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Magneto-Inertial Implosion Experiments on the OMEGA Laser

O. V. Gotchev et al.Laboratory for Laser EnergeticsUniversity of Rochester

Innovative Confinement Concepts WorkshopFebruary 12-14, 2007

College Park, Maryland

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Novel implosion experiments, using magnetic flux compression are underway on OMEGA

•A magnetized cylindrical target is imploded by OMEGA to compress a pre-seeded magnetic flux to high values.

•A ~0.1 MG seed magnetic field is generated with a double coil driven by a portable capacitive discharge system (MIFEDS)1.

•Proton radiography technique is used for detection of the compressed magnetic fields.

•Laser-driven flux compression will be used for thermal insulation of an ICF hot spot, laboratory astrophysics experiments and HEDP physics.

Summary

1 MIFEDS – Magneto-Inertial Fusion Electrical Discharge System

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FSCCollaborators

N. W. JangJ. P. KnauerM. D. Barbero

D. D. MeyerhoferR. Betti

R. D. PetrassoC. K. Li

Laboratory for Laser EnergeticsUniversity of Rochester

Plasma Science and Fusion CenterMassachusetts Institute of Technology

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Magneto-inertial fusion: ICF assisted by a magnetic field

•Ignition requirements and gain limits of conventional ICF

•Hot spot insulation with strong magnetic fields

•Feasibility of laser driven magnetic flux compression

•A seed magnetic field generator for OMEGA

•Design of laser-driven flux compression (LDFC) experiments

•Initial experiments and discussion

•Future directions and applications

Outline

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•Assuming ignition,

•Low implosion velocities Vi result in “cold” hot-spot:

•Conventional ICF designs have only moderate gain.

•A solution:

•Provide MGauss magnetic insulation to reduce thermal conductionlosses in the forming hot spot.

•An added benefit is increased hydrodynamic stability.

Massive ICF targets, imploded with low velocity provide higher gains*

1.3iLaser

Fusion

V1~

EEG =

* R. Betti and C. Zhou, Phys. Plasmas, 12 110702 (2005)

1.4ihs V~T

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Effects of a strong magnetic field on ICF target hot-spot parameters

At 10 MG compressed field: At 100 MG:

κ⊥≈0.01κ|| for ωceτe≈12

rα=27 µm α-particles magnetically trapped: rα/rhs ≈ 0.5

β≈4•104 κ⊥≈0.2κ|| for ωceτe≈1.2 β≈4•102

rα=270 µm rα/rhs > 5

•LILAC simulation of NIF 1.5 MJ, direct-drive point design* ρhs ≈ 30g/cc, Ths ≈ 7keV (before ignition), rhs ≈ 50µm.

•Braginskii conductivity used, anomalous effects not considered.

*P. W. McKenty, et al., Phys. Plasmas 8, 2315 (2001)

Tens of MG magnetic field is needed for effective reduction of the hot-spot thermal losses through magnetic insulation.

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High magnetic fields can be generated with compression of a seed field

•A seed field can be inserted in a spherical target via an exploding wire

D2

An azimuthal seed field is created by the current in an exploding lithium or carbon wire. Red lines show current path after gas ionization.

I0

B0

•Or in a cylindrical target using Helmholtz coils.

The axial seed field is created in a Helmholtz coil outside the target

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The imploding shell compresses the ionized gas fill that has trapped the magnetic field

•The magnetic Reynolds number Rem in OMEGA cylindrical implosions is high, due to the high implosion velocity and low plasma resistivity in the ionized gas fill.

•An average value of Rem~100 is obtained from simulations.

D2D2

Laser

)1/Re2(1

min

00maxz

m

RRBB

⎟⎟⎠

⎞⎜⎜⎝

⎛=

Shock

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The seed field is initially compressed by the ionizing front of the shock moving ahead of the CH shell.

LILAC-MHD simulation of 5-atm, D2-fill cylindrical implosion. B0=0.1 MGOMEGA pulse is 16 kJ, 1-ns “square”.

20

0 )()( ⎟⎟

⎞⎜⎜⎝

⎛≈

tRRBtB

Time evolution from t=1.8 ns to t=2.3 ns Time evolution from t=2.3 ns to t=3.0 ns

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The shell further compresses the ionized gas, amplifying the field, up to the time of stagnation

D2 gas fill

• Magnetic field levels at which rα/rhs ~1 are reached in the D2 hot spot.

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The reduction of (Braginskii) thermal conductivity leads to significant increase of the hot-spot temperature in D2

(κ⊥/κ|| )ions

(κ⊥/κ|| )e-

B0=0

Ths i

Ths e

• After effective B-field compression, the ion temperature in the hot-spot increases 6-fold.

• Anomalous effects are not included.

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The seed magnetic field is generated in a double coil configuration suitable for OMEGA implosions

1Radia Simulation (O. Chubar, P. Elleaume, J. Chavanne, J. Synchrotron Rad. (1998). 5, 481-484)

• Coil dimensions:

— d=4.4 mm and R=2 mm

• Coil parameters:

— L~25 nH and R~0.1 Ω

d=4.4 mm

R=d

Simulated B-field along the coil axis1

1.8 m

0.3 m

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A TIM-based, fast pulser delivers energy efficiently, while reducing the transmission distance and EMI issues.

• Capacitive discharge system that can safely store up to 130 Joules of energy (at 36 kV).

• Low-impedance (<1Ω) transmission line delivers the energy to the low-inductance coil.

• The device is contained in a shielded air box.

TIM boat

Charging

block

Energy storage

Spark Gap switch

Capacitors

Trigger beam

• Self-contained, needs low-power 24 VDC power supply.

• The SG trigger laser delivers 30 mJ in a ~5-ns IR pulse.

70 μm thick Cu foil(~2 skin depths @ 2 MHz)

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-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-1.00E-06 0.00E+00 1.00E-06 2.00E-06 3.00E-06

Time(s)

Rel

ativ

e In

tens

ity30 kV 07/24/0630 kV 07/06/06'30kV 07/13/06

We have measured 0.1 to 0.15 MG seed magnetic field with the prototype system charged to 25 - 30 kV

MGmm10radV,1mmd,(t)dBV(t)θ

(t))(θcosI(t)I

z

zzrot

rot2

0DET

===

=

Oscilloscope

MIFEDS prototype

Diagnostic TIM

0.15MGB MAXz_

MIFEDS in DTIM

200 nF, 40kV max

Probe laserPolarizer

Polarizer Detector

Transmission lineHelmholtz coil

Vacuum chamber

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The target is compressed by 40 OMEGA beams (~16 kJ) while 20 (8 kJ) are used for proton radiography

1C. K. Li et al., Phys. Rev. Lett. 97, 135003 (2006)

Cylindrical implosion target860 μm diam. and 1.5 mm long

Cylindrical target stalk

Backlighter target stalk

•Compression and fields are measured with proton radiography1.

•14.7 MeV D+3He fusion protons are produced by imploding a D3He filled glass microballoon.

MIFEDS coil4 mm diam. 500 μm wide

• Distance from backlighter to target is 9 mm.

• Distance to the CR-39 detector is ~10.5 cm.

Backlighter target

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Proton radiograph of an imploded cylindrical D2-filled shell without fields shows imploded core.

• No seed field present in this shot.

• The dense core slows-down the 14.7-MeV proton below detection threshold

1.5 mm

CR-39 track density map Track diameter mapStalk

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One cylindrical implosion with the seed field on, was performed. The protons through the core are not detectable with current set up.

• For our June 2007 experiments, the filter thickness in front of the CR-39 has been reduced to record the protons traveling through the core.

1.5 mm

Track density map Track diameter map

Stalk

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Low-adiabat, low-velocity implosions of magnetized ICF (MIF) targets will be pursued in the future.

• Magnetic field compression in cylindrical and spherical geometry in the context of inertial fusion.

• 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.

B

Petawatt Beam

Compressed field

OMEGA EPbeam

OMEGA beams

1500 μm

500 μm

Wire targete+e-

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

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Novel implosion experiments, using magnetic flux compression are underway on OMEGA

•A magnetized cylindrical target is imploded by OMEGA to compress a pre-seeded magnetic flux to high values.

•A ~0.1 MG seed magnetic field is generated with a double coil driven by a portable capacitive discharge system (MIFEDS)1.

•Proton radiography technique is used for detection of the compressed magnetic fields.

•Laser-driven flux compression will be used for thermal insulation of an ICF hot spot, laboratory astrophysics experiments and HEDP physics.

Summary

1 MIFEDS – Magneto-Inertial Fusion Electrical Discharge System

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Magnetic flux ratio and conservation:

where

- effective flux compression for Rem >> 1

Controlled megagauss magnetic fields have been generated with magnetic flux compression

),Re

1(1R(t)

v2R(t)

)v2(vdtdB

B1

m

ifi −=−

=

2

min

00

0

2

min

00max R

RBΦΦ

RRBB ⎟⎟

⎞⎜⎜⎝

⎛=⎟⎟

⎞⎜⎜⎝

⎛=

)/Re12(1

min

00max

m

RRBB

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎪⎪⎩

⎪⎪⎨

==

===⎟⎠⎞

⎜⎝⎛−=

ημLv

vvRe

,v2R

η2RLμ

RL

dtdlnΦτ

0i

f

im

f

0

sh

sh1

Supplemental

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• Small interaction volume at TCC requires low mass, single turn coils. (Low inductance system ~ tens of nH).

• The current rise must be fast in order to minimize the action integral that determines the lifetime of the small coil (due to Joule heating).

• Need high voltages to maximize energy (Estored=CV2/2) density.

• The energy must be delivered via low-impedance transmission line through a fast switch.

Macroscopic seed field changing little on the timescale of an Omega shot is needed.

t)(EtIL2

tt2

I T)R(B,t)(E m2max

2max

j ΔΔ

=Δ≈Δττ

Supplemental

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•The resistance in the circuit becomes

after the pulse peak.

30 kV charge 13 July 2006

-0.02

0.00

0.02

0.04

0.06

0.08

0.10-5.0E-07 0.0E+00 5.0E-07 1.0E-06 1.5E-06 2.0E-06 2.5E-06

Time (s)

Volta

ge (V

) VoltageFit

The MIFEDS circuit goes from underdamped to critically damped after the current peak

Ω0.772RCL ≈>

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−−−

=

0

4

220max22

0

0

10235I

(t)I arcCosx.(t)i

t]αωt]Sin[αExp[CVαω

ω(t)i

DETEXP

MOD• The current from the model is converted to the equivalent Faraday rotation signal.

76kAi(t)MAX ≈-0.02

0.00

0.02

0.04

0.06

0.08

0.100.0E+00 1.0E-07 2.0E-07 3.0E-07 4.0E-07 5.0E-07

Time (s)

Volta

ge (V

)

Voltage

Fit

Supplemental

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Proton radiography is used as the primary diagnostic in the flux compression experiments

• Proton source is a Gaussian with FWHM=45 μm.

• Distance to the CR-39 detector is ~30 cm.

• Expected 2x107 protons in the detector aperture (12 cm).

• Of those, 1.5x107 are deflected by either the background (seed) field or the compressed core.

• About 3000 protons are deflected by the 20 μm wide compressed cylindrical core.

Geant4 simulation of the proton deflection by a 30 MG compressed flux (R=20 μm). The box is 6x6 cm (1 pixel/cm), upper edge is on axis.

Def

lect

ion

Supplemental

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Filter - detector media arrangement in the performed experiments. Images of a Tantalum edge

Incident proton energies (MeV)15.0 11.1 10.7 2.5 (ranged out 85 μm into Al)

15.0 14.7 9.7 3.3 (ranged out in CR 39)

15.0 MeV proton source150 μm Ta foil

50 μm Al foil1 mm CR 39

500 μm Al foil1 mm CR39

Incident proton energies (MeV)15.0 11.1 10.7 2.5 (ranged out 85 μm into Al)

15.0 14.7 9.7 3.3 (ranged out in CR 39)

15.0 MeV proton source150 μm Ta foil

50 μm Al foil1 mm CR 39

500 μm Al foil1 mm CR39

Supplemental


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