Magnetic Collimation of Fast Electrons using Structured Targets

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Magnetic Collimation of Fast Electrons using
Structured Targets

• A.P.L.Robinson, M.Sherlock, P.A.Norreys
• (Central Laser Facility, STFC RAL)
• M.Zepf, and S.Kar.
• (Queens University, Belfast)

Presentation at 35th EPS Plasma Physics Conference
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Why Collimate Fast Electron Beams?
gt 200keV
I gt 1018 Wcm-2

• Put as much flux/energy as possible into a small
  area/volume.
• Fast Ignition Inertial Confinement Fusion
• Proton/Ion Acceleration
• X-ray backlighter
• Heating solids to high temperatures.

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Magnetic Collimation

• Collimation can result from resistive generation
  of magnetic field.

Current Balance
B-field
r
LASER
jf jc 0
z
Electric Field E -?jf
Magnetic Diffusion other terms
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Problems with Natural Collimation
Field too weak to bend electrons around.
Electrons too divergent.
Low resistivity
TOO HOT!

• Collimation does not necessarily occur.
• See Bell Kingham, Phys.Rev.Lett., 035003 (2003)
• Many experiments indicate that fast electron
  flows are not strongly collimated.
• e.g. Lancaster et al., Phys.Rev.Lett., 98, 125002
  (2007)

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Strucured Collimator Concept

• Enhance generation of collimating magnetic field
  by structuring the target resistivity, i.e. by
  using different Z materials.

Electric Field E -?jf
Published in Phys.Plasmas, 14, 083105
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Structured Collimator Concept
E -?jf
dB/dt -curl E
B-fields initiate collimation
Fast electron spray
Net Curl of E-field
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Analytic Model

• Use a Rigid Beam model.
• Resistivity gradient builds field.
• Sufficient to deflect fast
• electrons.

Rigid Beam Static, Specified jf
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LEDA simulations

• LEDA is a 2D hybrid Vlasov-Fokker-Planck code.

Fast Electrons (VFP, KALOS)
Background (hybrid)
Milchberg resitivity, Thomas-Fermi Model for
s.h.c.
Fields (hybrid)
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Target Set-up

• Use Al fibre with Li cladding. One laser pulse
  (5 x 1019Wcm-21ps).

This shows the Target Z, i.e the ion charge.
Z13 regions are Al, and Z3 regions are Li.
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A Typical Run
I 5 x 1019Wcm-2 (1 micron wavelength). Fast
electron Divergence half-angle of 340. Al target
initially at 200eV.
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Comparison
Same laser conditions. Fast electron density
profiles at 1ps.
Homogeneous Al target
Structured Collimator
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B-field in this run
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Magnetic Field Growth
Greatly helped by positive feedback
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Fibre Width
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Cold Target Effects Examined

• Simulations carried out for 1eV start.

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Works in Reverse Too
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3D Struc.Coll.s
1. Slab Geometry
Al
Sn
No enhancement to confinement parallel to slab.
2. Cylindrical Geometry
Simulate using a 3D particle-hybrid code.
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3D simulation of slab confinement
Al-Sn-Al target
Pure Al target
x-y midplane plot of fast electron density
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3D Transport Patterns
3x1026m-3 fast electron density isosurface(s)
Pure Al Conical Spray Pattern Ballistic Transport
Al-Sn-Al Fan Pattern Magnetic Guiding
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Bz field in 3D
Bz grows at material interface creating a
magnetic wall to confine fast electrons.
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Zepf-Kar Experiment
Sn (10 um wide)
Al
Al
532 nm
700 nm
Total signal is twice the reference
Total signal is twice the reference
slide courtesy of S.Kar
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3D Wire Confinement
Al with 40 micron Fe wire
Al only
1019 Wcm-2 500fs pulses. Fast electron Density
plots at 1.5ps.
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Summary

• Structured Collimator Simple concept that
  exploits the induction equation at a basic level.
• Positive Feedback Once collimation is initiated
  it helps itself.
• Cold Target Effects May not be a significant
  problem.
• Geometry and Materials These are important
  considerations, but there is flexibility.
• Experimental Realization Results from Zepf, Kar,
  and co-workers suggest that this has worked in
  the slab geometry.