s.n. bland et al- use of faraday probing to estimate current distribution in wire array z-pinches

8/3/2019 S.N. Bland et al- Use of Faraday Probing to Estimate Current Distribution in Wire Array Z-Pinches

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Use of Faraday Probing to Estimate Current

Distribution in Wire Array Z-Pinches

S.N. Bland, S.C. Bott, A. Guite, G.N. Hall, S. M. Hardy,

S.V. Lebedev, P. Shardlow, A. Harvey-Thompson, F. Suzuki

Blackett Laboratory, Imperial College London

D.J. Ampleford

Sandia National Laboratories, Albuquerque

K. H. KwekPhysics Dept, University of Malaysia, Kuala Lumpur, Malaysia

This research was sponsored by Sandia National Laboratories, Albuquerque,

and NNSA under DOE Cooperative Agreement DE-F03-02NA00057


2/29

Wire array z-pinches

B

xBz

Wires heat, ablate into plasma

JxB force towards axis

On stagnation, X-ray pulse 280TW, 2MJ soft X-rays@ 20% efficiency

Large questions over physics behind implosions

% of implosion time0 0 0 0

Implosion trajectory

Ablation of wires

240x7.5um W on 120x7.5um W on Z


3/29

Interest in arrays spurred by huge X-ray powers (>200TW)

Already used to provide temperatures for NIF hohlraums

Possible ICF drive already >97% symmetries at capsule

Perhaps even IFE as highly efficient (>15%)

CRUCIAL to understand plasma formation and dynamics and learn to control it

ICF and arrays

Sanford et al,


4/29

Arrays also serve as a highly versatile source of plasma

Precursor ni ~1017 1019 cm-3, T ~10 -100eV

Stable inertially confined body of plasma,

effects of coupling cannot be ignored Stagnated plasma ni > 10

20 cm-3, T > 400eV

CRUCIAL to understand plasma formation and dynamics and learn to control it

Arrays and HEDP

Precursor can be redirected into jet

Jet scalable to astrophysical jets

Can be interacted with gases/foils


5/29

J^B force acts

just to accelerate

coronal plasmaaround core

Streams then flow

force free to axis

Wire core remainsstationary

Cold relatively densecore ~250m in Al

Core ablates to coronal plasmav~1.5x105 ms-1

Ablation axially modulated

MAGPIE 16x15m Al 124ns

16mm

20 Ir4

BIdtdmv ==

Phenomenological model

of ablation:

Radiography (3-5kV)Laser probing

(ne ~ 1017 cm-3)

Plasma Formation in Wire Arrays


6/29

Ablation of cores axially

modulated

Until ~80% of 0-D time

ablation continuesGaps form in cores and

implosion occurs as

snowplough accreting pre-

filled mass

Implosion of an aluminium array

Stagnation &

x-ray pulse

Core-corona formation

Implosion not like a

shell snowploughscoronal plasma

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

Radius(mm)

% of implosion time

Precursor on axis

Imploding debris

field

Gaps form incores

snowploughdebris

debris

implodedPeak X-raysprecursor

Gaps

Implosion Dynamics in Arrays


7/29

Current distribution in arrays

The distribution of current throughout the various stages of array evolution will stronglyeffect plasma dynamics

Prior to implosion it is usually assumed that the majority of current remains

concentrated close to the wire cores.

Supported by observations of a stable precursor column and inductance calculations But current could accelerate coronal plasma flowing towards axis

This could significantly change ablation estimates

During implosion, trailing mass is observed after the snowplough

Current switching back into the trailing mass causes it to implode

This could Limit X-ray production at stagnation

XUV images of an array

implosion showing trailing mass

implodes after peak X-rays

peak-15ns +15ns


8/29

1-1.4MA, 240ns rise time

High impedance generator

Good diagnostic access

return at 7.5cm


9/29

Traditional measurements of I

Pick up or B-dot coil:

Rogowski groove:

B

I

B

Vpickup B-dot positioned

with Z-pinch

dt

dVpickup

=

dt

SdBdnVpickup = .

dt

dI

r

nAV opickup

2

=

Faradays law:

For n turns:

Sub for B:

I

B B

Vgroove

A machined groove effectively acts as a single turn coil

dt

dI.

a

bln

2

dt

dr2

Id

zV 0

b

a

0

groove

==

z

r

Can be made and positioned accurately More easily shielded from electric field effects


10/29

Problems with pick up coilsElectron flow early in time Shielding by plasma

Electric field pick up Breakdown to probe

I

B B Vgroove

I

e-

At early times, e- flow

from transmission line

Can short out/shield

B Flow ofplasma

In high conductivity plasmas

magnetic flux can be trapped in the

flow, shielding the probe

High fields can lead to breakdown

through probes themselves

destroys probe, damages scope

and disturbs pinch

Before

After

coilCapacitive voltage pick

up of coilI B

+Ve

E

V

t

Opposite wound coils

can quantify this


11/29

Faraday Probing

EM waves passing through optically active

materials in a magnetic field have a difference in

wave velocities for the right hand and the left

hand nodes of a circularly polarized wave

wave rotates as propagating -Faraday Rotation

Can be monitored be examining intensities of

different polarisations

In a plasma, the rotation , is a function of plasma density:

= dlBn

1

m

e

2c

1

e22e0

3Solving for B allows I to be

determined

Alternately, a rod of active solid material, such as quartz or Verdet glass can be used

= dlB where is the Verdet constant


12/29

Faraday Probing and Arrays

2 ways to use Faraday Probing with arrays: Imaging Faraday and Time resolved

Use short pulse laser to provide polarised images of array and

examine transmitted intensities can provide information on

where current is flowing in plasma if density is known

MAGPIE 16x15m Al 124ns

Alternatively can use CW laser, and examinepolarised transmission across a chord in time.

To remove uncertainties in plasma density, laser

passes through Verdet material e.g. quartz

To analysers

and scope


13/29

Faraday Probing Imaging set-up

Input SBS compressedNd YAG pulse

~300mJ, 532ns, 0.7ns

Front telescope Polarizer

8-bit CCD

8-bit CCD

Non-polarizing

beamsplitter

Analyser in parallel light

Extinction ~ 104

Faraday line

Mach-Zehnder line

Shadowgraphy line

16-bit cooled CCD

Because the degree of rotation is small, a polariser is required before array

Analyser in parallel light (at focus of telescope) via non-polarising beamsplitter

Faraday, interferometry and shadowgraphy all share same (low) acceptance angle


14/29

Faraday Probing Imaging set-up

The analyser (a second polariser) is set at a small angle A to extinction

Current flowing through the z-pinch will set up a magnetic field around it

On one side the field will be towards the beam, on the other away2 intensities result on the camera dark side and light side

)(cosI 20 = Abright I

)(cosI 20 += Adark I

Providing we know background intensity (Io), or

how it is changing shot to shot, monitoring bright

and dark allows to be calculated

Then knowing electron density profile we can find B

From M. Tatarakis et al, Phys. Plas. 5, P682 (1998)


15/29

Faraday Probing Imaging results

Shot 0607:176ns, A positive Shot 0611: 188ns, A negative4x18um W array background

16mm precursor wires

During shot intensity on one side of the precursor higher than other

Idark and Ibright swap sides when A swaps direction

indicates current present in precursor


16/29


600 700 800 900 10002.0

2.5

3.0

3.5

4.0

4.5

5.0

density(+18)(cm-3)

radius (m)

600 700 800 900 1000 1100

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

rotatio

n(deg)

radius (um)

600 700 800 900 1000

20

21

22

23

24

magneticfie

ld(T)

radius (m)

0

20

40

6

0

80

100

120

current(k

A)

Assuming cylindrical symmetry of

precursor, its density can bedetermined from interferometry

Rotation and density suggest a

current of ~100kA through

precursor (11% total I)


17/29


8x13um W array 183ns

16mm

8x13um W array 198ns

Small, if any, rotation

observed in 8 wire

arrays,


18/29

Faraday Probing Imaging limitations

In addition, absorption, and refraction limit the density that can be measured

accurately in the interferogrammes to ~1019 cm-3

= dlBn

1

me

2c1 e22

e0

3

Plasma provide only small rotations:

Stability arguments suggest that the precursor - say a 2mm body of ~5x1018 e- cm-3

- carries


19/29

Time resolved Faraday set-up

CW laser

532nm, 35mWVerdet rod either

besides or in array Cube polariser asanalyser

DET210 highspeed diode

The laser is already well polarised, and

angle of rotation is so large (>/8) only

an analyser is required

Rod must be protected from both EMradiation (it could scintillate), shock and

debris

Thor Labs DET210 detector at 532nm

with 50 load:V = 14xinput power in W

Time response ~1ns

DET210 high

speed diode

Faraday rod in

protection tube next

to short circuit load


20/29

High Verdet Glass characteristics

In order to allow small sample lengths to be used (say ~1mm) localising

measurements to precursor and wires - high Verdet constant glass is used to

provide a measurable rotation.

MR3-2 faraday glass was supplied by Xian Aofa Optoelectronic technology inc

Previous time resolved Faraday systems have used quartz rods, Verdet constant

Verdet constant:

0.327min/Oe-cm or 108 rad /TmRods of 3.15mm diameter, initially

13mm length

Verdet constant ~ 0.02 min/Oe-cm or 6.6rad /Tm at 532 nm

For the precursor, if we want to

measure a minimum of 10kA (1%peak current) in a 2mm section of

rod, placed 2mm from axis:

Rotation

MR3-2 ~ 0.1rads or 12degreesQuartz ~ 0.006 rads or 0.4degrees


21/29

CW Diode laser characteristics

CW Diode pumped Nd-YAG laser supplied by Wicked Lasers35mW CLASS 3B, 532nm

TEM00, Beam diameter ~2mm, Divergence


22/29

Time resolved Faraday test

Rod placed in loop of wire carrying fast rising current:

I ~ 3Ka, 300ns

rise time

( )( )2

322

2

0

xr

1I(t)

2

rxB

+=

From Biot Savart Law:

Integrating, and substituting into the rotationequation with r =7mm and length 13mm:

I(t)8.5x10dlB(t) 7==

where r is

the radius of

the coil

Therefore at peak current we expect arotation of~0.28radians or ~16degrees 0 1000 2000 3000 4000 5000

-3

-2

-1

0

1

2

3

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Expectedrotation(rads)

Current(k

A)

Time (ns)

Measured current through loop

and expected rotation



23/29


Opposite signals from the 2 diodessuggest Faraday rotation is taking place

Intensity peaks with peak current as

expected

0 1000 2000 3000-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.2

0.3

0.4

0.5

0.6

0.7

0.80.9

1.0

cos

2(rotation)

Expectedrotation(rads)

Time (ns)

+/16+/8+/4

)(cosII A2

0diode1 =

)(cosII A20diode2 +=Unfortunately uncertainty in the initial

polarisation A makes analysis difficult

future experiments require A to beknown and set before experiment

ie Rotate polarisation to 0 on diode 1,

max on diode 2

-1000 0 1000 2000 3000

0.00

0.05

0.10

0.15

Diodevolta

ge(V)

Time (ns)

Diode s polarDiode p polar


24/29

Time resolved Faraday on MAGPIE

Short circuits were used to test the system on MAGPIE

M10 bolt (short circuit) Faraday rod inside protection

tube bolted into position

Top down view

( )I(t)1.5x10

2d

Ltan

tIdlB(t) 710 =

==

Again Biot Savart can be used to calculate the field expected at the rod. Integration

and substituting for rotation:

Hence at peak current of 1MA, the rotation should be 16.6rads.


25/29

Time resolved Faraday on MAGPIE

0 50 100 150 200 250 3000

200

400

600

800

1000

0.0

0.2

0.4

0.6

0.8

1.0

cos2(rotation)

Current(kA)

Time (ns)

The MAGPIE current pulse model:

)2

t(sinII(t) 20=

0 50 100 150 200 250 300-0.02

0.00

0.02

0.04

0.06

0.08

0.10

The intensity measured on the diodes

expected to show at least 5 minima

over the current pulse

Diodevolta

ge(V)

Time (ns)

Diode 1

Diode 2

where I0 = 1MA, = 240ns

In experiment any real signal is swampedby noise both electrical and optical

Need to knowt


26/29

currentdistribution in

wire array

Imaging Faraday

system

Successfully usedto examine current

in precursor

In experiment swamped byelectrical/optical noise

Questions remain as todisturbance of saturation or rod

and disturbance of plasma inexperiment

Small rotations makeaccuracy difficult

Suffers from absorption/refraction problems

Summary

Measures rotationin polarised laser

image

Time resolvedFaraday system

Successfullytested offline

Uses CW laser throughVerdet glass rod

positioned close to pinch


27/29

Future Improvements

Imaging faraday will be improved via:

a) Better input beam Improvements in the laser system will remove many of the

spatial features present in intensity

b) improved polarizers Glan-Taylor Prisms provide 105 extinction

Time resolved faraday requires electrical and optical noise present at the diode tobe reduced, or the introduction of a far more powerful laser:

a) The optical shielding will be increased with better interference filters.

b) The 30mW CW laser currently used will not improve the basic signal level. One

option would be a more powerful CW laser. BUT DET210 detectors have amaximum input of 100mW CW not much improvement

Pulsed train from main MAGPIE laser

Input 100mJ, 7ns

PlatePolarizer Faraday

rotator

97%beamsplitter

0 50 100 150 2000

50

100

150

200

250

300

350

400

450

Ex

pectedpower(K

W)

Time (ns)


28/29

References and Acknowledgements

J.H.Hammeret al, Phys. of Plasmas Vol6 P2129 (1999).

T.W.L.Sanford et al, Phys. Rev. Letters Vol77 P5063 (1996).

C.Deeney et al, Phys. Rev. Lett. Vol81 P4883 (1999).

G. Bennett et al, Phys. Plasmas Vol10, P3717 (2003). S.V. Lebedev et al, Phys. Plasmas Vol8 P3734 (2001).

M. Tatarakis et al, Phys. Plas. Vol5 P682 (1998).

F.J.Wessel et al, Rev. Sci. Instrum. Vol57 P2246 (1986).

Wasif Syed of Cornell University for useful conversations on Faraday

Rotation and high Verdet constant glass


29/29

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