1. University of Rochester Fusion Science Center Review of electron beam divergence for Fast Ignition LLNL Livermore, Ca. August 4 th to 6 th 2010 Michael Storm The Ohio State University

2. Outline Introduction. Principle Diagnostic Techniques. Additional Experimental Concerns Results. Summary.

3. 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 I  10 19 Wcm -2, ~1 MeV. The electrons must propagate ~50 to ~100 µm along a density gradient that rises from 10 21 to 10 26 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 = 1MeV, a collimated electron beam carrying ~27 kJ 1 must deposit all its energy. 1.Atzeni, Phys Plasmas 15 056311 (2008)Atzeni, Phys Plasmas 15 056311 (2008) For  e  35%, this implies a PW laser energy of  77 kJ

4. The PW laser energy requirements increase significantly as the electron beam diverges Assuming an initial 20 µm radius solid-beam of uniformly distributed electrons Propagation distance 77 kJ

5. In experiments the electron beam divergence is 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.

6. The laser pulse peak intensity, leading edge and far field 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.

7. 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. K α x-ray imaging of buried layers. Coherent transition radiation. Incoherent transition radiation.

8. Side-on optical probing shows collimated jet-like structures originating from the laser interaction region 1.Gremillet et al, PRL 83 5015 (1999)Gremillet et al, PRL 83 5015 (1999) Ionization channels 100’s µm long with  20 µm diameters indicate electrons (total energy < 0.1% E laser ) propagate along the direction of the laser at a velocity close to c 1. Slower electrons with v  0.53c  E e = (  -1)mc 2  93 keV expand isotropically 1. E L  10J,  L  350fs 1 Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR.

9. Optical probing reveals the transverse size of the rear-surface fast-electron-generated plasma 1 1.Lancaster et al, PRL 98 125002 (2007)Lancaster et al, PRL 98 125002 (2007) 2.Tatarakis et al, PRL 81 999 (1998)Tatarakis et al, PRL 81 999 (1998) 25 µm Cu 50 µm Cu 75 µm Cu E L  250J,  L  450fs, I L  5 x 10 20 Wcm -2,  ½  38 o (after 200 ps) Other studies of the rear surface plasma suggest a 1 o focusing of the beam 2. Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR.

10. Thermal radiation is associated with fast electrons reaching the target rear surface 1.Kodama et al, Nature 412 798 (2001)Kodama et al, Nature 412 798 (2001) 2.Lancaster et al, PRL 98 125002 (2007)Lancaster et al, PRL 98 125002 (2007) Based on the size of the individual emission size, the electron beam divergence is  ½  25 o, 12 o, 7 o respectively. Collectively from 40 µm to 500 µm,  ½  5 o. Other experiments show the rear surface emission decreasing with increasing target thickness 2. UV images from Al, E L = 20J 1 40 µm 200 µm500 µm 200 µm Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR. Laser Target e-e- Rear surface emission

11. 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. E x B 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)Nakatsutsumi et al, IFSA 2007 112 022063 (2008) 2.Lancaster et al, PRL 98 125002 (2007)Lancaster et al, PRL 98 125002 (2007) 3.Forslund et al, PRL 48 1614 (1984)Forslund et al, PRL 48 1614 (1984) 2mm x 2.5mm x 40µm Cu/Al 1 400 x 360 x 40µm 3 Cu/Al 1 Refluxing 1 Thermal emission cannot reliably determine the electron beam divergence. Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR.

12. Nuclear activation by high-energy bremsstrahlung photons diagnoses the divergence of the most energetic electrons Activation typically requires photon energies ≥ 10 MeV. The bremsstrahlung opening angle is  ½ ~1/  so for E e = 10 MeV,  ½ ~2.7 o. Magnetic fields broaden the bremsstrahlung distribution by perturbing the electron trajectories (Calculation : 20 MeV collimated electrons reproduce  ½ =19 o  distribution ) 1. TLDs are sensitive to photons > 200 keV 2 E L  600J, I L  6x10 20 Wcm -2 indicates  ½  50 o[2] 1.Zepf et al, Phys Plasmas 8 2323 (2001)Zepf et al, Phys Plasmas 8 2323 (2001) 2.Hatchett et al, Phys Plasmas 7 2076 (2000)Hatchett et al, Phys Plasmas 7 2076 (2000) Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR. The beam directionality was seen to vary by ± 35 o[2]. Activated atom fraction X-ray > 200 keV (TLD)

13. K α radiation imaging measures the electron divergence using buried fluorescent layers Fluor Laser Propagation layer e-e- 20µm Cu in 130µm Al 1 1.Stephens et al, PRE 69 066414 (2004)Stephens et al, PRE 69 066414 (2004) Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR. Cu Kα Ti Kα (inset) Slowing down Linear fit Monte Carlo x The K α spot size remains constant over the first 100 µm after which it diverges as  ½  20 o[1]

14. K α imaging is a leading candidate for correctly determining the electron divergence The K α 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 K α. Higher energy K α is desirable (Ag). The effect of the impedance mismatch needs to be quantified experimentally 1. Resistive interface between materials leads to magnetic field generation: dB = ∫(  x J) dt Laser Propagation layer e-e- Electron slowing down region Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR. 1.Davies et al, PRE 58 2471 (1998)Davies et al, PRE 58 2471 (1998) Electrons with diverging trajectories are perturbed or trapped at the interface. 11 22 11 33

15. 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. CTR from 30 µm Au foil irradiated with E L  5J, I L  2x10 19 Wcm -2 x10 4 0 25 50 25 0 50 1 2 0 y (  m) x (  m)  ½  16 o 1.Storm et al, PRL 102 235004 (2009)Storm et al, PRL 102 235004 (2009) Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR. Laser e-e- CTR

16. 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 pulse 1. 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 material 2. 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)Baton et al, PRL 91 105001 (2003) 2.Storm et al, PRL 102 235004 (2009)Storm et al, PRL 102 235004 (2009) The reliability of the CTR technique to identify divergence should be determined Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR.

17. Incoherent transition radiation (ITR) diagnoses the divergence of all electrons that reach the rear surface Experiments using Al foils with E L  10J, I L  1x10 19 Wcm -2. Time resolved images of the rear surface emission 1.Santos et al, PRL 89 025001 (2002)Santos et al, PRL 89 025001 (2002) Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR.  ½  17 o Laser e-e- ITR

18. 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)Santos et al, PRL 89 025001 (2002) Inside probe. Surface probe. Thermal imaging. Bremsstrahlung. K α imaging. CTR. ITR. 35 µm Aluminum target 1 ITR

19. Divergence versus Diagnostic  ½ (degrees) Diagnostic 20 o  280 kJ and 611 kJ PW for 50 and 100 µm propagation respectively

20. Additional concerns and experimental results The laser pulse leading: – Displacement and shocks – Double pulse – Pre-plasma Compressed matter Resistive Channels

21. The laser pulse leading edge leads to target expansion, 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 material 1. 1.Santos et al, Phys. Plasmas 14 103107 (2007)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) time (ns) Density Map g/cc 2.09 1.05 0 3.14 4.19 5.24 CHIVAS 1D Hydro 1 40 µm Al LASER Front surface initially at z = 0. Density profiles z = 0 Rear surface stable at t 0 for thicker targets. t0t0

22. Accounting for target overdense thickness changes the inferred value of divergence 1.Santos et al, Phys. Plasmas 14 103107 (2007)Santos et al, Phys. Plasmas 14 103107 (2007) Pre-pulse -Shocks. -Double pulse. -Pre-plasma. Compression. Resistive Channel Inferred angle is larger when considering the calculated over dense thickness. Thermal radiation CTR Thermal radiation

23. Pre-plasma effects on the divergence were diagnosed using activation Ta targets were irradiated at 45 o. The pre-plasma scale-length was varied. 1.Santala et al, PRL 84 1459 (2000)Santala et al, PRL 84 1459 (2000) 2.Lasinski et al, Phys. Plasma 6 2041 (1999)Lasinski et al, Phys. Plasma 6 2041 (1999) 3.Ren et al, PRL 93 185004 (2004)Ren et al, PRL 93 185004 (2004) Large plasma Small plasma Two e - beams Pre-pulse -Shocks. -Double pulse. -Pre-plasma. Compression. Resistive Channel The scale length determines the dominant laser absorption mechanism. Rippling of the critical surface 2 or self-generated fields can seed the directionality 3. Vacuum JxB overlaps 18 o 28 o Laser filamentation/hosing…

24. Electron beam divergence in cylindrically compressed matter has been measured 1 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)Perez et al, Plasma Physics and Controlled Fusion 51 124035 (2009) 200 µm Ni plate Cu plate Reduced penetration, resistive confinement and shell truncation may explain the decreasing emission size with delay for densities that are initially low Pre-pulse -Shocks. -Double pulse. -Pre-plasma. Compression. Resistive Channel Penetration decreases with increasing delay

25. 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)Scott et al, CLF annual report 65 (2007/2008) No clear reduction in the rear surface spot size was observed with Ti K  Pre-pulse -Shocks. -Double pulse. -Pre-plasma. Compression. Resistive Channel

26. Recent studies using resistive channels to seed magnetic guiding show promising results 1,2 The targets use a high resistivity core and a low resistivity cladding. The sign of the resistive gradient should be maintained during heating. CTR 1 25 µm or 50 µm Fe 250 µm Al HOPG X-ray pinhole X-ray imager Guiding = full symbols Foil = open symbols Pre-pulse -Shocks. -Double pulse. -Pre-plasma. Compression. Resistive Channel. 1.Kar et al, PRL 102 055001 (2009)Kar et al, PRL 102 055001 (2009) 2.Ramakrishma (to be published) (2010)Ramakrishma (to be published) (2010)

27. Analysis of the previous work suggests appreciable 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

28. 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