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A world-class ultraintense laser LFEX at ILE, Osaka University directly heated a CD shell target, imploded by GEKKO XII(GXII) laser. Illuminating LFEX energy of 246 J increased the core internal energy by $23\pm 3$ J, leading to the conclusion that the heating efficiency is $9\pm 0.8$ %. The results encourage the fast ignition scheme fusion as a hopeful candidate of the fusion machine.

For the fast ignition fusion[ref1], the direct illumination of an ultraintense laser onto the core is the simplest technical and economical way. To demonstrate the feasibility of direct core heating, we have performed experiments with difficult illumination configurations, such that (a) LFEX is coaxial to the GXII bundled beams axis (Fig. 1(a)), and (b) LFEX is transverse to the axis (Fig.1(b)). (a) mode will be the simplest scheme, but the cutoff point is far from the core and much plasma clouds may block the hot electron and ion transports[ref2]. (b) mode may not be so simple to operate the power plant, but the cutoff point is close to the core and there are less cloud plasmas, which block the transport[ref3]. However, because the transverse mode results are not yet confirmed, we concentrate to the axial (a) mode. Counter illuminating 6 beams from the GXII has imploded a CD shell target. Ratio of shell radius $R$ to focal distance $d/R$ is -3. LFEX laser is directly focused to the core center.

The intensity on target is $0.5\sim 1\times10^{19}$ W/cm$^2$. We have estimated the LFEX fast heating efficiency from the following procedures.

Without LFEX illumination, Fig. 2(a) shows a DD reacted proton energy peak (3.02 MeV) shift down to 750 keV (red arrow in Fig.2 (a)) due to the core plasma, yields an areal density of 0.016 g/cm$^2$ along the transverse direction. Peak shift to 1500 keV (green arrow in Fig. 2 (a)) yields 0.011 g/cm$^2$ to the axial direction[ref4]. Considering an ellipsoidal core figure, these results lead us to the core density $\rho=2.8\pm 0.3$ g/cm$^3$ and volume $V = 3.2\times10^{-7}$ cm$^3$.

An x-ray streak camera, in Fig. 2 (b), shows both the core emissions due to the implosion +200 ps after the GXII peak and the LFEX heating +600 ps after. The intensity of core emission here is same as that without LFEX, but once LFEX is just on the compression, as in Fig. 2 (c), the core emission becomes $\sim$20 times stronger than the emissions without LFEX. The stagnation period $\tau$, within which the maximum compression continues, $\leq 50$ ps. We assume that the neutron generation period is also close to $\tau$.

$3.5\times10^6$ neutron yields(Ny) without LFEX illumination in Fig.3 (a) gives us the ion temperature $T_i$ to be 700 eV, if we assume $Ny = n_i^2/4<\sigma v >_{Ti} V \tau$. While, with LFEX at +200 ps, Ny of Fig.3 (b), $9.8\times10^6$ gives $T_i\sim$1.0 keV. The ion temperature increment $\Delta T_i$ is 0.3 $\sim$ 0.4 $T_i$, or $\sim$300 eV.Supposing $T_i \sim T_e$ in equilibrium, then $\Delta T_e\sim\Delta T_i\sim300$ eV with LFEX. The intensity of x-ray emission of the core (Fig.3(d)) is 4 times larger than the Fig.3 (c), leading to the electron temperature increment $\Delta T_e$ is ($4^{1/4}$-1)$T_e=0.4T_e$, if the core is yet in equilibrium. The increment of core energy is given by $\Delta E = \Delta E_e + \Delta E_i = 3/2(n_e\Delta T_e + n_i\Delta T_i) V$, where $\Delta E_e$ and $\Delta E_i$ are the electron and ion contributions, respectively. Assuming the core plasma is fully ionized, then $n_e=Z_{CD}n_i$, where $Z_{CD}$ is total charges of a CD ion and also using $\Delta T_e\sim\Delta T_i$, we could estimate $\Delta E$$ = 3/2V\Delta T_i n_i(Z_{CD}+1)$$ = 23\pm3$ J. Since the LFEX energy is 246 J, we expect the heating efficiency to be $9\pm 0.8$ % for the axial mode. Without LFEX, the implosion efficiency, defined as a core internal energy divided by an implosion laser energy (now GXII), is $53\pm7 {\rm J}/1.7 {\rm kJ} = 3.1\pm7$ %. With LFEX, we can estimate that the total implosion efficiency is improved to 85 J/1946 J = 4.4 %.

We will discuss the transverse mode later on.

**[References]**

[ref1]Y. Kitagawa *et al.*, J. Physics: Conf. Series **688** 012049 (2016).

[ref2]Y. Kitagawa *et al.*, Phys. Rev. E **71** 016403 (2005): J. Plasma Fusion Res. **81** 384 (2005).

[ref3]Y. Kitagawa *et al.*, Phys. Rev. Lett. **114** 195002 (2015): Nucl. Fusion **57** 076030 (2017).

[ref4]Y. Kitagawa *et al.*, Phys. Rev. Lett. **75** 3131 (1995).

Affiliation | The Graduate School for the Creation of New Photonics Industries |
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Country or International Organization | Japan |