s.v. lebedev- effect of discrete wires on the implosion dynamics of wire array z-pinches
TRANSCRIPT
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8/3/2019 S.V. Lebedev- Effect of discrete wires on the implosion dynamics of wire array Z-pinches
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Effect of discrete wires on the implosion
dynamics of wire array Z-pinches
S.V. Lebedev
Imperial College
In collaboration with
J.P. Chittenden, D. Ampleford, F.N Beg, S.N. Bland, C. Jennings,
M. Sherlock and M.G. Haines (IC)
S. Pikuz, T. Shelkovenko, D. Hammer (Cornell)
This work is supported by Sandia National Lab and US DOE
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Outline: life story of a wire array
Wires do not convert into plasma instantaneously
(at least in experiments at 1 - 3 MA)
wires plasma shell
?
Two-stage implosion dynamics:
Ablation of wires and redistribution of mass
Snowplough-like final implosion phase
Behaviour of nested arrays and foam targets
Scaling of the implosion dynamics to 20MA ?
0.5 1.00.0
0.5
1.0
Radiu
s
time
coro
nal
pla
sma
Trailing mass
StagnationPrecursor pinch
Snowplow-like
final implosion0-D
Ablation of wire cores
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Experimental set-up and diagnostics
X-ray radiography with X-pinch in return current path
1ns, 10m resolutionh 2-5keV
Wire arrays:
Diameter 16mm (8mm)
N < 64
Timpl = 200-300ns
I = 1 MA
Diagnostics:
Laser probingOptical streaks
X-ray imaging
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Core-corona structure of plasma
Radiography shows wire cores until ~80% of implosion
Inward streaming of the coronal plasma
Precursor on axis at t ~ 50% timp
Implosion starts at t~ 80% timp
End-on laser probing
Radial optical streak
0.0 0.5 1.0 1.5 2.0
16
18
20
Al
250m
array
edge
Filmdensity(a.u.)
Radial position (mm)
0.5 1.0 1.5
W
100m
two
wires
End-on XUV
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Axial non-uniformity of plasma formation
Non-uniformity of coronal plasma formation imprints
on the cores
Laser probing Radiography
same
Coronal plasma: Wire cores:
~ core size, const(t) The same at t~ 80% timp
No obvious correlation between instabilities in different wires
Wire cores remain on the initial array radius until
they run out of material in some axial positions
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Non-0-D implosion trajectories of Al andW wire arrays
Similar trajectory was observed on 4 MA ANGARA-5
In the first 80% of time the JxB force is not applied to
the cores, accelerating instead the coronal plasma.
The available JxB force can only implode < 50% ofthe initial mass in the last 20% of time.
Radial optical streaks: universal 80% trajectories
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.00-D
Al
N=16
N=32
W
N=32
N=64
R/
R0
t / timp
N=32, 8mm
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Ablation of wire cores in wire arrays
Momentum balance gives an estimate of ablation rate
0-D implosion
Ablation
Redistribution of mass by precursor flow:
By 80% of implosion
time ~40% of mass has
been removed from the
cores!
Snowplough-like implosion of the distributed mass
Stabilisation by density profile
Does all mass participate in the implosion?
rI
dtrdm
4
2
0
2
2
0 =
0
2
0
4 R
I
dt
dmV
=
2
0
2
2
00
8
)]([),(
VrR
Itr
=
V
rRt
= 00
0 2 4 6 80.0
0.2
0.4
0.6
0.8
1.0
massfraction
radius (mm)
1E-5
1E-4
1E-3 wire
cores
precursor
density(g/cm
3)
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Formation of gaps in wire cores
Only ~1/2 of mass left in the cores at 80% of timp
axial modulation of ablation rate
all mass could be ablated in some axial positions
Start of the implosion two possible scenarios:
Al W
No current through the gaps Current re-strike
Trailing mass All mass implodes
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Final phase of implosion: 32 x 15m Al array
Snowplough-like implosion of distributed mass
End-on x-ray imaging
Vpiston / Vshock~ 1.4 ~ ( + 1)/2 ?
Only
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Snowplough-like implosion in W arrays
Laser probing of 32 x 4 m tungsten wire array
-8 -6 -4 -2 0 2 4 6 80
50
100
150
200
initial array diameter
imploding
plasma
piston
precursor
Op
ticaldensity(a.u.)
Radius (mm)
-8 -6 -4 -2 0 2 4 6 850
100
150
200
250 precursor
initial array diameterOpticaldensity(a.u.)
Radius (mm)
Imploding current sheath
Some mass fraction is left behind the implosion
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Material is left behind the implosion
Laser probing of 32 x 15m Al wire array
Global m=0 structure on X-ray images from t~0.8 timp
Some current reconnects
through the gaps during the
implosion phase
Secondary implosions are seen on streak images
Radial optical streak
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
X-ray pulse and the implosion dynamics
Radiation from inelastically accreted plasma during the
snowplough phase
Rising part of the main X-ray pulse:
Compression of precursor plasma column by JxB force,terminated by the onset of m=0 MHD instability?
Outward current diffusion - re-strike through the trailing
mass?
Secondary implosions of trailing mass:
- is this responsible for the yield exceeding 0-D kinetic energy?
0.6 0.8 1.0 1.2 1.40
2
4
6
precursor
keV
radiation5m
1.5m
xrd1s0601
xrd4s0601
X
RD(a.u.)
t / timp
Compression
Radius
terminated
by onset of MHD instabilities?
PIN0601
0.0
0.5
1.0
0.6 0.8 1.0 1.2 1.4
Current re-strike
& secondary implosions
of traling mass
Snowplow
implosion
phase
rad.sn.10
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Nested wire arrays in a current switchingmode
Current pulse through the inner array is controlled by thephase transitions in the wires of outer and then inner arrays
Inner array retain high transparency (~98%)
Core sizes (Al):
Outer array ~250m
Inner array ~30m
(initial wire diameter 15m)
X-ray radiography
0 10 20 30 40 500
2
4
6 6% of total
currentcurrent in
inner array
current(kA)
time (ns)
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Implosion phase of nested wire arrays
No momentum transfer
to the inner array at
strike
(paper TU-O1-4C by S. Bland)
Current from the sheath
switches into the inner
array at strike
Decay of snowplough
emission, plasma piston
coasts to the axis
No X-ray pulse at stagnation of the outer array on axis
nested
sinlge arrayradius(mm)
0
4
8
150 200 250 3000
5
10single array
PCD(a.u.)
time (ns)
nested
array
Radial optical streak
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
X-ray pulse-shaping in nested wire arrays
Variation of the inner array diameter controls radiation
power during the snowplough phase
Smaller inner diameter
Longer duration of the
snowplough phase
Larger foot of the X-raypulse
Optimisation of nested wire arrays?
0
4
8
radius(mm)
0
1x1010
2x1010
3x1010
Rin=4mm
nested:
Rin=8mm
single
power(W/cm)
150 200 250 300
0
1
PCD(a.u.)
time (ns)
pcd3s0802
pcd3s0830
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Lebedev S.V. et al., BEAMS-DZP, Albuquerque, NM, June 24, 2002
Radiation during the snowplow implosion
Radiation power from the inelastically accreted plasma:
20mm diameter W wire array on Z(c. f. M. Cuneo and G. Chandler, SNL)
Density from the ablation model
(Va=2x107
cm/s)
~ 30% of the array mass is left behind the implosion
Agreement in implosion trajectory and in absolute
power of the x-ray pulse foot.
Talk TU-O1-3I by M. Cuneo on Tuesday.
32 )(),()(21)( aa VVtr
dtdr
dtdmtP =
0.0 0.2 0.4 0.6 0.8 1.00
2
4
6
Vpiston
= Vabl
Density profile for Vabl
=2x107
cm/s
stationary at t=73.4ns
along the implosion trajectory
Density(mg/cm
3)
Radius (cm)
0 20 40 60 80 1001200
2
4
6
8
10
snowplow
radius(mm)
time (ns)
0-D radius
Z674
0
50
100
X-raypower(TW)
t0
= 73.4ns
M0
(piston) = 0.35
Vcor
= 2x107
cm/s
power from
snowplow
2.45E-006 2.50E-006 2.55E-006
XRD5A1KM
20
0
22
0 )]([8
),(aa V
rRtI
rRVtr
=
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Lebedev S.V. et al., paper GI1.005 at APS-DPP, Long Beach, CA, October 30, 2001
Pre-conditioning of foam targets by theprecursor plasma flow
The flow of precursor plasma is equivalent to ~20 keV ionbeam with j ~ 200 kA/cm2
Rate of energy deposition:
(expansion)
Kinetic pressure:
(compression)m.f.p.
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Lebedev S.V. et al., paper GI1.005 at APS-DPP, Long Beach, CA, October 30, 2001
X-ray radiography shows compression ofCH foam by precursor plasma flow
Radiography by 3-5 keV radiation from X-pinch
Compression of the foam (15mg/cc) is consistent with 0-D
implosion driven by kinetic pressure of the precursor flow
What happens with foam targets on Z?
0 50 100 150 200 2500.0
0.2
0.4
0.6
0.8
R15mg
R10mg
R.fort
Radius(mm)
time (ns)
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Lebedev S.V. et al., paper GI1.005 at APS-DPP, Long Beach, CA, October 30, 2001
Ablation of wire cores in a wire array
Ablation rate increases with global magnetic field
Radiation from the wires:
scales as R-2/3
radiated energy per ablated ion
What ismechanism of energy deposition into the cores?
Direct ohmic heating ?
Thermoconduction
Radiative heating
(P ~ 2x107 W/cm2)
32 x 15 m Al wire arrays
100 150 200 250 300 3500
5
10
15> 370ns
230ns
175nsR(mm)
time (ns)
Radiography
0 50 100 150 200 2500.0
0.5
1.0R = 8mm
PCD_
R8m
m(GW/cm)
time (ns)
scaled ~ R-2/3
R = 4mm
R = 18mm
0.0
0.5
1.0R = 4mm
R = 8mm
R = 18mm
BRVR
I
dt
dm= 1
0
2
0
4
eVdtdm
PE rad 300
/~
3.1Rdt
dm
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Lebedev S.V. et al., paper GI1.005 at APS-DPP, Long Beach, CA, October 30, 2001
Symmetry of the current sheath formation
Variations in the ablation rate lead to non-
simultaneous breakage of the wires
Statistics of axial perturbations in individual wires:
Wire number
provides
averaging
Systematic variations in the global magnetic field:
Al0.0 0.2 0.4 0.6 0.80
5
10
15 = 0.51 mm
sd ( ) = 0.1mm
frequency
"wavelength" (mm)
Missed wire (XUV images)Conical array (laser probing)
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Summary: two-stage implosion in wirearrays
1.Radial redistribution of mass by the precursor flow
from stationary wire cores
Role of wire number more uniform pre-fill
2.Final implosion phase starts after formation of gaps in
wire cores
Implosion of current sheath (current transfer to the
array axis)
Stabilisation by the density profile?
Trailing mass
Role of wire number better statistics in formation ofgaps
3-D modelling is required for the 1st
stage!
1-D and 2-D could be adequate for the 2nd
stage.