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)
FSCB=0
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