s.v. lebedev- effect of discrete wires on the implosion dynamics of wire array z-pinches

8/3/2019 S.V. Lebedev- Effect of discrete wires on the implosion dynamics of wire array Z-pinches

1/21

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


2/21


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


3/21


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


4/21


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


5/21


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


6/21


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


7/21


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)


8/21


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


9/21


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


10/21


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


11/21


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



12/21


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


13/21


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)


14/21


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



15/21


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


16/21


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

=


17/21

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.


18/21


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)


19/21


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


20/21


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)


21/21

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.

s.v. lebedev- effect of discrete wires on the implosion dynamics of wire array z-pinches

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