Pann

istiweeith

n prodely to

4 mm) gold targets at the newly completed short-focus targetchamber TC1 to study hot electron, gamma-ray and positron pro-duction. Even though no positronwas convincingly detected due tothe high background, this experiment allowed us to determine the

1.1. Hot electron and pair production

rget, superthermalc energy approxi-

e laser wavelengthconverted into hotnsity is such that

Ehot > 2mc2), these hot electrons can then pair-produce inside ahigh-Z target [1]. Experimentally, the emergent hot electron spec-trum is often quite complicated and depends on details of the target(Z, thickness, density etc) and laser properties (intensity, contrast,polarization, duration, incident angle, focal spot size etc, see Ref.[14] for review). Some experiments measuring mainly the lowenergy (

spectrometer is borrowed from UT-Austin to cover the energyrange 1021 W/cm2.However, during our experiment, the laser was kept belowmaximum power to avoid damage to the f/3 focusing optics. Thuswe saw an energy range of 40e60 J, and a longer pulse duration onthe order of 200e300 fs, focused to a maximum intensity of

the LSU Mary Bird Perkins Cancer Center Elekta clinical beams atBaton Rouge, which has monoenergetic electron beams of w6e

Fig. 2. Magnetic spectrometer with Al case and 3 mm pinhole. The outer case di-mensions are 3.5 inches 4.5 inches 12 inches. It can measure e/e energies fromw1 MeVe50 MeV.

Fig. 4. A schematic of the background prole. The pink regions (a) are the magnets andare excluded. The blue regions (b) are the spaces in the cavity between the signal andthe magnets that are used to create the background prole. The background is taken asan average of the top and bottom of the cavity between magnets (blue regions (b)).(For interpretation of the references to color in this gure legend, the reader is referredto the web version of this article.)

D. Taylor et al. / High Energy Density Physics 9 (2013) 363e368 365signicantly diverted from the central axis until they are within thegap. This helps to improve the lower energy resolution of thespectrometer. The downside of using Fe yoke is that Fe uorescencecreates more internal background. Because of the fringe magneticeld geometry at the magnet edges and the width of the magnet,electrons tend to be focused toward the mid-plane of the gap,which enhances the signal to background on the image plates.

Because the image plates are slightly magnetic, they attach tothe magnets automatically without any special holder. A thin cavityis etched into the Al siding of the spectrometer to accommodate theplates, which measure 100 600 and run the length of the gap. Theouter case has room for up to 400 of front shielding. We used alter-nating layers of 0.500 Pb and 0.500 of Cu with a total thickness of 20. A3 mm collimating pinhole is bored through the shielding (Fig. 2).

3.2. Calibration

The low energy calibration can be accomplished with a standardradioactive source. 90Sr was used because the emitted electronenergy cutoff is relatively high at 2.28 MeV. To calibrate the highenergies, it is necessary to go to an electron beam line [4,8]. We usedFig. 3. Calibrated electron energy spectrum from LSU data points [8] and 90Sr source.22 MeV, allowing multiple calibration points. Several data pointswere taken with different beam energies in early 2012 to verify theMonte Carlo simulated energy spectrum based on the 3D-measuredB-eld map. In Fig. 3 we show that the LSU electron beam data andthe simulated position data are found to agree to better than

Fig. 6. Example of background subtraction for a 1 mm shot. The shot data is summed vertically (red line) and the data along two strips between the signal and the magnets is takens tak

spectrum in log linear plot showing the exponential tail.

D. Taylor et al. / High Energy Density Physics 9 (2013) 363e368366secondary electrons. Other background is due to the electronsstriking the magnets. To removemost of the background signal, thebackground is chosen to be the average of the signal inside thecavity above and below the electron signal. As can be seen in Fig. 4,the dened background offers reasonable agreement with theelectron signal prole. Unfortunately, simulations indicate that thelowest energy point spread functions have a large vertical spread.This would indicate that our method for background subtractionwill remove some of the lowest energy electrons. Regardless, thismethod seems more accurate than removing only the backgroundrecorded in themagnet region (pink area), which is the backgroundonly due to external radiation.

4.2. Image deconvolution

With the background removed from the image plate, we mustnow vertically integrate the signal to get a position spectrum. Fromthe position spectrum, we wish to extract the energy spectrum. Todo this, we must rst construct a response matrix for the system.The response matrix is constructed from point spread functions

to be the background (blue line). When no peak is visible as in (b), the resultant signal ithe reader is referred to the web version of this article.)generated using the GEANT4 Monte Carlo code from CERN. Thepoint spread functions are created in 0.1 MeV increments to allowfor ne energy deconvolution. Sample PSFs are displayed in Fig. 5.

Fig. 7. A sample deconvolved spectrum from the data presented in Fig. 6a. The deconvolutspectrum in log-linear plot showing the exponential tail.The energy-position spectrum is well matched to the calibrationpoints gathered from the LSU MBPCC electron beam lines [6,8] anda 90Sr source.

We next deconvolve the shot data using this response matrix.The deconvolution is non-trivial since we have to solve a largematrix equation of the form Ax b, whereA is our responsematrix,x is the unknown incident energy spectrum, and b is the measuredposition spectrum. Simply inverting the matrix may not producedesirable or smooth results since the problem is not well posed. It istherefore necessary to verify and improve the inverted spectrum byperforming a minimization routine. The minimization routine isused to optimize the solution of jjAx bjj2 0.

Taking the position spectrum, and using the Monte Carlo-generated response matrix, we can convert the data from posi-tion space to energy space. We present the deconvolved spectrumin 1 MeV energy bins. The error is taken to be the standard devi-ation of the position spectrum from the IP data. To estimate theerror in the nal energy spectrum, the input position spectrum isvaried in a normal random distribution based on the standard de-viation of the data in the position space. We then pass this position

en as an upper limit. (For interpretation of the references to color in this gure legend,spectrum through the response matrix many times to estimate anerror for the energy spectrum based on the error from the positionspectrum. A sample result is given in Fig. 7.

ion is done in 1 MeV bins. Left is the spectrum in linearelinear plot. Right is the same

4.3. Peak energy and effective kT

As we see in Fig. 7, the typical deconvolved hot electron spec-trum can be characterize by two key parameters, the peak energyEpk where the spectrum turns over, and the effective kT of the

exponential tail (slope in a log-linear plot). In Section 5 we studythe correlation between these empirical parameters and incidentlaser intensity. The effective kT is extracted by tting the high en-ergy tails of the deconvolved spectrum to an equation of the formNw exp(E/kT) where N is the signal and E is energy. An exampleof this tting mechanism can be seen in Fig. 8.

5. Main results and interpretations

After completing the analysis, we were not able to detect anyconvincing positron signal above the background (Fig. 6). This is notunexpected since the laser intensity was below 1020W/cm2 and theX-ray background was very high, especially at low energies. How-ever, we were able to extract useful hot electron spectra. From thedata we can compare Epk and effective kT and their relation toincident laser intensity as noted in Fig. 9.

In examining the energy spectra, the most surprising feature isthe steep turnover of low-energy spectrum

20 MeV may be indicative of underdense acceleration mechanismsin the pre-plasma, such as LWFA [15] or reverse sheath accelerationdue to electron-ion charge separation [14]. These results remain tobe conrmed in future TPW experiments. We see a positive cor-relation between intensity and peak energy in Fig. 9a. While thebest-t slope favors kT w I0.5 instead of kT w I0.34 scaling, the ab-solute kT values are higher than those given by the relation inSection 1.1. We also observe a weak positive correlation between kTand intensity in Fig. 9b. Finally, in Fig. 9c, we see a tight correlationbetween Epk and kT. More data is needed to conrm these trends,and the physics behind such correlations remains to be understoodfrom rst principles.

have covered the outside surface of the target chamber withdozens of gamma-ray dosimeters. The total gamma-ray doseagrees with the Monte Carlo simulated dose using the hot elec-tron spectra of Section 4, to within a factor 2. Gamma-ray dataanalyses and calibration are still in progress, and will be reportedin a future paper.

Acknowledgments

This work was supported by the DOE grant DE-SC-SC-000-1481and Rice University Faculty Initiative Fund.

Appendix A. Table of Shot Parameters

[1] E. Liang, et al., Phys. Rev. Lett. 81 (1998) 4887;D. Gryaznykh, et al., JETP Lett. 67 (2002) 257;K.. Nakashima, H. Takabe, Phys. Plasmas 9 (2002) 1505;J. Myatt, et al., Phys. Rev. E 79 (2009) 066409;J. Shearer, et al., Phys. Rev. A 8 (1973) 1582.

[2] H. Chen, et al., Rev. Sci. Instrum. 79 (2008) 033301.[3] H. Chen, et al., Phys. Rev. Lett. 102 (2009) 105001.[4] J.O. Deasy, et al., Med. Phys. 23 (1996) 675.[5] K.A. Tanaka, et al., Rev. Sci. Instrum. 76 (2005) 013507.[6] M. Martinez, et al., Proc. SPIE 5991 (2005), 59911N-1.[7] E. Liang, High Energy Density Phys. 6 (2010) 219e222.[8] K. Hogstrom, et al., AAPM Conf. Abstract, 2012.[9] S. Wilks, et al., Phys. Rev. Lett. 69 (1992) 1383.[10] W. Heitler, Quantum Theory of Radiation, Oxford, UK, 1954.[11] H. Chen, et al., Phys. Plasmas 16 (2009) 020705.[12] H. Chen, et al., Phys. Rev. Lett. 105 (2010) 015003.[13] E. Gaul, et al., Appl. Opt. 49 (2010) 9.[14] P. Gibbon, Short Pulse Laser Interactions with Matter, Imperial College, Lon-

don, UK, 2005.[15] T. Tajima, J. Dawson, Phys. Rev. Lett. 43 (1979) 267.

D. Taylor et al. / High Energy Density Physics 9 (2013) 363e3683686. Discussions

The difculty of extracting positron signal could be due to acombination of several factors: (a) our laser energy per shot isonly w 50 J. This is much lower than the Titan and Omega-EPshots by Chen et al. [3,11,12]. (b) Lower laser energy meansfewer exiting hot electrons and lower sheath electric eld, whichrenders emergent positrons to have too low an energy to beobserved above the background. (c) Our background may be toohigher compared with Titan and Omega-EP shots due to insuf-cient shielding. Future TPW experiments should improve on all ofthese.

The decit of low energy electrons and the narrow electronpeak make the TPW-driven hot electron distribution different fromother reported hot electron spectra. This may be caused by theunique properties of the TPW laser, especially its short pulse(