and right W arrays on both MAGPIE and COBRA using axesnormalized to the time of formation and minimum diameters in each caseput Al/W labels on plots.

FIG. 8. Laser shadowograms of W arrays from left COBRA at 150 ns andright MAGPIE at 160 ns showing formation of the precursor column ini-tially at the anode in both cases.

FIG. 9. Streak image and magnification of a W load on COBRA showingplasma structure around precursor column formation time.




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In addition to measurements of the precursor columndensity, radiography was used to examine the axial densitycontrast across the flare structure close to the wire positionsfor W experiments ablation flares for Al experiments pro-vided too low a contrast on radiographs to perform similarmeasurements. An example radiograph is given in Fig. 12which shows a 2.5 mm section of a W wire along with alineout in calibrated areal density. From these data, the aver-age mass density contrast ratio, stream /gap, is 1.6. These

FIG. 10. Radiographs with areal density lineouts for upper W 150 ns andlower Al 130 ns arrays on COBRA.

FIG. 11. plots of the precursor column mass density as a function of timecompared to the rocket model.

FIG. 12. Radiograph and lineouts of W axial flares on COBRA 0.5 mmfrom wire position.




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values are in good agreement with recent results from 80 kAX pinches and 1 MA cylindrical wire arrays on MAGPIE,72

the 250 kA GenASIS machine at UCSD and 3D MHDmodeling67 which also demonstrate a low axial density con-trast across the ablation flare structure. The average wave-length of the flare structure in Fig. 12 is 30090 m for

this array, which is comparable to measurements on othergenerators.73

The precursor column temperature was determined byanalysis of the XUV spectra recovered from arrays on CO-BRA. The best results were obtained using a time-integratedsetup. Since overmassed loads were used, there were no im-plosion or stagnation phases, and hence no emission strongerthan that of the precursor formation. This is confirmed by thePCD signals shown in Fig. 5. The time-integrated XUV spec-tra therefore reported the maximum temperature of the pre-cursor column, and an example is given in Fig. 13. Datafrom MAGPIE experiments is given in Ref. 54, which wasobtained using a gated detector on the same spectrograph.

The image time is shortly after column formation when thecolumn is expected to be at its maximum temperature, and soprovides a good comparison to the COBRA spectra. A spec-tral lineout was taken from both the MAGPIE and COBRAspectra indicated in Fig. 13 and several lines identified. Thecomparison of the experimental line position to the NISTAtomic Spectra Database74 gave a series of ionized Al spe-cies assignments which are indicated on the spectra in Fig.

13.The MAGPIE precursor column spectrum shows line

emission assignable to Al IVVIII 50300 and previousanalysis54 estimated a temperature of 5060 eV. Note thatemission from the precursor column is not observed at wave-lengths below 50 in this spectrum. The COBRA precursorcolumn spectrum shows additional emission from Al XIXIIspecies 2550 . The column on COBRA is therefore morehighly ionized, and so at a greater temperature given a simi-lar density, than that on MAGPIE. The rapid falloff in emis-sion at wavelengths shorter that 25 suggests ionizationabove Al XII is very limited. Higher ionization transitions

may appear close to the zero order on the above spectrum, soin order to determine if this is the case, the spectrum fromthe mica spherical crystal spectrometer fielded on the sameshot can be examined. This shows no line emission in the510 1.22.5 keV range. The appearance of the Al XIand Al XII lines, but without emission at shorter wavelengthscan be used to infer a temperature range in the assumption oflocal thermal equilibrium using the density obtained from theradiography results above. For =1.2 kg m3 a temperaturein the range of 70165 eV is estimated.

The temperatures reported in this work are significantlylower than those reported on the ZEBRA facility 1 MA, 100

ns at the Nevada Terawatt Facility by Kantsyrev et al.75

andmore recently Coverdale et al.76 who inferred precursor col-umn temperatures of 400 eV for Cu array experiments.Temperatures were inferred from time-resolved crystal spec-troscopy measurements which included Cu and stainlesssteel L-shell emission at 700 eV. This difference is likelydue to the difference in array configurations between the ex-periments. In the present work, arrays using 16 wires on a 16mm diameter provide relatively good inductive shielding ofthe axis, and so the amount of current in the precursor at anytime is 2% of the drive current for Al or W on eithergenerator. This is inferred from the lack of MHD instabilitiesobserved by imaging diagnostics even at very late time.55 Inthe ZEBRA experiment, loads used lower wire numbers, andthis rather more open geometry is likely to results in amuch larger fraction of the drive current being carried at theaxis through the precursor column once it is formed. In thiscase, the high temperatures would be due to direct Ohmicheating of the precursor column. In addition the experimentsof Coverdale et al. used Cu wires with 4% Ni as a spectro-scopic tracer. The behavior of Ni in wire arrays is somewhatanomalous, and loads using Ni wires typically show a sig-nificant fraction of current convected to the axis.77 This mayalso be a factor in the precursor column stability and tem-peratures recorded in Ref. 76.

FIG. 13. Top XUV spectra from Al arrays on upper COBRA time inte-grated and lower MAGPIE time gated at precursor column formationRef. 54, with bottom spectral lineouts of each.




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V. SUMMARY AND DISCUSSION

The experimental data presented above can be comparedto the predictions made using the analytical model for theprecursor column formation parameters given in Sec. II, andthis is summarized in Table I. Note that the column tempera-tures for COBRA derived from pressure balance Eq. 2have been updated with the experimental values of the col-umn diameter determined from the experiments.

The aim of these studies was to gain insight into whetherthe rise time of the current drive specifically influences theablation physics. The radiography results, while showing areasonable agreement to the rocket model using the stan-dard ablation velocity of 1.5105 m s1, cannot be used toconstrain the likely ablation rates due to the relatively largeerrors associated with these measurements. However, to give

an estimate of the likely change in the effective ablationvelocity over the experiments carried out on the two genera-tors, the comparison of the timing of the precursor columnformation can be used, along with the analytical scaling de-rived from the rocket model.

The experimental formation time of the precursor col-umn on COBRA is 1165 ns for Al and 1467 ns for W,both of which are some tens of nanoseconds prior to forma-tion on MAPGIE as would be expected from the differencein current rise time. The column diameters are similar forboth materials over the two generators, and both show afinite expansion velocity after column formation. In bothcases the expansion rate is greater for Al than for W, with the

COBRA precursor showing greater values than forMAPGIE. The formation times predicted for COBRA arraysfor both Al and W values lie very close to those predicted,lying slightly outside the error bars arising from the experi-ment. The prediction for the column temperature, using themeasured column diameter in the pressure balance model, isalso in good agreement with the range inferred from spectro-scopic measurements.

The fact that the analytical model predictions for CO-BRA experiments are very close to the experimental valuessuggests that the assumptions used in the model are reason-ably accurate. These are that the ablation rate on both gen-erators is well described by the standard rocket model, with

Vabl=1.5105 m s1 and that the precursor column forma-

tion is triggered by the advent of a critical density ion line atthe axis. In fact, the predicted formation time is relatively

sensitive to the ablation velocity assumed Fig. 14, and wecan investigate what variation of this would be needed toproduce formation times inconsistent with the experiments.This gives an estimate of the possible variation in ablationvelocity between the MAGPIE and COBRA experiments.This discussion will again use the aluminum results sincecollisionless flow at the axis does not occur for this material.

For the MAGPIE experiments, the standard ablation ve-locity of 1.5105 m s1 was previously shown to matchwell to experiments, and demonstrated a precursor columnformation x-ray signature with a repeatability of5 ns. If wetake these experimental error bars of the formation time as anestimate of the variation of the ablation velocity we can sug-

gest that Vabl=1.5+ /0.15105 m s1.Given that the predictions made for the formation timing

on COBRA were not exact, we can suggest by how much the

TABLE I. Summary of precursor column characteristic on MAGPIE and COBRA along with analytical predictions for COBRA.

MAGPIE COBRAScaling modelfor COBRA

Al W Al W Al W

Formation timefrom x-ray peak ns 1555 1755 1165 1467 107 139 155a

Column diameter

at Formation mm 1.650.1 0.60.15 1.550.3 1.00.2

From

experiment

From

experimentColumn maximumtemperature eV 5060 ? 70165 ? 140175 140175

Postformation expansionrate mm/ns 10 2.5 40 10

Notcalculated

Notcalculated

MHD instabilities observedin precursor column? No

Yes 1%drive current No No

Notcalculated

Notcalculated

aW scaling model values: assuming collisional flow estimate including collisionless flow period.

FIG. 14. Variation in precursor column formation time with ablation veloc-ity assumed for COBRA current drive. Dotted line indicates Vabl=1.5105 ms1 giving formation time of 107 ns.




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ablation velocity would have to change in order to matchperfectly. This requires a formation time 9 ns later than pre-dicted, requiring a decrease in ablation velocity, and this canbe achieved using a value of 1.3105 m s1. Again the errorassociated with the formation x-ray signal was 5 ns foraluminum. For the faster current rise rate on COBRA, thisequates to a range of possible ablation velocities of1.30.1105 m s1. If we assume the ablation velocity

changes by a much greater factor than this, say by a factor of2, precursor column formation would be expected at 80 nsfor a higher Vabl, or 160 ns for a lower Vabl on COBRA. Thisis clearly not observed. From these arguments we can infer amaximum variation of the ablation velocity from one genera-tor to the other, by taking the extremes of the error barsaround the optimum values. The highest velocity will be theupper limit inferred from MAGPIE experiments, 1.65105 m s1, with the minimum being the lower limit forCOBRA experiments of being 1.2105 m s1. We cantherefore suggest that by reducing the current rise time orincreasing the rise rate by a factor of 2.5 from MAGPIEto COBRA, the effective ablation velocity is reduced by amaximum of 30%. The true value may be less than thisfigure, and indeed if the average values determined above areused the ablation velocity reduction is 15%.

Previous work has indirectly inferred that the mass ab-lation rate of wires in cylindrical arrays is a function of theinterwire gap or initial wire diameter,78,79 and results by Si-nars et al.80 represent the first direct experimental investiga-tion of the latter of these effects. Given that the aluminumarray results presented here used wires of 50, 30, and25 m, we should address this issue and assess whether thechange in diameter of the wires between the MAGPIE andCOBRA by a factor of 2 is likely to be a factor in this work.

As discussed above, the change in effective ablation velocitybetween the two generators is small, and from the resultspresented here do not vary by more than 30%. The inferenceis therefore that this change in wire diameter does not sig-nificantly affect wire ablation rates. This appears to contra-dict work in Ref 80, where the transmission recorded byradiography was compared to fits using the ablation rocketmodel, and this analysis suggested that change in initial di-ameter of W wires from 5.0 to 11.4 m increased the massablation rate i.e., reduced the ablation velocity by almost afactor of 2 for comparable arrays. Tungsten wires with diam-eters of 5.0, 7.4, and 11.5 m were used giving from 8 MAplots in Fig. 9 best fits to rocket models using Vabl=13, 11,

and 7 cm /s, an approximately linear dependence on initialwire size can be deduced, with larger wire having largermass ablation rate, and lower ablation velocity. Recent datafrom the COBRA generator also indicate a similarrelationship.81 Applying this scaling to larger wire sizeswould give unfeasibly high mass ablation rates for the wirediameters used in this study. It is important to note that the Zstudy examined W wires and we concentrate on Al here. Theuse of W results from 1 MA machines is complicated by theperiod of collisionless flow in these arrays, particularly sincewe rely on the formation time of the column in these discus-sions. If we simply apply a relative scaling to the presentresults, following Ref. 80, the factor of 1.7 change in wire

diameter here would induce a factor of about 1.5 change inthe ablation velocity and hence mass ablation rate givingvalues of Vabl=1.132.010

5 m s1, with MAGPIE thelower of these and COBRA the higher. This is considerablygreater than the limit of the variation inferred from thesestudies, and denotes a trend opposite to that discussed above.

There are several possible explanations for this discrep-ancy in data from the present study and that of Sinars et al.

The first is that Al arrays behave in a fundamentally differentfashion to W arrays, and display no observable variation inablation rate with initial wire size. This would seem to con-tradict much previous work, in which rocket model estimatesappear to be good fits to data for a range of materials andgenerator parameters, and is therefore unlikely to be the case.

A second possibility is the influence of the magneticfield topology for a given array configuration. The array ge-ometry in the MAGPIE and COBRA experiments was fixed,using 16 wires on a 16 mm diameter, giving nominal inter-wire gap to core ratios of 30 for W and 13 for Al as-suming 100 and 250 m core diameters, respectively. Themagnetic topology is therefore fixed and allows a direct com-parison to be made in this regard. However, the interwire gapto core ratio for the Z array examined by Sinars et al. was2, indicating that if magnetic field penetration between thewire locations plays a role in the 1 MA arrays, this is un-likely to be observed for Z arrays, and the two systems arenot directly comparable. A study of the effective ablationvelocity with wire number on MAGPIE by Lebedev et al.78

showed a significant decrease at smaller interwire gap, butrelative insensitivity at large interwire gap, and this may be akey factor in explaining the difference in the trend reportedhere.

A further scenario can be suggested by referring to dif-

ferences in the wire explosion behavior for different initialwire sizes as observed with radiography. The results in thisstudy used wire sizes of 25, 30, and 50 m for Al and 10and 13 m for W. The W wires are observed to behave in asimilar fashion to those in previous studies, in that a typicalcore corona is observed, i.e., a well defined core region100 m in diameter is observed on radiography arealdensity 104 kg m2 with a corona that is several ordersof magnitude less dense, and demonstrates the universalaxial flare structure. The Al array experiments show someinteresting differences with a change in the initial wire diam-eter. The 25 m wires appear to behave as have been ob-served previously and analogously to the W wires, demon-

strating core diameters of 250 m Fig. 15c. The 30and 50 m Al wires show distinctly different behavior.When viewed from behind Fig. 15b, the core appears tobe 650 m in diameter. When viewed from the side Fig.15a, the wires appear to show a core but with an expandedhigher density corona which is visible on radiography for aconsiderable radial distance 0.5 mm, with structure atthe outside edge of the wire. Both these dimensions are atleast a factor of 2 larger than observed for 25 m or smallerAl wires in arrays at 1 MA. Figure 15 also shows small scalestructure on the large wire cores when viewed from be-hind, similar to that reported for thin wires.44,45,67,82 Axialstructure in the coronal plasma flow is not clear on radio-




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graphs of Al arrays, but laser imaging both on COBRA andMAGPIE confirm the presence of the ablation flare structureon large wire core arrays at wavelengths of 0.5 mm con-sistent with previous work.48

Following such observations, it has been speculated thatthere is some critical diameter at which the wire explosionbehavior changes. Small wires may follow a scaling closeto that in Ref. 80, but large wires may follow a differenttrend, which includes the possibility that there is no variationof mass ablation with wire diameter. From various studies itwould seem that this critical diameter is 18 m for Wsince up to 11.4 m W in Ref. 80 was studied, this work

used up to 13 m W, and some conical wire array experi-ments used 18 m wires,83 all of which appeared to behavelike small wires, and indeed such a transition was observedin the range 1720 m from recent results on the COBRAgenerator.81 For Al, a change in behavior was observed be-tween 25 and 30 m. It should be noted here that the25 m wires were used in arrays with 28 wires, rather than16 wires for the 30 m wires, which may also influenceconclusions. In any event, it is clear that this change is sig-nificant at least for wire arrays with current levels of 1 MA,or 3365 kA/wire at rise rates for the array between 41012 and 11013 A /s. This is important in that futurelarger current devices will need to use a larger mass to main-

tain 100 ns implosion times, and one way to increase themass is to use larger diameter wires at fixed wire number. Inthis case, the changes in wire explosion behavior presentedhere will require further studies to assess the impact on suchmachines.

In addition to inferring a change in mass ablation ratewith initial wire size, Ref. 80 noted that in some cases theradial transmission profiles used to assess this cannot be fit

using a single velocity rocket model. If we wish to continueto use an analytical model, an alternative is to use more thanone ablation velocity to describe the radial density profile.Such an approach was used previously55 in an attempt toexplain the earlier formation of the precursor column in ar-rays on Z of the same parameters studies in Ref. 80; 300wire, 20 mm diameter W than predicted using the standardrocket model. This approach uses two ablation velocities.The higher of these, V1, is set by the observed formation timeof the precursor column by using the same scaling model inthis work. The average of the two velocities must equal theaverage ablation rate to that predicted by the standard rocketmodel since this fits well to implosion trajectories for these

arrays.5 This constrains the lower ablation velocity, V2, andthese quantities are related by Eq. 3,

f

V1+

1 f

V2=

1

V, 3

where f is the fraction of the wire length ablation at eachrate, which is assumed to be fixed at 0.5 in these estimates.For these arrays, V1 =3.510

5 m s1 and V2 =0.9105 m s1, ensuring that V=1.5105 m s1.

This two-velocity rocket model approach was not re-quired to explain experiments on MAGPIE, which leads to

some concern over the need to apply such a large perturba-tion on the model for Z experiments. However, measure-ments of the axial density contrast across the ablation flarestructure presented in this and other recent work72 may pro-vide further insight. If different ablation rates are occurringat different axial positions, as is clear from many experi-ments, the radial density profile must therefore also be dif-ferent at different axial positions. If the axial variation ofdensity is measured at a fixed radial location inside the wirearray, the density contrast essentially determines what thetwo ablation velocities must be in the simplest case. Itshould be noted that it is inherently assumed that any axialmotion of the plasma occurs very close to the wire core, as in

the standard rocket model, and any measurement location inthe flow is outside this region.In order to reproduce this axial density contrast using

two ablation velocities, or at least the maximum variation,these must vary only very little and again are constrained toaverage to the standard rocket model velocity. For MAGPIEand COBRA experiments, values ofV1 =1.810

5 m s1 andV2 =1.310

5 m s1 meet these requirements. It is interest-ing to note that these are the same values determined as thelimits for possible variation of the ablation velocities fromthe present set of experiments. For the Z case describedabove, the large difference in V1 and V2 leads to a large axialdensity variation, and calculations suggest that this should be

FIG. 15. Full array with radiographs along with magnified sections indi-cated by black box ofa side on large Al wire cores COBRA, 120ns, 110%rise time, b rear of same on MAGPIE 197 ns, 79% rise time, and ctypical small Al wire radiograph from MAGPIE 220ns, 88% rise time.




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approximately an order of magnitude at similar radial loca-tions to those measured in the lower current experiments.The axial density contrast that would be expected if a two-velocity ablation model is used to describe the flaring struc-ture can be calculated for the pairs of velocities obtained forthe MAGPIE and COBRA results the examples below usethe MAGPIE current drive and the predictions for Z. Theseare shown in Fig. 16. For the MAGPIE case the separation in

velocities is small, as dictated by the error bars from precur-sor column formation timing, and this gives an axial densitycontrast between 0.8 and 2. Close to the wire position, thisvalue is 2, which is in good agreement with experimentalmeasurement ofthis density variation measured in this workand elsewhere.72 For the Z case, the large spread in velocitiescreates a large density contrast. If measurements of the flarecontrast were possible on Z, values greater than an order ofmagnitude would be expected close to the wire positionright plot in Fig. 16. It is interesting to note that in bothcases the plasma density is expected to become more uni-form in the axial direction as the plasma moves toward theaxis at r=0. This perhaps suggests that the contrast ratio of

the flare structure is determined by the current level not therise rate. In this case the change of approximately an order ofmagnitude from 1 to 20 MA can be used to infer the changeexpected on a 60 MA ignition scale device. The factor of 23increase in drive current would change the axial density con-trast by only a small factor, perhaps by 50%, suggesting thatin this sense the ablation dynamics at 60 MA may be similarto those observed on Z. The use of the refurbished Z machineat 28 MA to investigate mass ablation rates in arrays usingboth long 400 ns and short 100 ns pulse mode shouldprovide a good basis for scaling to larger power devices.

VI. CONCLUSIONS

The experimental work presented demonstrates that theformation of the precursor column in cylindrical wire arrayson the COBRA generator 1 MA, 100 ns forms in a quali-tatively similar way to that of comparable arrays on MAG-PIE 1 MA, 250 ns. X-ray emission measurements alongwith radial streak images report the formation time of thecolumn for both Al and W arrays and laser shadowographyand axial gated XUV self-emission image sequences are di-rectly comparable to previous MAGPIE experiments. In ad-dition, XUV spectroscopy suggests that the precursor columnelectron temperature on COBRA is 70165 eV, which isgreater than the column temperature of 5060 eV for MAG-

PIE experiments, as a result of the higher kinetic pressure atthe column at formation due to the faster rise time. The timeof formation and column temperature show very good agree-ment with an analytical scaling model derived from therocket ablation model.

The ability to closely predict the behavior of the precur-sor column on the 100 ns rise-time COBRA generator fromresults on the 250 ns rise time MAGPIE generator using a

fixed ablation velocity is an indication that the scaled abla-tion rate is not strongly affected by the current rise time. Thecolumn formation time in particular, which relies on the ad-vent of a defined ion density at the array axis, appears toscale in a predictable way with the change in rise time ex-amined in this work. In addition, quantitative measurementsof the precursor column density for Al and W on both MAG-PIE and COBRA are close to estimates from the Rocketablation model using the same ablation velocity, 1.5105 m s1, in both cases. The good correlation of pre-dicted and measured precursor column temperatures also in-dicates that the use of a pressure balance model can be suc-cessfully applied for experiments on both generators.

The error bars on experimental measurements of the col-umn formation time allow an estimation of the extent towhich the ablation rate may change and still agree with mea-surements presented here. These calculations suggest that thevariation by a factor 2.5 in the current rise time could changethe effective ablation velocity by a maximum of30%. Thestudy also highlights other factors may play a role, primarilyin the qualitative and quantitative behavior of larger wiresizes in wire arrays. The work presented here demonstratesthe need to characterize more closely the variation of themass ablation rate with initial wire size in view of the needto use larger wire diameters on larger current drive machines,such as those currently under consideration as an ICF igni-tion driver.

ACKNOWLEDGMENTS

This work was supported by the DOE Junior FacultyUnder Grant No. DE-FG-05ER4842, and a grant from theCenter of Excellence for Pulsed Power Driven High EnergyDensity Physics, Cornell University. Work at Imperial Col-lege London was sponsored by the NNSA under DOE Co-operative Agreement No. DE-F03-02NA00057.

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