Self-generated and externalmagnetic fields in plasmas

J. P. KnauerLaboratory for Laser EnergeticsUniversity of Rochester

HEDSA Symposia on High Energy Density Plasmas

Atlanta, GA1 November 2009

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Self-generated and externally-generated magnetic fields are measured in OMEGA experiments

• Magnetic reconstruction has been measured laser-generated fields

• Magnetic fields have been observed in spherical implosions

• DRACO/MHD simulations show that the moderate external magnetic field of <10 Tesla can be compressed to hundreds of Mega-Gauss at the implosion stagnation

• Cylindrical targets embedded in a seed magnetic field of 10 - 60 kG have been imploded with 14 kJ of laser energy creating amplified fields of 10 – 40 MG

• Magnetic fields in HED plasmas open up new fields of investigation

Summary

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Self-generated and external magnetic fields in plasmas

Outline

Reconnection of Laser-Generated Magnetic Fields

Self-Generated Magnetic Fields

External Magnetic Fields

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Collaborators

O. Gotchev, P. Chang, N. W. Jang , O. Polomarov, R. Betti, D. D. Meyerhofer

J. A. Frenjie, C. K. Li, M. Manuel, R. D. Petrasso, F. H. Seguin

Laboratory for Laser EnergeticsDepartments of Physics and Mechanical Engineering

University of Rochester

Plasma Science and Fusion CenterMassachusetts Institute of Technology

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Reconnection of Laser-Generated* Magnetic Fields

* C. K. Li et al., Phys. Rev. Lett. 99 055001 (2007)

0

200

0 1 2 3 4 5

Position along lineout (mm)

Magnetic reconnection has been observed and quantified

5 mm

Bdℓ(MG-µm)

0.31 ns 0.51 ns 0 .69 ns 0.97 ns 1.24 ns 1.72 ns 2.35 ns

5mm

0.04 ns 0.67 ns 1.42 ns

Bdℓ(MG-µm)

0

200

0 1 2 3 4 5

Position along lineout (mm)

> 95% field strength was reduced in the region where bubbles overlap

C. K. Li et al., Phys. Rev. Lett. 99 055001 (2007)

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Since hydro dominated, characteristic times of this reconnection differ from “standard” experiments

Reconnect ~ expansion ~ L / Cs ~ 0.2 ns

SP ~ (resist Alfven )1/2 ~ 5 ns (Sweet-Parker)

Where: Alfven ~ L/ vA ~ 1 ns

resist ~ L2 /DB ~ 30 ns

As a consequence that β ~ 100, reconnection

energy ~ 0.01 nkT, currently immeasurable

The topology is dominated by hydrodynamics and isn’t strongly affected by fields, even though MG fields are present.

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Reconnection energy has little impact on the dynamics of the interacting bubbles for such high- plasma

Field energy plasma internal energy in the reconnection region

ER = (8LB2)-1∫ Bdℓ2 dV ~ 2.5102 J cm-3

Where LB = B/B

Taking ne around the bubble edge to be ~ 1-10% of the (nc ~ 1022 cm-3),

Te 1-10 eV

A small and presently immeasurable fraction ( 1%) of Te (~ 1 keV).

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Self-Generated Magnetic Fields*

* J. R. Rygg et al, Science (2008)

The MIT proton radiography experiments measureEM fields generation during ICF implosions

J. R. Rygg et al, Science (2008)

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Self-generated magnetic fields for non-uniformly irradiated laser implosions in MHD framework

Main mechanisms

1. Grad N x Grad T as a source.

2. Hot spot amplification (non-linear) due to

3. Tidman instability (linear) due to

4. RT instability.

5. Converging shock front instability or corrugation.

( ) .T eq B T ����������������������������

( )[ ] .T eB h Tq ������������� ���������������

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Magnetic fields are calculated to be in the corona

Anisotropic TTB~0.5MG

Isotropic TTB~0.02MG

Tele Tele

Shell

CoronaEdge

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Magnetic field persist into the compressed target

Anisotropic TTB~5MG

Isotropic TTB~0.2MG

TeleTele

Shock front

Shell

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External Magnetic Fields*

* O. Gotchev et al, to be published in Physical Review Letters

The performance of ICF targets can be improved by MG magnetic fields

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0

10

20

30

40

0 1 2 3 4 5

Temperature (keV)

Yie

ld/Y

ield

(1 k

eV)

OMEGA Implosions

NIF 1.5 MJ, direct-drive point design ρhs 30g/cc, Ths 7keV (before ignition), rhs 50µm

/ || ~ 0.2 for B = 10 MG

rL=27m ~1/2 rhs for B = 100 MG

Bhsrhs

Yn ~ 2 <v>

<v> ~ 1/T ½ e-a/T

for constant Phs

~ 1/T

MIFEDS provides in-target seed fields between 10 and 150 kG depending on coil geometry and energy settings FSC

Faraday rotation measurements of seed field

TIM

6

MIF

ED

S L

aserM

IFE

DS

MIFEDS is a compact, self-contained system, that stores less than 100 J and is powered by 24 VDC.It delivers ~110kA peak current in a 350 ns pulse

0

50

100

150

0.0 0.5 1.0 1.5 2.0 2.5

Time (s)

|Bz|

(k

G)

0.5 mm wide coil1.2 mm wide coil

Coil geometry and placement of the cylindrical target have been optimized for OMEGA implosionsFSC

BCylindricaltube

Cylindrical implosion target is positioned in a uniform field region between the coils

Coil geometryRadius = 2 mmSeparation = 5.25 mm

Cylindrical targetRadius = 430 mLength = 1.5 mmWall thickness = 20 mFill = 9 atm D2

B

Coil Contours of |B| Coil

High magnetic fields are generated through laser compression of a seed field1

In a cylindrical target, an axial field can be generated using Helmholtz like coils. The target is imploded by a laser to compress the field

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D2

=BzR2const

Reversing the polarity of the seed field reverses the deflection of the proton probe

Reversed polarity seed field

The minimum, average magnetic field matching this deflection is 40 MG

B0~ -6.2T

FSCStandard polarity seed field

The minimum, average magnetic field matching this deflection is 30 MG

1D-MHD simulations show a Tion with magnetic field ~ 2X Tion without magnetic field

Density and Temperature at stagnation

B-field compressed to ~100 MG at the hot spot center

The plasma beta is ~ 1 where the magnetic field peaks

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B-field and plasma beta

0 5 10 15 200

20

40

60

80

100

1

10

B

B (

MG

)r (m)

B = 60 kGB = 0 kG

Spherical implosions will be used to probe the effect of magnetic fields > 10 MG on fusion yield

I0

B0

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Spherical target inserted into a two coil axial magnetic field

Spherical target with an inserted with for an azitmuthal magnetic field

Magnetic fields may play a significant role in the collimation of astrophysical jets

FSCHubble Space Telescope images OMEGA jet

OMEGA laboratory jets have cocoon pressures of the order of 30 kBar equal to the magnetic pressure of a 0.8 MG field

The applications of laser driven flux compression go beyond ICF

B

OMEGA EPbeam

Compressed field

OMEGA EPbeam

OMEGA beams

1500 μm

500 μm

Wire target

e+

e-

1J. Myatt et al., Bull. Am. Phys. Soc. 51 (7), 25 (2006)

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B=10 MG

• Guiding fields for hot electrons in fast ignition.

• Generation of positron-electron plasma in the laboratory1.

• Propagation of plasma jets in large scale magnetic field.

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Self-generated and externally-generated magnetic fields are measured in OMEGA experiments

• Magnetic reconstruction has been measured laser-generated fields

• Magnetic fields have been observed in spherical implosions

• DRACO/MHD simulations show that the moderate external magnetic field of <10 Tesla can be compressed to hundreds of Mega-Gauss at the implosion stagnation

• Cylindrical targets embedded in a seed magnetic field of 10 - 60 kG have been imploded with 14 kJ of laser energy creating amplified fields of 10 – 40 MG

• Magnetic fields in HED plasmas open up new fields of investigation

Summary/conclusions

Protonbacklighter

Initial seedfield of B < 90 kG

CR-39 Detector

Cylindricaltarget

p

Proton deflectometry is used to measure the magnetic field in the compressed core

D + 3He → 4He + p (14.7 MeV)

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Hot spot

B

p

D

L

p p

e B Dev Bd

m m

~ /v v L v

pm vB D

eL~GEANT4 simulations are used for an accurate

interpretation of the data

Detector plate

B

Hot spot

Denseshell

p p p SIMULATION

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The protons with the largest deflection probethe highest B-field region in the target hot spot

Protons that travel through the hot spot loose less energy that the protons that only travel through the dense shell

2-D simulations of spherical implosions show higher ion temperatures with a magnetic fieldFSC