Effect of the plasma production rate on the implosion dynamics of cylindrical wire/fiber arrays with a profiled linear mass

ISSN 1063�780X, Plasma Physics Reports, 2013, Vol. 39, No. 10, pp. 809–821. © Pleiades Publishing, Ltd., 2013.Original Russian Text © V.V. Aleksandrov, K.N. Mitrofanov, A.N. Gritsuk, I.N. Frolov, E.V. Grabovski, Ya.N. Laukhin, 2013, published in Fizika Plazmy, 2013, Vol. 39, No. 10,pp. 905–918.

809

1. INTRODUCTION

The implosion of wire arrays under the action ofhigh�power current pulses in the Z�pinch regimeallows one to obtain dense high�temperature plasmawith multicharged ions and generate intense thermalradiation. Research in this field is necessary for solvingthe problems of high�density energy physics and iner�tial confinement fusion. At present, experiments onthe implosion of the quasi�spherical wire arrays aspromising sources of soft X�ray (SXR) emission arebeing carried out worldwide [1–4]. It was theoreticallyshown in [1] that, unlike the two�dimensional implo�sion of cylindrical arrays, the three�dimensionalimplosion of quasi�spherical array requires spatialprofiling of their mass. It was also shown that, underthese conditions (e.g., in the course of implosion ofdouble nested spherical arrays in the scheme ofdynamic hohlraum), the intensity of thermal radiationfilling the hohlraum cavity can increase by more thantwice.

Thus, in order to increase the efficiency of trans�formation of the electric energy of a super�high�powercurrent generator into thermal radiation in the courseof spherical gas�dynamic implosion of a wire array, it isnecessary to spatially profile the array linear mass andto take into account the effect of the opacity of plasmaconsisting of a mixture of ions of different materials onthe parameters of the generated X�ray pulse.

In numerical simulations of the three�dimensionalimplosion of quasi�spherical arrays, one of the mostimportant parameters is the plasma production rate,

which, as was shown in [5], determines the compres�sion dynamics of plasma flows and the spatial structureof the pinch formed on the array axis.

It was shown in [6, 7] that the magnetic field of thedischarge current is frozen in plasma and penetratesinto the wire array already in the stage of plasma pro�duction. The penetration of plasma with the frozen�inmagnetic field into the wire array is determined by theplasma production rate , which in turn depends onthe material of wires or fibers [8–10].

The dynamics of the pinch compression, the dissi�pation of the kinetic and magnetic energy, and thegeneration of the X�ray pulse during the implosion ofa cylindrical wire array depend on the mass and mate�rial of wires and the spatial distribution of the mag�netic field frozen in the plasma flows.

In this work, in order to obtain information on theplasma production rate, required for numerical simu�lations of the implosion of quasi�spherical arrays, wecarried out experiments on the implosion of cylindri�cal wire arrays with a spatial profiled mass ofwires/fibers made of different materials.

The objectives of the present study were as follows:

(i) to determine the plasma production rates formaterials deposited on wires/fibers of cylindricalarrays;

(ii) to examine how the spatial profiling of thewire/fiber linear mass affects the penetration ofplasma with the frozen�in magnetic field into a cylin�drical array;

( )m t�

PLASMA DYNAMICS

Effect of the Plasma Production Rate on the Implosion Dynamicsof Cylindrical Wire/Fiber Arrays with a Profiled Linear Mass

V. V. Aleksandrov, K. N. Mitrofanov, A. N. Gritsuk, I. N. Frolov, E. V. Grabovski, and Ya. N. Laukhin

Troitsk Institute for Innovation and Fusion Research, Troitsk, Moscow, 142190 Russiae�mail: [email protected]

Received February 28, 2013; in final form, April 12, 2013

Abstract—Results are presented from experimental studies on the implosion of arrays made of wires and met�alized fibers under the action of current pulses with an amplitude of up to 3.5 MA at the Angara�5�1 facility.The effect of the parameters of an additional linear mass of bismuth and gold deposited on the wires/fibers isinvestigated. It is examined how the material of the wires/fibers and the metal coating deposited on themaffect the penetration of the plasma with the frozen�in magnetic field into a cylindrical array. Information onthe plasma production rate for different metals is obtained by analyzing optical streak images of implodingarrays. The plasma production rate for cylindrical arrays made of the kapron fibers coated with bismuthis determined. For the initial array radius of R0 = 1 cm and discharge current of I = 1 MA, the plasma pro�

duction rate is found to be ≈ 0.095 ± 0.015 μg/(cm2 ns).

DOI: 10.1134/S1063780X13100012

Bim�

Bim�

810

PLASMA PHYSICS REPORTS Vol. 39 No. 10 2013

ALEKSANDROV et al.

(iii) to study the effect of the plasma productionrate on the implosion dynamics of cylindrical arrays.

2. EXPERIMENTAL SETUP

The experiments with quasi�spherical arraysrequire the profiling of the mass along the wire/fiber[3]. For example, in order to create an inhomogeneousdistribution of the mass m(θ) over the poloidal angle(along the wire), it is possible to either smoothly varythe wire diameter by etching or deposit a conductingmaterial with the required mass profile on the wire sur�face.

In this work, we used the second method—deposi�tion of various metals (such as aluminum, bismuth,and gold) on the wire surface. The deposition tech�nique was described in detail in [3]. Along with wires,we also used kapron fibers on which the above metalswere deposited. Different types of arrays made of wiresand metalized fibers with profiled masses are pre�sented in the table. The quality of the deposited coat�ing, its thickness, and the size of the deposition regionalong the wire/fiber was tested using a REMMA�202electron microscope with a LiF�crystal spectrograph�analyzer.

The azimuthal magnetic field in the wire arrayplasma was measured by absolutely calibrated mag�netic probes (see [6, 11, 12] for details). The probeswere located at different radii inside the wire array(from 0.5R0 to 0.9R0, where R0 is the initial arrayradius) and different distances from the anode elec�trode (Δh = 2–8.5 mm). The magnetic probes mea�sured the time derivative of the azimuthal magneticfield at given radii. The current Ip flowing inside agiven radius was calculated by numerically integratingthe signal from the probe located at this radius, assum�ing that the distribution of the magnetic field washomogeneous along the azimuth. The signal from theprobe was integrated until breakdown occurred on it.

The measurement accuracy of the magnetic field inplasma with allowance for the calibration error (~5%)was better than 20%. The probe positions with respectto the coated wire/fiber regions were checked usingphotographs of the wire array placed in the concentra�tor of the facility.

Figure 1 shows photographs of wire arrays in theelectrode gap of the facility. In the wire array shown inFig. 1a, bismuth was deposited over the entire lengthof the wires, whereas in the wire array shown inFig. 1b, the mass was profiled in the central part of thewire. Figure 1 also shows the profile of the integralwire brightness L (in arbitrary units) along the wires.The integral brightness technique is based on mea�surements of the difference between the intensities oflight reflected from the wire/fiber surface with andwithout the deposited coating. From this difference itpossible to determine the length of the coated regionand use it when positioning the probes with respect tothis region. When the Bi coating was deposited overthe entire wire/fiber length (see Fig. 1a), the bright�ness inhomogeneity along the wire ( ≈ 1.2)did not exceed 20%. When the Bi coating was depos�ited only in the central part of the wires/fibers, thebrightness ratio reached a value of ≈ 4.5. Theregion of length Δh coated with bismuth spanned forabout 4 mm upward and downward from the middle ofthe wire/fiber. In this region, the integral brightnessreached its maximum value and was nearly constant.There was a transition region between the wire seg�ments with and without the deposited coating. Thelength of the transition region was about 1–1.5 mm. Inthis region, the integral brightness gradually decreasesfrom the maximum to the minimum value (seeFig. 1b).

In our experiments, we also used tungsten wirescoated with gold. Such wire arrays consisted of 30 10�

max min/I I

max min/I I

Characteristics of cylindrical wire/fiber arrays

Shot no. Wire (fiber) material

Num

ber

of w

ires

(fi

bers

)

Wir

es (

fibe

r)

diam

eter

, µm

Arr

ay r

adiu

s R

0, m

m

Arr

ay h

eigh

t h,

mm

Lin

ear

mas

s w

itho

ut c

oati

ng,

µg/

cm

Coating parameters (material, coated region, thickness Δ, linear mass)

4921* W 40 6 10 16.5 220 Without coating

4876 W 40 6 10 15 220 Bi, over 0.5h ± 4 mm, Δ ~ 0.68 μm (56 μg/cm)

4872 W 40 6 10 15 220 Bi, over 0.5h ± 4 mm, Δ ~ 0.73 μm (60 μg/cm)

4685 kapron 40 25 10 15 220 Bi, over 0.5h ± 4 mm, Δ ~ 0.9 μm (264 μg/cm)

4595, 4596 96%W + 4%Au 30 10 10 15 360 Au, over h = 15 mm, Δ ~ 0.082 μm (15 μg/cm)

4687 kapron 40 25 10 15 220 Bi, over h = 15 mm, Δ ~ 1.0 μm (310 μg/cm)

4690 kapron 16 25 10 15 88 Bi, over h = 15 mm, Δ ~ 1.2 μm (154 μg/cm)

* Experiment on testing the method for measuring magnetic fields at different positions of the probe with respect to the anode.


EFFECT OF THE PLASMA PRODUCTION RATE 811

μm�diameter tungsten wires coated with a 0.082�μm�thick gold coating.

The total current I was measured using an eight�loop current detector and a magnetic probe locatedoutside the wire array at the radius of 20 mm. Below,the locations of the magnetic probes inside the wirearray will be specially indicated in the text for eachparticular case.

The dynamics of plasma flows from the wireregions coated with bismuth in the final stage ofimplosion was studied using an SFER�2 optical streakcamera, a four�frame MCP X�ray camera, and time�integrated pinhole camera.

The SXR power PSXR in the photon energy rangeabove 100 eV was measured using X�ray diodes behinddifferent filters.

3. EXPERIMENTAL RESULTS AND DISCUSSION

Below, we present results of experimental studies ofthe penetration of the current�carrying plasma into acylindrical array from the wire segments with andwithout the deposited coating. Special attention waspaid to the time at which the probe signal appearedand the magnitude of the recorded current (the mag�netic field).

3.1. Measurements of the Magnetic Field in Tungsten Wire Arrays without a Metal Coating

Since the magnetic probes located at the sameradius (about 0.5R0) could be placed at different dis�tances from the anode (from 0.5 to 8 mm), it was nec�

0

0.4

0.8

1.2

1.6

Y,

сm

Anode

Cathode0 0.5 1.0 1.5 2.0 0 20 40 60 80 100

LX, сm

Lmax/Lmin ≈ 1.2

Probe no. 1 Probe no. 2

0

0.4

0.8

1.2

1.6

Y,

сm

Anode

Cathode0 0.5 1.0 1.5 2.0 0 20 40 60 80 100

LX, сm

Imax/Imin ≈ 4.5

Bi deposition region


(a)

(b)

+4

mm

–4

mm

Region without a Bi coating

Imin Imax

Bi deposition region

Fig. 1. Photographs of 20�mm�diameter 15�mm�high wire arrays with a profiled mass along the wires: (a) ~1�μm�thick bismuthcoating deposited over the entire wire length (shot no. 4687) and (b) ~0.73�μm�thick bismuth coating deposited in the central partof the wires (shot no. 4872). The dashed rectangles show the regions in which the integral brightness was determined. The depen�dences of the integral wire brightness L (in half�tone shades of 0–255) along the wires are shown in the left parts of the panels.

812


ALEKSANDROV et al.

essary to check whether the probe distance from theanode affected the current measured by the probe.

To this end, we performed an experiment (shotno. 4921) with a tungsten wire array in which twoprobes were located at the same radius of 0.48R0.Probe no. 1 was installed at a distance of ~2 mm fromthe anode, while probe no. 2, at a distance of ~8 mm(see Fig. 2a). The wire array was made of 40 tungsten6 μm wires located at the radius of 10 mm. The arrayheight was 16.5 mm.

Figure 2b presents results of magnetic field mea�surements in such an array. It is seen that, although theprobes were located at different distances from theanode, they recorded practically the same (to withinmeasurement errors) current. The probe signalsappeared about 45 ns after the beginning of the currentpulse (see Fig. 2c). The precursor current at the timecorresponding to the front of the SXR pulse in thisshot was ~200 kA. At this time, the probes detected asharp increase in the current, which is associated withthe final compression of plasma at the wire array axis.The amplitude of the SXR power in this shot reacheda value of 3.5 TW.

Thus, it may be concluded that, when there is noprofiling of the wire mass in the array, the implosion ofplasma with the frozen�in magnetic field occursalmost simultaneously over the height of the wire array.

In the next section, we present results of experi�mental studies of the implosion of wire arrays with themass profiled along the wires (see Fig. 1b).

3.2. Measurements of the Magnetic Field in Arrays Made of Tungsten Wires or Kapron Fibers Coated

with a High�Z Material (Bismuth) in the Central Region of the Array. Comparison of the Rates of Plasma

Production from Kapron and Bismuth

Let us first consider results of the experiment witha tungsten wire array the parameters of which are givenin the table (shot no. 4876). The Bi coating with athickness of 0.68 μm was deposited in the central partof the wires, the total linear mass of bismuth being56 μg/cm.

Probe no. 1 (see Fig. 3) was placed at a distance of~1 mm from the anode and was used to study thedynamics of plasma generated from the region of thetungsten wires without a Bi coating. Probe no. 2 was

h


Cathode

Anode

Tungsten wire

I

I

~45 ns

200 kA

Ip(Probe no. 1)

Ip(Probe no. 2)

0.5

0.4

0.3

0.2

0.1

0

I, Ip, МА

750 770 790 810 t, ns

3

2

1

0750 800 850 900 t, ns

Ip

(Probe no. 1)(Probe no. 2)

I, Ip, МА P, TW

PSXR

6

5

4

3

2

1

0

Fig. 2. Experiment with a 20�mm�diameter 16.5�mm�high wire array made of 40 6�μm�diameter tungsten wires with a total linearmass of 220 μg/cm (without a metal coating) (shot no. 4921). The upper panel shows the arrangement of probe nos. 1 and 2,installed at the radius of r = 4.8 mm inside the wire array at distances of 2 and 8 mm from the anode, respectively. The lower panelsshow the time dependences of the current Ip measured by probe nos. 1 and 2, the total current I, and the SXR power PSXR(>100 eV).



placed deeper in the electrode gap (at a distance of 6–7 mm from the anode) and was used to study thedynamics of plasma generated from the wire regioncoated with bismuth. Both probes were installed atclose radii (r = 5–5.2 mm) inside the array.

The results of probe measurements of the magneticfields in these experiments are presented in Fig. 3. Thesignal from probe no. 1 appears 8 ns later than thatfrom probe no. 2 (see the time profiles of Ip). Thismeans that the plasma produced from the wire regionwithout a Bi coating propagates under the action of theAmpère force more slowly than the plasma producedfrom the region coated with bismuth. It is found that,at a given instant of time, the first portions of plasmafrom the region coated with bismuth carry a larger cur�rent than the first portions of plasma from the regionwithout a Bi coating (cf. the time profiles of Ip

recorded by probe nos. 2 and 1). From the regioncoated with bismuth in the middle of the wire array, acurrent of up to 0.8–1 MA penetrates to the probeposition at 100 ns from the beginning of the discharge,whereas from the wire region without a Bi coating,

only 200–300 kA penetrate to the probe position overthe same time. The current measured by the probeinstalled near the wire region without a Bi coating cor�responds to the precursor current recorded during theimplosion of single tungsten wire arrays without acoating (see, e.g., Fig. 2), which agrees well withresults of [7, 10]. Thus, the azimuthal magnetic fluxpenetrating in the course of implosion from the wireregions coated with bismuth differs substantially fromthat penetrating from regions without a Bi coating.The larger magnetic flux penetrating to the probe posi�tion in the former case is related to the lower rate ofplasma production from the Bi coating as compared tothat from tungsten wires without a Bi coating. Indeed,if a small portion of plasma proportional to is pro�duced under the action of the discharge current ateach instant of time, then this portion is acceleratedunder the action of the Ampère force and penetratesinto the array with a radial velocity Vr determined bythe expression

Vr ∝ (I/R0)2, (1)

m�

m�

h


Cathode

Anode

Tungsten wire +

II

~38 ns Ip(Probe no. 1)

Ip(Probe no. 2)0.5

0.4

0.3

0.2

0.1

0

I, Ip, МА

760 780 800 820 t, ns

3

2

1

0750 800 850 900 t, ns

I, Ip, МА P, TW

PSXR

1.5

0

Tungsten wire

Bi coating(Δ ≈ 0.68 μm)

840

~46 ns

Ip(Probe no. 2)

Ip

(Probe no. 1)

1.0

0.5

Fig. 3. Experiment with a 20�mm�diameter 15�mm�high wire array made of 40 6�μm�diameter tungsten wires with a total linearmass of 220 μg/cm (shot no. 4876). The Bi coating with a thickness of Δ ~ 0.68 μm (56 μg/cm) is deposited in the region of 0.5h ±

4 mm. The upper panel shows the arrangement of probe nos. 1 and 2 inside the wire array. Probe no. 1 is installed at the radius ofr = 5 mm at a distance of 1 mm from the anode (in front of the wire region without a Bi coating), and probe no. 2 is installed atthe radius of r = 5.2 mm at a distance of 7 mm from the anode (in front of the wire region coated with bismuth). The lower panelsshow the time dependences of the current Ip measured by probe nos. 1 and 2, the total current I, and the SXR power PSXR(>100 eV).

814


ALEKSANDROV et al.

where is the rate of plasma production from the wiresurface (in units of μg/(cm2 ns)). The rate of theplasma production from the Bi coating is lower thanthat from tungsten wires [7], i.e., < = (0.125–0.18) μg/(cm2 ns) under the same conditions (I =1 MA and R0 = 1 cm).

In the next experiment (shot no. 4685), the loadwas a fiber array made of 25�μm�diameter metalizedkapron fibers in the central part of which a 0.9�μm�thick Bi coating (with a total linear mass of264 μg/cm) was deposited, as was the case with tung�sten arrays. It should be noted that the total linearmasses of 25�μm�diameter kapron fibers and 6�μm�diameter tungsten wires were 5.5 μg/cm. The numberof fibers in the array (40 fibers placed at the radius of10 mm) was the same as the number of wires in thetungsten array. The array height was 15 mm.

The probes were installed in the same positions (seeFig. 4) as in the above experiment with tungsten arrays.Probe no. 1 was installed in front of the fiber regionwithout a Bi coating. This probe detected the penetra�

m�

Bim� Wm�

tion of the current�carrying plasma to the radius of r =5 mm about 6 ns earlier than probe no. 2 installed atthe same radius in front of the region coated with bis�muth. At 90 ns from the beginning of the discharge,the current carried by the plasma produced from thematerial of kapron fibers (~0.6 MA) was larger thanthe current carried by the plasma produced from theBi coating (~0.4 MA). It should be noted that thedynamics of the penetration of the current�carryingplasma produced from kapron fibers was similar tothat of the current�carrying plasma of single kapronfiber arrays studied in [7]. The optical streak cameradetected a nonsimultaneous start of compression ofthe Bi plasma and the plasma produced from kapronfibers in the region coated with bismuth (see Fig. 5a).Such a nonsimultaneous compression of plasmas pro�duced from the Bi coating and kapron fibers was alsoobserved during the implosion of arrays in which bis�muth was deposited over the entire fiber length (see,e.g., Fig. 8b).

The plasma produced from tungsten wires with adeposited Bi coating is more efficiently compressed

h


Cathode

Anode

Kapron fiber

II

~44 ns

Ip(Probe no. 1)

Ip(Probe no. 2)

0.7

0.4

0.3

0.2

0.1

0

I, Ip, МА

760 780 800 840 t, ns

3

2

1

0750 800 850 900 t, ns

Ip(Probe no. 1)

I, Ip, МА P, TW

PSXR

0.8

0

Probe no. 3

Kapron fiber +Bi coating

(Δ ≈ 0.9 μm)

(Probe no. 3)

0.4

Ip(Probe no. 2)

~50 ns

820

0.6

0.5

Fig. 4. Experiment with a 20�mm�diameter 15�mm�high fiber array made of 40 25�μm�diameter kapron fibers with a total linearmass of 220 μg/cm (shot no. 4685). The Bi coating with a thickness of Δ ~ 0.9 μm (264 μg/cm) is deposited in the region of 0.5h ±

4 mm. The upper panel shows the arrangement of probe nos. 1–3 inside the wire array. Probe nos. 1 and 2 are installed at theradius of r = 5 mm at distances of 2–3 mm from the anode (in front of the fiber region without a Bi coating) and 7 mm from theanode (in front of the fiber region coated with bismuth), respectively, and probe no. 3 is installed at the radius of 20 mm and mea�sures the total current. The lower panels show the time dependences of the current Ip measured by probe nos. 1 and 2, the totalcurrent I, and the SXR power PSXR (>100 eV).



toward the array axis than the plasma produced fromkapron fibers with the same Bi coating (see streakimages in Figs. 5a, 5b). No separate compression ofthe Bi and W plasmas is observed in the streak imagepresented in Fig. 5b, whereas in Fig. 5a, it is clearlyseen that the compressions of the Bi and kapron plas�mas are separated in time. The time of the start of thecompression of Bi and W plasmas in Fig. 5b and theinstant of the final plasma compression at the arrayaxis indicate that the entire mass of Bi and W isinvolved in the compression process.

Figure 5c shows X�ray frame images illustrating thecompression of the plasma of the fiber array in whichthe Bi coating was deposited in the central part of thefibers. These images were synchronized with the SXRpulse (>100 eV). It was found that the plasma sur�rounding the cores of kapron fibers in the region with�out a Bi coating radiates more weakly in the SXR rangethan the plasma in the region with the deposited Bicoating. The SXR power (>100 eV) in this shot was~0.4 TW. The relatively low SXR yield is related to thefact that the linear mass of the Bi coating (264 μg/cm)was not matched to the discharge current.

Comparison of tungsten wire arrays and kapronfiber arrays showed that, in the case of a tungsten wirearray with a Bi coating in the central part of the wires,the current precursor from the region coated with bis�muth penetrates earlier into the array. In contrast, inthe case of cylindrical fiber arrays with the same Bicoating, the penetration of the current precursor intothe array is observed earlier from the region without aBi coating. Most probably, this is related to the differ�ence in the rates of plasma production from kapronfibers, tungsten wires, and the deposited material (inour case, bismuth). According to the aforesaid andexpression (1), the rate of plasma production from theregion coated with bismuth is higher than the rate ofplasma production from kapron fibers [8], i.e., >

≈ (0.04–0.07) μg/(cm2 ns) under the same con�ditions (I = 1 MA and R0 = 1 cm).

Below, we present results of experiments on theimplosion of wire and fiber arrays with a uniform dep�osition of various high�Z materials over the entirewire/fiber length.

Bim�

kapronm�

1.00.80.60.40.2

0

750 800 850 900 t, ns

r, с

m

1.0

r, с

m

0.5

0

–0.5

–1.0

(a)

(c)

(b)

750 800 850 900 t, ns

0.4

0.2

0

PS

XR

, T

W

840 880 920 960 t, ns

W + Bi plasma

Array axis

Fiber

Array axis

plasma~35–40 nsBi plasma

Anode

Cathode Kapron Bi coating Kapron Bi coating

Fig. 5. (a) Optical streak image of the radial compression of the plasma produced from the region of kapron fibers with the Bicoating (the streak camera slit is located 10 mm above the cathode) (shot no. 4685), (b) optical streak image of the radial com�pression of the plasma produced from tungsten wires with the Bi coating (the streak camera slit is located 8.2 mm above the cath�ode) (shot no. 4872), and (c) frame X�ray images (>20 eV) of plasma synchronized with the SXR pulse (>100 eV) (shot no. 4685).The frame exposure is ~3 ns, and the time interval between frames is 20 ns.

816


ALEKSANDROV et al.

3.3. Measurements of the Magnetic Field in Arrays Made of Tungsten Wires or Kapron Fibers Coated

with a High�Z Material (Gold or Bismuth) over the Entire Array Length

We performed experiments with arrays consistingof wires (or plastic fibers) coated with bismuth or goldover their entire length. These experiments were aimedat studying the effect of the wire/fiber coating on theplasma dynamics in the stage of plasma production.The average velocity of plasma compression insidearrays with an additional deposited coating was esti�mated by the time�of�flight method.

In shot no. 4595, a wire array consisting of 3010�μm�diameter tungsten wires uniformly covered bya ~82�nm�thick gold coating with a total linear massof 15 μg/cm was used as a load. The other parametersof the wire array are given in the table. The magneticprobes were located at different radii: probe no. 1 atthe radius of 5 mm and probe no. 2 at the radius of9 mm. Both probes were installed at a distance of 3–4 mm from the anode (see Fig. 6). The results of probemeasurements are presented in Fig. 6.

A specific feature of these experiments was a rela�tively long (55 ns) time delay between the start of thecurrent and the penetration of the first portions of thecurrent�carrying plasma (the current precursor) to theradius of 5 mm as compared to that in the case of tung�sten wire arrays (~40 ns) [7, 9]. For arrays made oftungsten wires coated with gold, this time delay was onthe average 15–17 ns longer than for arrays made ofuncoated tungsten wires. Thus, the penetration of thefirst portions of plasma (the current precursor) fromtungsten wires coated with gold was mainly deter�mined by this coating. The 55�ns time delay of the cur�rent penetration for tungsten wires coated with cold iscomparable with the time delay measured in [9] foraluminum and copper arrays. In [9], the penetrationtime of the first portions of plasma (the current pre�cursor) to one�half of the array radius was determinedas a function of the sublimation heat of the wire mate�rial. Since the sublimation heats of gold(343.6 kJ/mol), aluminum (303.8 kJ/mol), and cop�per (315.0 kJ/mol) are close to one another, the pene�tration times of the current precursor into the arrays

h


Cathode

Anode

I

~44 nsIp

(Probe no. 1)

Ip(Probe no. 2)

2.0

0

I, Ip, МА

740 760 780 820 t, ns

3

2

1

0700 800 850 900 t, ns

Ip(Probe no. 1)

I, Ip, МА P, TW

PSXR

4.5

0

Probe no. 3

Tungsten wire +Au coating

(Δ ≈ 82 nm)

(Probe no. 3)

Ip(Probe no. 2)

~55 ns

800

I(Probe no. 3)

1.6

1.2

0.8

0.4

750

3.0

1.5

~200 kA

Fig. 6. Experiment with a 20�mm�diameter 15�mm�high wire array made of 30 10�μm�diameter tungsten wires with a total linearmass (W + 5% Au) of 375 μg/cm (shot no. 4595). The Au coating with a thickness of Δ ~ 82 nm (~15 μg/cm) is deposited overthe entire wire length (h = 15 mm). The upper panel shows the arrangement of probe nos. 1–3 inside the wire array. Probe nos. 1and 2 are installed at a distance of 3–4 mm from the anode at the radii of r = 5 and 9 mm, respectively, and probe no. 3 is installedat the radius of 20 mm and measures the total current. The lower panels show the time dependences of the current Ip measuredby probe nos. 1 and 2, the total current I, and the SXR power PSXR (>100 eV).



are also comparable in spite of the large difference inthe atomic masses.

From the difference between the times of the cur�rent penetration to the radii of 9 and 5 mm (see thetime profiles of Ip in Fig. 6), the average velocity ofplasma propagation toward the axis was found to be≈0.9 × 107 cm/s. At 100 ns from the beginning of thedischarge, the precursor current was ~300 kA. Up tothe beginning of the SXR pulse, about 80–90% of thedischarge current penetrates to the radius of 9 mm.Figure 7 shows a time�integrated X�ray image ofplasma obtained using the pinhole camera in shotno. 4596. One can see a compact highly radiatingpinch with a diameter of ~0.5 mm on the array axis.The SXR power (>100 eV) in these shots was up to4.5 TW.

Figures 8 and 9 present results obtained in shotnos. 4690 and 4687 with arrays made of kapron fiberscoated with bismuth of different thicknesses, ~1.2 and1.0 μm, with a total linear mass of 154 and 310 μg/cm,respectively. The number of fibers in the array was 16and 40, respectively. All fibers in the array were coatedwith bismuth over their entire length (see Fig. 1a). Thelocation of the probes was the same as in the experi�ments with tungsten wire arrays coated with gold: theprobes were placed at the radii of 0.5R0 and 0.9R0

inside the fiber array.Since the sublimation heat of bismuth

(188 kJ/mol) differs insignificantly from that of gold(343.6 kJ/mol) or aluminum (303.8 kJ/mol), one canexpect similar values of the time delays of the penetra�tion of the current precursor to the probe locations.Regardless of the number (or mass) of fibers in thearray, the average delay time of the penetration of thefirst portions of the current�carrying plasma mainlyconsisting of the deposited bismuth to one�half of thearray radius was about 50–55 ns. This agrees well withthe data of [9] on the penetration times of plasma withthe frozen�in magnetic field.

Thus, it was found that the dynamics of the pene�tration of the current (plasma) precursor in the stage ofthe plasma production toward the axis of a cylindricalarray made of wires or fibers coated with different met�als (bismuth, gold) depends on the thermodynamicand electric properties of the deposited metal.

It follows from the streak image of radial plasmacompression (Fig. 8b) that the bismuth plasma is firstcompressed toward the axis. Then, a radiating pinchforms on the axis. At the same time, the emission ofthe plasma produced from kapron fibers is observed atthe initial array radius. About 50 ns after the start of thecompression of the bismuth plasma and the formationof a radiating pinch, the plasma of kapron fibers beginsto be compressed toward the axis. It may be concludedthat the effect of radiation from the Z�pinch producedfrom the bismuth plasma promotes efficient plasmaproduction from the kapron fibers. A similar compres�sion of plasma produced from kapron fibers in the

presence of highly radiating plasma of high� andmedium�Z materials (tungsten and aluminum) wasearlier observed in [8].

Thus, it is experimentally demonstrated that, in thecourse of array implosion, the radiation of the formedpinch substantially intensifies plasma production fromthe material remaining at the array periphery. Thiseffect should be taken into account in the numericalcalculations of the implosion of wire arrays.

When an additional metal coating is depositedalong the entire wire/fiber length, the dynamics of thepenetration of the current precursor toward the arrayaxis in the stage of plasma production is determined bythe parameters of the plasma of the deposited mate�rial. Therefore, the proper choice of the depositedmetal at a given growth rate of the discharge currentallows one to control such parameters of the currentprecursor as the radial plasma propagation velocityand the value of the current carried by the plasma. Onthe other hand, the parameters of the plasma precur�sor determine the radial compression of the pinch andthe profile of the SXR pulse in the final stage of implo�sion.

3.4. Determination of the Instant of Termination of Plasma Production from Optical Streak Images

and Estimation of the Plasma Production Rate

It is known that the implosion of wire arrays under“cold start” conditions [13] is characterized by pro�longed plasma production [14–16]. This means thathot emission is continuously produced from relativelycold dense products of the wire explosion (wire core)under the action of energy fluxes from the surroundinghot rarified plasma (plasma corona). Under the actionof the magnetic pressure of the discharge current, thenewly formed plasma is carried from the region ofplasma production toward the array axis. This resultsin the formation of plasma jets—continuous plasmaflows extended from each wire toward the axis. Theinteraction between these plasma flows on the array

Anode

Cathode

Probes

h = 15 mm

Fig. 7. Time�integrated X�ray pinhole image of plasma(>20 eV) of a tungsten wire array with a 4 wt % gold coating(shot no. 4596).

818


ALEKSANDROV et al.

axis and the transformation of their energy into SXRemission is determined by the plasma production rate.

Therefore, the experimental determination of thetime dependence of the rate of plasma productionfrom the wire surface is necessary for the correct( )m t�

description of the process of plasma production innumerical simulations of wire array implosion.

At present, there are several models of wire arrayimplosion that take into account the phenomenon ofprolonged plasma production. One such model—a

h


Cathode

Anode

I

~17 ns

Ip(Probe no. 1)

Ip

(Probe no. 2)

3

0

I, Ip, МА

760 780 800 t, ns

3

2

1

0750 800 850 900 t, ns

Ip(Probe no. 1)

I, Ip, МА P, TW

PSXR

Probe no. 3

Kapron fiber + Bi coating

(Δ ≈ 1.2 μm)

(Probe no. 3)

Ip

(Probe no. 2)

~55 ns

820

I(Probe no. 3)

2

1

1.0

3

2

1

0

(a)

(b)

Array axis

Fiber plasma~50 ns

Bi plasma

Pinch

800 850 900 t, ns

0.5

0

–0.5

–1.0

r, с

m

Fig. 8. Experiment with a 20�mm�diameter 15�mm�high fiber array made of 16 25�μm�diameter kapron fibers with a total linearmass of 88 μg/cm (shot no. 4690). The Bi coating with a thickness of Δ ~ 1.2 μm (154 μg/cm) is deposited over the entire fiberlength (h = 15 mm). The upper panel in plot (a) shows the arrangement of probe nos. 1–3 inside the wire array. Probe nos. 1 and2 are installed at a distance of 3–4 mm from the anode at the radii of r = 5 and 9 mm, respectively, and probe no. 3 is installed atthe radius of 20 mm and measures the total current. The lower panels in plot (a) show the time dependences of the current Ipmeasured by probe nos. 1 and 2, the total current I, and the SXR power PSXR (>100 eV). Plot (b) shows the optical streak imageof the radial compression of the plasma produced from kapron fibers with a Bi coating (the streak camera slit is located 5 mmabove the cathode).



heterogeneous load with prolonged plasma produc�tion—has been developed by the team of the Angara�5�1 facility [14, 17]. Another such model is the so�called “rocket” model developed at the MAGPIEfacility [16]. There is also a combination of these twomodels [18].

According to the heterogeneous load model [14,17], the time dependence of the plasma productionrate required for the maintenance of a steady�stateradial outflow of plasma from the region of plasmaproduction with a fixed outer boundary is described bythe expression

, (2)

where (in units of μg/(ns cm2)) is the mass ofplasma produced per unit time from the unit area ofthe side surface of a cylindrical array; I(t) is the totalcurrent (in MA) flowing through the array; R0 is thearray radius; Δ is the interwire distance; d is the diam�eter of the cloud of the cold products of the initial wire

0

( )( )

I t dm t KR

μ α

β

⎛ ⎞= ⎜ ⎟

Δ⎝ ⎠�

( )m t�

explosion; and α, β = 0.1–0.4, K, and μ are numericalcoefficients.

The previous experiments on the implosion of con�ical arrays [5] and their numerical simulations have

shown that the factor , which takes into accountthe spatial inhomogeneity of the plasma sources is ofminor importance; therefore, in this model of plasmaproduction, it was assumed to be unity. This assump�tion corresponds to a plasma source with a uniformdistribution of over the azimuthal angle. Numeri�cal simulations of conical array implosion performedwith a similar plasma source have shown that the char�acteristic features of the radiating pinch and the profileof the SXR pulse obtained in such simulations agreewell with experimental data.

Therefore, we use this model of the plasma sourcewhen interpreting the results of experimental studiesof the implosion of different types of wire arrays.

In [7], the coefficients K and μ for a tungsten wirearray were found to be 0.12–0.18 and 1.8–2, respec�tively. The coefficients for wire arrays made of othermaterials were determined in [10]. For arrays made of

d α β

Δ

( )m t�

h


Cathode

Anode

I

~20–22 ns

Ip(Probe no. 1)

Ip

(Probe no. 2)

1.5

0

I, Ip, МА

760 780 800 840 t, ns

3

2

1

0750 800 850 950 t, ns

Ip(Probe no. 1)

I, Ip, МА P, TW

PSXR

0.3

0

Probe no. 3

Kapron fiber +Bi coating(Δ ≈ 1 μm)

(Probe no. 3)

0.1

Ip(Probe no. 2)

~50 ns

820

1.0

0.5

I(Probe no. 3)

900

0.2

Fig. 9. Experiment with a 20�mm�diameter 15�mm�high fiber array made of 40 25�μm�diameter kapron fibers with a total linearmass of 220 μg/cm (shot no. 4687). The Bi coating with a thickness of Δ ~ 1 μm (310 μg/cm) is deposited over the entire fiberlength (h = 15 mm). The upper panel shows the arrangement of probe nos. 1–3 inside the wire array. Probe nos. 1 and 2 areinstalled at a distance of 3–4 mm from the anode at the radii of r = 5 and 9 mm, respectively, and probe no. 3 is installed at theradius of 20 mm and measures the total current. The lower panels show the time dependences of the current Ip measured by probenos. 1 and 2, the total current I, and the SXR power PSXR (>100 eV).

820


ALEKSANDROV et al.

dielectric (kapron) fibers, the coefficient К is in therange of 0.04–0.07 [8], while for aluminum arrays, it isabout 0.2. The determination of the coefficient K informula (2) for bismuth, which is used for the initialmass profiling along the wires/fibers, is of interestfrom the standpoint of optimization of the design of aquasi�spherical wire array. In our experiment, bismuthwas deposited on kapron fibers by the method of ther�mal evaporation of metals in vacuum [3].

Below, we present results of measurements of theinstant of termination of plasma production tpp for bis�muth. The measurements were performed by twomethods: from streak images of the radial plasma com�pression (tpp(optic)) and from the current and voltagewaveforms (tpp(electric)).

Experiments on the implosion of wire arrays haveshown that, up to the time tpp(optic), which corre�sponds to the start of final plasma compression deter�mined from optical streak images, about 70–80% ofthe initial linear mass M0 (μg/cm) of the array materialtransforms into plasma [7, 19–21]. The remainingmass of the wires is the so�called trailing (or lost) mass.Taking into that, up to the time tpp, about 70–80% ofthe array linear mass M0 transforms into plasma, wecan write the following equality:

. (3)

On the other hand, it was shown in [22] that thestart of final plasma compression (tpp(optic)) in opticalstreak images coincides well with the abrupt increasein the inductance (tpp(electric)) determined from the

0 0

0

2 ( ) (0.7 0.8)ppt

R m t dt Mπ ≈ −∫ �

equation relating the waveforms of the discharge cur�rent and the voltage measured near the tungsten wirearray,

. (4)

As was shown in [22], Eq. (4) is applicable when theresistive component of the voltage, I(t)R(t), is muchless than its inductive component (less than 10%), i.e.,starting from the formation of the plasma coronaaround the wires (at 5–15 ns from the beginning of thedischarge) and up to the generation of the SXR pulse.In [22] (and later in [10]), it was also shown that, in thestage of plasma production, the linear inductance var�ies by no more than 7% of its change in the stage offinal plasma compression.

In the stage of plasma production, it is possible todisregard variations in the wire array inductance(dL/dt = 0); then, Eq. (4) takes the form

. (5)

According to Eq. (5), the abrupt increase in thearray inductance, which corresponds to the start offinal plasma compression, begins at the time tpp(elec�tric), when the voltage fails to be proportional to thetime derivative of the total current (see, e.g., Fig. 10a;curves 1, 2).

Thus, the instant corresponding to the end ofplasma production and the start of final plasma com�pression was determined from optical streak imagesand the waveforms of the current and voltage. Experi�ments carried out with arrays made of tungsten wiresand kapron fibers covered by Bi coatings with different

( ) ( ) ( )dI dLU t L t I tdt dt

= +

( ) dIU t Ldt

≈

0.2

0

–0.2

–0.4

–0.6

–0.81.0

0.5

0

–0.5

–1.0700 750 800 850 900 950

t, ns

r, с

mdI

/dt,

1014

А/s

1 2

0.2

0

–0.2

–0.4

–0.6

–0.8

(а) (b)

U,

MV

tpp(electric)

tpp(optic)

Array axis

Start of compression(termination of plasmaproduction)

W, 220 µg/сm

100

95

90

85

80

75

t pp(

elec

tric

), n

s

75tpp(optic), ns

80 85 90 95 100

no. 4921

no. 4685

no. 4690

Bi, 264 µg/сm

Bi, 154 µg/сm

Fig. 10. (a) Method for determining the instant of termination of plasma production from the measured waveforms of the currentand voltage and from the optical streak image of radial plasma compression by using shot no. 4921 as an example: (1) time deriv�ative of the total discharge current; (2) voltage waveform; (b) comparison of the instants of termination of plasma production ina wire array obtained from the optical streak image, Δtpp(optic), and the measured waveforms of the current and voltage,Δtpp(electric). For shot nos. 4690 and 4921, the times corresponding to the start of plasma compression obtained from two opticalstreak images are given.



linear masses showed good coincidence between thetimes tpp(optic) and tpp(electric) (see Fig. 10b).

Solving Eq. (3) with respect to and usingexpression (2), it is possible to find the coefficient К.Using the experimental data for fiber arrays with 264�and 154�µg/cm Bi coatings (shot nos. 4685 and 4690,respectively), the rate of bismuth plasma production

at a discharge current of I = 1 MA and an initialarray radius of R0 = 1 cm was found to be (0.095 ±0.015) µg/(cm2 ns).

In the same way, the value of for a tungstenarray (shot no. 4921) was found to be about0.18 µg/(cm2 ns), which agrees with the estimate forthe plasma production rate obtained in [7].

4. CONCLUSIONS

It is shown experimentally that the implosiondynamics of cylindrical arrays made of wires or metal�ized fibers with a profiled linear mass depends sub�stantially on the plasma production rate . Thisshould be taken into account when performingnumerical simulations of different types of loads, e.g.,quasi�spherical wire arrays.

The obtained experimental results allow us to drawthe following conclusions.

(i) At a discharge current of I = 1 MA and an initialarray radius of R0 = 1 cm, the rate of plasma produc�tion from the Bi coating deposited on tungstenwires amounts to (0.095 ± 0.015) µg/(cm2 ns), whichcorresponds to the inequalities < < .

(ii) Radiation generated in the pinch formed in thecourse of array implosion substantially acceleratesplasma production from the material remaining at thearray periphery. This effect should be taken intoaccount in numerical calculations aimed at optimiz�ing the power of the SXR pulse.

It is also worth noting the following features of theimplosion dynamics of cylindrical arrays.

(i) The dynamics of the penetration of the current�carrying plasma during the implosion of tungstenarrays without mass profiling is found to be homoge�neous over the array height.

(ii) During the implosion of a cylindrical tungstenwire array with a Bi coating in the central part of thewires, the current precursor from the deposited Bicoating penetrates earlier into the array. In contrast,during the implosion of a cylindrical array made ofkapron fibers with the same Bi coating, the currentprecursor from the fiber regions without a Bi coatingpenetrates into the array earlier. This is related to dif�ferent rates of plasma production from kapron fibers,tungsten wires, and the deposited material (bismuth inour case).

( )m t�

Bim�

Wm�

m�

Bim�

kaprm� Bim� Wm�

ACKNOWLEDGMENTS

We are grateful to the team of the Angara�5�1 facil�ity for the engineering and technical support of theseexperiments. This work was supported in part by theRussian Foundation for Basic Research, projectnos. 13�02�00013 and 13�02�00482.

REFERENCES

1. V. P. Smirnov, S. V. Zakharov, and E. V. Grabovski,JETP Lett. 81, 442 (2005).

2. E. V. Grabovski, A. N. Gritsuk, V. P. Smirnov, et al.,JETP Lett. 89, 315 (2009).

3. V. V. Aleksandrov, G. S. Volkov, E. V. Grabovski, et al.,Plasma Phys. Rep. 38, 315 (2012).

4. S. V. Lebedev, D. J. Ampleford, S. N. Bland, et al., inProceedings of the 6th International Conference on DenseZ�Pinches, Oxford, 2006, Ed. by J. Chittenden, AIPConf. Proc. 808, 69 (2006).

5. E. V. Grabovski, V. V. Aleksandrov, G. S. Volkov, et al.,Plasma Phys. Rep. 34, 815 (2008).

6. E. Grabovsky, G. Zukakishvili, K. Mitrofanov, et al., inProceedings of the International Conference on AdvancedDiagnostics for Magnetic and Inertial Fusion, Varenna,2001, Ed. by P. E. Stott, A. Woottom, G. Gorini, et al.(Academic, New York, 2002), p. 257.

7. G. G. Zukakishvili, K. N. Mitrofanov, V. V. Aleksan�drov, et al., Plasma Phys. Rep. 31, 908 (2005).

8. V. V. Aleksandrov, E. V. Grabovski, A. N. Gritsuk, et al.,Plasma Phys. Rep. 36, 482 (2010).

9. V. V. Aleksandrov, V. A. Barsuk, E. V. Grabovski, et al.,Plasma Phys. Rep. 35, 200 (2009).

10. K. N. Mitrofanov, E. V. Grabovski, G. M. Oleinik,et al., Plasma Phys. Rep. 38, 797 (2012).

11. E. V. Grabovski, G. G. Zukakishvili, K. N. Mitrofanov,et al., Preprint TRINITI No. 0091A (Moscow, TsNII�ATOMINFORM, 2002).

12. I. V. Glazyrin, E. V. Grabovski, G. G. Zukakishvili,et al., Vopr. At. Nauki Tekh., Ser. Termoyad. Sintez,No. 2, 67 (2009).

13. V. V. Aleksandrov, E. V. Grabovski, M. V. Zurin, et al.,JETP 99, 1150 (2004).

14. V. V. Aleksandrov, A. V. Branitsky, G. S. Volkov, et al.,Plasma Phys. Rep. 27, 89 (2001).

15. E. P. Yu, B. V. Oliver, D. B. Sinars, et al., Phys. Plasmas14, 022705 (2007).

16. S. V. Lebedev, F. N. Beg, S. N. Bland, et al., Phys. Plas�mas 8, 3734 (2001).

17. V. V. Alexandrov, I. N. Frolov, M. V. Fedulov, et al.,IEEE Trans. Plasma Sci. 30, 559 (2002).

18. P. V. Sasorov, B. V. Oliver, E. P. Yu, and T. A. Mehlhorn,Phys. Plasmas 15, 022702 (2008).

19. M. E. Cuneo, E. M. Waisman, S. V. Lebedev, et al.,Phys. Rev. E 71, 046406 (2005).

20. S. V. Lebedev, F. N. Beg, S. N. Bland, et al., Phys. Plas�mas 9, 2293 (2002).

21. C. J. Garasi, D. E. Bliss, T. A. Mehlhorn, et al., Phys.Plasmas 11, 2729 (2004).

22. V. V. Aleksandrov, E. V. Grabovski, K. N. Mitrofanov,et al., Plasma Phys. Rep. 30, 568 (2004).

Translated by L. Mosina

Documents

Effect of the plasma production rate on the implosion dynamics of cylindrical wire/fiber arrays with a profiled linear mass