Heating efficiency evaluation with mimicking plasma conditions of integrated fast-ignition experiment

A series of experiments were carried out to evaluate the energy-coupling efficiency from heating laser to a fuel core in the fast-ignition scheme of laser-driven inertial confinement fusion. Although the efficiency is determined by a wide variety of complex physics, from intense laser plasma interactions to the properties of high-energy density plasmas and the transport of relativistic electron beams (REB), here we simplify the physics by breaking down the efficiency into three measurable parameters: (i) energy conversion ratio from laser to REB, (ii) probability of collision between the REB and the fusion fuel core, and (iii) fraction of energy deposited in the fuel core from the REB. These three parameters were measured with the newly developed experimental platform designed for mimicking the plasma conditions of a realistic integrated fast-ignition experiment. The experimental results indicate that the high-energy tail of REB must be suppressed to heat the fuel core efficiently.

Figure 1

Schematic drawings [(a) and (b)] and a photograph (c) of a target used in experiments. (a) A gold cone attached hemishell is mounted on a high-$Z$ (Sn and Ta) metal block. REB generated at the cone-tip is converted into $K\alpha$ and Bremsstrahlung x-rays in the block. Absolute spectrum and angular distribution of x-rays were measured to determine the absolute number and energy distribution of the REB. (b) A Cu tracer layer is located on a C block to measure spatial profile of the REB by measuring Cu-$K\alpha$ x-ray emission profile. The C block is a REB damper to prevent Cu-$K\alpha$ emission by refluxing electrons around the tracer layer.

Figure 2

(a) Comparison between energy distribution of vacuum electrons and that obtained from hard x-ray spectrum. Gray dots represent energy distributions of energetic electrons, so-called vacuum electrons, escaped from the metal block into vacuum, which were measured with an electron energy spectrometer. Error of vacuum electron numbers is $\pm 5\%$ owing to uncertain of analyzer detector response for electrons, and error of electron energy is $\pm 4.5\%$ owing to uncertain of its calibration. Blue broken and red solid lines are Boltzmann distributions calculated with $T_{\mathrm{REB}1}=1$ and $T_{\mathrm{REB}2}=15$ MeV of slope temperature and $A=0.95$ of relative coefficient. Slope temperature of higher-energy component ($T_{\text{REB2}}$) was obtained by fitting the energy distribution of the vacuum electrons in the range of $E>$ 10 MeV with the function $[exp(-E/T_{\text{REB2}})]$. The lower-energy component ($T_{\mathrm{REB}1}$) and coefficient ($A$) were evaluated from measured hard x-ray signal. (b) $\text{Cu-K}\alpha$ emission from a Cu tracer layer was measured with a spherically bent quartz crystal. The spot diameter corresponds to REB diameter at the dense fuel core position. The radius of the $K\alpha$ spot highlighted by the circle shows $r_{\text{REB}}=40\pm 10\mu \mathrm{m}$ FWHM. The white cross is a spatial scale of 200 $\mu \mathrm{m}$ in the image plane.

Figure 3

Relative x-ray doses (red solid circles) recorded on imaging plates in HEXSs located at (a) ${180}^{\circ }$, (b) $159.1^{\circ }$, and (c) $110.9^{\circ }$ from the LFEX laser incident axis were compared with Monte Carlo calculations. The curves were calculated for three cases of REB energy distribution; [Case A (blue solid line)] $A=0.95, T_{\mathrm{REB}1}=1$ MeV, and $T_{\mathrm{REB}2}=15$ MeV; [Case B (orange broken line)] $A=0.5, T_{\mathrm{REB}1}=1$ MeV, and $T_{\mathrm{REB}2}=15$ MeV; [Case C (green dash-dot line)] $A=1, T_{\mathrm{REB}1}=1$ MeV, respectively. Errors in the measured doses are caused by uncertain of IP calibration for x rays. (d) Sensitivity of fitting of calculations to the experimental doses for varying relative coefficient ($A$) and lower slope temperature ($T_{\mathrm{REB}1}$) with fixed higher slope temperature ($T_{\mathrm{REB}2}=15$ MeV) and divergence angle (${\theta }_{\text{div}}={41}^{\circ }$ FWHM). The fitting residual values defined as in the text are color coded and the white broken line is a contour line of 0.12.

Figure 4

Comparison between computed spatial distributions of REB (red broken line) and $K\alpha$ emission profile (blue solid line). The REB profile is almost identical to $K\alpha$ emission profile calculated with consideration of cross-section and spatial and energy distributions of the REB after transport through the cone tip and the plasma. Details of the REB transport simulation is described in the text.

Figure 5

REB transport was computed in a tracer target with a simulation code to confirm that is not modulated by structures of the tracer target. (a) Two-dimensional (2D) density profile of the REB transport region that was calculated with a 2D radiation-hydrodynamic simulation code. Computed 2D profiles of REB energy density in erg/s ${\mathrm{cm}}^3$ unit (b) and strength of azimuthal magnetic field in T unit (c) generated by the REB itself. Structures of the tracer target do not modulate the REB transport.

Figure 6

X-ray backlight images of solid CD ball compressed by nine laser beams at 0.44 and 0.84 ns after the peak of the laser pulse. Nine beams of GEKKO-XII laser irradiate asymmetrically on the CD ball. (c) Density profile was obtained from the shadow image after Abel inversion. Peak density and areal density are $22\pm 6\text{g}/{\mathrm{cm}}^3$ and $54\pm 9\text{mg}/{\mathrm{cm}}^2$, respectively.

Figure 7

Transport of the REB in a fuel core was computed with a simulation code. (a) Density profile of the fuel core used in the computation. Temperature profile of bulk electrons heated by experimentally characterized REB (b), REB with 1 MeV single slope temperature and ${40}^{\circ }$ divergence angle (c), and REB with 1 MeV single slope temperature and $0^{\circ }$ divergence angle (d). Units of the color (gray) scales are ${\mathrm{g}/\mathrm{cm}}^3$ (a) and keV (b, c, d). The energy coupling efficiency from the REB to the core ($\rho >1\text{g}/{\mathrm{cm}}^3$) are 1.3% (b), 11% (c), and 27% (d), respectively.