Fig. 1. Schematic of ultrafast probing of ion temperature in a hot ¹¹B plasma by Doppler broadening of NRF. An intense γ-ray beam can be efficiently generated from submicrometer wires irradiated by a recently available PW laser. After collimation, the γ-ray beam is fired into a ¹¹B pellet, which is located 11 cm downstream from the wire position and has a small radius of 2 mm, whereupon NRF interactions are excited. This is followed by emission of the characteristic photons. Owing to Doppler broadening, the NRF emission spectra contain information about ion temperature. To record these NRF signals efficiently, 24 high-purity germanium (HPGe) detectors are distributed in two concentric rings and are located at 90° and 135° with respect to the incident γ beam. The distance between the detectors and the pellet is 30 cm. For each detector, the germanium crystal used is 8.6 cm thick and has radius 4.2 cm. In our case, owing to the small size of the ¹¹B pellet, a large number of energetic γ rays will penetrate through the pellet, forming a transmitted γ-ray beam. For better visualization, the figure is not to scale.

Fig. 2. (a) Dependence of Doppler-broadened cross section on ¹¹B ion temperature at E_r = 5.020 MeV. (b) Doppler-broadened cross section of ¹¹B as a function of photon energy.

Fig. 3. Spectral–angular distribution of γ-ray pulses emitted from laser-illuminated wires under laser powers P₀ = 0.5 PW (a), 1.0 PW (b), 2.5 PW (c), and 5.0 PW (d).

Fig. 4. Spectra of the γ-ray beams with collimation angle <1° at four different laser peak powers. The tails of these spectra are overlaid with exponential temperature fits, shown by broken lines.

Fig. 5. Simulation results for a collimated intense γ-ray beam with effective temperature T_γ = 70 MeV at a laser power of 2.5 PW. (a) γ-ray intensity recorded by 24 HPGe detectors as a function of observing angle θ and energy (which is represented by the radius in the polar figure). (b) γ-ray spectrum showing five NRF signatures and a few escape peaks. The inset shows an enlarged view of one NRF signature at 5.020 MeV. The dashed line is a fitting curve of a Gaussian distribution.

Fig. 6. (a) Fitting curves of NRF peaks at 5.020 MeV. A collimated intense γ-ray beam with temperature T_γ = 70 MeV at laser power 2.5 PW is used for the simulation. (b) Values of δE_sim, δE, 2.355Δ, and δE_D at 5.020 MeV as functions of ion temperature T_i.

Fig. 7. Dependence of the detected NRF yield (a) and areal density (b) on laser peak power with ¹¹B ions at resonance energies of 2.125, 4.445, 5.020, 7.286, and 8.920 MeV. The NRF yield is fixed at 100 for calculating the required areal density in (b).

Fig. 8. Threshold areal density required for four aneutronic fusion materials. The resonance energy E_r is selected to be 3.563, 0.478, 5.020, and 6.324 MeV for ⁶Li, ⁷Li, ¹¹B, and ¹⁵N, respectively. A collimated intense γ-ray beam with temperature T_γ = 38 MeV at 1.0 PW laser power is used.

Table 1. Integrated NRF cross sections I_σ for principal transitions 0 → r → 0 in ^6,7Li, ¹¹B, and ¹⁵N at their characteristic energies E_r and the estimated thresholds to probe ion temperature under the premise that δE_sim ≥ 2δE_D.