Self-generated and external magnetic fields in plasmas J. P. Knauer Laboratory for Laser Energetics University of Rochester HEDSA Symposia on High Energy Density Plasmas Atlanta, GA 1 November 2009 FSC

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 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 FSC

Self-generated and external magnetic fields in plasmas Outline Reconnection of Laser-Generated Magnetic Fields Self-Generated Magnetic Fields External Magnetic Fields FSC

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 Energetics Departments of Physics and Mechanical Engineering University of Rochester Plasma Science and Fusion Center Massachusetts Institute of Technology FSC

Reconnection of Laser-Generated * Magnetic Fields * C. K. Li et al., Phys. Rev. Lett (2007)

Magnetic reconnection has been observed and quantified 5 mm   B  d ℓ  (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   B  d ℓ  (MG-µm) > 95% field strength was reduced in the region where bubbles overlap C. K. Li et al., Phys. Rev. Lett (2007) FSC

Since hydro dominated, characteristic times of this reconnection differ from “standard” experiments  Reconnect ~  expansion ~ L / C s ~ 0.2 ns  SP ~ (  resist  Alfven ) 1/2 ~ 5 ns (Sweet-Parker) Where:  Alfven ~ L / v A ~ 1 ns  resist ~ L 2 /D B ~ 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. FSC

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 E R = (8  L B 2 ) -1 ∫  B  dℓ  2 dV ~ 2.5  10 2 J cm -3 Where L B = B/  B Taking n e around the bubble edge to be ~ 1-10% of the (n c ~ cm -3 ),   T e  1-10 eV A small and presently immeasurable fraction (  1%) of Te (~ 1 keV). FSC

Self-Generated Magnetic Fields* * J. R. Rygg et al, Science (2008)

The MIT proton radiography experiments measure EM fields generation during ICF implosions J. R. Rygg et al, Science (2008) FSC

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. FSC

Magnetic fields are calculated to be in the corona Anisotropic TT B~0.5MG Isotropic TT B~0.02MG Tele Shell Corona Edge FSC

Magnetic field persist into the compressed target Anisotropic TT B~5MG Isotropic TT B~0.2MG Tele Shock front Shell FSC

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 FSC NIF 1.5 MJ, direct-drive point design ρ hs  30g/cc, T hs  7keV (before ignition), r hs  50µm   /  || ~ 0.2 for B = 10 MG r L  =27  m ~1/2 r hs for B = 100 MG B hs r hs Y n ~  2 ~ 1/T ½ e -a/T for constant P hs  ~ 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 MIFEDS Laser MIFEDS 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

Coil geometry and placement of the cylindrical target have been optimized for OMEGA implosions FSC B Cylindrical tube Cylindrical implosion target is positioned in a uniform field region between the coils Coil geometry Radius = 2 mm Separation = 5.25 mm Cylindrical target Radius = 430  m Length = 1.5 mm Wall thickness = 20  m Fill = 9 atm D 2 B CoilContours of |B| Coil

High magnetic fields are generated through laser compression of a seed field 1 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 FSC D2D2  =  B z R 2  const

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 B 0 ~ -6.2T FSC Standard polarity seed field The minimum, average magnetic field matching this deflection is 30 MG

1D-MHD simulations show a T ion with magnetic field ~ 2X T ion 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 FSC B-field and plasma beta B   B (MG) r (  m) B = 60 kG B = 0 kG

Spherical implosions will be used to probe the effect of magnetic fields > 10 MG on fusion yield I0I0 B0B0 FSC 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 FSC Hubble 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 EP beam Compressed field OMEGA EP beam OMEGA beams 1500 μm 500 μm Wire target e+ e+ e-e- 1 J. Myatt et al., Bull. Am. Phys. Soc. 51 (7), 25 (2006) FSC B=0 B=10 MG Guiding fields for hot electrons in fast ignition. Generation of positron-electron plasma in the laboratory 1. Propagation of plasma jets in large scale magnetic field.

FSC 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 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

Proton backlighter Initial seed field of B < 90 kG CR-39 Detector Cylindrical target p Proton deflectometry is used to measure the magnetic field in the compressed core D + 3 He → 4 He + p (14.7 MeV) FSC Hot spot B  p D L GEANT4 simulations are used for an accurate interpretation of the data

Detector plate B Hot spot Dense shell p p p SIMULATION FSC The protons with the largest deflection probe the 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 field FSC