university of rochester fusion science center review of electron beam divergence for fast ignition...

University of Rochester Fusion

Science Center

Review of electron beam divergence for Fast Ignition

LLNLLivermore, Ca.August 4th to 6th 2010

Michael StormThe Ohio State University

Outline

• 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

• Experiments and calculations indicate e = 10 to 50%.

• The energy spectrum is approximately Maxwellian with, at I1019 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.

1. Atzeni, Phys Plasmas 15 056311 (2008)

For e 35%, this implies a PW laser energy of 77 kJ

The PW laser energy requirements increasesignificantly as the electron beam diverges

Assuming an initial 20 µm radius solid-beam of uniformly distributed electrons

Propagation distance

77 kJ

In experiments the electron beam divergenceis associated with a cone angle

• 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:– 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 farfield distribution need careful characterization

• 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

• 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 structuresoriginating from the laser interaction region

1. Gremillet et al, PRL 83 5015 (1999)

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.

EL 10J, L 350fs1

Inside probe.Surface probe.Thermal imaging.Bremsstrahlung.Kα imaging.CTR.ITR.

Optical probing reveals the transverse size of therear-surface fast-electron-generated plasma1

1. Lancaster et al, PRL 98 125002 (2007)2. Tatarakis et al, PRL 81 999 (1998)

25 µm Cu 50 µm Cu 75 µm Cu

EL 250J, L 450fs, IL 5x1020Wcm-2, ½ 38o (after 200 ps)

• Other studies of the rear surface plasma suggest a 1o focusing of the beam2.


Thermal radiation is associated with fast electrons reaching the target rear surface

1. Kodama et al, Nature 412 798 (2001)2. Lancaster et al, PRL 98 125002 (2007)

• 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.

UV images from Al, EL = 20J1

40 µm 200 µm 500 µm

200 µm


Laser

Target

e-Rearsurfaceemission

The distribution of thermal radiation is influenced by refluxing, penetration depth, surface propagation effects and temperature

• 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.

1. Nakatsutsumi et al, IFSA 2007 112 022063 (2008)2. Lancaster et al, PRL 98 125002 (2007)3. Forslund et al, PRL 48 1614 (1984)

2mm x 2.5mm x 40µm Cu/Al1 400 x 360 x 40µm3 Cu/Al1 Refluxing1

Thermal emission cannot reliably determine the electron beam divergence.


Nuclear activation by high-energy bremsstrahlung photonsdiagnoses the divergence of the most energetic electrons

• 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.

TLDs are sensitive to photons > 200 keV2 EL 600J, IL 6x1020 Wcm-2 indicates ½ 50o[2]

1. Zepf et al, Phys Plasmas 8 2323 (2001)2. Hatchett et al, Phys Plasmas 7 2076 (2000)


The beam directionality was seen to vary by ± 35o[2].

Activated atom fraction

X-ray > 200 keV (TLD)

Kα radiation imaging measures the electrondivergence using buried fluorescent layers

Fluor

Laser

Propagation layer

e-

20µm Cu in 130µm Al1

1. Stephens et al, PRE 69 066414 (2004)


Cu KαTi Kα (inset) Slowing downLinear fitMonte Carlo

x

The Kα spot size remains constant over the first 100 µm after which it diverges as ½ 20o[1]

K α imaging is a leading candidate for correctlydetermining the electron divergence

• The Kα emission indicates the location of electrons whose energy is above the threshold for the process.

• In thin targets refluxing smears the desired image.

• Numerical calculations are needed to extract the spatial distribution of first-pass electrons from the spatial distribution of Kα.

• Higher energy Kα is desirable (Ag).

• The effect of the impedance mismatch needs to be quantified experimentally1.

Resistive interface between materials leads to magnetic field generation: dB = ∫( x J) dt

Laser

Propagationlayer

e-

Electron slowing down region


1. Davies et al, PRE 58 2471 (1998)

Electrons with diverging trajectories are perturbed or trapped at the interface.

1 2 1 3

Coherent transition radiation (CTR) diagnoses thedivergence 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.

CTR from 30 µm Au foil irradiated with EL 5J, IL 2x1019Wcm-2

x104

0 25 50

25

0

50

1

2

0

y (m)

x (

m)

½ 16o

1. Storm et al, PRL 102 235004 (2009)


Lasere-

CTR

CTR generating electrons account for only a fraction(0.1%)1 of the electrons that were accelerated by the laser

• 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.

1. Baton et al, PRL 91 105001 (2003)2. Storm et al, PRL 102 235004 (2009)

The reliability of the CTR technique to identify divergence should be determined


Incoherent transition radiation (ITR) diagnoses thedivergence of all electrons that reach the rear surface

• Experiments using Al foils with EL 10J, IL 1x1019Wcm-2.

Time resolved images of the rear surface emission

1. Santos et al, PRL 89 025001 (2002)


½ 17o

Lasere-

ITR

ITR imaging requires a high resolution temporal gate

• 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.

1. Santos et al, PRL 89 025001 (2002)


35 µm Aluminum target1

ITR

Divergence versus Diagnostic

½ (degrees)

Dia

gnos

tic

20o 280 kJ and 611 kJ PW for 50 and 100 µm propagation respectively

Additional concerns and experimental results

• The laser pulse leading: – Displacement and shocks

– Double pulse

– Pre-plasma

• Compressed matter

• Resistive Channels

The laser pulse leading edge leads to targetexpansion, heating and pre-plasma generation

• 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.

1. Santos et al, Phys. Plasmas 14 103107 (2007)

Pre-pulse-Shocks.-Double pulse.-Pre-plasma.Compression.Resistive Channel

-50 0 50

1

3

2

0

5

6

4

8

7

z (µm)tim

e (ns)

Density Mapg/cc

2.09

1.05

0

3.14

4.19

5.24

CHIVAS 1D Hydro1

40 µm Al

LASER

Front surface initially at z = 0.

Density profiles z = 0

Rear surface stable at t0 for thicker targets.

t0

Accounting for target overdense thicknesschanges the inferred value of divergence

1. Santos et al, Phys. Plasmas 14 103107 (2007)


Inferred angle is larger when considering the calculated over dense thickness.

Thermal radiation

CTR CTR

Thermal radiation

Pre-plasma effects on the divergencewere diagnosed using activation

• Ta targets were irradiated at 45o.

• The pre-plasma scale-length was varied.

1. Santala et al, PRL 84 1459 (2000)2. Lasinski et al, Phys. Plasma 6 2041 (1999)3. Ren et al, PRL 93 185004 (2004)

Large plasma

Small plasma

Two e- beams

Two e- beams


• The scale length determines the dominant laser absorption mechanism.

• Rippling of the critical surface2 or self-generated fields can seed the directionality3.

Vacuum

JxB

overlaps

18o

28o Laser filamentation/hosing…

Electron beam divergence in cylindricallycompressed matter has been measured1

• Cu doped foam or CH filled cylinders are imploded.

• Divergence increases or decreases with compression evolution depending on the initial density.

Delay

1. Perez et al, Plasma Physics and Controlled Fusion 51 124035 (2009)

200 µm

Niplate

Cuplate

• Reduced penetration, resistive confinement and shell truncation may explain the decreasing emission size with delay for densities that are initially low


Penetration decreases with increasing delay

Double pulse experiments attempt to demonstrate divergence control

• The lower-intensity, pulse preheats the target to form a resistive magnetic channel.

1. Scott et al, CLF annual report 65 (2007/2008)

No clear reduction in the rear surface spot size was observed with Ti K


Recent studies using resistive channels to seedmagnetic guiding show promising results1,2

• The targets use a high resistivity core and a low resistivity cladding.

• The sign of the resistive gradient should be maintained during heating. CTR1

25 µm or50 µm Fe

250 µm Al HOPG

X-ray pinhole

X-ray imager

Guiding = full symbolsFoil = open symbols

Pre-pulse-Shocks.-Double pulse.-Pre-plasma.Compression.Resistive Channel.

1. Kar et al, PRL 102 055001 (2009)2. Ramakrishma (to be published) (2010)

( )fastfast .t

ηη∂

= × ×∇ ∇∂

BJ+J

Analysis of the previous work suggestsappreciable electron divergence

• 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.

Summary

Acknowledgements

Dimitri BataniTony BellClaudio BelleiRiccardo BettiJonathon DaviesRoger EvansRichard FreemanLaurent GremilletDavid MeyerhoferChristopher RidgersMark SherlockAndrey SolodovRichard StephensDouglas WertepnyLinn Van WoerkomSentoku Yasuhiko

university of rochester fusion science center review of electron beam divergence for fast ignition...

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