LLNL-PRES-741326 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC X-ray sources from laser-plasma acceleration: development and applications for high energy density sciences HEDS Center Seminar Presented by Félicie Albert [email protected]LLNL May 9 th 2019
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LLNL-PRES-741326This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC
X-ray sources from laser-plasma acceleration: development and applications for high energy density sciences
Ping et al 84, RSI 123105 (2013)- X-ray absorption spectroscopy
Bailey et al, Nature 517, 56 (2015)- X-ray opacity
Jarrott et al, POP 21 031201 (2014)
Albert et al, PRL 118, 134801 (2017)Albert et al, PRL 111, 235004 (2013)Lemos et al, PPCF 58 034108 (2016)Lemos et al, PRL (in review)
Sandia Z – 3 ns
Broadband emissionOMEGA – 100 ps
Betatron radiationps
Line emissionNIF – 1 ns
Bremsstrahlung Titan – 10 ps
Ê
Ê
Ê
1 2 5 10 20 50 100
105
107
109
1011
1013
Photon energy @keVD
PhotonsêeVêSrêps
LWFA
5F. Albert – HEDS seminar – May 9th 2019
Outline
§ Laser-plasma acceleration: an alternative for high brightnessx-ray sources
§ Self modulated and blowout laser-wakefield accelerationregimes for high brightness x-ray source development
§ X-ray source development at LLNL and applications
§ Betatron x-ray source development at LCLS and applications
§ Conclusion and perspectives
6F. Albert – HEDS seminar – May 9th 2019
Outline
§ Laser-plasma acceleration: an alternative for high brightnessx-ray sources
§ Self modulated and blowout laser-wakefield accelerationregimes for high brightness x-ray source development
§ X-ray source development at LLNL and applications
§ Betatron x-ray source development at LCLS and applications
§ Conclusion and perspectives
7F. Albert – HEDS seminar – May 9th 2019
Conventional x-ray light sources are large scale national facilities
3 km
X-ray free electron laser: LCLS Synchrotron: APS
SLAC, CA Argonne Nat. Lab., IL
8F. Albert – HEDS seminar – May 9th 2019
Sources driven by laser-plasma accelerators offer an alternative
Synchrotron Free Electron Laser Laser-plasma
Hard X-rays (up to MeV)High brightnessSmall scaleUltrafast (fs)Some spatial coherence
Soft X-rays (8 keV)Very High brightnessOne beamlineUltrafast (fs)Coherent
Hard X-raysHigh brightnessMultiple beamlinesNot ultrafast (ps)Not coherent
Electrons from storage ring wiggled by undulators
Electrons from linac wiggled by undulators
Electrons from laser-produced plasma wiggled by plasma
LCLSAPS
✓✓
✓✓✓
✓✓
✓✓✓
✓✓
✓✓✓
> 1km
F. Albert, Laser wakefield accelerators: Next Generation Light Sources, Optics and Photonics News, 29, 1, 42-49 (2018)
9F. Albert – HEDS seminar – May 9th 2019
Plasmas can naturally sustain large acceleration gradients
E0 =mcω p
eω p =
nee2
mε0ne =1018 cm−3 → E0 = 96 GV/m
Plasma frequencyAcceleration gradient
RF Cavity Gas cell – laser plasma
100 MV/m 100 GV/m
10F. Albert – HEDS seminar – May 9th 2019
Plasma wave behind a laser
Intense laser pulses drive electron plasma waves
Wake behind a boat
Nuno Lemos, LLNL
Width of human hair
11F. Albert – HEDS seminar – May 9th 2019
Plasma wave behind a laser
Intense laser pulses drive electron plasma waves
Wake behind a boat
Nuno Lemos, LLNL
Width of human hair~50 µm
12F. Albert – HEDS seminar – May 9th 2019
Plasma wave behind a laser
Intense laser pulses drive electron plasma waves
Wake behind a boat
Nuno Lemos, LLNL
~50 µm
13F. Albert – HEDS seminar – May 9th 2019
Laser pulse
Electron plasma wave
F. Albert et al, Laser wakefield accelerator based light sources: potential applications and requirements, Plasma Phys. Control. Fusion 56 084015 (2014)
14F. Albert – HEDS seminar – May 9th 2019
Laser pulse
Electron plasma wave
F. Albert et al, Laser wakefield accelerator based light sources: potential applications and requirements, Plasma Phys. Control. Fusion 56 084015 (2014)
Trapped Electron
15F. Albert – HEDS seminar – May 9th 2019
Laser pulse
Electron plasma wave
F. Albert et al, Laser wakefield accelerator based light sources: potential applications and requirements, Plasma Phys. Control. Fusion 56 084015 (2014)
Trapped Electron
16F. Albert – HEDS seminar – May 9th 2019
Laser pulse
Electron plasma wave
F. Albert et al, Laser wakefield accelerator based light sources: potential applications and requirements, Plasma Phys. Control. Fusion 56 084015 (2014)
Trapped Electron
BetatronX-ray beam
17F. Albert – HEDS seminar – May 9th 2019
Beam divergence 𝜽 ~ 𝑟#𝑛%𝛾
20 mrad
Laser pulse
Electron plasma wave
F. Albert et al, Laser wakefield accelerator based light sources: potential applications and requirements, Plasma Phys. Control. Fusion 56 084015 (2014)
Trapped Electron
BetatronX-ray beam
18F. Albert – HEDS seminar – May 9th 2019
X-ray energy [keV]
Inte
nsity
[a.u
.] Ec
Critical energy Ec ~ 𝛾'𝑛%𝑟#
Laser pulse
Electron plasma wave
F. Albert et al, Laser wakefield accelerator based light sources: potential applications and requirements, Plasma Phys. Control. Fusion 56 084015 (2014)
Trapped Electron
BetatronX-ray beam
19F. Albert – HEDS seminar – May 9th 2019
Laser wakefield acceleration can produce x-ray and gamma-ray sources using several processes
ElectronX-raysBetatron x-ray radiation
keV
ElectronLaser photon
Scattered photon
Compton scatteringkeV – MeV
+BremsstrahlungMeV
Gamma-ray photon
Nucleus
Electron
1
2
3
20F. Albert – HEDS seminar – May 9th 2019
1 5 10 50 100 500 1000
105
108
1011
1014
1017
X!ray energy !keV"
AverageX!rayflux!pho
tons#s#0.1
"BW" APS(SPX)
LCLS
Compton
Betatron
ALS(slicing)
Unique properties§ Broadband (keV - MeV)
§ Ultrafast (fs-ps)
§ Collimated (mrad)
§ Small source size (µm)
§ Synchronized with drive laseror XFEL within <ps
X-ray sources from LWFA have unique properties compared to conventional light sources
21F. Albert – HEDS seminar – May 9th 2019
X-ray sources from LWFA have unique properties compared to conventional light sources
1 5 10 50 100 500 1000
105
108
1011
1014
1017
X!ray energy !keV"
AverageX!rayflux!pho
tons#s#0.1
"BW" APS$(SPX)$
LCLS$
Compton$
Betatron$
ALS$(slicing)$
X"ray&absorp+on&
XPCI&
Plasma Phys. Control. Fusion 56 (2014) 084015 F Albert et al
parameter increases, the photon spectrum tends towards asynchrotron-like broad spectrum, extending to much higherphoton energies than the shifted fundamental.
The emission of photons in such processes clearlyindicates that a force is applied to the electron to conservemomentum. This radiation force has a classical form, which isself-consistent within the limits that the acceleration timescaleis much larger than τ0 = 2e2/3mc3 = 6.3 × 10−23 s [58],which is principally a damping of motion due to loss ofmomentum to the radiation. One of the interesting phenomenaarising from this laser-electron interaction is that the radiationdamping is theoretically predicted to be so extreme that for asufficiently intense laser, the electron beam may lose almost allits energy in the interaction time [59–61]. This means that theradiation force is comparable to the accelerating force, whichhas the implication that the spectrum of the radiation shouldbe strongly modified.
3. Review of x- and γ-ray applications
This section discusses three specific promising applicationsof laser–plasma accelerator-based light sources: x-ray phasecontrast imaging (XPCI), x-ray absorption spectroscopy, andnuclear resonance fluorescence (NRF). While this list is notintended to be exhaustive, here we describe the basic principlesof these applications and discuss ongoing and future effortsto improve them with either betatron radiation or Comptonscattering from laser–plasma accelerators.
3.1. X-ray phase contrast imaging
XPCI records the modifications of the phase of an x-ray beamas it passes through a material, as opposed to its amplituderecorded with conventional x-ray radiography techniques.When x-rays pass through matter, elastic scattering causes aphase shift of the wave passing through the object of interest.The cross-section for elastic scattering of x-rays in low-Zelements is usually much greater than for absorption [62]. Thetotal phase shift induced on an x-ray wave when it travels adistance z through a sample with complex index of refractionn = 1−δ +iβ is due to the real part of the index and calculatedwith the relation:
$(z) = 2π
λ
∫ z
0δ(x)dx, (4)
where λ is the x-ray wavelength. For two distinct low-Zelements, the difference in the real part of the complex index ofrefraction is much larger than the difference in the imaginarypart. It means that for quasi transparent objects such asbiological samples or tissues, this technique is more sensitiveto small density variations, and offers better contrast thanconventional radiography. For the past decade, XPCI hasbeen a very active topic of research for medical, biological,and industrial applications. Consequently, several XPCItechniques have been developed based on interferometry [62],gratings [63] and free space propagation [64]. In combinationwith these techniques, XPCI has been done with various x-raysources. Examples includes images of a small fish recordedwith a standard x-ray tube and gratings [65], images of abee obtained with a Mo K-alpha laser-based source [66] and
Figure 3. Single-shot x-ray phase contrast image of a cricket takenusing the Astra Gemini Laser. This 200 TW laser produces 1 GeVelectron beams and very hard x-rays (with critical energy > 30 keV).The image shows minimal absorption, indicative of high flux ofphotons at energies > 20 keV, for which the phase-shift cross-sectiongreatly exceeds (> 100×) that for absorption.
phase contrast radiography using x-pinch radiation [67]. Eventhough, as suggested by equation (4), it is suitable to use amonochromatic x-ray source for XPCI, polychromatic sourceswith high spatial coherence can also be used [68, 69]. Inthis case, the scheme is much simpler and does not requireusing complex and expensive x-ray optics. Much of thesources currently used for XPCI do not have a high temporalresolution desirable to take snapshots of laser-driven shocksor other phenomena. XPCI measurements of shocks doneat synchrotrons were limited to a temporal resolution of∼ 100 ps [70]; betatron x-ray radiation, where the sourcesize is less than a few micrometers [38], has the potentialto offer three orders of magnitude better time resolution.For a source size of 2 µm and a critical energy of 8 keV,the transverse coherence length of betatron radiation wasmeasured at Ltrans = 3 µm 5 cm away from the source, whichis sufficient to observe Fresnel diffraction fringes [37]. Usingfree space propagation techniques, proof-of-principle XPCImeasurements of biological samples have recently been done[9, 10] with betatron radiation. These promising results haveled to an extension of this technique to higher x-ray energies[71], with an example shown in figure 3.
To generate a single-shot image, a large photon numberis required. As an approximate threshold, a megapixel(1024×1024 pixels) is a reasonable number of elements tomake an image. The relative fluctuations from Poisson
statistics will scale as 1/
√Nij , where Nij is the average
number of detected photons per pixel. Therefore, for alow noise image the number of photons per shot should beN ≫ 106, assuming the x-rays uniformly fill the detector andare detected. In practice N ≫ 108 is more realistic, given
4
Absorption spectroscopy
The demonstrated spatial and spectral qualities of ourgamma-ray source satisfy totally the necessary conditionsfor radiography of dense objects with very high resolution.
We have used the optimised gamma-ray source to radio-graph a complex and dense tungsten object. This object isspherical, hollow, and etched on the inner part with sinusoi-dal structures with cylindrical symmetry (cf., Figs. 4(a) and4(b)).
The spherical object with 20 mm diameter was placedon the laser axis, at 60 cm from the convertor and imaged onthe imaging plate phosphor screen with a magnification of afactor 3. The resulting experimental image is shown on Fig.4(c). The clear details of the inner sinusoidal lobes confirmthe 30 lm-level resolution and validate the possibility of
dense object radiography with the demonstrated gamma-raysource.
In summary, experimental results from a high-qualitygamma-ray source were detailed in this article. This sourcewas achieved using a compact laser-plasma accelerator. Thegamma-ray source size was measured and reveals a value inthe range of 30 lm. Such excellent resolution was obtainedby using the optimum parameters (geometry and thickness ofthe convertor) resulting from previous numerical studies.18
The presented gamma-ray sources, with such high tem-perature, dose, and 10 lm-range size, are beneficial for fastand ultra-precise radiographies for example in automotiveand aeronautics industries. These sources have the capabilityto identify sub-millimetric manufacturing defects, such ascracks, incomplete welds and other flaws that develop duringservice.
These gamma-ray sources are also an alternative for lineradiations such as Ka line radiations produced when intenselaser pulses irradiated a solid target. Such radiations areemitted in all directions and require a large amount of energy(in the 100 J level) to be useful for the case of implodingcapsule radiograph. The source characteristics presented inthis paper show that this required level of laser energy couldbe significantly reduced by keeping the same imaging qual-ity. In addition, according to numerical simulations, the du-ration of the studied gamma-ray pulse is expected to be inthe sub-picosecond range. This duration makes this sourcealso of interest for the dynamical studies of imploding pelletsin inertial confinement fusion experiments (studies of implo-sion stability, hydrodynamics instabilities, etc…).
The authors acknowledge collaboration with Mr. LoicLe-Dain from CEA-DAM Bruyeres-le-Chatel. This work hasbeen partially supported by ERC contract “PARIS”, byAIMA OSEO contract and by DGA Contract No. 06.34.013.
1T. Tajima and J. Dawson, Phys. Rev. Lett. 43, 267 (1979).2V. Malka et al., Science 1596, 298 (2002).3S. P. D. Mangles et al., Nature 431, 535 (2004).4C. G. R. Geddes et al., Nature 431, 538 (2004).5J. Faure et al., Nature 431, 541 (2004).6J. Faure et al., Nature 444, 737 (2006).7C. Rechatin et al., Phys. Rev. Lett. 102, 164801 (2009).8W. P. Leemans et al., Nat. phys. 2, 696 (2006).9S. Kneip et al., Phys. Rev. Lett. 103, 035002 (2009).
10D. H. Froula et al., Phys. Rev. Lett. 103, 215006 (2009).11N. A. M. Hafz et al., Nature Photon. 2, (2008).12A. Giulietti et al., Phys. Rev. Lett. 101, 105002 (2008).13R. D. Edwards et al., Appl. Phys. Lett. 80, 12 (2002).14Y. Glinec et al., Phys. Rev. Lett. 94, 025003 (2005).15C. Courtois et al., Phys. Plasmas 18, 023101 (2011).16S. Semushin and V. Malka, Rev. Sci. Instrum. 72, 7 (2001).17Y. Glinec et al., Rev. Sci. Instrum. 77, 103301 (2006).18A. Ben-Ismaıl et al., Nucl. Instrum. Methods Phys. Res. A, 629 382
(2011).19G. W. Forbes, J. Opt. Soc. Am. A 5, 1943 (1988).20S. Agostinelli et al., Nucl. Instrum. Methods Phys. Res. A 506, (2003).
FIG. 4. (Color online) (a) Photo of the 20 mm diameter tungsten object,(b) a schematic A-A0 cut, and (c) the resulting radiograph with the optimizedgamma-ray source.
264101-3 Ben-Ismail et al. Appl. Phys. Lett. 98, 264101 (2011)
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:128.15.43.113 On: Mon, 04 Jan 2016 19:56:07
X-ray Imaging
Gamma-rayradiography
Unique properties§ Broadband (keV - MeV)
§ Ultrafast (fs-ps)
§ Collimated (mrad)
§ Small source size (µm)
§ Synchronized with drive laseror XFEL within <ps
22F. Albert – HEDS seminar – May 9th 2019
The sources and techniques we are developing are important for applications in HED science
1 5 10 50 100 500 1000
105
108
1011
1014
1017
X!ray energy !keV"
AverageX!rayflux!pho
tons#s#0.1
"BW" APS$(SPX)$
LCLS$
Compton$
Betatron$
ALS$(slicing)$
X"ray&absorp+on&
XPCI&
Plasma Phys. Control. Fusion 56 (2014) 084015 F Albert et al
parameter increases, the photon spectrum tends towards asynchrotron-like broad spectrum, extending to much higherphoton energies than the shifted fundamental.
The emission of photons in such processes clearlyindicates that a force is applied to the electron to conservemomentum. This radiation force has a classical form, which isself-consistent within the limits that the acceleration timescaleis much larger than τ0 = 2e2/3mc3 = 6.3 × 10−23 s [58],which is principally a damping of motion due to loss ofmomentum to the radiation. One of the interesting phenomenaarising from this laser-electron interaction is that the radiationdamping is theoretically predicted to be so extreme that for asufficiently intense laser, the electron beam may lose almost allits energy in the interaction time [59–61]. This means that theradiation force is comparable to the accelerating force, whichhas the implication that the spectrum of the radiation shouldbe strongly modified.
3. Review of x- and γ-ray applications
This section discusses three specific promising applicationsof laser–plasma accelerator-based light sources: x-ray phasecontrast imaging (XPCI), x-ray absorption spectroscopy, andnuclear resonance fluorescence (NRF). While this list is notintended to be exhaustive, here we describe the basic principlesof these applications and discuss ongoing and future effortsto improve them with either betatron radiation or Comptonscattering from laser–plasma accelerators.
3.1. X-ray phase contrast imaging
XPCI records the modifications of the phase of an x-ray beamas it passes through a material, as opposed to its amplituderecorded with conventional x-ray radiography techniques.When x-rays pass through matter, elastic scattering causes aphase shift of the wave passing through the object of interest.The cross-section for elastic scattering of x-rays in low-Zelements is usually much greater than for absorption [62]. Thetotal phase shift induced on an x-ray wave when it travels adistance z through a sample with complex index of refractionn = 1−δ +iβ is due to the real part of the index and calculatedwith the relation:
$(z) = 2π
λ
∫ z
0δ(x)dx, (4)
where λ is the x-ray wavelength. For two distinct low-Zelements, the difference in the real part of the complex index ofrefraction is much larger than the difference in the imaginarypart. It means that for quasi transparent objects such asbiological samples or tissues, this technique is more sensitiveto small density variations, and offers better contrast thanconventional radiography. For the past decade, XPCI hasbeen a very active topic of research for medical, biological,and industrial applications. Consequently, several XPCItechniques have been developed based on interferometry [62],gratings [63] and free space propagation [64]. In combinationwith these techniques, XPCI has been done with various x-raysources. Examples includes images of a small fish recordedwith a standard x-ray tube and gratings [65], images of abee obtained with a Mo K-alpha laser-based source [66] and
Figure 3. Single-shot x-ray phase contrast image of a cricket takenusing the Astra Gemini Laser. This 200 TW laser produces 1 GeVelectron beams and very hard x-rays (with critical energy > 30 keV).The image shows minimal absorption, indicative of high flux ofphotons at energies > 20 keV, for which the phase-shift cross-sectiongreatly exceeds (> 100×) that for absorption.
phase contrast radiography using x-pinch radiation [67]. Eventhough, as suggested by equation (4), it is suitable to use amonochromatic x-ray source for XPCI, polychromatic sourceswith high spatial coherence can also be used [68, 69]. Inthis case, the scheme is much simpler and does not requireusing complex and expensive x-ray optics. Much of thesources currently used for XPCI do not have a high temporalresolution desirable to take snapshots of laser-driven shocksor other phenomena. XPCI measurements of shocks doneat synchrotrons were limited to a temporal resolution of∼ 100 ps [70]; betatron x-ray radiation, where the sourcesize is less than a few micrometers [38], has the potentialto offer three orders of magnitude better time resolution.For a source size of 2 µm and a critical energy of 8 keV,the transverse coherence length of betatron radiation wasmeasured at Ltrans = 3 µm 5 cm away from the source, whichis sufficient to observe Fresnel diffraction fringes [37]. Usingfree space propagation techniques, proof-of-principle XPCImeasurements of biological samples have recently been done[9, 10] with betatron radiation. These promising results haveled to an extension of this technique to higher x-ray energies[71], with an example shown in figure 3.
To generate a single-shot image, a large photon numberis required. As an approximate threshold, a megapixel(1024×1024 pixels) is a reasonable number of elements tomake an image. The relative fluctuations from Poisson
statistics will scale as 1/
√Nij , where Nij is the average
number of detected photons per pixel. Therefore, for alow noise image the number of photons per shot should beN ≫ 106, assuming the x-rays uniformly fill the detector andare detected. In practice N ≫ 108 is more realistic, given
4
Absorption spectroscopy
X-ray Imaging
§ High pressure and shock physics
§ Equation of state
§ Material strength
§ Phase transitions
§ Opacity
§ Laboratory astrophysics
Applications
TargetDrive laser
probe
Gamma-rayradiography
The demonstrated spatial and spectral qualities of ourgamma-ray source satisfy totally the necessary conditionsfor radiography of dense objects with very high resolution.
We have used the optimised gamma-ray source to radio-graph a complex and dense tungsten object. This object isspherical, hollow, and etched on the inner part with sinusoi-dal structures with cylindrical symmetry (cf., Figs. 4(a) and4(b)).
The spherical object with 20 mm diameter was placedon the laser axis, at 60 cm from the convertor and imaged onthe imaging plate phosphor screen with a magnification of afactor 3. The resulting experimental image is shown on Fig.4(c). The clear details of the inner sinusoidal lobes confirmthe 30 lm-level resolution and validate the possibility of
dense object radiography with the demonstrated gamma-raysource.
In summary, experimental results from a high-qualitygamma-ray source were detailed in this article. This sourcewas achieved using a compact laser-plasma accelerator. Thegamma-ray source size was measured and reveals a value inthe range of 30 lm. Such excellent resolution was obtainedby using the optimum parameters (geometry and thickness ofthe convertor) resulting from previous numerical studies.18
The presented gamma-ray sources, with such high tem-perature, dose, and 10 lm-range size, are beneficial for fastand ultra-precise radiographies for example in automotiveand aeronautics industries. These sources have the capabilityto identify sub-millimetric manufacturing defects, such ascracks, incomplete welds and other flaws that develop duringservice.
These gamma-ray sources are also an alternative for lineradiations such as Ka line radiations produced when intenselaser pulses irradiated a solid target. Such radiations areemitted in all directions and require a large amount of energy(in the 100 J level) to be useful for the case of implodingcapsule radiograph. The source characteristics presented inthis paper show that this required level of laser energy couldbe significantly reduced by keeping the same imaging qual-ity. In addition, according to numerical simulations, the du-ration of the studied gamma-ray pulse is expected to be inthe sub-picosecond range. This duration makes this sourcealso of interest for the dynamical studies of imploding pelletsin inertial confinement fusion experiments (studies of implo-sion stability, hydrodynamics instabilities, etc…).
The authors acknowledge collaboration with Mr. LoicLe-Dain from CEA-DAM Bruyeres-le-Chatel. This work hasbeen partially supported by ERC contract “PARIS”, byAIMA OSEO contract and by DGA Contract No. 06.34.013.
1T. Tajima and J. Dawson, Phys. Rev. Lett. 43, 267 (1979).2V. Malka et al., Science 1596, 298 (2002).3S. P. D. Mangles et al., Nature 431, 535 (2004).4C. G. R. Geddes et al., Nature 431, 538 (2004).5J. Faure et al., Nature 431, 541 (2004).6J. Faure et al., Nature 444, 737 (2006).7C. Rechatin et al., Phys. Rev. Lett. 102, 164801 (2009).8W. P. Leemans et al., Nat. phys. 2, 696 (2006).9S. Kneip et al., Phys. Rev. Lett. 103, 035002 (2009).
10D. H. Froula et al., Phys. Rev. Lett. 103, 215006 (2009).11N. A. M. Hafz et al., Nature Photon. 2, (2008).12A. Giulietti et al., Phys. Rev. Lett. 101, 105002 (2008).13R. D. Edwards et al., Appl. Phys. Lett. 80, 12 (2002).14Y. Glinec et al., Phys. Rev. Lett. 94, 025003 (2005).15C. Courtois et al., Phys. Plasmas 18, 023101 (2011).16S. Semushin and V. Malka, Rev. Sci. Instrum. 72, 7 (2001).17Y. Glinec et al., Rev. Sci. Instrum. 77, 103301 (2006).18A. Ben-Ismaıl et al., Nucl. Instrum. Methods Phys. Res. A, 629 382
(2011).19G. W. Forbes, J. Opt. Soc. Am. A 5, 1943 (1988).20S. Agostinelli et al., Nucl. Instrum. Methods Phys. Res. A 506, (2003).
FIG. 4. (Color online) (a) Photo of the 20 mm diameter tungsten object,(b) a schematic A-A0 cut, and (c) the resulting radiograph with the optimizedgamma-ray source.
264101-3 Ben-Ismail et al. Appl. Phys. Lett. 98, 264101 (2011)
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:128.15.43.113 On: Mon, 04 Jan 2016 19:56:07
23F. Albert – HEDS seminar – May 9th 2019
Outline
§ Laser-plasma acceleration: an alternative for high brightnessx-ray sources
§ Self modulated and blowout laser-wakefield accelerationregimes for high brightness x-ray source development
§ X-ray source development at LLNL and applications
§ Betatron x-ray source development at LCLS and applications
§ Conclusion and perspectives
24F. Albert – HEDS seminar – May 9th 2019
LWFA light sources are typically produced with ultrashort laser pulses in the blowout regime (cτ ~ lp/2)
e-de
nsity
ne
0
cτ
lp=c/ωp~ 1/ne1/2
To drive a wake we need P > Pc~ 1/ne ~ τ2
Condition to be in the blowout regime cτ ~ 1/ne1/2
30 fs ne~ 1019 cm-3
1 ps ne~ 1016 cm-3
30 fs Pc~ 2 TW
1 ps Pc~ 2 PW
25F. Albert – HEDS seminar – May 9th 2019
Self modulated laser wakefield acceleration (SMLWFA) is easier to achieve with picosecond scale lasers (cτ >> lp)
e-de
nsity
ne
0
cτ
lp=c/ωp~ 1/ne1/2
To drive a wake we need P > Pc~ 1/ne
Condition to be in the self modulated regime cτ >>~ 1/ne1/2 1 ps ne~ 1019 cm-3
1 ps Pc~ 2 TW
26F. Albert – HEDS seminar – May 9th 2019
The laser propagates in the plasma and decays into an electron plasma wave and forward scattered waves
of x rays through elements of the system (Al, Mylarwindows) and the calibrated image plates’ absorptionand efficiency [24]. For photon energies between 1 and30 keV, we utilize the filter wheel. Assuming that thebetatron motion of the electrons dominates the observedx-ray emission in this range, we consider an intensitydistribution per unit photon energy dE and solid angle dΩas a function of the photon energy E of the form:
d2IdEdΩ
∝!EEc
"2
K22=3½E=Ec"; ð1Þ
which is valid for betatron x rays on axis [25]. Here, Ec isthe critical energy of the betatron spectrum, and K2=3 is amodified Bessel function. The distribution function iscalculated through the different filters of the wheel andintegrated to obtain the corresponding signal that it wouldyield on the image plate. The filters are sufficiently thin toneglect the effects of scattering for our range of energies.Both the experimental and theoretical data are normalizedso that the sum of the signals of the filters is equal to 1. Thedata are analyzed through a least squares fitting method byminimizing the number
PiðDi − TiÞ2, where Di and Ti
are, respectively, the measured and calculated normalizedsignals for each filter. One example is shown in Fig. 3(a)for a0 ¼ 3.05 and ne ¼ 1019 cm−3. Here, the best fit isobtained for Ec ¼ 10 keV. In our experimental conditions,the highest critical energy Ec ¼ 20 keV was measured fora0 ¼ 3.02 and ne ¼ 1.3 × 1019 cm−3. By differentiating thesignal obtained in the iron-chromium Ross pair (filters 6and 5, see image of Fig. 1), we can deduce the x-ray photonyield Nx at 6.5& 0.5keV. At constant electron density ne¼1.3×1019cm−3, it goes from Nx¼ 3×108photons=eVSr fora0 ¼ 1.44 to Nx ¼ 1.45 109 photons=eVSr for a0 ¼ 3.02.A sharp stainless-steel edge placed 22 cm from the sourcecasts a clear shadow on the first image plate detector,indicating that for energies below 30 keV, the main sourceof x rays originates at the gas jet, consistent with betatronemission. We do not expect any significant hard x-ray
bremsstrahlung emission from the very underdense plasma.The measured 1=e2 source diameter has an upper valueof 35 μm.To quantify the x-ray spectrum at photon energies
between 10 and 500 keV, we use the stacked image platespectrometer. In addition to the betatron spectrumdescribed by Eq. (1), we assume an additional high-energyphoton background so that the total number of photons perunit energy on axis is:
dNx
dE∝
1
E
!EEc
"2
K22=3½E=Ec" þ A exp½−E=ET "; ð2Þ
where ET is the temperature of the exponentially decayingbremsstrahlung spectrum and A its amplitude relative tothe betatron spectrum. We propagate Eq. (2) through thedifferent materials of the experiment and through thecalibrated stacked image plate spectrometer [23,26].The number RT;i ¼ PT;0=PT;i is calculated, where PT;0 isthe total theoretical yield in the first plate (plate C0 in Fig. 1)and PT;i the total theoretical yield in subsequent plates fori ¼ 1∶7. These values are compared to the experimentalresults RE;i ¼ PE;0=PE;i to minimize the residue
PiðRE;i −
RT;iÞ2 by varying the parameters ET and A. The betatroncritical photon energy is set at Ec ¼ 10 keV in agreementwith the Ross pair filters measurements. The best fit [inset ofFig. 3(a) with the experimental data] is obtained for ET ¼200 keV andA ¼ 0.00014. The residue is higher by a factorof 10 if we fit using only betatron or bremsstrahlungdistributions separately. We deduce that the total x-ray yieldobserved in our experiment and shown in Fig. 3(b) is acombination of betatron radiation (dominant up to 40 keV)and bremsstrahlung (dominant above 40 keV). The brems-strahlung, inevitable whenever relativistic electrons areproduced, is likely due to lower energy (<500 keV) elec-trons being strongly deflected by the magnet onto the wallsof the target chamber.To explain the observed betatron x-ray spectra, we
performed 2D PIC simulations with OSIRIS for a varietyof conditions [27]. We illustrate the salient observationsfrom one simulation that uses an a0 ¼ 3, τ ¼ 0.7 ps, λ0 ¼1.053 μm laser pulse focused to a spot size of 15 μm(1=e2 intensity radius) into a 200 μm density up ramp. Thepulse duration and a0 were chosen to match the exper-imental values, and the spot size matches the value obtainedfrom the Gaussian fit (1=e2 intensity radius) of themeasured spot. The pulse then propagates through a3 mm-long fully ionized helium plasma of constant electrondensity ne ¼ 1 × 1019 cm−3. The simulation utilizes amoving window with box dimensions of 500 μm in thelongitudinal (laser propagation) direction and 150 μm inthe transverse direction. The corresponding resolutions are,respectively, 60 and 7.2 cells per λ0. To calculate betatronx-ray emission in these conditions, we select 750 randomelectrons in energy to match the overall spectrum[Fig. 4(c)]. The simulation is run again while also tracking
1 5 10 50 100
105
106
107
108
109
1010
X ray Energy keV
Phot
ons
eVSr
2 4 6 8 10
0.05
0.10
0.15
0.20
0.25
Filter number
Xra
yin
tens
ityno
rmal
ized
Betatron Ec=10 keV
Bremsstrahlung T = 200 keV
1 2 3 4 5 6 70.4
0.5
0.6
0.7
0.8
0.9
Plate
Rat
ioPl
ate
Plat
e0 (a) (b)
FIG. 3. (a) Normalized x-ray yield through filters of Fig. 1 (reddots) for a0 ¼ 3.05 and ne ¼ 1019 cm−3 and critical energy fitscalculated with Eq. (1), with Ec ¼ 5 keV, 10 keV, and 15 keV(solid, dashed, and dotted lines). Inset: stacked image plate dataRE;i (red dots) and fit RT;i for a photon distribution [Eq. (2)] withEc ¼ 10 keV, A ¼ 0.000 14, and T ¼ 200 keV. (b) Deducedbetatron and bremsstrahlung spectra (see text for details).
PRL 118, 134801 (2017) P HY S I CA L R EV I EW LE T T ER Sweek ending
Electrons accelerated in the SMLWFA regime produce betatron x-rays
X =
Ec = 10 keV
2 4 6 8 10 12
0.05
0.10
0.15
FilterYield@NormalizedD
of x rays through elements of the system (Al, Mylarwindows) and the calibrated image plates’ absorptionand efficiency [24]. For photon energies between 1 and30 keV, we utilize the filter wheel. Assuming that thebetatron motion of the electrons dominates the observedx-ray emission in this range, we consider an intensitydistribution per unit photon energy dE and solid angle dΩas a function of the photon energy E of the form:
d2IdEdΩ
∝!EEc
"2
K22=3½E=Ec"; ð1Þ
which is valid for betatron x rays on axis [25]. Here, Ec isthe critical energy of the betatron spectrum, and K2=3 is amodified Bessel function. The distribution function iscalculated through the different filters of the wheel andintegrated to obtain the corresponding signal that it wouldyield on the image plate. The filters are sufficiently thin toneglect the effects of scattering for our range of energies.Both the experimental and theoretical data are normalizedso that the sum of the signals of the filters is equal to 1. Thedata are analyzed through a least squares fitting method byminimizing the number
PiðDi − TiÞ2, where Di and Ti
are, respectively, the measured and calculated normalizedsignals for each filter. One example is shown in Fig. 3(a)for a0 ¼ 3.05 and ne ¼ 1019 cm−3. Here, the best fit isobtained for Ec ¼ 10 keV. In our experimental conditions,the highest critical energy Ec ¼ 20 keV was measured fora0 ¼ 3.02 and ne ¼ 1.3 × 1019 cm−3. By differentiating thesignal obtained in the iron-chromium Ross pair (filters 6and 5, see image of Fig. 1), we can deduce the x-ray photonyield Nx at 6.5& 0.5keV. At constant electron density ne¼1.3×1019cm−3, it goes from Nx¼ 3×108photons=eVSr fora0 ¼ 1.44 to Nx ¼ 1.45 109 photons=eVSr for a0 ¼ 3.02.A sharp stainless-steel edge placed 22 cm from the sourcecasts a clear shadow on the first image plate detector,indicating that for energies below 30 keV, the main sourceof x rays originates at the gas jet, consistent with betatronemission. We do not expect any significant hard x-ray
bremsstrahlung emission from the very underdense plasma.The measured 1=e2 source diameter has an upper valueof 35 μm.To quantify the x-ray spectrum at photon energies
between 10 and 500 keV, we use the stacked image platespectrometer. In addition to the betatron spectrumdescribed by Eq. (1), we assume an additional high-energyphoton background so that the total number of photons perunit energy on axis is:
dNx
dE∝
1
E
!EEc
"2
K22=3½E=Ec" þ A exp½−E=ET "; ð2Þ
where ET is the temperature of the exponentially decayingbremsstrahlung spectrum and A its amplitude relative tothe betatron spectrum. We propagate Eq. (2) through thedifferent materials of the experiment and through thecalibrated stacked image plate spectrometer [23,26].The number RT;i ¼ PT;0=PT;i is calculated, where PT;0 isthe total theoretical yield in the first plate (plate C0 in Fig. 1)and PT;i the total theoretical yield in subsequent plates fori ¼ 1∶7. These values are compared to the experimentalresults RE;i ¼ PE;0=PE;i to minimize the residue
PiðRE;i −
RT;iÞ2 by varying the parameters ET and A. The betatroncritical photon energy is set at Ec ¼ 10 keV in agreementwith the Ross pair filters measurements. The best fit [inset ofFig. 3(a) with the experimental data] is obtained for ET ¼200 keV andA ¼ 0.00014. The residue is higher by a factorof 10 if we fit using only betatron or bremsstrahlungdistributions separately. We deduce that the total x-ray yieldobserved in our experiment and shown in Fig. 3(b) is acombination of betatron radiation (dominant up to 40 keV)and bremsstrahlung (dominant above 40 keV). The brems-strahlung, inevitable whenever relativistic electrons areproduced, is likely due to lower energy (<500 keV) elec-trons being strongly deflected by the magnet onto the wallsof the target chamber.To explain the observed betatron x-ray spectra, we
performed 2D PIC simulations with OSIRIS for a varietyof conditions [27]. We illustrate the salient observationsfrom one simulation that uses an a0 ¼ 3, τ ¼ 0.7 ps, λ0 ¼1.053 μm laser pulse focused to a spot size of 15 μm(1=e2 intensity radius) into a 200 μm density up ramp. Thepulse duration and a0 were chosen to match the exper-imental values, and the spot size matches the value obtainedfrom the Gaussian fit (1=e2 intensity radius) of themeasured spot. The pulse then propagates through a3 mm-long fully ionized helium plasma of constant electrondensity ne ¼ 1 × 1019 cm−3. The simulation utilizes amoving window with box dimensions of 500 μm in thelongitudinal (laser propagation) direction and 150 μm inthe transverse direction. The corresponding resolutions are,respectively, 60 and 7.2 cells per λ0. To calculate betatronx-ray emission in these conditions, we select 750 randomelectrons in energy to match the overall spectrum[Fig. 4(c)]. The simulation is run again while also tracking
1 5 10 50 100
105
106
107
108
109
1010
X ray Energy keV
Phot
ons
eVSr
2 4 6 8 10
0.05
0.10
0.15
0.20
0.25
Filter number
Xra
yin
tens
ityno
rmal
ized
Betatron Ec=10 keV
Bremsstrahlung T = 200 keV
1 2 3 4 5 6 70.4
0.5
0.6
0.7
0.8
0.9
Plate
Rat
ioPl
ate
Plat
e0 (a) (b)
FIG. 3. (a) Normalized x-ray yield through filters of Fig. 1 (reddots) for a0 ¼ 3.05 and ne ¼ 1019 cm−3 and critical energy fitscalculated with Eq. (1), with Ec ¼ 5 keV, 10 keV, and 15 keV(solid, dashed, and dotted lines). Inset: stacked image plate dataRE;i (red dots) and fit RT;i for a photon distribution [Eq. (2)] withEc ¼ 10 keV, A ¼ 0.000 14, and T ¼ 200 keV. (b) Deducedbetatron and bremsstrahlung spectra (see text for details).
PRL 118, 134801 (2017) P HY S I CA L R EV I EW LE T T ER Sweek ending
31 MARCH 2017
134801-3
45F. Albert – HEDS seminar – May 9th 2019
Electrons accelerated in the SMLWFA regime produce betatron x-rays
of x rays through elements of the system (Al, Mylarwindows) and the calibrated image plates’ absorptionand efficiency [24]. For photon energies between 1 and30 keV, we utilize the filter wheel. Assuming that thebetatron motion of the electrons dominates the observedx-ray emission in this range, we consider an intensitydistribution per unit photon energy dE and solid angle dΩas a function of the photon energy E of the form:
d2IdEdΩ
∝!EEc
"2
K22=3½E=Ec"; ð1Þ
which is valid for betatron x rays on axis [25]. Here, Ec isthe critical energy of the betatron spectrum, and K2=3 is amodified Bessel function. The distribution function iscalculated through the different filters of the wheel andintegrated to obtain the corresponding signal that it wouldyield on the image plate. The filters are sufficiently thin toneglect the effects of scattering for our range of energies.Both the experimental and theoretical data are normalizedso that the sum of the signals of the filters is equal to 1. Thedata are analyzed through a least squares fitting method byminimizing the number
PiðDi − TiÞ2, where Di and Ti
are, respectively, the measured and calculated normalizedsignals for each filter. One example is shown in Fig. 3(a)for a0 ¼ 3.05 and ne ¼ 1019 cm−3. Here, the best fit isobtained for Ec ¼ 10 keV. In our experimental conditions,the highest critical energy Ec ¼ 20 keV was measured fora0 ¼ 3.02 and ne ¼ 1.3 × 1019 cm−3. By differentiating thesignal obtained in the iron-chromium Ross pair (filters 6and 5, see image of Fig. 1), we can deduce the x-ray photonyield Nx at 6.5& 0.5keV. At constant electron density ne¼1.3×1019cm−3, it goes from Nx¼ 3×108photons=eVSr fora0 ¼ 1.44 to Nx ¼ 1.45 109 photons=eVSr for a0 ¼ 3.02.A sharp stainless-steel edge placed 22 cm from the sourcecasts a clear shadow on the first image plate detector,indicating that for energies below 30 keV, the main sourceof x rays originates at the gas jet, consistent with betatronemission. We do not expect any significant hard x-ray
bremsstrahlung emission from the very underdense plasma.The measured 1=e2 source diameter has an upper valueof 35 μm.To quantify the x-ray spectrum at photon energies
between 10 and 500 keV, we use the stacked image platespectrometer. In addition to the betatron spectrumdescribed by Eq. (1), we assume an additional high-energyphoton background so that the total number of photons perunit energy on axis is:
dNx
dE∝
1
E
!EEc
"2
K22=3½E=Ec" þ A exp½−E=ET "; ð2Þ
where ET is the temperature of the exponentially decayingbremsstrahlung spectrum and A its amplitude relative tothe betatron spectrum. We propagate Eq. (2) through thedifferent materials of the experiment and through thecalibrated stacked image plate spectrometer [23,26].The number RT;i ¼ PT;0=PT;i is calculated, where PT;0 isthe total theoretical yield in the first plate (plate C0 in Fig. 1)and PT;i the total theoretical yield in subsequent plates fori ¼ 1∶7. These values are compared to the experimentalresults RE;i ¼ PE;0=PE;i to minimize the residue
PiðRE;i −
RT;iÞ2 by varying the parameters ET and A. The betatroncritical photon energy is set at Ec ¼ 10 keV in agreementwith the Ross pair filters measurements. The best fit [inset ofFig. 3(a) with the experimental data] is obtained for ET ¼200 keV andA ¼ 0.00014. The residue is higher by a factorof 10 if we fit using only betatron or bremsstrahlungdistributions separately. We deduce that the total x-ray yieldobserved in our experiment and shown in Fig. 3(b) is acombination of betatron radiation (dominant up to 40 keV)and bremsstrahlung (dominant above 40 keV). The brems-strahlung, inevitable whenever relativistic electrons areproduced, is likely due to lower energy (<500 keV) elec-trons being strongly deflected by the magnet onto the wallsof the target chamber.To explain the observed betatron x-ray spectra, we
performed 2D PIC simulations with OSIRIS for a varietyof conditions [27]. We illustrate the salient observationsfrom one simulation that uses an a0 ¼ 3, τ ¼ 0.7 ps, λ0 ¼1.053 μm laser pulse focused to a spot size of 15 μm(1=e2 intensity radius) into a 200 μm density up ramp. Thepulse duration and a0 were chosen to match the exper-imental values, and the spot size matches the value obtainedfrom the Gaussian fit (1=e2 intensity radius) of themeasured spot. The pulse then propagates through a3 mm-long fully ionized helium plasma of constant electrondensity ne ¼ 1 × 1019 cm−3. The simulation utilizes amoving window with box dimensions of 500 μm in thelongitudinal (laser propagation) direction and 150 μm inthe transverse direction. The corresponding resolutions are,respectively, 60 and 7.2 cells per λ0. To calculate betatronx-ray emission in these conditions, we select 750 randomelectrons in energy to match the overall spectrum[Fig. 4(c)]. The simulation is run again while also tracking
1 5 10 50 100
105
106
107
108
109
1010
X ray Energy keV
Phot
ons
eVSr
2 4 6 8 10
0.05
0.10
0.15
0.20
0.25
Filter number
Xra
yin
tens
ityno
rmal
ized
Betatron Ec=10 keV
Bremsstrahlung T = 200 keV
1 2 3 4 5 6 70.4
0.5
0.6
0.7
0.8
0.9
Plate
Rat
ioPl
ate
Plat
e0 (a) (b)
FIG. 3. (a) Normalized x-ray yield through filters of Fig. 1 (reddots) for a0 ¼ 3.05 and ne ¼ 1019 cm−3 and critical energy fitscalculated with Eq. (1), with Ec ¼ 5 keV, 10 keV, and 15 keV(solid, dashed, and dotted lines). Inset: stacked image plate dataRE;i (red dots) and fit RT;i for a photon distribution [Eq. (2)] withEc ¼ 10 keV, A ¼ 0.000 14, and T ¼ 200 keV. (b) Deducedbetatron and bremsstrahlung spectra (see text for details).
PRL 118, 134801 (2017) P HY S I CA L R EV I EW LE T T ER Sweek ending
31 MARCH 2017
134801-3
46F. Albert – HEDS seminar – May 9th 2019
Electrons accelerated in the SMLWFA regime produce betatron x-rays
Not the same slopefor cr-SiO2(higher density ?)(substrate ?)
These averageswill be resp. usedto estimate thepre-edge integral
450 550500 600 650
0
Abso
rban
ce0.4
0.8
1.2
1.6
X-ray energy (eV)
Amorphous SiO2 330 shotsCrystalline SiO2 60 shots
Cold absorption spectra
→B
81F. Albert – HEDS seminar – May 9th 2019
We have demonstrated the use of betatron x-rays as a tool for absorption spectroscopy
MeV
70
90
150
Electronspectrometer
Ellipsoidal mirrorX-ray CCD200 nm SiO2
Energy (eV)
700450100 µm
Cold/warm absorption spectra
Pump1015 W/cm2
0
0.4
0.8
1.2
1.6
450 500 550 600 650
Cold / Hot XANES spectra averageover all the delay scan [smooth 7 eV]
(normalized over [550-575 eV])am-SiO2 sample only
Mean cold 330 shotsMean hot 330 shots
Abso
rban
ce
Energy (eV)
Integration rangeof each hot - cold avg= [500 - 545] eV
Alternatively= [500 - 535] eV
Pre-edge
450X-ray energy (eV)
550500 600 650
0
Abs
orba
nce
0.4
0.8
1.2
1.6 Mean cold SiO2 330 shotsMean hot SiO2 330 shots
→B
82F. Albert – HEDS seminar – May 9th 2019
We have demonstrated the use of betatron x-rays as a tool for absorption spectroscopy with sub ps resolution
MeV
70
90
150
Electronspectrometer
Ellipsoidal mirrorX-ray CCD200 nm SiO2
Energy (eV)
700450100 µm
Pump1015 W/cm2
→B
0.48 +/- 0.18 ps rms rise time
3. Time-resolved XANES (4/5)!
• Pre-edge level extracted from integration of “hot” – “cold” averaged"– Pre-edge time evolution versus delay gives an upper limit for temporal resolution"
! Just considering date on am-SiO2 … but the run #568 seems to be aberrant"! Without it, the best fit gives a temporal resolution = 0.48 ± 0.13 ps rms"
-2
0
2
4
6
8
10
-2 0 2 4 6 8 10 12
Delay scan on am-SiO2 sampleXANES spectra normalized
then substracted to avg coldand integrated over ≠ spectral range
Cold over [500-545] eVCold over [500-535] eVHot over [500-545] eVHot over [500-535] eV
Inte
grat
ed s
pect
ra h
ot -
avg
cold
(eV)
Delay (ps)
run #568
Error estimated from cold data :0.8 rms over [500-545]0.6 rms over [500-535]=> reported on error bars
Courtesy of S. Mangles and J. Woods, Imperial College
Relaxation of metals driven by XFEL x-raysSample
Betatron
X-FEL
Spectrometer
Radiativedecay
Auger decay(KLL)
K-Shellphotoionization
LCLS
KL
M
e- hv e-
84F. Albert – HEDS seminar – May 9th 2019
Conclusions and future work § We have demonstrated the production of novel x-ray sources from laser-plasma accelerators
§ They are broadband (keV - MeV), ultrafast (fs -ps), collimated (mrad), synchronized with drive laser
§ They enable new applications— Study of ultrafast non-thermal melting in
SiO2— Phase contrast imaging of laser-driven shocks— Study of opacity in HED matter
§ Future work and challenges— Improving sources stability and flux— Applications from proof-of-principle to
practical— LWFA sources as probes for HED science
experiments
X-ray sources – Picosecond phenomena
Sandia Z – 3 ns
Broadband emissionOMEGA – 100 ps
Betatron radiationps
Line emissionNIF – 1 ns
Bremsstrahlung Titan – 10 ps
Ê
Ê
Ê
1 2 5 10 20 50 100
105
107
109
1011
1013
Photon energy @keVD
PhotonsêeVêSrêps
LWFA
N. Lemos et al, PPCF 58 034108 (2016)F. Albert et al, PRL 118 134801 (2017)F. Albert et al, POP 25 056706 (2018)N. Lemos et al, PPCF 60, 054008 (2018) P. King et. al, Rev. Sc. Instr. 90, 033503 (2019)F. Albert et al, Nuclear Fusion, 59, 032003 (2019)N. Lemos et. al, PRL (in review)
85F. Albert – HEDS seminar – May 9th 2019
It is an exciting time for short pulse laser science – LaserNetUSestablished in August 2018