Simon Bott, Farhat Beg

Application of pulsed power driven plasmas to study

astrophysical jets and supersonic outflows

Simon Bott, Farhat Beg

University of California, San Diego

Sergey Lebedev, Jerry Chittenden

Imperial College London, UK

Presented at the first U.S. Plasma Jet Workshop, which was sponsored by the

DOE Office of Fusion Energy Sciences and held at Los Alamos National

Laboratory on January 24-25, 2008

Ablating wires

Introduction

2

0IdmVabl

µ−=

• Mass ablation rate described by Rocket model (S.Ledebev, Phys Plasmas, 8, p3734, (2001)) 16mm

04 RdtVabl

π−=

• Mass ablated determined by Imax

• Timescale determined by τ

Ge

nera

tor

Dri

ve C

urr

ent

/ M

A

IMAX

abl

Time-slice from 3D Resistive MHD Gorgon Code (J.Chittenden, Plasma Phys Control Fusion 46, B457 (2004)

0 50 100 150 200 250 300 350

Ge

nera

tor

Dri

ve C

urr

ent

/ M

A

Time/ nsτ

Generator Location Imax ττττMAGPIE Imperial College 1MA (2MA) 250nsGenASIS UCSD 0.25 MA 150ns

X-Pinch Driver UCSD 0.08 MA 50ns

Supersonic Plasma Flow

• Plasma density (Nion): 1x1014 - 5x1017cm-3

• Plasma Velocity: 1.5x105 ms-1

• T = 5-15 eV

Supersonic precursor

plasma flowFlow Parameters

16mm

• Te = 5-15 eV

• Mach number: 3-5

• Rm < 1 (experimental)

2/ln8 44

42

ππλ

Λ=

ion

ablionperp

neZ

vm

Collisionality

133ns 171nsWAl

Time-slice from 3D Resistive MHD Gorgon Code (J.Chittenden, Plasma Phys Control Fusion 46, B457 (2004)

MAGPIE

Al : typically <1mm

W : >8mm for ~140ns

UCSD:

Some collisionless flow

even for Al

16mm

Gated axial XUV self-emission images from 16 wire arrays on MAGPIE

Shock formation in supersonic plasma flow

Collisional systems:

• e.g. Nested Wire Arrays at >1MA

Outer array wires

Plasma flowfrom outer array

Inner array wires

Axis

Shock formation in supersonic plasma flow

Collisional systems:

• e.g. Nested Wire Arrays at >1MA

• Data from 32 outer and 16 inner Al wires on MAGPIE

Outer arrayposition

Outer array wires

Plasma flowfrom outer array

Axial gated XUV self-emission imaging of nested Al arrays on MAGPIE (D.J.Ampleford in prep. PRL)

on MAGPIE

• Bow shocks formed around inner wires

• Secondary shocking also observed

• D.J.Ampleford at HEDLA

Shock formation in supersonic plasma flow

Collisional systems:

• e.g. Nested Wire Arrays at >1MA

• Data from 32 outer and 16 inner Al wires on MAGPIE

Outer arrayposition

Outer array wires

Plasma flowfrom outer array

Collisionless systems:

Axial gated XUV self-emission imaging of nested Al arrays on MAGPIE (D.J.Ampleford in prep. PRL)

XUV Spectroscopy

on MAGPIE

• Bow shocks formed around inner wires

• Secondary shocking also observed

• D.J.Ampleford at HEDLA

Generator

Axis

• UCSD experiments will provide collisionless flow,

• E.g. Laser driven experiments by Bell et

al Phys Rev A, 38, p1363 (1998)

• Good diagnostic access and shot rate

Ireturn Iwire

J x Bwire return

Ablated plasma flowaccelerated by JxB force

CATHODE ANODE

P = vflow ρ2

Single metal wireX

Radiography andimaging diagnostics

Obstruction

Precursor Column parameters

• Nion : 1018-1022 cm-3 (0.1 – 1 kg/m3)

• Z: (Al) ~7, (W) ~ 14

• Te ~ 60eV – 100 eV

• Diameter: 0.5-3 mm

Dense precursor

condensation on

axis

Inertially Confined plasma column formed

• Diameter: 0.5-3 mm

ArrayAxis

-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Film

contr

ast

/ arb

. units

Scale / mm

133ns

163ns

193ns

3.0

3.5

4.0

4.5

5.0Radiography Data

COBRA

MAGPIE

Rocket Model

precursor radius = 0.6mm

Vabl

= 1.5 x 105 ms

-1

COBRA

MAGPIE

Den

sity /

kg

m-3

Axis

Axial (lineouts right) and radial gated XUV self-emission images, along with column density with time for MAGPIE and COBRA W experiments (Bott et al, Phys Rev E, 74 046403 (2006))

Radiatively cooled and steady state (several shock transit times)

0 25 50 75 100 125 150 175 200 225 250 275 300

0.0

0.5

1.0

1.5

2.0

2.5 MAGPIE

Den

sity /

kg

m

Time / ns16mm

Optical Streak Photograph from MAGPIE of 32 wire Al array

Typical Parameters scale well

to astrophysical jets

Hydrodynamic Jet formation

General flow variablesLength (cm) 2

Width (cm) 0.1Dynamical time Scale 100nsElectron temperature (eV) 10Jet tip velocity (km/s) ~200

Conical

Wire

Array

Jet tip velocity (km/s) ~200�Jet density, (g/cm3) 10−4

Validity of fluid description

Localisation parameter 10−4

Reynolds Number (Re) 105 − 108

Peclet number (Pe) 2 − 2 × 103

Jet scalingMach number, M > 20Density Contrast, 100/ ~ 1

Cooling Parameter, 1S.Lebedev et al, ApJ 564, p113 (2002)S.Lebedev et al, ApJ, 616, p988 (2004)

2mm

Gated XUV Emission Laser Shadowgram 100 years 300 years5mm

Jet

CH Foil

Internal shock structure during deflectionD.J.Ampleford, Astro & Space Sci , 307, p29 (2007)

Ciardi et al, ApJ (accepted)A.Frank, Astro. Space Sci , 298, p107 (2005)

WIND

5mmX-UV

emissions

Foil holder

Side

Wind

Bally & Reipurth. ApJ, 546, p299 (2001)

HH502

Variation of jet parameters: Jets at UCSD• Range of jet parameters possible using different currents (e.g. 2 Generators at UCSD &

MAGPIE)

• First free propagating jets from x-pinches recently measured at UCSD at 80 kA

ρ (cm-2) 4.5

Are

al E

lectr

on

Density (

x 1

0 c

m)

17

-2

166 ns

D.M.Haas at APS 2007, and in prep. APL

5.5 x 1017

1 x 1016

8 x 1017

ρe (cm-2)

3

-1 0 1 2 3 4 5 6 7 8 91

1.5

2

2.5

3.5

4.5

4

Distance From top of Anode (mm)

AverageBackground

Level

Are

al E

lectr

on

Density (

x 1

0 c

m)

17

-2

2mm

Parameter 80 kA X-pinch measured 250 kA Conical Expected (HEDLA)Vjet 3.3 x 104 ms-1 1 x 105 ms-1 (100 km/s)cs (radial exp) 5.5 x 103 ms-1

M 4-8 M > 10ρe (cm-3 ) few x 1017 ~ 1018 - 1019

T (eV) ~15 ~15 Z ~5 ~ 5

D.M.Haas at APS 2007, and in prep. APL

Magnetically Driven Jets

Radial Wire Arrays• Wires show magnetic bubble structure and

jet formation (Lebedev AIP Conf. 2006)

• Foils loads show repeat formation of this structure during one current pulsestructure during one current pulse

• Recently foils performed with and without a gas fill (see F.Suzuki-Vidal at upcoming HEDLA conference)

Ciardi et al, Phys. Plasmas 14, 056501 2007

Magnetically Driven Jets

6 µm

Al FoilAnode

Radial Wire Arrays• Wires show magnetic bubble structure and

jet formation

• Foils loads show repeat formation of this structure during one current pulse

Cathode

structure during one current pulse

• Recently foils performed with and without a gas fill (see F.Suzuki-Vidal at upcoming HEDLA conference)

current cathod

e

foil

Magnetically Driven Jets

Radial Wire Arrays• Wires show magnetic bubble structure and

jet formation

• Foils loads show repeat formation of this structure during one current pulsestructure during one current pulse

• Recently foils performed with and without a gas fill (see F.Suzuki-Vidal at upcoming HEDLA conference)

current cathod

e

foil

Future Studies at UCSD

UCSD Drivers

• Good diagnostic access, high shot rate• 2 generators to give plasma source, and independent

B-field or second plasma

Jet

GenASIS

250 kALTD

10

mm

Single metal wire

20 - 40 mm

Parameter space accessible

Can adjust Plasma ρ : nion ~1014 – 1017 cm-3

B-field: Variable up to ~50T (200 kA)

Difficult to adjust: Plasma velocity (ablation physics)T: 10eV in flow, 60-100 eV in column

Material At No. below 6(C) (typ. 13, Al)

Physical Conditions: Collisionality of flowMagnetization of ions

β

Jet propagation into B-field

Ireturn Iwire

X-Pinch

80 kA

10 m

m

AnodeCathode X-Pinch80 kA

Marx

10

mm

10 mm

Low T limits plasma to low βNeed to investigate application to cosmic shocks (Drake PoP 2000)

Modelling

• GORGON for hydro and magnetic jets (J. Chittenden & A.Ciardi)

• Also use of LSP, h2d, and ePlas at UCSD

Kinetic compression of exploding foil

P = vflow ρ2

Single metal wire

GenASIS250 kA

LTD

80 kAMarx

MetalFoil

Cathode Anode

20 - 40 mm

10 m

m

Imperial College / UCSD Collaborative Studies

Imperial College: High current drive, extensive diagnostics, experienced team

UCSD: 2 drivers, high shot rate in simplified set-ups

Precursor Compression of targets using ablated

Iarray

Ablated plasmaflow

Precursor Column

WIRES

P = vflow ρ2

JxB force ANODE

Compression of targets using ablated plasma flow

Pressures: 1 – 100 kbar

AXIS

Bglobal CATHODE

Imperial College / UCSD Collaborative Studies

Imperial College: High current drive, extensive diagnostics, experienced team

UCSD: 2 drivers, high shot rate in simplified set-ups

Bz Compression of targets using ablated

Iarray

Ablated plasmaflow

WIRES

P = vflow ρ 2

JxB force ANODE

Bz

Iφ

Compression of targets using ablated plasma flow

Pressures: 1 – 100 kbar

Magnetic field in precursor column

Twisted Arrays

Bglobal CATHODE

Imperial College / UCSD Collaborative Studies

Imperial College: High current drive, extensive diagnostics, experienced team

UCSD: 2 drivers, high shot rate in simplified set-ups

Compression of targets using ablated

Iarray

A blated plasmaflow

WIRES

P = vflow ρ 2

JxB force ANODE

Current DriveMarx or

inductive split

Compression of targets using ablated plasma flow

Pressures: 1 – 100 kbar

Magnetic field in precursor column

Twisted ArraysInductive split from main current

Bglobal CATHODE

current

Additional generator

Imperial College / UCSD Collaborative Studies

Imperial College: High current drive, extensive diagnostics, experienced team

UCSD: 2 drivers, high shot rate in simplified set-ups

B Compression of targets using ablated

Iarray

Ablated plasma

flow

Thin-WalledMetal tube

WIRES

P = vflow ρ 2

JxB force ANODE

Bz Compression of targets using ablated plasma flow

Pressures: 1 – 100 kbar

Magnetic field in precursor column

Twisted ArraysInductive split from main current

Bglobal CATHODE

current

Additional generator

B-field flux compression

Imperial College / UCSD Collaborative Studies

Imperial College: High current drive, extensive diagnostics, experienced team

UCSD: 2 drivers, high shot rate in simplified set-ups

Precursor Column

Iarray

Bglobal

Ablated plasmaflow

P = vflow

ρ2

JxB force

Jet

Jet Interaction Experiments

Use of radial / conical arrays for interaction with

Precursor plasma column

Magnetised precursorJet

Counter-propagating jet

Jets and outflows from pulsed power driven plasmas

Well characterised……

• Generation and deflection of hydrodynamic jets

• Generation of magnetically driven jets• Generation of magnetically driven jets

Systems developing…..

•Multi-stage magnetically driven jets

•Low jet/ambient medium density ratio experiments

•Hydro Jet work at UCSD

•Jets with angular momentum (Ampleford, PRL 100, p035001, 2008)

To come……

•Compression of magnetised plasmas

•Propagation of plasma into B-field / magnetised targets

•Collisionless shock systems