Ultrahigh acceleration in the range above 1020cm/s2 of plasma blocks was numerically predicted by laser pulses of ps duration and intensities of 1018W/cm2 (Hora, Reference Hora1981) where a non-thermal direct conversion of optical energy into macroscopic plasma motion was determined by nonlinear (ponderomotive) forces using the dielectrically modified Maxwellian stress tensor. This was experimental verified at plane geometry laser-plasma interaction by Doppler effect line shifts (Sauerbrey, Reference Sauerbrey1996) using 350 fs laser pulses of 3.5 × 1017W/cm2 pulses from a KrF laser. These accelerations were 100,000 times higher than ever measured before in a laboratory and reproduced (Földes et al., Reference Földes, Bakos, Gal, Juhasz, Kedves, Kocsis, Szatmari and Veres2000) in agreement with the theory of the nonlinear force (Hora et al., Reference Hora, Badziak, Read, Li, Liang, Liu Hong, Zheng-Ming, Jie, Miley, Zhang, He, Peng, Glowacz, Jablonski, Wolowski, Skladanowski, Jungwirth, Rohlena and Ullschmied2007).
Necessary condition was that the contrast ratio had to be >107 for cutting off prepulses in order to avoid relativistic self-focusing. Another essential condition is to work with single mode laser pulses. This was fulfilled in the experiments (Sauerbrey, Reference Sauerbrey1996; Földes et al., Reference Földes, Bakos, Gal, Juhasz, Kedves, Kocsis, Szatmari and Veres2000) with the KrF lasers. This condition is not fulfilled in most other lasers where the results could not be reproduced. In retrospect, it confirms the extreme high quality of the Titan-sapphire single mode laser of Zhang et al. (Reference Zhang, He, Chen, Li, Zhang, Wong, Li, Feng, Zhang, Tang and Zhang1998) used in the experiment where from anomalously low X-ray emission it could be concluded, how relativistic self-focusing was avoided for the plane geometry interaction process supporting the ultrahigh acceleration.
Thanks to the now available 3 PW laser pulses (Li et al., Reference Li2013; Chu et al., Reference Chu, Liang, Yu, Xu, Xu, Ma, Lu, Liu, Leng, Li and Xu2013) on the way to exawatt (Mourou et al., Reference Mourou, Brlocklesby, Tajima and Limpert2013), the initiation of a fusion flame in solid density deuterium-tritium (DT) fuel by interpenetration of very fast picoseconds plasma blocks (Hora, Reference Hora1983; Hora et al., Reference Hora and Miley2005) could be studied numerically (Hora, Reference Hora2009) where fusion energy from the extremely difficult 11B (HB11) reaction with protons changed into the level of the conditions of DT.
After the fusion results were manifested for infinite plane geometry, the problem was the problems of cylindrical lateral energy losses when working with finite diameter laser beams. One way out was to use spherical geometry (Hora et al., Reference Hora, Lalousis and Moustaizis2014) where, however, the fusion gains are limited by fuel exhaustion if not laser pulses above exawatt are used. Another way is to use cylinder-parallel magnetic fields (Hora et al., Reference Hora, Lalousis and Moustaizis2012) (Fig. 1) where fields up to 100 Tesla were not sufficient (Moustaizis et al., Reference Moustaizis, Lalousis and Hora2013). This situation changed dramatically after the recent laser operated 10 kilotesla magnetic fields were developed (Fujioka et al., Reference Fujioka, Zhang, Ishihara, Shigemori, Hironaka, Johzaki, Sunahara, Yamamoto, Nakashima, Watanabe, Shiraga, Nkishimura and Azechi2013), resulting in high gains, however still needing exawatt laser pulses (Lalousis et al., Reference Lalousis, Moustaizis, Hora and Miley2014). The computations use the multi-fluid code as used before (Lalousis et al., Reference Lalousis, Hora, Eliezer, Martinez-Val, Moustaizis, Miley and Mourou2013; Hora et al., Reference Hora, Miley, Lalousis, Moustaizis, Clayton and Jonas2014a; Reference Hora, Lalousis and Moustaizis2014b) based on the general genuine two-fluid plasma hydrodynamics (Lalousis et al., Reference Lalousis and Hora1983; Hora et al., Reference Hora, Lalousis and Eliezer1984). From a series of cases with each irradiation of ps laser pulses of 248 nm wave length and 1020 W/cm2 intensity at an interaction diameter of 0.1 mm radius on solid density HB11 for initiation of fusion, Figures 2 and 3 show the resulting densities of the electrons N e, protons N h, and boron nuclei N b along the radial coordinate r at times 100 ps and 1000 ps, respectively, of the figures. From the initial radius of 0.1 mm, the plasma has expanded showing depletion at the cylinder axis up to the radius but with some compression at higher radius. Above 0.4 mm the plasma has the untouched densities. Figure 4 shows at 100 ps the magnetic field which is 104 T in the axis-parallel z-direction while the curve on the left-hand side is the density N a of the generated alpha particles centered inside the plasma. The fact of the ignition can be seen in Figure 5 where the density of the generated alpha particles is shown increasing on time.
Fig. 1. (Color online) Magnetic trapping of a cylindrical nuclear fusion volume: (1, 2) is the loop for generating a magnetic field, (3) is the fusion fuel for one or two sided irradiation (4) of ps laser pulses to initiate a fusion flame, (5) is the magnetic field parallel to the cylindric symmetry, and (6) is the complete fuel not directly irradiated by the laser.
Fig. 2. (Color online) Dependence on the radius r of the electron density N e, the proton density N h, and the 11B nuclear density N b (maxima decreasing respectively) at time 100 ps for solid state HB11 fuel at an irradiation radius of 0.1 mm of a 248 wave length laser pulse of 1 ps duration.
Fig. 3. (Color online) Same as Figure 2 at time 1000 ps.
Fig. 4. (Color online) Same case of Figure 2 with the magnetic field B z parallel to the cylindrical axis z merging into 10 kilotesla above the radius 0.3 mm, with the curve at the left showing the density of the generated alpha particles N a.
Fig. 5. (Color online) Alpha density N a depending on the radius r at different times showing ignition from the increase of the curves on time.
All these calculations are similar to the DT fusion as binary reactions. The secondary reactions of the 2.9 MeV alphas when hitting a boron nucleus and transferring about 600 MeV energy at central collision are not included in the computations (Hora et al., Reference Hora, Lalousis, Moustaizis, Földes, Miley, Yang, He, Eliezer and Martinez-Val2013). The gyro radius of the alpha particles at 10 kilotesla magnetic fields is 42.5 µm and their mean free pass for collective stopping at solid state density is nearly independent on the electron temperature in the range of 60 µm at solid state density such that an avalanche multiplication is resulting in an exponential increase of the fusion gain until fuel depletion. Similar estimations as for spherical geometry (Hora et al., Reference Hora, Lalousis and Moustaizis2014a) show how a laser energy input into the block for the initiation of the flame of 30 kJ can produce alpha energy of 1 GJ. By this way, the requested fusion gain for DT of 10,000 postulated by Nuckolls et al. (Reference Nuckolls and Wood2002) for a power station with his relativistic electron beam fast ignition arrives at comparable values for HB11. It is remarkable that the alpha-avalanche process is arriving at comparable values with clean HB11 fusion compared with DT, but without the neutrons produced by DT and their difficulties with the generation of radioactivity (Tahir et al., Reference Tahir and Hoffmann1997).
