INTRODUCTION
Fiber glass lasers for amplification of pulses of lower than picosecond (ps) duration and powers of petawatt (PW) up to exawatt (EW) and higher by the ICAN project using chirped pulse amplification (CPA) (Mourou et al., Reference Mourou, Brlocklesby, Tajima and Limpert2013) are of interest for electron or hadron accelerators with many applications including cancer therapy, as well as for generating PeV particles or high energy physics for exploring extremely high field processes as pair production in vacuum. Another application is for nuclear fusion for generating energy where the problem of the dangerous radioactive radiation of all presently developed nuclear energy schemes can be reduced below the radiation from burning coal, i.e., below any dangerous level. The scheme “has the potential to be the best route to fusion energy” (Haan, Reference Haan2010) and is one of the applications opened by the CPA discovery (Strickland et al., Reference Strickland and Mourou1985) which led to the CPA-ICAN lasers (Mourou et al., Reference Mourou, Brlocklesby, Tajima and Limpert2013).
This application for laser driven fusion was not easy to be opened and because this was realized only on a rather narrow line of research though the principals involved with the nonlinearity of laser physics have a long tradition. The ICAN technique provides very favorable conditions for this application for fusion as it will be adding to the groundbreaking new aspects (Mouroou et al., 2013). The key measurement is the experimental confirmation of the ultrahigh acceleration using the very short laser pulses with the very high power by CPA, first measured by Sauerbrey (Reference Sauerbrey1996) when using extremely high contrast ratios to cut-off laser-prepulses by a higher ratio than 107 until a time of about 1 ps before the main laser pulse arrived at the target. The repetition of this experiment was possible only by using the extreme quality of laser pulses by Földes et al. (Reference Földes, Bakos, Gal, Juhasz, Kedves, Kocsis, Szatmari and Veres2000), while any slight reduction of the quality prevented the measurement of this effect. This was clarified by the teams of Zhang et al. (Reference Zhang, He, Chen, Li, Zhang, Wong, Li, Feng, Zhang, Tang and Zhang1998), Badziak et al. (Reference Badziak, Kozlov, Makowksi, Parys, Ryc, Wolowski, Woryna and Vankov1999), and Klaus Witte (Kaluza et al., Reference Kaluza, Schreiber, Sandala, Tsakiris, Eidmann, Meyer-Ter-Vehn and Witte2004).
The measured ultrahigh acceleration (Sauerbrey, Reference Sauerbrey1996) of 2 × 1020cm/s2 was 100,000 times higher than ever measured before in a laboratory. This extremely high acceleration was predicted numerically in 1978 (see Hora, Reference Hora1981) in details (Hora et al., Reference Hora, Badziak, Read, Li, Liang, Liu, Sheng, Zhang, Osman, Miley, Zhang, He, Peng, Glowacz, Jablonski, Wolowski, Skladanowski, Jungwirth, Rohlena and Ullschmied2007) as nonlinear-force (ponderomotive) collective acceleration of plasma blocks. On top, the discovery of ultrahigh ion current densities in the space charge neutral accelerated plasma blocks above 1013Amps/cm2 is more than million times higher than can produce accelerators (Hora et al., Reference Hora, Badziak, Boody, Höpfl, Jungwirth, Kralikova, Kraska, Laska, Parys, Perina, Pfeifer and Rohlena2002; Badziak et al., Reference Badziak, Glowacz, Jablonski, Parys, Wolowski and Hora2004).
After considering the new aspects of the fiber option (Mourou et al., Reference Mourou, Brlocklesby, Tajima and Limpert2013) for PW to EW and more powerful laser pulses, we report on laser fusion of uncompressed solid density deuterium-tritium (DT) fuel at spherical irradiation where the properties can realistically followed up on numerous confirming preceding computations. The use of solid density HB11 fuel resulted in similar gains when using the same presumptions as for DT (Hora, Reference Hora2009; Hora et al., Reference Hora, Miley, Ghoranneviss, Malekynia and Azizi2009). This was not including the secondary reactions of the generated alpha particles when hitting protons leading to an avalanche of reactions with an essentially much higher total fusion gain, even to higher values than with DT. One may note, that the HB11 reaction is then the first to realize a neutron-free reaction (Tahir et al., Reference Tahir and Hoffmann1997; Labaune et al., Reference Labaune, Depierraux, Goyon, Loisel, Yahia and Rafelski2013), which the highly supported DT fusion schemes cannot provide, for which the classical approach has not arrived at the break-even level yet. The generated neutrons for the DT reaction decay with a half-life of 12 min into protons and electrons to produce water but before reaching this, the neutrons can react with stable nuclei to produce large amounts of radioactivity. These problems are eliminated with the neutron-free HB11 reaction.
Without the availability of details of the essential secondary reactions of the alpha particles (Hora et al., Reference Hora, Sadighi-Bonabi, Yazdani, Afaideh, Nafari and Ghoranneviss2012), an evaluation of estimations for the fusion gain is possible for the conditions of irradiating spheres of solid density HB11 fuel by converging ICAN laser pulses.
BENEFITS OF THE FIBER ICAN
The application to nuclear fusion was based on the Chu-Bobin scheme (Chu, Reference Chu1972; Bobin, Reference Bobin, Schwarz and Hora1974) of side-on ignition of a fusion flame in uncompressed solid density deuterium-tritium where it was shown that the flame can be initiated by a ps energy input into the fuel having an energy flux above 108 J/cm2. It was completely impossible to be realized with the lasers in 1972 and the thermal compression and ignition of the fusion fuel by nanosecond laser pulses only could be followed up using indirect drive (Lind et al., Reference Lindl and Moses2011; Haan et al., Reference Haan and Lindl2011), fast ignition (Azechi et al., Reference Azechi and Mima2011), or direct drive (Hora et al., Reference Hora, Azechi, Kitagawa, Mima, Murakami, Nakai, Nishihara, Takabe, Yamanaka, Yamanaka and Yamanaka1998; Hora, Reference Hora2013). However, when using CPA (Sauerbrey, Reference Sauerbrey1996; Hora et al., Reference Hora, Badziak, Boody, Höpfl, Jungwirth, Kralikova, Kraska, Laska, Parys, Perina, Pfeifer and Rohlena2002; Hora, Reference Hora2004) the unexpected conditions of the Chu-Bobin scheme could be fulfilled for the side-on ignition of uncompressed solid density fuel. This was initially evaluated for DT fusion fuel for irradiating laser pulses in plane geometry (Hora, Reference Hora2009).
For a fusion power station, problems of lateral energy losses of the plane irradiation can be overcome by using spherical irradiation. For this case, the ICAN fiber laser offers a solution as can be seen from Figure 1 (Mourou et al., Reference Mourou, Brlocklesby, Tajima and Limpert2013). The output of the amplified beam before the focusing of mirror 6 is from parallel fibers and has a plane wave front. In practical cases, the beam of 100 cm2 cross-section may be a pulse with 1 kJ energy and of ps duration representing 1 PW. The wave front is of such a quality that focusing in 7 has been shown (Mourou et al., Reference Mourou, Brlocklesby, Tajima and Limpert2013) to go to a diameter of 10 µm such that intensities at about 1021 W/cm2 are reached. The fibers permit an exceptionally high quality of the beam uniformity as it was shown in Figure 2 (Mourou, Reference Mourou2013) where the usual undesired maxima in the beam profile with glass lasers are automatic eliminated due to the fiber optics quality.
Fig. 1. (Color online) ICAN laser (Mourou et al., Reference Mourou, Brlocklesby, Tajima and Limpert2013).
Fig. 2. (Color online) Intensity distribution (schematic) across the laser beam after amplification (a) from a solid state laser (upper part) with irregular hot spots (maxima) in contrast to (b) the ideal output from an ICAN fiber laser (Mourou, Reference Mourou2013; Mourou et al., Reference Mourou, Brlocklesby, Tajima and Limpert2013).
A further advantage of the fiber optics is by avoiding the focusing mirror 6 in Figure 1, when taking the axes at the ends of the fibers not parallel at the end. Instead of the plane wave fronts from parallel axes of the fibers in Figure 1, the axes should be directed radial to a spherical center 2 as shown in Figure 3 such that a whole sphere 1 produces a spherical converging laser pulse front towards the center 3 where a fusion fuel pellet 3 is located. The fiber ends should fill nearly completely the whole sphere 1. If the radius of 1 is 1 m or more, a converging laser pulse with 1 ps duration and a power of more than EW will be generated for hitting the fuel pellet 2. Based on kJ energy per 100 cm2 output from a sphere of about 2 m diameter, a spherical laser pulse of EW and 1 ps duration would be generated.
Fig. 3. (Color online) Generation of a spherical shrinking laser pulse from radially directed fiber ends at a radius 1 to irradiate a spherical solid state fusion fuel 3 with ta concentric grid 2 of positive electric charge for slowing down the generated alpha particles from the HB11 reactions.
RESULTS WITH DEUTERIUM-TRITIUM FUEL
In order to understand the mechanisms in the spherically irradiated solid density fuel, results from computations using the genuine two-fluid hydrodynamics are being shown. In this model case, the radius of the pellet is taken 0.5 mm similar to the cases evaluated before (Moustaizis et al., Reference Moustaizis, Lalousis, Hora, Hein, Korn and Silva2013) with a laser intensity of 1020 W/cm2 for the initiating ps laser pulse. Figure 4 shows the ion density n i within the sphere at a sequence of times, Figure 5 the fusion reaction rate and Figure 6 the electron temperature. The main push is in the radial directed ions while the complete hydrodynamic code shows the highly delayed heating of the electrons in the collectively accelerated plasma blocks in Figure 6.
Fig. 4. (Color online) Initiation of a fusion flame in a solid DT sphere of 0.5 mm radius in the center of Figure 3 irradiated by a 1 ps laser pulse of 1020 W/cm2. The profile of the ion density is shown at different time after the initiating ps laser pulses deposited the energy to the driving plasma block.
Fig. 5. (Color online) The reaction rate for the case of Figure 4.
Fig. 6. (Color online) The electron temperature from the slowly thermalizing of the directed ion energy of the nonlinear force accelerated plasma blocks.
The conditions for the numerical evaluation of the initiation of the fusion flame by ultrahigh acceleration of nonlinear force driven plasma blocks by non-thermal direct conversion of laser energy into the collective driving process involves the result of Chu (Reference Chu1972) that the energy flux density E* threshold for the picosecond laser pulses of 4 × 108 J/cm2 has to be reduced by a factor 20 (Hora et al., Reference Hora, Malekynia, Ghoranneviss, Miley and He2008) for DT to
$$E^{\ast} = 2 \times 10^{7}\, \hbox{J}/\hbox{cm}^{2}.$$The reason for this reduction is the fact that at the time of the work of Chu, the inhibition factor for the reduction of thermal conduction in inhomogeneous plasmas was not known and the collective stopping power of Denis Gabor was not used as needed for high density plasmas. The experimental confirmation of these processes was shown while the quantum correction of the collision frequency is important only for longer times than the ps interactions (Hora et al., Reference Hora, Sadighi-Bonabi, Yazdani, Afaideh, Nafari and Ghoranneviss2012).
The collective block acceleration could best be seen, e.g., from the very low energy of the space charge neutralizing electrons between the directed motion of the blocks where the main energy is in the ions. The computations with the general hydrodynamic code (Lalousis, Reference Lalousis and Hora1983; Hora et al., Reference Hora, Lalousis and Eliezer1984; Reference Hora, Lalousis, Moustaizis, Miley, Yang., He, Eliezer and Martinez-Val2013; Hora, Reference Hora, Miley, Yang and Lalousis2011; Lalousis et al., Reference Lalousis, Földes and Hora2012; Reference Lalousis, Hora, Eliezer, Martinez-Val, Moustizis, Miley and Mourou2013) include the separate temperatures of the electrons and of the ions based on the genuine two-fluid model with complete inclusion of collisions in contrast to the initial computations (Chu, Reference Chu1972) with modifications (Malekynia et al., Reference Malekynia and Razavipour2013). The stopping power for the generated charged nuclear products was a first option based on the same collective model as for DT (Hora, Reference Hora2009; Hora et al., Reference Hora, Miley, Ghoranneviss, Malekynia and Azizi2009).
GENERATION OF A SPHERICAL FUSION FLAME FOR IGNITION OF HYDROGEN BORON
The stopping power for the generated charged nuclear products was as first option based on the same collective model as for DT (Hora, Reference Hora2009; Hora et al., Reference Hora, Miley, Ghoranneviss, Malekynia and Azizi2009). This is in strong contrast to the fusion of HB11 though it was very helpful that the nonlinear force driven block ignition of the fusion flame by picoseconds laser pulses led to fusion gains about 5 times more complicate only than for DT. With thermal nanosecond laser pulse driving to the fusion, HB11 was about 100,000 times more difficult (Stening et al., Reference Stening, Khoda-Bakhsh, Pieruschka, Kasotakis, Kuhn, Miley, Hora, Miley and Hora1992) and relaxed to a factor 1,000 due to a resonance process (Kouhi et al., Reference Kouhi, Ghoraneviss, Malekynia, Miley, Sari, Azizi and Razavpour2011).
It was then rather a surprise that computations of the fusion flame ignition of HB11 was only less than about 5 times more difficult than with DT fuel even with the pessimistic assumption that the stopping of the generated 2.89 MeV alpha particles was described by the collective electron interaction only, neglecting the enormous multiplication process of secondary alpha generation (Hora et al., Reference Hora, Sadighi-Bonabi, Yazdani, Afaideh, Nafari and Ghoranneviss2012a). This is important when considering the nuclear fusion of a sphere 3 in the center of Figure 3 of solid density HB11.
Based on the reaction
$$\,p + ^{11} B = 3\, {}^{4}\hbox{He} + 8.9\, \hbox{MeV}\comma \;$$where the resulting helium nuclei (alpha particles) have each the same energy of 2.89 MeV, the simplified assumption for the stopping power (Hora et al., Reference Hora, Miley, Ghoranneviss, Malekynia and Azizi2009) neglected the reaction by the pre-cursing alpha particles beyond the shock (Hora et al., Reference Hora and Miley2011a) of the fusion flame and used only stopping by electrons resulting in higher gains. As has been shown (Hora et al., Reference Hora, Sadighi-Bonabi, Yazdani, Afaideh, Nafari and Ghoranneviss2012a; Moustaizis et al., Reference Moustaizis, Lalousis, Hora, Hein, Korn and Silva2013) when discussing spherical irradiation geometry, an additional stopping is due to alpha-proton and alpha-boron collisions. This is not only important for shorter stopping lengths but the energy transferred from the alpha particles to protons is in the range of 600 keV where the HB11 fusion reaction cross-section is exceptionally high producing three new alpha particles of 2.89 MeV each. This is important for spherical compression where a density increase was also evaluated by hydrodynamics from extending the earlier numerical codes. Further, additional ion collisions in the range between 100 and 600 keV will increase this multiplication of the HB11 reactions producing an avalanched reaction. These secondary reactions are considerably increasing the gain and also the initial ignition process at the ps laser pulse interaction. If all fuel would react this is expressed by a factor F = 1. The reduction of the threshold of the energy flux density E 0* may be not so strong.
Combining the result (1) for DT with the higher value for HB11 without the secondary reactions in view of the result for DT (Hora et al., Reference Hora, Malekynia, Ghoranneviss, Miley and He2008)
$$E_{0}^{\ast} = \lpar 10^{8}\, \hbox{J}/\hbox{cm}^{2}\rpar \comma \;$$a reduction by a factor B > 1 takes into account the not yet known reduction of the ignition flux limit due to the secondary reactions.
$$E_{\rm r}^{\ast} = E_{0}^{\ast}/B\quad \lpar B \gt 1\rpar .$$The prediction of B is rather preliminary and may be around 5 but the most pessimistic case would be B = 1. The total HB11 fusion energy in a fuel sphere 2 of Figure 3 with radius R in cm is
$$E = 5.95 \times 10^{11} R^{3}\quad \hbox{Joule}.$$The minimum laser energy for producing the fusion flame is for the time t (in ps)
$$E_{\rm L} = 4R^{2}\ E_{r}^{\ast}/\lpar Bt\rpar .$$If the radius of the fuel sphere is 1 mm and the laser pulse duration 1 ps, the laser power has to be 12.5/B EW. This shows that the radius R has to be less than mm, if the laser pulse has to be 1 EW for the pessimistic B = 1. The gain is
$$G = 474\, BRtF.$$Where t is in ps.
As a first rough estimation, we assume that the laser energy produced by the ICAN spherical output of the laser pulse at the sphere 1 with a radius of 1 m may be 1 EW for driving the 1 ps laser pulse of MJ energy for igniting the fusion flame in the solid HB11 fuel 2. Using a factor B = 3, the diameter of the sphere 3 has to be 0.560 mm. The fusion energy from the reaction has then a maximum value of 69 MJ. If the reactor would work with a sequence of 20 Hz, the total nuclear power produced is then 1.38 GW in the produced alpha particles. This energy can be converted per slowing down of the alphas by electric fields up to about 1.4 MV such that with a minimum of losses, GW power (electric) can be produced.
It should be mentioned that a fiber laser ICAN with spherical fiber ends at a radius of 1 meter (Fig. 3) for Exawatt spherical converging laser pulses would consist of about 10 million thicker low cost polymer fibers (Fleming et al., Reference Fleming, Van Eijkelenborg, Sceats and Basset2001) instead of the thin glass fibers for telecommunication, providing ideal optical diffraction limit properties and CPR amplification with pulses of ps or shorter (Eggleton et al., Reference Eggleton, Luther-Davies and Richardson2011). This offers a solution for laser intensities of 1024 W/cm2 or higher.
SUMMARY
Due to the high energy flux necessary for side-on ignition of HB11 for ultrahigh plasma block acceleration, spherical contracting laser pulses of EW power and 1 ps duration are needed for a >15 Hz operation of a Gigawatt power station where the ICAN-fiber laser pulse system needs to have a spherical output diameter pulse of more than 2 m shrinking to the reactor core with a solid HB11 fuel pellet of 0.56 mm diameter for initiating the fusion reaction flame. The comparable high secondary reactions of the alpha particles produce an avalanche reaction of high efficiency. The spherical reactor core for the EW-ps laser pulses for initiating the reaction flame may lead to a fusion gain up to a factor 69 for a power station with Gigawatt (electric). Next topics of research focus on the secondary reaction of the generated alpha particles producing an avalanche process. The secondary reactions for determining the multiplication factor B for the energy flux density needs to be evaluated. The aim is to produce nuclear energy with less dangerous radioactive radiation than from burning coal per generated energy free from primary generation of neutrons (Weaver et al., Reference Weaver, Zimmerman and Wood1973; Hora et al., Reference Hora, Miley, Yang and Lalousis2011). This gain of nuclear energy without radiation problem is the essential difference offered with HB11 fuel through the ICAN-fiber laser by nonlinear collective interaction in contrast to the thermal-pressure dominated way for laser driven fusion energy from deuterium-tritium fuel used by NIF or related schemes.
