Исследование проникновения магнитного поля внутрь сжимаемого током лайнера на установке Ангара-5-1

22 Pages·0.783 MB·Russian

by  Александров В.В., Барсук В.А., Грабовский Е.В. и др.

ISSN 1063(cid:1)780X, Plasma Physics Reports, 2009, Vol. 35, No. 3, pp. 200–221. © Pleiades Publishing, Ltd., 2009.
Original Russian Text © V.V. Aleksandrov, V.A. Barsuk, E.V. Grabovski, A.N. Gritsuk, G.G. Zukakishvili, S.F. Medovshchikov, K.N. Mitrofanov, G.M. Oleinik, P.V. Sasorov, 2009,
published in Fizika Plazmy, 2009, Vol. 35, No. 3, pp. 229–250.
PLASMA
DYNAMICS
Studies of Penetration of the Magnetic Field into Electrically
Imploded Loads in the Angara(cid:1)5(cid:1)1 Facility
V. V. Aleksandrova, V. A. Barsuka, E. V. Grabovskia, A. N. Gritsuka, G. G. Zukakishvilia,
S. F. Medovshchikova, K. N. Mitrofanova, G. M. Oleinika, and P. V. Sasorovb
a Troitsk Institute for Innovation and Thermonuclear Fusion Research, Troitsk, Moscow oblast, 142190 Russia
b Institute for Theoretical and Experimental Physics, Bol’shaya Cheremushkinskaya ul. 25, Moscow, 117218 Russia
Received February 28, 2008; in final form, July 2, 2008
Abstract—Results are presented from measurements of the distributions of the azimuthal magnetic field in
aluminum, copper, molybdenum, tungsten and other wire arrays electrically imploded at currents of up to
3MA in the Angara(cid:1)5(cid:1)1 facility. It is shown that the time during which the magnetic field of the current pulse
reaches the array axis depends on the material of the wires or wire coating. The current of the precursor
formed on the array axis before the implosion of the main load mass is measured. It is shown that the pene(cid:1)
tration of the load material with the frozen(cid:1)in magnetic field into a polymer (agar(cid:1)agar) foam liner is drasti(cid:1)
cally different from that in the case of a wire array. It is found that the rate of current transfer to the array axis
is maximum for tungsten wire arrays. The rates of plasma production during implosion of loads made of dif(cid:1)
ferent materials are compared.
PACS numbers: 52.59.Qy
DOI: 10.1134/S1063780X09030039
1. INTRODUCTION action of the discharge current on a solid substance. As
a result, a heterogeneous structure forms that consists
In recent years, significant progress has been
of dense wire cores surrounded by plasma. The main
achieved in generating high(cid:1)power X(cid:1)ray pulses by
consequence of the cold start is the formation of a het(cid:1)
implosion of wire arrays in high(cid:1)current facilities
erogeneous core–plasma system (the core diameter
[1,2]. These results have inspired a renewed interest in
being less than the skin depth) and, accordingly, pro(cid:1)
studying the Z(cid:1)pinch discharge as an energy driver for
longed plasma production, which continues almost
indirect(cid:1)drive targets in various schemes of inertial
over the entire rise time of the discharge current. Since
confinement fusion [3].
the conductivity of the wire core plasma is relatively
The use of cylindrical wire arrays made of high(cid:1)Z
low, the discharge current primarily flows through the
materials significantly improved the efficiency of con(cid:1)
plasma corona. The wire cores remain at rest because
version of the electric pulse energy into X radiation [2,
their diameters (~20 µm) are much less than the skin
4, 5]. It was shown experimentally in the Z facility,
depth, which, for a plasma with the electron tempera(cid:1)
which was put into operation in the United States in
ture T ≈ 10–20 eV and typical time scales of ~100 ns,
the mid(cid:1)1990s, that the use of arrays formed of many e
is about 2 mm.
(>100) wires at currents of ~20 MA allows one to
obtain X(cid:1)ray pulses with a duration of 6–8 ns, a power The experiments performed in the Angara(cid:1)5(cid:1)1
of ~280 TW, and an energy of ~1.8 MJ in the photon (Russia) [6], MAGPIE (Great Britain) [7], and Z
energy range >200 eV. facilities (United States) have shown that prolonged
In spite of a great body of experimental data, the plasma production is inherent in the process of wire(cid:1)
process of implosion of a cylindrical wire array is not array implosion [4, 10, 11]. By prolonged plasma pro(cid:1)
fully understood and there is no model capable of ade(cid:1) duction we mean not only ionization but also the for(cid:1)
quately describing the parameters of the output X(cid:1)ray mation of a highly conducting plasma capable of car(cid:1)
pulse. rying the major fraction of the generator current. The
Current(cid:1)driven implosion of wire arrays [6, 7] dif(cid:1) magnetic field turns out to be frozen in the newly pro(cid:1)
fers substantially from that predicted by the classical duced plasma corona [12], which is permanently car(cid:1)
Leontovich–Osovets implosion model [8], because ried away toward the array axis. As a result, a radial
almost all of the experiments on the implosion of wire plasma distribution arises that is appreciably thicker
arrays have been performed under so(cid:1)called “cold than the skin depth. This distribution can be discon(cid:1)
start” conditions [9, 10]. In this case, phase transitions tinuous in the azimuthal direction. The plasma of an
(melting, ablation, sublimation, ionization, etc.) in imploding cylindrical wire array acquires the form of
the plasma(cid:1)forming load material occur under the separate jets extended along the wires and propagating
200
STUDIES OF PENETRATION OF THE MAGNETIC FIELD 201
toward the array axis. The acceleration of this plasma measurements inside wire arrays provide important
toward the system axis is provided by the Ampére information on the physics of the entire implosion
force, which acts on the entire plasma volume, rather process. This information can further be used to opti(cid:1)
than by a magnetic piston, the action of which on the mize the parameters of wire arrays and generated SXR
external boundary of the wire array plasma would give pulses [18].
rise to strong instabilities. Such a system is more stable Comparing the time dependence of the azimuthal
against the Rayleigh–Taylor instability than a thin magnetic field measured by probes at different radii
plasma sheath with a thickness less than the skin with theoretical curved calculated by the above one(cid:1)
depth. Obviously, there should be an optimal plasma
dimensional model for different profiles m(cid:1)(t), one can
thickness at which stable compact plasma implosion
leads to the generation of a high(cid:1)power soft X(cid:1)ray find the m(cid:1)(t) profile that best fits the probe signals.
(SXR) pulse [4]. Using this profile, one can then calculate the time evo(cid:1)
lution of the radial distributions of the current, plasma
In order to describe the process of prolonged
density, and radial plasma velocity in the course of wire
plasma production during the implosion of a tungsten
array implosion [12, 18].
wire array, the following one(cid:1)dimensional MHD
model was developed by the team of the Angara(cid:1)5(cid:1)1 Experiments with tungsten wire arrays performed
facility [6, 11]. According to this model, the plasma in the Angara(cid:1)5(cid:1)1 facility have shown that the mea(cid:1)
source consists of an infinite number of wires that are sured distributions of the magnetic field and matter
located at the initial array radius R and permanently can be used to test theoretical models that take into
0
account prolonged plasma production.
generate plasma, the rate of plasma production m(cid:1)(t)
Comparison of the measured distributions of the
being proportional to ~(I/R )2. The model describes
0 magnetic field and matter in imploding wire arrays
the formation of a magnetized radial plasma flow
made of various materials makes it possible to improve
propagating from the wires toward the array axis,
the existing theoretical models of wire array implosion
where a plasma precursor carrying a fraction of the
with allowance for the elemental composition of wires.
discharge current forms in the initial stage of implo(cid:1)
Knowing how the properties of the wire material affect
sion. Such a precursor was observed experimentally in
the initial stage of current(cid:1)driven implosion is very
[12]. At present, this model is being upgraded [13]. A
important for studies of wire array implosion.
similar model (a so(cid:1)called “rocket model”) was pro(cid:1)
posed by the MAGPIE team to describe the rate of The expansion rate of a single 25(cid:1)µm(cid:1)diameter
plasma production [14]. In that model, however, the wire exploding under the action of a sinusoidal current
precursor carries no magnetic field or current. pulse with an amplitude of up to 4 kA and a rise time
of 350 ns was studied in [19] as a function of the abla(cid:1)
As soon the material of wire cores is exhausted, the
tion energy for such wire materials as zinc, silver, alu(cid:1)
process of ablation terminates and the entire plasma
minum, gold, copper, lead, platinum, nickel, tung(cid:1)
implodes toward the axis. The inhomogeneity of abla(cid:1)
sten, and titanium. It was shown in that paper that the
tion results in the breakthrough of the magnetic flux
measured expansion rate of electrically heated wires
through the regions free of plasma sources. In [10],
made of low(cid:1)melting metals (such as gold, aluminum,
this process was called “a plasma rainstorm.”
silver, and zinc) range from 2 × 105 cm/s for gold to 5 ×
To better understand the process of wire array
105 cm/s for zinc. The corresponding expansion rates
implosion (and, probably, to control it), it is necessary
to more thoroughly study the processes and phenom(cid:1) for other wire materials are 2 × 104 cm/s for titanium,
ena that can substantially affect the total radiation 3 × 104 cm/s for tungsten, 4 × 104 cm/s for nickel, and
yield, such as the formation of a plasma precursor, the 5 × 104 cm/s for platinum. It is found that the structure
rate of plasma production, the phase of pinch com(cid:1) of the wire material changes during wire explosion
pression (stagnation), the residual load mass that [20–22]. It is shown that, for aluminum and copper
remains at the pinch periphery, the redistribution of wire arrays, the expansion rate of the wire material
the current density, repeated pinch compressions, the (~3.5–4 × 104 cm/s) is substantially higher than that
breakthrough of the magnetic flux, and the stability of for tungsten arrays (104 cm/s) [23].
pinch compression. It is also necessary to investigate
In this paper, we present results of experiments on
the generation of hard X(cid:1)ray emission and fast elec(cid:1)
studying the effect of the atomic number of the
tron beams, which can significantly influence the
plasma(cid:1)forming material on the implosion of hollow
parameters of a Z(cid:1)pinch X(cid:1)ray source.
cylindrical arrays made of metal wires and hollow
One line in this field of research is to measure the loads made of a low(cid:1)density foam. The experiments
magnetic field inside an imploding wire array. Such were performed in the Angara(cid:1)5(cid:1)1 facility. Magnetic
measurements are based on the Faraday effect [15] field measurements show that the time at which the
and/or employ microprobe techniques [16, 17]. current(cid:1)carrying plasma appears inside the array
The distributions of the magnetic field and matter depends on the load material. The plasma and mag(cid:1)
inside a wire array depend substantially on the time netic field penetrate into an array made of high(cid:1)melt(cid:1)
behavior of the plasma production rate. Magnetic field ing metals (molybdenum or tungsten) faster than into
PLASMA PHYSICS REPORTS Vol. 35 No. 3 2009
202 ALEKSANDROV et al.
0.9 R Wire array
0
Probes
(а) Magnetic probe (b) 0.5 R0
NbTi foil
m
Two loops m
0.5–0.8 mm 0
2. Anode
–
5
1.
m
m
0 Cathode
0
3
∅
Fig. 1. Design and arrangement of probes measuring the azimuthal magnetic field in the wire(cid:1)array plasma.
(а) (b) (c) (d) (e)
Agar(cid:1)agar foam Aluminum Copper Molybdenum Tungsten
(Z = 13) (Z = 29) (Z = 42) (Z = 74)
Fig. 2. Photographs of loads made of various plasma(cid:1)forming materials and magnetic probes placed inside them. The vertical size
of the loads is 15 mm.
arrays made of low(cid:1)melting metals (such as alumi(cid:1) 2. EXPERIMENTAL DESIGN
num, copper, stainless steel, and gold(cid:1)coated tung(cid:1)
The experiments on studying the rate of plasma
sten). It is found that the external boundary of a wire
production during the implosion of axisymmetric
array is compressed asynchronously in the radial
cylindrical wire arrays and hollow loads made of a low(cid:1)
direction; as a result, the brightness of the imploding
density foam were carried out in the Angara(cid:1)5(cid:1)1 facil(cid:1)
array is modulated in the axial direction. The spatial ity [24] at currents of up to 3 MA. The azimuthal mag(cid:1)
scale of this modulation depends on the plasma(cid:1)form(cid:1) netic field inside an electrically imploded load was
ing material. The growth rate of the spatial scale of measured by small(cid:1)size calibrated magnetic probes
axial modulation at the initial array radius is different [16]. Two 300(cid:1)µm(cid:1)diameter loops were used as detec(cid:1)
tors of the variable magnetic field. The loops were
for low(cid:1)melting (aluminum, copper, or iron) and
wound in opposite directions, so the probe provided
high(cid:1)melting (molybdenum or tungsten) metals. In a
two signals of opposite polarity (see Section 3.6). Such
hollow load made of a dielectric material (agar(cid:1)agar
a probe design allows one to be sure that the signals
foam), no plasma precursor is detected by magnetic measured in the presence of strong electromagnetic
probes on the array axis. fields are of magnetic origin. The measuring loops are
covered with an envelope made of a NbTi foil, which
By varying the parameters of the array (such as its
protects them from plasma fluxes and radiation, but
initial radius, linear mass, interwire distance, and wire
allows the variable magnetic field to penetrate into the
material), it is possible to control plasma production
probe. The design of the probe detector is shown in
in order to achieve compact plasma compression and Fig. 1a. The current flowing within the radius at which
generation of high(cid:1)power X(cid:1)ray pulses. the probe is located is calculated by integrating the
PLASMA PHYSICS REPORTS Vol. 35 No. 3 2009
STUDIES OF PENETRATION OF THE MAGNETIC FIELD 203
(а) Al Kα12 (b) Cu Kβ1 Cu Kα12 µm
0
15 µm 2
1
β1 Kβ
K u
α12Al 2C
K
Si
1.0 1.5 2.0 2.5 3.0 λ, Å
(d)
(c) 2
1
α
L
1 W
12 Lβ
m 1 Lα W 6 µm
µ20 o Lβ Mo
M
6
3 β
β2 L
Mo Lβ4 W L W Lγ3
W
Mo L
β3
1
Mo L Lγ 2
γ4 W He W LβLβ1
Mo Lγ23 W 2 W
2
2 3 4 5 6 7 λ, Å 1.0 1.5 2.0 2.5 3.0 λ, Å
Fig. 3. Optical microphotographs of the array wires and X(cid:1)ray spectra of the wire surface material, recorded using a LiF spec(cid:1)
trograph: (a) 15(cid:1)µm(cid:1)diameter aluminum wire, (b) 20(cid:1)µm(cid:1)diameter copper wire, (c) 20(cid:1)µm(cid:1)diameter molybdenum wire, and
(d)6(cid:1)µm(cid:1)diameter tungsten wire.
probe signals over time. The probes were installed at grated pinhole camera was ≈30 µm at photon energies
distances of ~3–4 mm from the anode both inside and of ≈200 eV.
outside of the load (see Fig. 1b). This allowed us to The spectral characteristics of X(cid:1)ray emission in
measure the currents at different radii inside and out(cid:1) the photon energy range 0.2–2 keV were monitored
side the load. with a VChD(cid:1)3 thermocouple calorimeter and four
vacuum X(cid:1)ray diodes equipped with X(cid:1)ray filters of
X(cid:1)ray images of the pinch in the photon energy
different hardness [25].
range over 20 eV were taken with a time(cid:1)integrated
pinhole camera and with four(cid:1)frame X(cid:1)ray pinhole In this work, the following types of loads were used
cameras based on an open microchannel(cid:1)plate matrix (Fig. 2):
with an exposure of 3 ns and a time interval between (i) cylindrical arrays (Figs. 2b–2e) made of alumi(cid:1)
frames of 5 ns. The object resolution of the time(cid:1)inte(cid:1) num, copper, molybdenum, tungsten, stainless steel,
PLASMA PHYSICS REPORTS Vol. 35 No. 3 2009
204 ALEKSANDROV et al.
(а) Kβ1 Kα12 (b) Kα12
Ni Ni Fe 10 µm
2
8.5 µm α1
K
r
C
1
β
K
12e
α F
K
Ni 2
β1 α1
K K
β1 r n
K C M
Ni
1.0 1.5 2.0 2.5 3.0 1.0 1.5 2.0 2.5 3.0
λ, Å λ, Å
2
(c) α1 2 (d)
L α1
u L
A W
+
1
β
L
W 10 µm
Lγ1 β2
Lβ1W W L Lβ6
Au W
3
2
β
L e 1
Au W H W Lβ 100 µm
2
1.0 1.5 2.0 2.5 3.0
λ, Å
Fig. 4. Optical microphotographs of the array wires and X(cid:1)ray spectra of the wire surfaces, recorded using a LiF spectrograph:
(a)8.5(cid:1)µm(cid:1)diameter nickel wire, (b) 10(cid:1)µm(cid:1)diameter stainless(cid:1)steel wire, and (c) 10(cid:1)µm(cid:1)diameter gold(cid:1)coated tungsten wire
(the thickness of 5 wt % gold coating is 1270 Å). In panel (d), an optical microphotograph of agar(cid:1)agar foam with a density of
2mg/cm3 and thickness of 150 µm is shown.
or gold(cid:1)coated tungsten wires (the parameters of wires Agar(cid:1)agar is a natural water(cid:1)soluble polymer
are presented in Figs. 3 and 4) and (С H O ) extracted from marine red algae. It con(cid:1)
14 18 9 n
(ii) cylindrical polymer loads made of a low(cid:1)den(cid:1) tains up to 90% hydrocarbons [26, 27]. A hollow cylin(cid:1)
sity agar(cid:1)agar foam (Fig. 2a). drical load was prepared from a low(cid:1)density microhet(cid:1)
erogeneous solid material (foam) (see Fig. 2a). The
The general view of a wire array is shown in Fig. 1b.
foam is a medium consisting of chaotically arranged
Equal(cid:1)diameters wires are stretched uniformly along
the cylinder generatrix between two equal(cid:1)size coaxial solid fibers with a mass density of ρf≈ 0.9–1 g/cm3 and
metal electrodes spaced by 15 mm. typical transverse size of d ≈ 1–5 µm. The interfiber
f
PLASMA PHYSICS REPORTS Vol. 35 No. 3 2009
STUDIES OF PENETRATION OF THE MAGNETIC FIELD 205
3
1
2 2
4
W
А
М T
, , P
I
1 1
2
∆t ≈ 53 ns
3
0 0
750 800 850 900
t, ns
Precursor
Anode
m
m
5
1
=
H
Cathode–29 ns –24 ns –19 ns
Fig. 5. On top: results of magnetic probe measurements in the plasma produced from an array made of 40 15(cid:1)µm(cid:1)diameter alu(cid:1)
minum wires. The array linear mass is 220 µg/cm, the array diameter is 20 mm, and the array height is 15 mm (shot no. 4524).
Curve 1 shows the waveform of the total current measured by a probe installed at a radius of 20 mm (outside the array), and curves
2 and 3 show the current waveforms measured by probes installed at radii of 0.8R and 0.5R , respectively. Curve 4 shows the time
0 0
dependence of the SXR power. Here and in subsequent figures, ∆t is the time interval between the beginning of the current pulse
and the appearance of a reliably detected signal from the magnetic probe. On bottom: frame X(cid:1)ray images of the imploding wire
array, taken in the photon energy range hν > 20 eV and synchronized with the above current waveforms. The zero time corre(cid:1)
sponds to the peak of the SXR pulse. The frame exposition is 3 ns, and the time interval between frames is 5 ns.
distance (the pore size) is r ≈ 10–50 µm (see The wire diameters were measured by comparing
pore
Fig.4d). There is also a small number of fibers with their electron microscopy photographs with photo(cid:1)
d ≈ 10 µm. The fiber length is l ≈ 10–50 µm graphs of reference objects. The wire diameters on
f f
(l (cid:1)d). segments a few centimeter long were determined using
f f
Table
Array linear
Wire material Array radius, cm Wire diameter, µm Number of wires Array height, cm
mass, µg/cm
Aluminum 220 1 15 40 1.5
Copper 224, 560 1 20 8, 20 1.5
Molybdenum 365, 456 1 20 16, 20 1.5
Tungsten 220 1 6 40 1.5
Gold(cid:3)coated tungsten 375 1 10 30 1.5
Stainless steel 248 1 10 40 1.5
PLASMA PHYSICS REPORTS Vol. 35 No. 3 2009
206 ALEKSANDROV et al.
3 3
1
2 2
4
W
А
T
М
,
, P
I
1 1
2
∆t ≈ 54 ns
3
0 0
750 800 850 900
t, ns
Probe
Anode
m
m
5
1
=
H
Cathode–11 ns –6 ns –1 ns
Fig. 6. On top: results of magnetic probe measurements in the plasma produced from an array made of 40 15(cid:1)µm(cid:1)diameter alu(cid:1)
minum wires. The array linear mass is 220 µg/cm, the array diameter is 20 mm, and the array height is 15 mm (shot no. 4525).
Curve 1 shows the waveform of the total current measured by a probe installed at a radius of 55 mm (outside the array), and
curves 2 and 3 show the current waveforms measured by probes installed at radii of 0.8R and 0.5R , respectively. Curve 4 shows
0 0
the time dependence of the SXR power. On bottom: frame X(cid:1)ray images of the imploding wire array, taken in the photon energy
range hν> 20 eV and synchronized with the above current waveforms. The zero time corresponds to the peak of the SXR pulse.
The frame exposition is 3 ns, and the time interval between frames is 5 ns.
optical microscopy. The wire composition was deter(cid:1) which is 13% of the depth of the analyzed layer. The
mined by the method of quantitative X(cid:1)ray microspec(cid:1) intensity ratio between the W and Au lines agrees with
troscopy with the help of an RÉMMA(cid:1)202 LiF spec(cid:1) this value.
trograph analyzer. Figure 4b shows a microphotograph of a stainless(cid:1)
Figures 3 and 4 present microphotographs of the steel wire with a nominal diameter of 10.0 µm. The fig(cid:1)
wires from which the arrays were produced (the focal ure also shows the X(cid:1)ray spectrum of the wire surface
depth is ≈150 µm). In all of the photographs, inhomo(cid:1) material, which corresponds to 12Kh18N10 stainless
geneities of the wire material and deviations from a steel.
perfect cylindrical shape (the wire diameter varies by The wire array parameters varied in our experi(cid:1)
≈1–5% for different materials) are seen. ments are listed in the table.
Figure 4c shows a microphotograph of a 10.0(cid:1)µm(cid:1)
diameter gold(cid:1)coated tungsten wire and the X(cid:1)ray
3. EXPERIMENTAL RESULTS
spectrum of the wire surface material. The L lines of
gold (Au) are clearly seen against the background of The subsequent figures present the results of mag(cid:1)
tungsten (W) lines. We note that, in this case, the netic field measurements performed at different radii
depth of the analyzed layer was ~1 µm (the accelerat(cid:1) both inside and outside the wire array plasma. In the
ing voltage was 30 kV). Simple estimates show that the former case, the current flowing within a certain
thickness of the Au layer with a nominal mass fraction radius was measured, while in the latter case, the total
of 5% on a 10(cid:1)µm(cid:1)diameter tungsten wire is ~1270 Å, current flowing through the array was determined. The
PLASMA PHYSICS REPORTS Vol. 35 No. 3 2009
STUDIES OF PENETRATION OF THE MAGNETIC FIELD 207
figures also show frame X(cid:1)ray images synchronized Probe
with the current waveforms.
Anode
3.1. Implosion of Aluminum Wire Arrays
In shots nos. 4524–4526, arrays made of 40 15(cid:1)µm(cid:1)
diameter aluminum wires mounted at a radius of m
10mm were used as loads. The total linear mass of the m
array was 220 µg/cm, and its height was 15 mm. The 15
total current in this series of shots was up to 2.7 MA. It =
H
is seen in Fig. 5 that the current within the radii 0.8R
0
and 0.5R appears in a certain time (≈35 and ≈53 ns,
0
respectively) after the beginning of the current pulse
(curves 2, 3). Taking into account that the distance
between the probes is ∆r = 3 mm and the time delay ∆t Cathode
between the probe signals is about 18 ns, we find that
the wire plasma propagates with an average radial
velocity of Vr = ∆r/∆t ≈ 1.6 × 107 cm/s. At the instant Fig. 7. Time(cid:1)integrated pinhole X(cid:1)ray image of the plasma
at which the pinch begins to emit X radiation (75 ns produced from an array made of 20 20(cid:1)µm(cid:1)diameter cop(cid:1)
per wires. The array linear mass is 560 µg/cm, the array
after the beginning of implosion), the current flowing
diameter is 20 mm, and the array height is 15 mm. The
within the radius 0.5R0 is ≈100 kA. On the bottom of image is taken in the photon energy range >20 eV.
Fig. 5, frame images of the wire array plasma propa(cid:1)
gating toward the axis are also shown. It is seen that,
29ns before the peak of the SXR pulse, the external
3.2. Implosion of Copper Wire Arrays
plasma boundary is discontinuous and looks like as it
is broken along the array radius. This means that, in In shots nos. 4532 and 4533, arrays made of 8 or 20
some places, plasma production at the initial array 20(cid:1)µm(cid:1)diameter copper wires, respectively, mounted
radius has already terminated. A plasma precursor [28] at a radius of 10 mm were used as loads. The total lin(cid:1)
is observed on the array axis 19 ns before the peak of ear masses of the arrays were 224 and 560 µg/cm,
the SXR pulse. In the optical range, such a precursor respectively, and their heights were 15 mm.
is usually observed much earlier, 50–70 ns before the In these shots, the penetration of the magnetic flux
peak of the SXR pulse. The SXR power reaches its was studied using magnetic probes installed at the radii
maximum (≈2 TW) 118 ns after the beginning of 0.8–0.9R and 0.5R . The SXR yield in experiments
0 0
implosion. with copper wire arrays ranged from 0.4 to 3 TW,
depending on the array parameters. Figure 7 shows a
Analysis of frame images of the plasma produced
time(cid:1)integrated pinhole image of the plasma, taken in
from an aluminum array (see Fig. 6) shows that plasma
its self(cid:1)emission in the photon energy range >20 eV.
production terminates asynchronously along the axial
The diameter of the brightly emitting axial plasma
direction (the array height). This is clearly seen in the
region is about 3 mm.
frame taken 11 ns before the peak of the SXR pulse.
Here, a “magnetic bubble” (a macroscopic volume in Figures 8 and 9 show typical waveforms of the cur(cid:1)
which the magnetic field is stronger and the plasma rents measured at these radii. It is seen that the cur(cid:1)
density is lower than those in the neighboring plasma rent(cid:1)carrying plasma penetrates to one(cid:1)half of the ini(cid:1)
regions) extended radially up to the array axis can be tial array radius 56–67 ns after the beginning of the
seen. It follows from the subsequent frames that the discharge. The experiments show that, for copper wire
bubble grows with time. The propagation of the mag(cid:1) arrays, the first portions of the current(cid:1)carrying
netic bubble toward the array axis indicates that, at this plasma penetrate to one(cid:1)half of the initial array radius
height, plasma production at the array periphery has in about the same time as for aluminum wire arrays,
already terminated and the plasma is compressed although the atomic weights of aluminum and copper
toward the array axis, where a Z(cid:1)pinch forms. Later (6 differ by a factor of 2.4. Most likely, this is related to
and 1 ns before the peak of the SXR pulse), this part of the fact that the first plasma portions from which the
the pinch is seen to be unstable against the develop(cid:1) precursor then forms on the axis are produced soon
ment of the m = 1 (“zigzag”) mode. In the third frame, after the beginning of the discharge.
taken 1 ns before the peak of the SXR pulse, one can It can be expected that, for wire materials with sub(cid:1)
see that the boundary of the magnetic bubble has limation heats close to those of aluminum and copper,
already been closed, so the current has been probably the initial breakdown and the formation of the first
reconnected. The SXR yield in experiments with alu(cid:1) portions of plasma will take place at nearly the same
minum wire arrays reached 2–3 TW. time, whereas for molybdenum or tungsten wires, the
PLASMA PHYSICS REPORTS Vol. 35 No. 3 2009
208 ALEKSANDROV et al.
3 1 1.2
А2 0.8W
М T
, I , P
2 4
1 0.4
∆t ≈ 56 ns
3
0 0
750 800 850 900 950 1000
t, ns
Anode
m
m
5
1
=
H
Cathode–61 ns –56 ns –51 ns –46 ns
Fig. 8. On top: results of magnetic probe measurements in the plasma produced from an array made of 20 20(cid:1)µm(cid:1)diameter copper
wires. The array linear mass is 560 µg/cm, the array diameter is 20 mm, and the array height is 15 mm (shot no. 4532). Curve 1
shows the waveform of the total current measured by a probe installed at a radius of 20 mm (outside the array), and curves 2 and
3 show the current waveforms measured by probes installed at radii of 0.8R and 0.5R respectively. Curve 4 shows the time depen(cid:1)
0 0
dence of the SXR power. On bottom: frame X(cid:1)ray images of the imploding wire array, taken in the photon energy range hν > 20eV
and synchronized with the above current waveforms. The zero time corresponds to the peak of the SXR pulse. The frame exposi(cid:1)
tion is 3 ns, and the time interval between frames is 5 ns.
corresponding times will be different. The results of region was determined by numerically processing the
magnetic field measurements for molybdenum and time(cid:1)integrated image shown in Fig. 12 by the method
tungsten are presented below. described in [29, 30]. It was found that this diameter
was about 2 mm.
It follows from the frame X(cid:1)ray images presented in
3.3. Implosion of Molybdenum Wire Arrays
Fig. 11 that the plasma continues to propagate toward
In shots nos. 4535 and 4536, arrays made of 20 or the array axis even at the peak of the SXR pulse. No
16 20(cid:1)µm(cid:1)diameter molybdenum wires, respectively, continuous wire cores (plasma sources) are observed at
mounted at a radius of 10 mm were used as loads. The the plasma periphery. This means that plasma produc(cid:1)
total linear masses of the arrays were 365 and tion at the periphery has already terminated. At the
456µg/cm, respectively, and their heights were instant corresponding to the peak of the SXR pulse, a
15mm. Figures 10 and 11 present the results of mag(cid:1) pinch is observed on the array axis. Then, the pinch
netic field (current) measurements in these shots. It is expands. The maximum SXR power in this shot was
seen that the first portions of the current(cid:1)carrying about 1.1 TW.
plasma penetrate to one(cid:1)half of the initial array radius
42–53 ns after the beginning of the discharge, i.e.,
15ns (on average) earlier than in experiments with 3.4. Implosion of Tungsten Wire Arrays
aluminum and copper wire arrays. The frame X(cid:1)ray
images presented in Fig. 10 show that, 44 ns before the In shot no. 4529, an array made of 40 6(cid:1)µm(cid:1)diam(cid:1)
peak of the SXR pulse, there is already a plasma pre(cid:1) eter tungsten wires mounted at a radius of 10 mm was
cursor on the axis, which is typical of imploding wire used as a load. The total linear mass of the array was
arrays. It is seen from X(cid:1)ray images that the plasma is 220 µg/cm, and its height was 15 mm. It should be
supplied from the array periphery and a pinch forms noted that the number of wires (40), the initial array
on the array axis. The diameter of the radiating plasma radius (R =10 mm), and the total liner mass of the
0
PLASMA PHYSICS REPORTS Vol. 35 No. 3 2009
STUDIES OF PENETRATION OF THE MAGNETIC FIELD 209
3 3
1
4
2 2
W
А
М T
,
, P
I
1 1
2
∆t ≈ 67 ns
3 0
0
750 800 850 900 1000
t, ns
Anode
m
m
5
1
=
H
Cathode –34 ns –29 ns –24 ns –19 ns
Fig. 9. On top: results of magnetic probe measurements in the plasma produced from an array made of eight 20(cid:1)µm(cid:1)diameter
copper wires. The array linear mass is 224 µg/cm, the array diameter is 20 mm, and the array height is 15 mm (shot no. 4533).
Curve 1 shows the waveform of the total current measured by a probe installed at a radius of 20 mm (outside the array), and curves 2
and 3 show the current waveforms measured by probes installed at radii of 0.9R and 0.5R , respectively. Curve 4 shows the time
0 0
dependence of the SXR power. On bottom: frame X(cid:1)ray images of the imploding wire array, taken in the photon energy range hν>
20 eV and synchronized with the above current waveforms. The zero time corresponds to the peak of the SXR pulse. The frame
exposition is 3 ns, and the time interval between frames is 5 ns.
array (220 µg/cm) were the same as those of aluminum external plasma boundary subject to instabilities is
wire arrays used in the above experiments. observed in place of dense wire cores.
Figure 13 show the results of magnetic field (cur(cid:1)
rent) measurements at different radii inside and out(cid:1) 3.5. Implosion of Gold(cid:1)Coated Tungsten Wire Arrays
side the tungsten wire array. It is seen that the first In shot no. 4595, an array made of 30 10(cid:1)µm(cid:1)diam(cid:1)
plasma portions penetrate to one(cid:1)half of the initial eter tungsten wires coated with an ~0.1 µm(cid:1)thick gold
array radius in a time of about 40 ns after the beginning layer (with a relative mass of 5%) and mounted at a
of the discharge, i.e., earlier than for aluminum and radius of 10 mm was used as a load. The total linear
copper wire arrays. The precursor appears on the array mass of the array was 375 µg/cm, and its height was
axis 20 ns before the peak of the SXR pulse. The pre(cid:1) 15mm. This experiment was aimed at studying the
cursor current measured 100 ns after the beginning of effect of wire coating on the production of plasma and
the discharge is about 300 kA (≈15% of the total cur(cid:1) its implosion toward the array axis. The results of mag(cid:1)
netic field (current) measurement for this shot are pre(cid:1)
rent at that instant). The current measured at the
sented in Fig. 14. Figure 15 shows a time(cid:1)integrated
radius 0.8R 100 ns after the beginning of the discharge
0 pinhole X(cid:1)ray image of the imploding plasma. A dis(cid:1)
is almost equal to the total discharge current. This
tinctive feature of this experiment is that the first por(cid:1)
means that plasma production at the array periphery
tions of the current(cid:1)carrying plasma begin to penetrate
has already been terminated and the plasma carrying inside the array volume much later than in the case of
the major fraction of the current has begun to implode a tungsten wire array. On the average, the time delay
toward the array axis. This is confirmed by frame X(cid:1)ray increased to ≈56 ns after the beginning of the dis(cid:1)
images taken at this instant. In these frames, a diffuse charge, i.e., by 15–17 ns in comparison with an array
PLASMA PHYSICS REPORTS Vol. 35 No. 3 2009