Transcript University of Rochester Fusion Science Center

University of Rochester
Fusion
Science Center
Review of electron beam divergence for
Fast Ignition
Michael Storm
The Ohio State University
LLNL
Livermore, Ca.
August 4th to 6th 2010
Outline
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Introduction.
Principle Diagnostic Techniques.
Additional Experimental Concerns Results.
Summary.
Optimizing the laser-to-electron conversion efficiency, mean electron
energy and electron directionality are essential for the viability of FI
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Experiments and calculations indicate e = 10 to 50%.
The energy spectrum is approximately Maxwellian with, at I1019 Wcm-2, <E> ~1 MeV.
The electrons must propagate ~50 to ~100 µm along a density gradient that rises from
1021 to 1026 cm-3 to a region of radius ~20 µm in ~20 ps.
For a fuel density of  = 300 gcm-3 and an exponential electron energy distribution with
<E> = 1MeV, a collimated electron beam carrying ~27 kJ1 must deposit all its energy.
For e 35%, this implies a PW laser energy of 77 kJ
1.
Atzeni, Phys Plasmas 15 056311 (2008)
The PW laser energy requirements increase
significantly as the electron beam diverges
Assuming an initial 20 µm radius solid-beam of uniformly distributed electrons
PW energy (kJ)
1000
77 kJ
Propagation
distance
800
50 um
100 um
600
400
200
0
0
5
10
15
1/2 (degrees)
20
25
In experiments the electron beam divergence
is associated with a cone angle
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The angle is obtained from the ratio of the measured transverse spatial distribution
of some emission and the emission depth.
The angle can be characterized in numerous ways:
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Half angle or full angle.
Containment fraction.
The full, half or some width of a fitted curve.
For a series of shots there are the maximum, mean, rms… angles.
These definitions of divergence are used in numerical calculations.
A consensus on how to define and report the divergence is needed.
The laser pulse peak intensity, leading edge and far
field distribution need careful characterization
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FWHM, Peak Intensity, energy containment fractions… are commonly used to describe
the intensity.
Experiments and numerical calculations suggest a connection between electron
directionality/divergence and the laser intensity/leading edge profile.
Properly determining the laser pulse parameters and establishing
commonality in reporting them at different facilities is desirable.
Principle Diagnostic Techniques
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Optical probing inside transparent targets.
Optical probing of the target surface blow-off plasma.
Thermal imaging of the target rear surface.
High energy bremsstrahlung angular distribution.
Kα x-ray imaging of buried layers.
Coherent transition radiation.
Incoherent transition radiation.
Side-on optical probing shows collimated jet-like structures
originating from the laser interaction region
Inside probe.
Surface probe.
Thermal imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
EL 10J, L 350fs1
Ionization channels 100’s µm long with 20 µm diameters indicate electrons (total
energy < 0.1% Elaser) propagate along the direction of the laser at a velocity close to c1.
Slower electrons with v  0.53c  Ee = (-1)mc2  93 keV expand isotropically1.
1.
Gremillet et al, PRL 83 5015 (1999)
Inside probe.
Surface probe.
Thermal imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
Optical probing reveals the transverse size of the
rear-surface fast-electron-generated plasma1
25 µm Cu
50 µm Cu
75 µm Cu
EL 250J, L 450fs, IL 5x1020Wcm-2, ½  38o (after 200 ps)
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Other studies of the rear surface plasma suggest a 1o focusing of the beam2.
1.
2.
Lancaster et al, PRL 98 125002 (2007)
Tatarakis et al, PRL 81 999 (1998)
Inside probe.
Surface probe.
Thermal
imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
Thermal radiation is associated with fast
electrons reaching the target rear surface
UV images from Al, EL = 20J1
Laser
eTarget
Rear
surface
emission
40 µm
200 µm
500 µm
200 µm
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Based on the size of the individual emission size, the electron beam divergence is ½ 
25o, 12o, 7o respectively.
Collectively from 40 µm to 500 µm, ½ 5o.
Other experiments show the rear surface emission decreasing with increasing target
thickness2.
1.
2.
Kodama et al, Nature 412 798 (2001)
Lancaster et al, PRL 98 125002 (2007)
The distribution of thermal radiation is influenced by refluxing,
penetration depth, surface propagation effects and temperature
2mm x 2.5mm x 40µm Cu/Al1
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400 x 360 x 40µm3 Cu/Al1
Inside probe.
Surface probe.
Thermal
imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
Refluxing1
The transverse size decreases in thicker targets because the electrons fail to penetrate.
ExB drift along the rear surface contributes to the size of the thermal emission.
Higher frequency emission terminates sooner.
Thermal emission cannot reliably determine the electron beam divergence.
1.
2.
3.
Nakatsutsumi et al, IFSA 2007 112 022063 (2008)
Lancaster et al, PRL 98 125002 (2007)
Forslund et al, PRL 48 1614 (1984)
Nuclear activation by high-energy bremsstrahlung photons
diagnoses the divergence of the most energetic electrons
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Inside probe.
Surface probe.
Thermal imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
Activation typically requires photon energies ≥ 10 MeV.
The bremsstrahlung opening angle is ½ ~1/ so for Ee = 10 MeV, ½ ~2.7o.
Magnetic fields broaden the bremsstrahlung distribution by perturbing the electron
trajectories (Calculation : 20 MeV collimated electrons reproduce ½ =19o  distribution)1.
Activated atom
fraction
TLDs are sensitive to photons > 200 keV2
X-ray > 200 keV
(TLD)
EL 600J, IL 6x1020 Wcm-2 indicates ½ 50o[2]
The beam directionality was seen to vary by ± 35o[2].
1.
2.
Zepf et al, Phys Plasmas 8 2323 (2001)
Hatchett et al, Phys Plasmas 7 2076 (2000)
Inside probe.
Surface probe.
Thermal imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
Kα radiation imaging measures the electron
divergence using buried fluorescent layers
Fluor
Laser
e-
x
Propagation
layer
Cu Kα
Ti Kα (inset)
Slowing down
Linear fit
Monte Carlo
20µm Cu in 130µm Al1
The Kα spot size remains constant over the first
100 µm after which it diverges as ½  20o[1]
1.
Stephens et al, PRE 69 066414 (2004)
Inside probe.
Surface probe.
Thermal imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
K α imaging is a leading candidate for correctly
determining the electron divergence
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The Kα emission indicates the location of
Resistive interface between materials leads to
electrons whose energy is above the
magnetic field generation: dB = ∫( x J) dt
threshold for the process.
In thin targets refluxing smears the
desired image.
1 2 1
3
Laser
eNumerical calculations are needed to
extract the spatial distribution of firstElectron slowing
Propagation
pass electrons from the spatial
down region
layer
distribution of Kα.
Higher energy Kα is desirable (Ag).
Electrons with diverging trajectories are
perturbed or trapped at the interface.
The effect of the impedance mismatch
needs to be quantified experimentally1.
1.
Davies et al, PRE 58 2471 (1998)
Inside probe.
Surface probe.
Thermal imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
Coherent transition radiation (CTR) diagnoses the
divergence in the absence of refluxing
Refluxing reduces the correlation between propagating electrons so that electrons that
return to the rear surface no longer generate CTR.
Laser
e-
CTR
½  16o
x104
50
x (m)
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2
25
1
0
0
0
25
50
y (m)
CTR from 30 µm Au foil irradiated
with EL 5J, IL 2x1019Wcm-2
1.
Storm et al, PRL 102 235004 (2009)
Inside probe.
Surface probe.
Thermal imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
CTR generating electrons account for only a fraction
(0.1%)1 of the electrons that were accelerated by the laser
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The CTR emission duration is 50 fs for a 400 fs long laser pulse1.
The CTR signal strength has a dependence on target material, suggesting scattering is
important, but in the divergence which should be influenced by scattering is independent
of target material2.
The CTR signal is brighter than competing emission processes.
Due to velocity dispersion, the CTR generating electron cutoff energy is ~ 1MeV.
The reliability of the CTR technique to identify divergence should be determined
1.
2.
Baton et al, PRL 91 105001 (2003)
Storm et al, PRL 102 235004 (2009)
Inside probe.
Surface probe.
Thermal imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
Incoherent transition radiation (ITR) diagnoses the
divergence of all electrons that reach the rear surface
Laser
e-
ITR
Time resolved images of the rear surface emission
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Experiments using Al foils with EL
10J, IL 1x1019Wcm-2.
½  17o
1.
Santos et al, PRL 89 025001 (2002)
Inside probe.
Surface probe.
Thermal imaging.
Bremsstrahlung.
Kα imaging.
CTR.
ITR.
ITR imaging requires a high resolution temporal gate
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ITR radiation is characterized by a prompt
bright emission of duration a few times
longer than the laser pulse duration.
In thin targets the ITR signal will be smeared
by refluxing.
Refluxed electrons are less energetic and
more diffuse than the electrons during their
first pass through the target.
High-resolution, time-resolved imaging of
the ITR could be used to benchmark the
CTR emission.
ITR
35 µm Aluminum target1
1.
Santos et al, PRL 89 025001 (2002)
Diagnostic
Divergence versus Diagnostic
20o  280 kJ and 611 kJ PW for 50 and 100 µm propagation respectively
 ½ (degrees)
Additional concerns and experimental results
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The laser pulse leading:
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Displacement and shocks
– Double pulse
– Pre-plasma
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Compressed matter
Resistive Channels
Pre-pulse
-Shocks.
-Double pulse.
-Pre-plasma.
Compression.
Resistive Channel
The laser pulse leading edge leads to target
expansion, heating and pre-plasma generation
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The laser pulse peak interacts with a non-zero scale-length plasma
Self focusing and filamentation modify the laser intensity and focal spot distribution.
Shocks heat, compress and displace the bulk target material1.
Density Map
g/cc
Density profiles z = 0
8
5.24
5
3.14
4
2.09
3
40 µm Al
1.05
LASER
0 -50
0
z (µm)
Rear surface stable at
t0 for thicker targets.
CHIVAS
1D Hydro1
2
1
50
time (ns)
7
6
4.19
t0
0
Front surface
initially at z = 0.
1.
Santos et al, Phys. Plasmas 14 103107 (2007)
Pre-pulse
-Shocks.
-Double pulse.
-Pre-plasma.
Compression.
Resistive Channel
Accounting for target overdense thickness
changes the inferred value of divergence
Thermal radiation
CTR
Thermal radiation
CTR
Inferred angle is larger when considering the calculated over dense thickness.
1.
Santos et al, Phys. Plasmas 14 103107 (2007)
Pre-pulse
-Shocks.
-Double pulse.
-Pre-plasma.
Compression.
Resistive Channel
Pre-plasma effects on the divergence
were diagnosed using activation
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Ta targets were irradiated at 45o.
The pre-plasma scale-length was varied.
JxB
Large plasma
18o
Small plasma
Two e- beams
Two e- beams
Laser filamentation/hosing…
28o
overlaps
Vacuum
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The scale length determines the dominant laser absorption mechanism.
Rippling of the critical surface2 or self-generated fields can seed the directionality3.
1.
2.
3.
Santala et al, PRL 84 1459 (2000)
Lasinski et al, Phys. Plasma 6 2041 (1999)
Ren et al, PRL 93 185004 (2004)
Pre-pulse
-Shocks.
-Double pulse.
-Pre-plasma.
Compression.
Resistive Channel
Electron beam divergence in cylindrically
compressed matter has been measured1
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Cu doped foam or CH filled cylinders are imploded.
Divergence increases or decreases with compression evolution depending on the initial
density.
Penetration decreases with increasing delay
Delay
200 µm
Cu
plate
Ni
plate
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Reduced penetration, resistive confinement and shell truncation may explain the
decreasing emission size with delay for densities that are initially low
1.
Perez et al, Plasma Physics and Controlled Fusion 51 124035 (2009)
Pre-pulse
-Shocks.
-Double pulse.
-Pre-plasma.
Compression.
Resistive Channel
Double pulse experiments attempt to
demonstrate divergence control
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The lower-intensity, pulse preheats the target to form a resistive magnetic channel.
No clear reduction in the rear surface spot size was observed with Ti K
1.
Scott et al, CLF annual report 65 (2007/2008)
Pre-pulse
-Shocks.
-Double pulse.
-Pre-plasma.
Compression.
Resistive Channel.
Recent studies using resistive channels to seed
magnetic guiding show promising results1,2
B
   Jfast  +   Jfast .
t
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The targets use a high resistivity core
and a low resistivity cladding.
The sign of the resistive gradient should
be maintained during heating.
25 µm or
50 µm Fe
CTR1
X-ray pinhole
250 µm Al
HOPG
X-ray imager
Guiding = full symbols
Foil
= open symbols
1.
2.
Kar et al, PRL 102 055001 (2009)
Ramakrishma (to be published) (2010)
Summary
Analysis of the previous work suggests
appreciable electron divergence
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No specific angle or “narrow” range of angles is evident.
Access to previous raw data and shot sheets would allow for a comprehensive and
consistent assessment of the previous work.
A common way to characterize the laser pulse is needed.
A common way to characterize divergence is necessary.
It necessary to determine which diagnostics are reliable.
Conduct concentrated experimental campaigns.
Acknowledgements
Dimitri Batani
Tony Bell
Claudio Bellei
Riccardo Betti
Jonathon Davies
Roger Evans
Richard Freeman
Laurent Gremillet
David Meyerhofer
Christopher Ridgers
Mark Sherlock
Andrey Solodov
Richard Stephens
Douglas Wertepny
Linn Van Woerkom
Sentoku Yasuhiko