Abstract
Transport of relativistic electrons in a solid Cu wire target has been modeled with the implicit hybrid particleincell code LSP to investigate the electron energy distribution and energy coupling from the highintensity, shortpulse laser to electrons entering to the wire. Experiments were performed on the TITAN laser using a 1.5 mm long Cu wire attached to a Au cone tip at the laser intensity of 1 × 10^{20} W/cm^{2} which was irradiated into the cone. The simulated Cu Kα wire profile and yields matched the measurements using a twotemperature energy distribution. These modeling results show that the cold component of the energy spectrum can be determined with ±100 keV accuracy from the fit to the initial experimental falloff of the Kα emission while the simulated profiles were relatively insensitive to the hotter component of the electron distribution (>4 MeV). The slope of measured escaped electrons was used to determine the hotter temperature. Using exponential energy distributions, the lasertoelectroninwire coupling efficiencies inferred from the fits decreased from 3.4% to 1.5% as the prepulse energy increases up to 1 J. The comparison of the energy couplings using the exponential and Relativistic Maxwellian distribution functions showed that the energy inferred in the cold component is independent of the type of the distribution function.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DEAC5207NA27344 and by Fusion Science Center under Contract DEFC0204ER54789. H. Sawada and T. Ma would additionally like to acknowledge the assistance of D. Hey, C. Murphy, B. Westover, T. Yabuuchi, K. U. Akli, R. R. Freeman, G. E. Kemp, A. G. Krygier, L. D. Van Woerkom, R. Fedosejevs, H. Friesen, Y. Y. Tsui, S. D. Baton, M. Koenig, D. Turnbull, D. Price, and R. Combs in preparing the manuscript and implementing the experiment.
I. INTRODUCTION
II. CONEWIRE EXPERIMENT WITH ARTIFICIALLY CREATED PREPLASMA
III. LSP SIMULATION CONDITIONS
IV. FAST ELECTRONTRANSPORT MODELING OF A Cu WIRE
V. COMPARISONS OF LSP MODELING TO THE MEASUREMENTS
A. One and twotemperature fits
B. Twotemperature fits to measurements for prepulse energies of 17, 100, 500, and 1000 mJ
C. Coupling efficiencies inferred using exponential and relativistic Maxwellian distributions
VI. CONCLUSION
Key Topics
 Copper
 29.0
 Electron beams
 18.0
 Electron scattering
 16.0
 Electronic transport
 14.0
 Electron spectrometers
 9.0
H05H1/46
Figures
(a) TITAN conewire experimental setup and diagnostic layout. (b) Measured Cu Kα emission from 1.5 mm long Cu wire.
(a) TITAN conewire experimental setup and diagnostic layout. (b) Measured Cu Kα emission from 1.5 mm long Cu wire.
Transversely integrated lineouts along the Cu wire from the Kα imager for various prepulse energies of 17, 100, 500, and 1000 mJ. The lineouts were normalized to their peak.
Transversely integrated lineouts along the Cu wire from the Kα imager for various prepulse energies of 17, 100, 500, and 1000 mJ. The lineouts were normalized to their peak.
Contours of fast electron density (n_{fast}), radial electric field (E_{R}) and azimuthal magnetic field (B_{θ}) simulated at 1.0, 4.5, and 7.5 ps. The electrons using the twotemperature distribution are injected at z = 0 with 40° Gaussian spread.
Contours of fast electron density (n_{fast}), radial electric field (E_{R}) and azimuthal magnetic field (B_{θ}) simulated at 1.0, 4.5, and 7.5 ps. The electrons using the twotemperature distribution are injected at z = 0 with 40° Gaussian spread.
Fast electron particle plots at 5.0 ps for three energy groups: (a) less than 50 keV, (b) between 0.5 and 2.5 MeV and (c) >3.5 MeV. The energy of electrons surfing along the wire is ∼1 MeV as shown in (b). The electron bunch between 500 and 1500 μm corresponds to the timeofflight of electrons at speed of light for 0.7 ps duration. The vertical edge of the bunch is due to aspect ratio.
Fast electron particle plots at 5.0 ps for three energy groups: (a) less than 50 keV, (b) between 0.5 and 2.5 MeV and (c) >3.5 MeV. The energy of electrons surfing along the wire is ∼1 MeV as shown in (b). The electron bunch between 500 and 1500 μm corresponds to the timeofflight of electrons at speed of light for 0.7 ps duration. The vertical edge of the bunch is due to aspect ratio.
Energy partition of fast electron transport simulation with T_{cold} = 800 keV and T_{hot} = 6 MeV for the intrinsic prepulse case. The total injected energy (blue) is distributed to the fast electron energy (pink), thermal energy (red), field energy associated with the electrons (light blue), ionization (black) and energy into radiation loss (green). The energy carried by electrons leaving from the simulation boundaries is shown in dottedblue. The energy error of the simulation is plotted in dottedred.
Energy partition of fast electron transport simulation with T_{cold} = 800 keV and T_{hot} = 6 MeV for the intrinsic prepulse case. The total injected energy (blue) is distributed to the fast electron energy (pink), thermal energy (red), field energy associated with the electrons (light blue), ionization (black) and energy into radiation loss (green). The energy carried by electrons leaving from the simulation boundaries is shown in dottedblue. The energy error of the simulation is plotted in dottedred.
Comparisons of the measured wire profile for the 17 mJ to simulations using single temperature: (a) T = 500, 800, and 1200 keV and (b) T = 4, 8, and 12 MeV. (c) The simulated escaped electron spectra for 1.2, 4, 6, 8, and 12 MeV. They are compared with the measured electron spectrum for the intrinsic prepulse case (shot 17s5). (d) Comparison of the measurement and model with twotemperature distribution (T_{cold} = 700 keV, T_{hot} = 6 MeV, E_{hot}/E_{total} = 70%).
Comparisons of the measured wire profile for the 17 mJ to simulations using single temperature: (a) T = 500, 800, and 1200 keV and (b) T = 4, 8, and 12 MeV. (c) The simulated escaped electron spectra for 1.2, 4, 6, 8, and 12 MeV. They are compared with the measured electron spectrum for the intrinsic prepulse case (shot 17s5). (d) Comparison of the measurement and model with twotemperature distribution (T_{cold} = 700 keV, T_{hot} = 6 MeV, E_{hot}/E_{total} = 70%).
Result of least square fitting for the measurement at 17 mJ shot. The input electron distribution was varied by changing T_{cold} and energy fraction in the cold component while T_{hot} = 6 MeV and the total injected current were fixed. The contour is plotted in log scale of the least square values normalized by the minimum. The dotted line represents twice the minimum of lease squares (log10(2) = 0.3).
Result of least square fitting for the measurement at 17 mJ shot. The input electron distribution was varied by changing T_{cold} and energy fraction in the cold component while T_{hot} = 6 MeV and the total injected current were fixed. The contour is plotted in log scale of the least square values normalized by the minimum. The dotted line represents twice the minimum of lease squares (log10(2) = 0.3).
Comparisons of the measured Kα wire profile for the 17 mJ case with the simulated for different initial angular momentum. The spread of the electrons was modeled with a Gaussian function (exp[ − (θ/dθ)^{2}]) and dθ = 5, 40, and 80°.
Comparisons of the measured Kα wire profile for the 17 mJ case with the simulated for different initial angular momentum. The spread of the electrons was modeled with a Gaussian function (exp[ − (θ/dθ)^{2}]) and dθ = 5, 40, and 80°.
Fits of LSP simulations of the Kα wire profiles to the measurements for the prepulse energies of 17(open circle), 100 (open square), 500 (asterisk), and 1000 mJ (open diamond). In the fitting, T_{cold} and total injected energies were varied with fixed T_{hot} of 6 MeV. As the prepulse energy increases, the slope of the falloff decreases from 700 keV to 400 keV while the energy percentage in the hot component increases from 70.0% to 96.6%. The total electron energy entering the wire decreases from 5.2 J to 2.2 J.
Fits of LSP simulations of the Kα wire profiles to the measurements for the prepulse energies of 17(open circle), 100 (open square), 500 (asterisk), and 1000 mJ (open diamond). In the fitting, T_{cold} and total injected energies were varied with fixed T_{hot} of 6 MeV. As the prepulse energy increases, the slope of the falloff decreases from 700 keV to 400 keV while the energy percentage in the hot component increases from 70.0% to 96.6%. The total electron energy entering the wire decreases from 5.2 J to 2.2 J.
(a) The coupling efficiencies inferred from the fits using exponential and relativisticMaxwell distributions as a function of the prepulse energy. The coupling efficiencies were calculated for the coupling from the laser to all electrons into the wire and from the laser to 13 MeV electrons. (b) The electron energy distributions using the inferred parameters from the fits to the measurements for 17 mJ (solid) and 1000 mJ (dotted) cases. The distributions were reconstructed with exponential (red) and relativistic Maxwellian (black) distributions.
(a) The coupling efficiencies inferred from the fits using exponential and relativisticMaxwell distributions as a function of the prepulse energy. The coupling efficiencies were calculated for the coupling from the laser to all electrons into the wire and from the laser to 13 MeV electrons. (b) The electron energy distributions using the inferred parameters from the fits to the measurements for 17 mJ (solid) and 1000 mJ (dotted) cases. The distributions were reconstructed with exponential (red) and relativistic Maxwellian (black) distributions.
(a) The measured Kα spectrum of the conewire shot for 17 mJ was compared with modeled Cu Kα spectra with FLYCHK for 10, 50, and 100 eV temperature. The modeled spectra were convolved with the instrument function. (b) Calculated total Kα signals within the crystal bandwidth as a function of electron temperature. The signals were normalized by that for 20 eV.
(a) The measured Kα spectrum of the conewire shot for 17 mJ was compared with modeled Cu Kα spectra with FLYCHK for 10, 50, and 100 eV temperature. The modeled spectra were convolved with the instrument function. (b) Calculated total Kα signals within the crystal bandwidth as a function of electron temperature. The signals were normalized by that for 20 eV.
Tables
Summary of inferred electron spectrum parameters using exponential energy distribution for the prepulse energies considered.
Summary of inferred electron spectrum parameters using exponential energy distribution for the prepulse energies considered.
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