Abstract
The energy and angular distributions of the fast electrons predicted by particleincell (PIC) simulations differ from those historically assumed in ignition designs of the fast ignition scheme. Using a particular 3D PIC calculation, we show how the ignition energy varies as a function of sourcefuel distance, source size, and density of the precompressed fuel. The large divergence of the electron beam implies that the ignition energy scales with density more weakly than the scaling for an idealized beam [S. Atzeni, Phys. Plasmas 6, 3316 (1999)], for any realistic source that is at some distance from the dense deuteriumtritium fuel. Due to the strong dependence of ignition energy with sourcefuel distance, the use of magnetic or electric fields seems essential for the purpose of decreasing the ignition energy.
This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. DEAC5207NA27344.
I. INTRODUCTION
II. IGNITION WITH NONIDEAL PARAMETERS
III. PIC SOURCE AND ZUMAHYDRA
A. Particleincell simulation and resulting hot electrondistribution function
B. Particle injection into Zuma
C. Scaling the source to different parameters
IV. BURN CALCULATIONS
V. SUMMARY AND CONCLUSIONS
Key Topics
 Particleincell method
 56.0
 Electron beams
 17.0
 Particle distribution functions
 12.0
 Hot carriers
 11.0
 Electron scattering
 8.0
H05H1/02
Figures
Minimum electron energy required for ignition as a function of laser irradiance , for different fuel densities and assuming that the energy is deposited in the ideal beam diameter. Solid lines refer to the “PIC” distribution of Eq. (5) and scale as . Broken lines refer to the exponential distribution , with Tp being the ponderomotive temperature, and scale as . The lines at constant ebeam ignition energy refer to the minimum ignition energy of Eq. (2) .
Minimum electron energy required for ignition as a function of laser irradiance , for different fuel densities and assuming that the energy is deposited in the ideal beam diameter. Solid lines refer to the “PIC” distribution of Eq. (5) and scale as . Broken lines refer to the exponential distribution , with Tp being the ponderomotive temperature, and scale as . The lines at constant ebeam ignition energy refer to the minimum ignition energy of Eq. (2) .
Ignition energy as a function of target density and sourcefuel distance, for an energy spectrum of the fast electrons given by Eq. (5) . The left column assumes a second harmonic laser of NdYAG ( ) and the right column considers its third harmonic ( ). The top row assumes a beam with , the bottom row assumes . The numbers in the white boxes of panel (a) are results from the numerical simulations described in Sec. III .
Ignition energy as a function of target density and sourcefuel distance, for an energy spectrum of the fast electrons given by Eq. (5) . The left column assumes a second harmonic laser of NdYAG ( ) and the right column considers its third harmonic ( ). The top row assumes a beam with , the bottom row assumes . The numbers in the white boxes of panel (a) are results from the numerical simulations described in Sec. III .
Laser intensity corresponding to the case (a) of Fig. 2 , as a function of fuel density and sourcefuel distance. For distances larger than , the optimal focal spot was limited by the maximum value allowed of . Note that at small distances, it is convenient to focus the beam to small focal spots despite the increased hot electron temperature.
Laser intensity corresponding to the case (a) of Fig. 2 , as a function of fuel density and sourcefuel distance. For distances larger than , the optimal focal spot was limited by the maximum value allowed of . Note that at small distances, it is convenient to focus the beam to small focal spots despite the increased hot electron temperature.
Normalized figures of merit of the distribution function of the hot electrons, for all the hot electrons with energy in the region . This distribution function belongs to the time t = 440 fs after the beginning of the simulation (that is, about 400 fs after the beginning of the interaction). Filled circles show the resolution used for each variable, resulting in a matrix with elements to be sampled in subsequent ignition calculations.
Normalized figures of merit of the distribution function of the hot electrons, for all the hot electrons with energy in the region . This distribution function belongs to the time t = 440 fs after the beginning of the simulation (that is, about 400 fs after the beginning of the interaction). Filled circles show the resolution used for each variable, resulting in a matrix with elements to be sampled in subsequent ignition calculations.
(a) Dependence of the angular distribution vs. angle θ, for three different ranges in r. (b) Dependence of the angular distribution vs. angle , for three different ranges in r. These figures show the correlation between angular and spatial variables.
(a) Dependence of the angular distribution vs. angle θ, for three different ranges in r. (b) Dependence of the angular distribution vs. angle , for three different ranges in r. These figures show the correlation between angular and spatial variables.
Sampling of the multivariate distribution function with 500 particles/time step and a temporal resolution of 0.5 fs produces figures of merit of the distribution, which are close to the original particleincell calculation. Red circles are obtained after collecting particles within of distance from the injection plane in Zuma, for a beam propagating through a DT plasma at 10 g/cc and temperature of 100 eV. The original PSC figures of merit are shown in blue (same as Fig. 4 ).
Sampling of the multivariate distribution function with 500 particles/time step and a temporal resolution of 0.5 fs produces figures of merit of the distribution, which are close to the original particleincell calculation. Red circles are obtained after collecting particles within of distance from the injection plane in Zuma, for a beam propagating through a DT plasma at 10 g/cc and temperature of 100 eV. The original PSC figures of merit are shown in blue (same as Fig. 4 ).
Energy contained in a box ahead of the injection plane in Zuma, normalized with respect to the energy contained in the collisionless PSC simulation. In the Zuma calculation, the electron beam propagates through a 10 g/cc DT plasma, with the inclusion of stopping and scattering.
Energy contained in a box ahead of the injection plane in Zuma, normalized with respect to the energy contained in the collisionless PSC simulation. In the Zuma calculation, the electron beam propagates through a 10 g/cc DT plasma, with the inclusion of stopping and scattering.
Maps of the energy density (left) and longitudinal current (right) during propagation of the hot electron beam in a 30 g/cc DT plasma. For this Zuma simulation, the effects of scattering and stopping are included, electric and magnetic fields are switched off.
Maps of the energy density (left) and longitudinal current (right) during propagation of the hot electron beam in a 30 g/cc DT plasma. For this Zuma simulation, the effects of scattering and stopping are included, electric and magnetic fields are switched off.
Map of the longitudinal flux (left) and corresponding axial lineout (right) radially averaged over , for the same parameters of Figure 8 .
Map of the longitudinal flux (left) and corresponding axial lineout (right) radially averaged over , for the same parameters of Figure 8 .
Dependence of the laser ignition energy as a function of sourcefuel distance , for (left) and (right). Colors are associated with different peak densities; the thickness of the different bands represents the uncertainty on the ignition energy: simulations did (did not) ignite on the upper (lower) bound of each band.
Dependence of the laser ignition energy as a function of sourcefuel distance , for (left) and (right). Colors are associated with different peak densities; the thickness of the different bands represents the uncertainty on the ignition energy: simulations did (did not) ignite on the upper (lower) bound of each band.
Dependence of the laser ignition energy as a function of beam size multiplier , for (left) and (right). For and , no solution was found below 4 MJ.
Dependence of the laser ignition energy as a function of beam size multiplier , for (left) and (right). For and , no solution was found below 4 MJ.
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