s.v. lebedev- implosion dynamics of wire array z-pinches

Implosion dynamics of wire array Z-pinches

S.V. LebedevMini-course on Z-pinches

Monterey, CA 18-19 June 2005

Imperial College London

S.V. Lebedev, Implosion dynamics of wire array Z-pinches. Z-pinch mini-course, Monterey, CA, June 19, 20052

Acknowledgements

D.J. AmplefordS.N. BlandD. Bliss S.C. BottJ.P. ChittendenM. CuneoJ. DavisC. DeeneyJ. GoyerC. Jennings M.G. Haines G.N. Hall D.A. Hammer J.B.A. Palmer S.A. Pikuz

D.D. RyutovT. SanfordT.A. ShelkovenkoD. SinarsA. VelikovichE. Waisman

………………

Experiments at Imperial College are supported by Sandia National Laboratories and by NNSA DOE


Outline

• Introduction: why wire arrays?

• Overview of the implosion dynamics

• Early stages of plasma formation

• Implosion phase in wire arrays and the X-ray pulse

• Trailing mass and trailing current

• Different implosion modes of nested wire arrays

• Possible non-MHD effects

• Other configurations/applications of wire array Z-pinches


0-D implosion

RIBRRm

πμ

μπ

422

20

0

2

0 −=⋅−=&&

22

2

)(ττ

fd

rdr ⋅Π−=⋅

Thin conducting shell with axial current

Equation of motion of a shell driven by the pressure of magnetic field (m0 is mass per unit length) :

200

2max

2max0

4 RmtI

πμ

≡Π

In dimensionless variables

r = R / R0, τ = t / tmax f(τ) = I(τ) / Imax

Π is a dimensionless scaling parameter:identical implosions for identical values of Πand the same current pulse shape (f(τ))

0.0 0.5 1.00.0

0.5

1.0

0.0

0.5

1.0

Time

Π=20

Π=5

Rad

ius

Cur

rent

I ~ sin2(t)

Implosion trajectory


X-ray power from Z-pinch implosion or why wire arrays?

rayXWmVCU−⇒⇒

22

22

VRWP X δτ

τ~∝

Imploding plasma shell Energy Power

•Small mass to maximize implosion velocity

•Wire array is equivalent to ~50nm thick foil and wires should rapidly merge into a shellWire array Z-pinch

Wire array Shell

This transition does not happen!

3-D effects are important throughout the implosion!


Wire array Z-pinches: two stage implosion dynamics

Two-stage implosion dynamics

• “Slow” ablation of wires and radial redistribution of mass

• Snowplough-like final implosion phase, stabilised by the peaked on axis density profile

Wires survive for ~3/4 of the implosion time!

0.5 1.00.0

0.5

1.0

Rad

ius

time

coronal

plasma

Trailing mass

StagnationPrecursor pinch

Snowplow-likefinal implosion

0-D

Ablation of wire cores


Wires in wire array (magnetic field configuration)

wNRgap δπ

>>= 02

0 2 4 6 8 10x, mm

0

2

4

6

Inter-wire separation >> initial wire diameter

“Global” and “private” magnetic flux

∑= −⋅−+

−⋅−⋅=

N

CosrrrrCosrr

NIB

122

00

)(2)(

2 β βββ

ββθ θθ

θθπ

μ

∑= −⋅−+

−⋅⋅=

N

r CosrrrrSinr

NIB

122

00

)(2)(

2 β βββ

ββ

θθθθ

πμ

0.6 0.8 1.0 1.2 1.4 1.6-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

B/B

shel

l

radius

shell

array:between wires

array:through wire

Magnetic field lines (N=8)

Magnetic field distribution (N=16)

( )π

δπδ

μπ

μ2

@2

/2

00 gapNIBRIB wireshell =≡=≡

( >200μm) ( ~5-20 μm)

Magnetic field distribution[ Felber & Rostoker, Phys. Fluids 1981]


Wires in a wire array (R and L)

HNr

RNR

RhLwire

oretout

10

0

0 108.6)ln1(ln2

−⋅≈⋅

+=π

μ

Typical Ohmic heating time to ~Tmelt:

τ ~9ns

Typical “cold” array resistance: R~25 mΩ/cm for 6mg, N=300 tungsten array

Typical inductance:

Typical array resistance at T=Tmelt:

R~8.7 Ω/cm 0 2 4 6 8 100.0

0.1

0.2

0.3

0.4

0.5

0

1000

2000

3000

4000

R (O

hm)

time (ns)

T

R

I (kA)

T (K

), I (

kA)

Z arrayW 6mg, 1cm longN=300

After plasma formation current is in the coronal plasma: Rplasma =?

L/Rcold ~ 30ns


Experimental set-up: MAGPIE (1MA) and Z (20MA)

Wire arrays:

X-pinch in current return Z-Beamlet and spherical crystals

MAGPIE Z

1ns, 10μm

hν ~ 3-5keV

MAGPIE Z

R (mm) 4-8mm 10-20mm

N ~32 ~300

timplosion ~250ns ~100nsCurrent per wire

30 kA 60 kADiagnostics: X-ray/optical imaging, laser probing

Radiography:


Core-corona structure of plasma in wire arrays (1MA)

Wires remain at initial positions until ~80% of implosion

Non-uniformity of coronal plasma formation imprints on the cores

Sharp outward and a shallow inward edges of wire cores

Radiography Laser probing Radiography

Same λ

Dense, stationary wire cores surrounded by low density coronal plasma

0.0 0.5 1.0 1.5 2.0

16

18

20Al

250μm

arrayedge

Film

den

sity

(a.u

.)

Radial position (mm)0.5 1.0 1.5

W100μm

twowires

Shape of wire cores is not cylindrical


Core-corona structure of plasma in wire arrays (1MA)

Wires remain at initial positions until ~80% of implosion

Non-uniformity of coronal plasma formation imprints on the cores

Maximum ablation and maximum plasma flow are at different axial positions!

Radiography Laser probing Radiography

Same λ

Radiography Laser probing

Dense, stationary wire cores surrounded by low density coronal plasma

flow

gap


Precursor plasma flow in wire arrays (1MA)

Inward streaming of the coronal plasmaEnd-on laser probing End-on XUV Radial optical streak

X-ray image of precursor

• Plasma on axis at t ~50% timpl

(V~15cm/μs from end-on measurements)

• “Inertially confined” precursor column on axis

• Implosion starts at t ~80% timpl


Core-corona structure of plasma in wire arrays (Z)

Radiography shows wire cores until ~60% of implosion

Non-uniformity of coronal plasma formation

Maximum ablation and maximum plasma flow are in different axial positions!

Precursor column on axis

Radiography Visible imagingD. Sinars et al, PoP 2005. D. Bliss et al, ICOPS 2004.

End-on X-ray imageM. Cuneo et al., PRE 2005

precursor


“Delayed” implosion trajectories

MAGPIE Z

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

0-D Al

N=16 N=32

W N=32 N=64

R /

R0

t / t imp

shell-likeimplosion

N=32, 8mm

• During the first 80% - 60% of time the JxBforce is not applied to the cores, accelerating instead the coronal plasma

• Fast acceleration – not all mass participates

• Rate of plasma formation is the most important parameter during the first phase

M. Cuneo et al., PRE 2005

0-D


Ablation rate of wires in a wire array

Ablation in conical array Ablation time depends on array radius

The JxB force of the “global” magnetic field determines the ablation rate of wires in an array

32x15μm Al arrays driven by the same current pulse have different ablation times

Direct application of single wire results is not possible !


“Rocket” model of ablation and mass redistribution

0

20

4 RI

dtdmV

πμ

−=

∫=t

abl

dtIRV

tm0

2

0

0

4)(

πμδ

Ablation of stationary wire cores

(Rocket model)

rI

dtrdm

πμ4

20

2

2

0 −=

Ablated mass:

Momentum balance:

JxB force is only acting on the coronal plasma

(0-D model)

ablVRI

dtdm

0

20

4πμ

−=

202

02

0 )]([8

),(ablabl V

rRtIVrR

tr −−⋅=

πμρ

Ablation rate:

Radial profile of the ablated material:

Concept of “ablation velocity” (Vabl) highlights the main dependence of the ablation rate on current and array radius (Vabliis a weak function)

Lebedev et al., PoP 2001


Ablation rate of wires in a wire array

Ablation in conical array Ablation time depends on array radius

Starting time of the implosion is consistent with ablation of about half of array mass:

32x15μm Al arrays driven by the same current pulse have different ablation times

Direct application of single wire results is not possible !

∫=t

abl

dtImRVm

tm

0

2

00

0

0 4)(

πμδ


Early time XUV radiation as indicator of ablation rate

Linear wire array

abl

global

VBI

dtdm

⋅

×−=

2

32x15μm Al arrays driven by the same current pulse show different level of XUV emission

)(/4~),(/300~/

~ WionkeVAlioneVdtdm

PE rad

The same current, but larger Bgl (x6.6)


Variation of ablation rate with inter-wire gap

Ablation time of an array “Ablation velocity” versus inter-wire gap

0 5 10 15 20 25 30 350.0

0.5

1.0

1.5

2.0N=8R=8mm

N=16R=8mm

N=32R=8mm

N=64R=8mm

N=16, R=4mm

N=32, R=4mm

N=64, R=4mm

Vab

l (10

7 cm

/s)

gap / core size

Al Wπ (critical ratio)

Rapid increase of ablation rate for the gaps below “critical”:

change in the magnetic field topology at δcr ~ 3 x (core size)

Could be an additional dependence of Vabl on wire diameter [D. Sinars et al., PoP 2005]

0 2 4 6 8 10x, mm

0

2

4

6

7 8 9 10x, mm

0.0

0.5

1.0

1.5

2.0

Magnetic field

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−−⋅=

4.3exp15.1)( xxf

∫=t

abl

dtImRVm

tm

0

2

00

0

0 4)(

πμδ


Implosion similarity of wire arrays

max0max /)()ˆ(/ˆ/ IItfRrrtt ττ ===

22

2

)(ττ

fd

rdr ⋅Π−=⋅)

)

200

2max

2max0

4 RmtI

πμ

≡Π

0-D similarityIn dimensionless variables:

0-D dimensionless scaling:identical implosions for identical Πand the same current pulse shape f(τ)

How the similarity criteria should change to account for the redistribution of mass by the precursor plasma?

∫⋅=

t

abl

dtIRVmm

tm

0

2

00

0

0 4)(

πμδ

ablVRI

dtdm

0

20

4πμ

−=

Ablation rate:

Ablated mass:


Implosion similarity of “ablating” wire arrays

)//()ˆ,ˆ(ˆ/ˆ/ 2000 RmtrRrrtt m ρρτ ===

[ ]22

))ˆ1((ˆˆ2

),ˆ(ˆ rKIr

Kr −⋅−⋅⋅

⋅Π= τπ

τρ

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0 Π ~ 6

Cur

rent

time

Abl

ated

mas

s fra

ctio

n

K=0.2(Magpie)

K=0.7(Z ?)

Ablated mass fraction:

∫∫ ⋅⋅Π=⋅⋅

⋅⋅

=ττ

ττπμτδ

0

2

0

20200

220

0

)~()~(4

)( dIKdItV

RRm

tImm

mabl

m

Πis fixed ⇒ the same 0-D implosion time and the same trajectory+K is fixed ⇒ the same degree of mass redistribution

Dimensionless variables:

Density profile:Π K

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

Π ~ 6

K=0.7, τ =0.7(Z ?)

K=0.2, τ = 0.97(Magpie)

Den

sity

Radius

KMagpie ~0.2

KAngara ~0.2

KZ ~ 0.4 - 0.7

KSphinx ~0.7


Distribution of mass at the start of implosion phase

Implosion phase:Snowplough-like implosion of the distributed mass

Stabilisation by density profile

Does all mass participate in the implosion?

~50% of mass is inside the array

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Π ~ 6

K=0.2, τ = 0.97(Magpie)

K=0.7, τ =0.7(Z ?)

Mas

s fra

ctio

n

Radius

~50% of mass in wire cores at R0


Axial non-uniformity of the ablation rate

Axial modulation of the ablation rate is responsible for existence of trailing mass in wire array Z-pinches

Process of wire ablation is the same for 1MA and 20MA currents

1MA

MAGPIE

20MA

Z (SNL)


Transition to the implosion phase

Axial modulation of ablation rate formation of “breaks” in the wires

Imploding current sheath, formed by a number of “magnetic bubbles”

Laser probing (Al, N=16) XUV images (Cu, N=8)

precursor


Snowplough-like implosion in W arrays

Laser probing of 32 x 4 µm tungsten wire array

Implosion of current sheath through the plasma pre-fill

-8 -6 -4 -2 0 2 4 6 850

100

150

200

250 precursor

initial array diameterOpt

ical

den

sity

(a.u

.)

Radius (mm)-8 -6 -4 -2 0 2 4 6 8

0

50

100

150

200

initial array diameter

implodingplasmapiston

precursor

Opt

ical

den

sity

(a.u

.)

Radius (mm)


Snowplough implosion phase

implosion trajectory

10%

60%mass fractionin the piston:

0% 10% 60%

Rad

ius

(mm

)

time (ns)100 150 200 250 300 3500

2

4

6

80-D

experiment streak

x-ray: outer inner

Two possible implosion scenarios:No current through the gaps Current re-strike

Trailing mass All mass implodes

ρ(r) from “rocket” model

Initial piston mass is adjusted to fit implosion trajectory

~40% of array mass is left behind

32 x 15µm Al array on MAGPIE

Imploding sheath on end-on X-ray images


Snowplough implosion phase on Z facility

202

02

0 )]([8

),(ablabl V

rRtIVrR

tr −−⋅=

πμρ 32 )(),()(

21)( ablp VVtr

dtdr

dtdmtP −⋅∝⋅= ρ

0 2 4 6 8 100

2

4

6

dens

ity (m

g/cc

)

Radius (mm)

Density profile along implosion trajectory

Vabl = 1.45x107 cm/s

Vpiston = Vabl

Density profile from the ablation model:

Radiation power from the inelasticallyaccreted plasma:

0

5

10

60 80 100 120 1400.01

0.1

1

10

100

60 80 100 120 140

time (ns)

P_exp

Rad

ius

(mm

)

Shot674nf rpeak

Vabl = 1.45x107 cm/s

t0 = 71.4ns

Pow

er (T

W)

P_model

time (ns)

R0D rad

The “foot” of the X-ray pulse is produced by the snowplow radiation

~35% of array mass is left behind



Expansion of precursor during the implosion phase

dtdm

RVP

p

ablkin ⋅=

π2 lRETnZP

pith 23

2)1(π

⋅=+=

Equilibrium radius of precursor during wire ablation phase:


dtdmlV

ERabl ⋅⋅

⋅=34

radQFdtdE

dtdR

⋅−⋅=∝ )1( α

Kinetic pressure of plasma flow is equal to the precursor thermal pressure

TlnRZE ip2)1(

23 π+=

Equilibrium precursor radius:

Heating of precursor by the snowplow radiation leads to increase of equilibrium radius


Implosion and stagnation phase

Laser probingXUV images (32x10μm Al)X-ray peak

Transition from small λ modulation on wires to the global m=0 mode with λ ~2mm (Al)

Fraction of mass is left behind, and it is gradually reducing with time

Significant fraction of mass is left behind even at the time of the X-ray peak

Development of m=1 mode after the peak of X-ray pulse


Implosion and stagnation phase

X-ray signals

XUV images (32x10μm Al)X-ray peak

Expansion of precursor during the implosion phase

Start of the main X-ray pulse at ~time of the current sheath collision with precursor

Fast electrons (~100keV e-beam) during the X-ray pulse phaseX-ray>10keV


Spatial structure of stagnated pinch (MAGPIE)

Axially resolved X-ray spectrum (Al)

Correlation between positions of “hot spots”and the most pronounced m=0 structures in the trailing plasma

Al K-shell spectral lines

Continuum radiation from localised “hot spots”

Similar “hot spots” emitting continuum radiation were observed on Z [Sinars et al., JQSRT, in press]


Spatial structure of stagnated pinch (Z)

X-ray image of W array on Z Radiography of W wire array on Z[Deeney et al., PRL 1998] [Sinars et al., PRL 2004]

The spatial structure of the stagnated pinch could be related to the axial distribution of the trailing mass?

Pinch diameter ~1.5mm


Trailing mass at the time of the radiation pulse

Laser probing X-ray image

~10 -30% of mass is trailing at time of X-ray peakgradual clearing of trailing mass throughout the X-ray pulse

Trailing mass on Z (Cuneo et al. PRE 05)

Trailing mass could prevent efficient delivery of current (magnetic energy) to the radiating pinch

X-ray peakX-ray peak

Diameter of X-ray emitting region is a small fraction of the plasma diameter





Secondary implosions could act as a mechanism transporting magnetic energy to stagnated pinch





Dynamic modes of nested wire arrays

Model of two plasma shells:

• Mitigation of R-T instability by the inner shell

• X-ray pulse at the strike

3-D reality:

• No current in the inner array

• Initial array transparency > 99%

• Interpenetration of the arrays and implosion due to fast transfer of current to the inner array

Plasma shell

Wires Davis et al., APL 1997, Deeney et al., PRL 1998, Terry et al. PRL 1999,

Lebedev et al., PRL 2000, Deeney et al., PRL 2004, Cuneo et al PRL 2005


Current division in nested wire arrays

)ln1(ln2

0

NrR

NRRhL

wire

arr

arr

retarr ⋅

+=π

μ)(ln

20

arr

ret

RRhM

πμ

=

Inductive current division

For large wire number arrays (e.g. on Z) only a small fraction of total current (~2%) should be in the inner array

For arrays with N~16 (e.g. on MAGPIE) current fraction is ~ 20%

Resistivity could play a role in the current division

)ln()2(

)(Nr

RMLL

MLII

wire

o

inout

out

total

inner

⋅∝

−+−

=

Array inductance Mutual inductance

Current fraction in the inner array

A. Velikovich et al., PoP 2002


Nested wire arrays operating in a current switching mode

Current pulse through the inner array is suppressed

0 10 20 30 40 500

2

4

6 6% of totalcurrentcurrent in

inner array

curr

ent (

kA)

time (ns)

Current pulse through the inner array is controlled by the phasetransitions in the wires of outer and then inner arrays

Small core size of the inner array wires

Inner array retain high transparency (~98%)

Lebedev et al., PRL 2000, Bland et al, PoP 2003


Nested wire arrays operating in a current switching mode

No momentum transfer at “strike”

nested

sinlge arrayradi

us (m

m)

0

4

8

150 200 250 3000

5

10single array

PC

D (a

.u.)

time (ns)

nestedarray

Trajectory and the X-ray pulse

Current from the sheath switches into the inner array at “strike”

Decay of snowplough emission, plasma piston coasts to the axisAblation phase of the inner array after current pulse [Cuneo et al., PRL 2005]

Interaction radiation pulse in talk by M. Cuneo


Nested wire arrays offer control of the radiation pulse shape

150 200 250 3000

1nestedRin=2mm

pcd3s0802 pcd3s0830

PCD

(a.u

.)

time (ns)

0

5

10

nestedRin=4mmP

CD

(a.u

.)

pcd1s0726 pcd1s0802

02468

singlearray

nested

radi

us (m

m)

0.0

0.5

1.0

curr

ent (

MA

)

time (ns)0

1

2

3

PC

D (a

.u.)

stagnationstrike

precursor

b

current

X-ray PCD

0 50 100 150 200 250 3000

2

a

singlearray

nestedarray

PC

D (a

.u.)

0.0

0.2

0.4

0.6

0.8 experiment: nested array

0-D, 100% currenttransfer

I = 100%(single array)

Rad

ius

(cm

)

c

experiment: single array

100 150 200 250 3000.0

0.2

0.4

0.6

0.8

Different current division between the outer and the inner array affects the X-ray pulse shape

Effect of inner array radius on X-ray pulse shape

Implosion trajectories X- ray pulses

Iout = 65%

Iout = 78%

Rad

ius

(cm

)

time (ns)

d

Iin = 22%

Iin = 35%

I = 100%(single array)


Some “hot” topics (very subjective)

“Optimal” wire number

Effect of electric field polarity on plasma formation

Non-MHD effects?

Effects of turbulence on plasma resistivity?


Effect of wire number on X-ray power

0 5 10 15 20 25 30 350.0

0.5

1.0

1.5

2.0

2.5

3.0

Vab

l (10

7 cm

/s)

gap / core size

N=300

N=120N=50

f(x) = 2.2*(1-exp(-x/3.4))

N=600

Rise-time of the X-ray pulse for Al and W arrays

Mazarakis et al., Pl. Dev. Oper. 2005

0 2 4 6 8 100

1

2

3

4

5

6

dens

ity (m

g/cc

)

radius (mm)

V=0.8, t_0=61.6ns V=1.0, t_0=65.1ns V=1.2, t_0=68.1ns V=1.45, t_0=71.5ns V=2.2, t_0=80ns 0.8

11.21.45

2.2

Change in the density profile along the implosion trajectory

Expected scaling of Vabl withwire number for Z conditions

Optimal wire number in wire array implosions:• at large gaps – improvement with wire number due to statistics of uncorrelated perturbations

• small gaps – degradation due to less stabilisation of the R-T by the density profile


Non-MHD or “initial conditions” effects?

The wires in the array should have the same current.

However, the top and the bottom halves show very different dynamics!

The reason for this appears to be in the sign of the radial electric field on the wires


Effect of polarity of the radial electric field

-1 -0.5 0 0.5 10

20

40

60

80 Distance (mm)

Electric Field (AU)

“Standard” array:

Er <0

“Long” array:

Er <0 at the top

Er >0 at the bottom half

Long single array Electric field in“long” array

The polarity of the radial electric field changes in the middle of the “long” array

Difference in:•time of plasma formation •core size•ablation rate (Vabl)•implosion time

The half with Er>0 behaves as a standard array (in which Er<0) !?

Holes in electrodes

8mm

MITL

Anode


Effect of polarity of the radial electric field

The polarity of the radial electric field changes in the middle of the “long” array

Laser probing High resolution XUV image

Size of the wire core shadows:

Standard array “Long” array

300-350μm bottom half ~350μm

top half ~100μm

Later “breakage” of the wires and later start of the implosion for the top half of the array

Different ablation rate:Standard /bottom half top halfVabl ~15cm/μs Vabl ~40cm/μs


Axial plasma flow: two-fluid MHD?

Plasma has an axial velocity component (from cathode to anode), especially on the outward side of the wires

Is this related to the mechanism responsible for the axial modulation of ablation rate?

MAGPIE Z


X-ray pulse: kinetic energy or current convergence?

0.0

0.1

0.2

0.3

0.0

0.5

1.0

curr

ent o

n ax

is (M

A)

Iin0117

Iin0121

Iin0128

tota

l cur

rent

(MA

)

Id0117

Id0121

Id0128

0 100 200 3000

1

2

3

4

time (ns)

pcd

(a.u

.) pcd1s0117

pcd1s0121

pcd1s0128

Configuration with post-convolute transfers a fraction of current from the wires into precursor column, leading to delay in implosion

m=1 instability in the precursor

Total current

Precursor current

X-ray pulse

220 240 260 280 300

0

1

2

3

4

5

6

0

5

10

15

20

PC

D (a

.u.)

time (ns)

pcd5s0921 pcd5s1013

pcd2s0921 pcd2s1013

Different current left in the wires different array mass to keep the same implosion time

different kinetic energy ( x2)

The same current after stagnation and the same X-ray pulse





Trailing mass on Z (Cuneo et al. PRE 05)





What limits the current flowing through the trailing mass?

)21~( −⋅=> ξξ scrit Cuu

For Spitzer resistivity all current should remain in the trailing mass• High non-uniformity of the trailing mass

• Anomalous resitivity – Ion Acoustic Turbulence:

The following conditions should be satisfied(see e.g. Ryutov et al., RMP, 72, 167 (2000)):

1. Current velocity should exceed critical velocity:

i

i

i

ies m

Tm

TZTC

22 ⋅>

+=

ZTT i

e 7>

2. Ion sound speed should exceed ion thermal speed by, e.g., factor of 2:

For typical Z array(m0 =6mg, tungsten)

If mtr / m0 = 10%

u > ucrit for Itr > 3 MA

For high Z plasma satisfied even for Te=Ti


Is I.A.T. responsible for sub-quadratic power scaling?

secrite Cenuenj ⋅=⋅= ξ

∫ ⋅== trp

str m

AmZeCrdrrjI ξπ2)(

Current density in the trailing mass is saturated at the threshold of ion acoustic turbulence:

Total trailing current is proportional to the trailing mass:

Ohm’s law with Ion Acoustic Turbulence

Only the current flowing through the radiating pinch is useful!

0 5 10 15 20 25 300.0

0.5

1.0

1.5

2.0

2.5

0

200

400

Ene

rgy

(MJ)

current (MA)

0-D R=10mm R=20mm Exp R=10mm Exp R=20mm

Pow

er (T

W)

(τ=5

ns)

Z ZR

R=2cm

R=1cm

A =183, Z =8, T =30eV, α = 0.1, ξ = 1.1

Trailing plasma parameters:

)ln()(4

020

0

ptr R

RIIhW −⋅=π

μ

Magnetic energy delivered to the array axis:


Some other configurations of wire arrays

Radiatively cooled supersonic plasma jets:“hydrodynamic” “magnetic”


The “dynamic” life story of wire array Z-pinches

0.5 1.00.0

0.5

1.0

Rad

ius

timecoronal

plasma

Trailing mass

StagnationPrecursor pinch

Snowplow-likefinal implosion

0-D

Ablation of wire cores


References used in this talk1. D. D. Ryutov, M. S. Derzon, M. K. Matzen, “The physics of fast Z pinches”, Rev. Mod. Physics 72, 167 (2000)

2. M. K. Matzen, Phys. Plasmas 4, 1519 (1997)

3. T. W. L. Sanford et al, - “Improved Symmetry Greatly Increases X-Ray Power from Wire-Array Z-Pinches”, Phys. Rev. Lett. 77 5063 (1996)

4. M. K. Matzen et al., - “Pulsed-power-driven high energy density physics and inertial confinement fusion research”, Phys. Plasmas 12, 055503 (2005)

5. F.S. Felber, N. Rostoker, “Kink and displacement instabilities in imploding wire arrays”, Phys. Fluids 24 1049 (1981)

6. M.E. Cuneo et al., - “Characteristics and Scaling of Tungsten-Wire-Array Z-Pinch Implosion Dynamics at 20 MA”, Phys. Rev., E71, 046406 (2005).

7. S.V. Lebedev et al., - “Physics of Wire Array Z-Pinch implosions: Experiments at Imperial College”, Plasma Physics and Controlled Fusion, 47, A91 (2005)

8. S.V Lebedev. et al., – “Snowplow-like behaviour in the implosion phase of wire array Z pinches” , Phys. Plasmas, 9, 2293 (2002)

9. S.V. Lebedev et al., - “Effect of discrete wires on the implosion dynamics of wire array Z pinches” , Phys. Plasmas, 8, 3734 (2001)

10. C. Deeney et al., - ” Enhancement of X-Ray Power from a Z Pinch Using Nested-Wire Arrays”, Phys. Rev. Letters, 81, 4883 (1998)

11. S.V., Lebedev et al.,– “Plasma formation and the implosion phase of wire array Z-pinch experiments”, Laser and Particle Beams, 19, 355 (2001)

12. D. B. Sinars et al., - ” Mass-Profile and Instability-Growth Measurements for 300-Wire Z-Pinch Implosions Driven by 14–18 MA”, Phys. Rev. Letters, 93, 145002-1 (2004)

13. D. B. Sinars et al., “Measurements of the mass distribution and instability growth for wire-array Z-pinch implosions driven by 14–20 MA”, Phys. Plasmas, 12, 056303 (2005)


References used in this talk14. A. L. Velikovich, I. V. Sokolov, A. A. Esaulov, - ” Perfectly conducting incompressible fluid model of a wire array

implosion”, Phys. Plasmas, 9, 1366 (2002)

15. D.B. Sinars et al., - ” Measurements of K-shell Ar spectra from z -pinch dynamic hohlraum experiments made using a focusing spectrometer with spatial resolution”, JQSRT – (in press)

16. E. M. Waisman et al., - “Wire array implosion characteristics from determination of load inductance on the Z pulsed-power accelerator”, Phys. Plasmas, 11, 2009 (2004)

17. J. Davis, N. A. Gondarenko, A. L. Velikovich, - “Fast commutation of high current in double wire array Z-pinch loads”, Appl. Phys. Letters, 70, 170 (1997)

18. R. E. Terry et al., - “Current Switching and Mass Interpenetration Offer Enhanced Power from Nested-Array Z Pinches”, Phys. Rev. Letters, 83, 4305 (1999)

19. S.N. Bland et al., – “Nested wire array z-pinch experiments operating in the current transfer mode”, Phys. Plasmas, 10, 1100 (2003)

20. C. Deeney et al., - “Spectroscopic Diagnosis of Nested-Wire-Array Dynamics and Interpenetration at 7 MA”, Phys. Rev. Letters, 93, 155001-1 (2004)

21. M. E. Cuneo et al., - “Direct Experimental Evidence for Current-Transfer Mode Operation of Nested Tungsten Wire Arrays at 16–19 MA”, Phys. Rev. Letters, 94, 225003-1 (2005)

22. S.V. Lebedev et al., - “Effect of core-corona plasma structure on seeding of instabilities in wire array z-pinches”, Phys. Rev. Lett. 85, 98 (2000)

23. C. A. Coverdale et al., - “Optimal Wire-Number Range for High X-Ray Power in Long-Implosion-Time Aluminum Z Pinches”, Phys. Rev. Letters, 88, 065001-1 (2002)

24. M. G. Mazarakis et al., - “Tungsten wire number dependence of the implosion dynamics at the Z-accelerator”, Plasma Devices and Operations, 13, 157 (2005)


References used in this talk25. C. Deeney, C.A. Coverdale, M.R. Douglas, - “A review of long-implosion-time z pinches as efficient and high-power

radiation sources”, Laser and Particle Beams 19, 497 (2001)

26. S.V. Lebedev et al., - “Two different modes of nested wire array Z pinch implosions” - Phys. Rev. Lett., 84 1708 (2000)

27. S. N. Bland et al., – “Use of linear wire array Z-pinches to examine plasma dynamics in high magnetic fields”, Phys. Plasmas, 11, 4911 (2004)

28. S.V. Lebedev et al., - “The dynamics of wire array z-pinch implosions”, Phys.Plasmas, 6, 2016 (1999)

29. W. A. Stygar et al., - “X-ray emission from z pinches at 107 A: Current scaling, gap closure, and shot-to-shot fluctuations”, Phys. Rev. E 69, 046403 (2004)

30. V. V. Aleksandrov et al., - “Dynamics of Heterogeneous Liners with Prolonged Plasma Creation”, Plasma Physics Reports, 27, 89 (2001)

31. I. K. Aivazov, V. D. Vikharev, G. S. Volkov, L. B. Nikandrov, V. P. Smirnov, and V. Ya Tsarfin, JETP Lett. 45, 28 (1987)

32. Bekhtev M B et al, Sov. Phys.—JETP 68 955 (1989)

33. C. Deeney et al., - “Power enhancement by increasing the initial array radius and wire number of tungsten Z pinches”, Phys. Rev. E 56, 5945 (1997)

s.v. lebedev- implosion dynamics of wire array z-pinches

Documents

xray emitting

ion acoustic

prevent efficient

radial electric

wire arraydirect

stagnation

4vabl r0 m0

maximum plasma