1. Fast Electron Temperature Scaling and Conversion Efficiency Measurements using a Bremsstrahlung Spectrometer Brad Westover US-Japan Workshop San Diego, CA March 12, 2010

2. Motivation What is the fraction of laser energy that is converted to fast electrons? Is the spectrum of electrons generated hotter or colder than what is predicted by ponderemotive scaling? What is the angular distribution of the electrons?

3. Target and Laser Parameters Experimental and Diagnostic Setup TITAN LASER Energy: 150 J Pulse Length: 0.7 ps Spot Size: 7 um FWHM Wavelength: 1054 nm Intensity: 2x10 20 W/cm 2 peak Al/Ag Targets 10 um Al 250 um Ag Incident laser

4. High Energy X-Ray and Bremsstrahlung Spectrometer (HXBS) Magnet to deflect electrons The HXBS consists of thirteen stacked image plates behind filters of varying thickness and material (increasing in Z from Al to Pb) A model of the target is generated using the Integrated Tiger Series 3.0 code (ITS 3.0); this code simulates the bremsstrahlung and K-alpha radiation that will be from a given electron distribution A model of the spectrometer is also made using the same code

5. Testing Electron Single-Temperature Models Simple one- temperature models were considered Red and Green lines represent Beg and Ponderemotive scaling applied to average intensity

6. The single temperature model described above is too simple The laser spot does not have uniform spatial intensity We use an equivalent plane monitor (EPM) to record the spatial profile of the beam on each shot The equivalent plane image is time-integrated, so we assume a Gaussian temporal profile Using the Equivalent Plane Monitor to Constrain Electron Spectra

7. The peak intensity is above 10 20 W/cm 2, but that only about 10% of the energy is in this region About 40% of the energy is delivered to the target at between 10 18 and 10 19, while 50% is between 10 19 and 10 20 W/cm 2 (time-averaged) Intensity Distributions Derived from the Equivalent Plane

8. The electron distributions produced in this way are not well approximated by a one- or two- temperature model Typical Electron Spectrum Generated by Pointwise Ponderemotive Scaling

9. Forward Analysis Techniques A Ponderemotive Scaling Law is Applied to the Intensity distributions from Equivalent Plane The first scaling law to test is a ponderemotive scaling law, where the fit parameters are the overall conversion efficiency and the temperature scale (the fraction of the ponderemotive temperature) A and B are the fit parameters: CE = A Temp. = B*0.511*((1+I/(1.37*10 18 )) 1/2 -1)MeV

12. A scaling model that uses an I 1/3 temperature scaling model is also tested A and B are the fit parameters: CE = A Temp. = B*0.215*(I/10 18 ) 1/3 MeV Forward Analysis Techniques cont. An I 1/3 Scaling Law is Applied to the Intensity distributions from Equivalent Plane

15. Electron Divergence Models Compared The electron divergence models studied were as follows: Line – all electrons forward going, perpendicular to the target surface Narrow – divergence is uniform within a 15 o half angle EDA – electrons given divergence angles based on energy PIC – divergence given by a Cos 2 distribution with 30 o half- width half-maximum Wide – divergence in uniform within a 75 o half angle

20. Conclusions High-energy X-ray spectrometers can be very useful tools for diagnosing the temperature of fast electrons as they propagate through a target Two different types of scaling laws are tested: ponderemotive and I 1/3 scaling Several models of the divergence angles of electrons were studied, and how they affect the resulting conversion efficiencies and temperature scales was quantified Future work will involve having multiple spectrometers for better angular resolution and beam-pointing measurements Work supported by the U.S. Department of Energy, Office of Fusion Energy Sciences under contracts DE-FC02-04ER54789 (Fusion Science Center) and DE-AC52- 07NA27344(ACE).

21. We use a High-Energy X-ray and Bremsstrahlung Spectrometer (HXBS) to measure bremsstrahlung and K-alpha radiation created by fast electrons as they move in a target Using information from the spectrometer, as well as supplemental information from an equivalent plane monitor, we can infer the spectrum of electrons generated The spectrum of electrons is compared to predictions of two electron temperature scaling laws Overview of Analysis Procedure

22. Electron Divergence Models Compared Up until now, we have made assumptions about the divergence angle of the electrons produced at the target surface Specifically, we have used a model in which the electrons have a divergence angle which is dependent on their energy, the higher the energy, the narrower the angle into which the electrons are produced, with the high energy >1MeV electrons sent into a very narrow cone angle Recent PIC simulations and experimental results suggest that the divergence of the electron beam may be much higher, and does not diminish for high-energy electrons We have compared several models of the electron divergence

23. Why bremsstrahlung? Other diagnostics have attempted to infer the energy of electrons generated by the short pulse laser by measuring the energy of the escaping electrons However, these electrons may undergo shifts in energy as they move through the target, and may not be representative of the actual electron population K-alpha signals are sensitive to the number, but not the temperature of the electrons that move through the fluor layer Bremsstrahlung radiation is produced by the electrons while they are inside the bulk of the target, and the spectrum produced contains information about both the number and temperature of the electron population

24. Bremsstrahlung Distributions The angular distribution of the bremsstahlung, as well as the total energy in bremsstrahlung that escapes the target, depends highly on the angular distribution of electrons that are input More focused (narrower angle) of electron beam produces more focused bremsstrahlung response The total energy in bremsstrahlung that reaches the detector (at 17 o ) depends on these distribution The conversion efficiency and temperature scale will also be affected