Avalanche proton-boron fusion based on elastic nuclear collisions Shalom Eliezer, Heinrich Hora, Georg Korn, Noaz Nissim, and Josè Maria Martinez Val Citation: Physics of Plasmas 23, 050704 (2016); doi: 10.1063/1.4950824 View online: http://dx.doi.org/10.1063/1.4950824 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/23/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Kinetic advantage of controlled intermediate nuclear fusion AIP Conf. Proc. 1479, 2407 (2012); 10.1063/1.4756680 Modeling Nuclear Fusion with an Ultracold Nonneutral Plasma AIP Conf. Proc. 926, 66 (2007); 10.1063/1.2768833 Proton core imaging of the nuclear burn in inertial confinement fusion implosions Rev. Sci. Instrum. 77, 043503 (2006); 10.1063/1.2173788 Laser-cluster interaction for nuclear fusion AIP Conf. Proc. 611, 264 (2002); 10.1063/1.1470311 A fusion-driven gas core nuclear rocket AIP Conf. Proc. 420, 1377 (1998); 10.1063/1.54763 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 121.216.144.135 On: Mon, 16 May 2016 17:44:41 PHYSICS OF PLASMAS 23, 050704 (2016) Avalanche proton-boron fusion based on elastic nuclear collisions Shalom Eliezer,1 Heinrich Hora,2 Georg Korn,3 Noaz Nissim,4 and Josè Maria Martinez Val1 1 Institute of Nuclear Fusion, Polytechnic University of Madrid, Madrid, Spain Department of Theoretical Physics, University of New South Wales, Sydney, Australia 3 Institute of Physics, ASCR, ELI-Beamlines Project, Prague, Czech Republic 4 Applied Physics Department, Soreq NRC, Yavne 81800, Israel 2 (Received 26 February 2016; accepted 3 May 2016; published online 16 May 2016) Recent experiments done at Prague with the 600 J/0.2 ns PALS laser interacting with a layer of boron dopants in a hydrogen enriched target have produced around 109 alphas. We suggest that these unexpected very high fusion reactions of proton with 11B indicate an avalanche multiplication for the measured anomalously high nuclear reaction yields. This can be explained by elastic nuclear collisions in the broad 600 keV energy band, which is coincident with the high nuclear p-11B fusion cross section, by the way of multiplication through generation of three secondary alpha particles from a single primarily produced alpha particle. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4950824] The fusion reaction of protons with 11B nuclei (pB11) is interesting for controlled generation of fusion energy, primarily, since no neutrons are produced1 apart from alpha particles, H þ 11 B ¼ 3 4 He þ 8:9 MeV: (1) This ideal energy source is extremely more difficult to achieve than the usually studied fusion reaction of deuterium (D) and tritium (T) where the generated neutrons are a problem. In the standard proposals of p-11B inertial confinement fusion (ICF) with nanosecond laser pulses,2 densities of above 100 000 times of the solid state are necessary. Using lasers, the first p-11B 1000 reactions just above the level of sensitivity were measured.3 A special combination of highly intense proton beams, of energies far above MeV, by picosecond laser pulses and a second irradiated laser beam produced more than one million reactions.4 A recent experiment at Prague PALS facility with the targets containing high boron concentration doped in silicon crystals produced one billion alpha particles per steradian,5,6 using an iodine laser pulse of few hundred joules energy with the duration of 100 ps range at a maximum laser irradiance. In Ref. 6, a straightforward explanation of the results is presented; however, the electromagnetic interactions, leading to a large stopping power effect for the alphas and protons, are not mentioned. This effect causes the ions to lose their energy before the fusion interaction can occur at the maximum of the cross section at around 600 keV. In order to avoid the stopping power effect, a collective phenomenon such as the plasma block interactions7–9 was suggested. The Prague experiment is a very important step to the p-11B clean nuclear fusion energy solution as recently suggested by Hora et al.7–9 This reactor design was based on a many years research showing that lasers produce forces (fNL) in plasmas apart from the thermal pressure p, resulting in f ¼ rp þ f NL : 1070-664X/2016/23(5)/050704/3/$30.00 The force fNL is given by Maxwell’s stress tensor as Lorentz and gauge invariant nonlinear force by quadratic terms of the force quantities E (electric field) and H (magnetic field).10 The non-linear force is dominating against the thermal forces,11 resulting in the acceleration of a plasma block causing non-thermal fusion ignition.7–9,12,13 In particular, the p-11B fusion can be explained by an avalanche process. A detailed explanation of the avalanche process is possible by the following evaluation of the elastic collisions14 of the generated alpha particles. These alpha particles transfer energy in a broad energy range around 600 keV in the high density p-11B plasma. An initially resting 11B or proton nucleus of mass m2 gains energy from the energy Ea of an alpha particle of mass m1. The maximum energy which can be acquired in the collision by a particle at rest is14 E2; final ðinitially at restÞ ¼ ½4m1 m2 =ðm1 þ m2 Þ2 E1;initial : (3) After a first collision of an alpha particle with a boron one gets 176 11 Þ ð Ea ¼ 2270 ½keV; Elab B ¼ 225 11 1 176 Ea ¼ 189 ½keV; Ecm pB ¼ 12 225 where Elab(B11) is the energy of the boron after the collision in the lab frame. While Ecm(pB11) is the center-of-mass system energy of that boron and a proton at rest in the lab frame. After a first collision of an alpha particle with a proton, one gets (2) 23, 050704-1 16 Ea ¼ 1860 ½keV; 25 11 16 Ea ¼ 1701 ½keV; Ecm pB11 ¼ 12 25 Elab ð pÞ ¼ Published by AIP Publishing. Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 121.216.144.135 On: Mon, 16 May 2016 17:44:41 050704-2 Eliezer et al. where Elab(p) is the energy of the proton after the collision in the lab frame. While Ecm(pB11) is the center-of-mass system energy of that proton and a boron at rest in the lab frame. After an alpha particle with an energy Ea ¼ 2900 keV has its second collision with a proton and this proton collides with a 11B, one gets in their center-of-mass system of reference an energy Ecm(pB11) 11 16 9 Ea ¼ 612:5 ½keV : (4) Ecm pB11 ¼ 12 25 25 This energy is within the maximum cross section rmax of p-11B.15 We get the energy for p-11B maximum cross section from the alpha’s collisions with protons that then collide with B11 to get the fusion. We call this mechanism avalanche, because of the multiplication through generation of three secondary alpha particles by one primarily produced alpha particle. The avalanche scheme is described in Figure 1. The alpha collisions with protons are more probable since the probability ratio is Phys. Plasmas 23, 050704 (2016) ðnp rap em ua Þ=ð nB raB em ua Þ ðnp =nB Þ½ð1 þ ma =mp Þ2 =ð1 þ ma =mB Þ2 ½1=ðZB 2 Þ ð1=2Þðnp =nB Þ; where the Rutherford cross section (rapem, raBem) has been used for the appropriate cross sections and ZB is the boron ionization degree. Since the hydrogen density is larger than the boron density by a factor of 10, we get the main chain of reactions as described in Figure 1. In this process, we get 2 classes of proton densities, np1 that did not have any alpha collision and np2 that collided with alpha, and got the right energy to have a p-11B collision at maximum nuclear cross section. It is conceivable to assume for this experiment6 np ¼ np1 þ np2 and np1 np2 ¼ na =3 yielding the rate equation for the alpha particles, dna ¼ 3np1 nB hrviT þ 3np1 nB hrviNT þ 3np2 nB rmax u dt 3np1 nB hrviNT þ na nB rmax u: The first term on the right hand side of Equation (5) is given in Ref. 6 in order to explain the Prague experimental data.5 However, this term is dependent on the ion temperature created in the laser plasma interaction 2 cm3 13 5=6 17:7080 ¼ 6:3820 10 f hrviT s T 1=3 53:1240 1=3 exp f T 1=3 148 15 3=2 exp þ 5:41 10 T T f¼1þ FIG. 1. The avalanche scheme. (5) 59:3570T 1:0404T 2 þ 9:1653 103 T 3 103 þ 201:65T þ 2:7621T 2 þ 9:8305 104 T 3 ion temperature T in keV. In the Prague experiment, a total number of Na ¼ 4 108 alpha particles per laser pulse were observed from a number of protons measured experimentally to be NH ¼ npDV ¼ 1011 in a time interval of Dt ¼ 109 s. Calculating Na ¼ 3NH nBhrviTDt according to the first term of Equation (5), with nB ¼ 2 1021 cm3 at the plasma, according to hydrodynamic simulation,6 and hrviT ¼ 6.625 1017 for T ¼ 100 keV yields Na ¼ 4 107 which is an order of magnitude less than the measured Na. Furthermore, we claim that for laser irradiance of 3 1016 W/cm2 as reported in the Prague experiment, an ion temperature of 100 keV is not conceivable. Moreover, the authors are unaware of any laser experiment of expanding plasma into vacuum with such laser and plasma parameters, which provided ion temperatures as high as 100 keV. The second term in Equation (5) is a non-thermal equilibrium quantity that is related to the proton spectrum measured in Ref. 5. The last term of Equation (5) is caused by the protons that collided with the alphas and are returned back into the target by the inverted double layer (DL) simulations.16 Taking the data from the Prague experiment, Equation (5) can be solved numerically. In particular, the proton energy distribution as given in this experiment can be written as dNp/dE ¼ N0 [MeV1] for 0 < E < 1 MeV and dNp/dE ¼ 0 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 121.216.144.135 On: Mon, 16 May 2016 17:44:41 050704-3 Eliezer et al. Phys. Plasmas 23, 050704 (2016) for E > 1 MeV, where Np is the proton volume integrated density number and N0 ¼ 1011 is the total number of protons under consideration. This distribution implies 1 ð 1=2 f ðEÞrðEÞE hrviNT ¼ rmax u f ðEÞ ¼ 0 ( 1 ð dE 0 f ðEÞdE pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1:2 bÞ 0:6 MeV promising to achieve a p-11B fusion reactor. The measured strong elevation of the p-11B fusion gain could be only explained as the result of the secondary p-11B reactions caused by the avalanche process as suggested in this paper. 1 0:40 N0 ¼ 1011 ½MeV1 for 0 < E < 1 MeV (6) 0 for 1 MeV < E: Therefore to a good approximation, we get the following solution: hrviNT ð s=sA s Na ¼ Np e 1Þ 0:4N0 rmax u sA 1 : (7) sA nB rmax u N0 is of the order of few times 1011 and Na of the order of 109 are accordingly the volume integrated density numbers as given in the Prague experiment. sA is defined as the avalanche time and the interaction time s to create alphas. In the Prague experiment, sA is of the order of 100 ns (nB ¼ 1022 cm3, rmax ¼ 1.2 b and u ¼ 109 cm/s) which means that alphas are created during a couple of nanosecond. The exponential term in our solution of Equation (7) will be very large for ssA in a pB11 fusion scheme as suggested in Ref. 7 by using a magnetic field to confine the laser produced plasma. In this case, the avalanche process will dominate and therefore its application for a nuclear fusion reactor might be viable for the clean proton-boron11 fusion. Computations7,9,10 done for cylindrical trapping with ultrahigh magnetic fields under the assumption of the avalanche show that a 30 kJ laser pulse of ps duration could produce more than GJ energy in alpha particles. This laser energy is G. H. Miley, Fusion Energy Conversion (American Nuclear Society, Hinsdale, IL, 1972). 2 M. Kouhi, M. Ghoraneviss, B. Malekynia, H. Hora, G. H. Miley, A. H. Sari, N. Azizi, and S. S. Razavipour, Laser Part. Beams 29, 125 (2011). 3 V. S. Belyaev, A. P. Matafonov, V. I. Vinogradov, V. P. Krainov, V. S. Lisitsa, A. S. Roussetski, G. N. Ignatyev, and V. P. Andrianov, Phys. Rev. E 72, 026406 (2005). 4 C. Labaune, C. Baccou, S. Deprierraux, C. Goyon, G. Loisel, V. Yahia, and J. Rafelski, Nat. Commun. 4, 2506 (2013). 5 A. Picciotto, D. Margarone, A. Velyhan, P. Bellutti, J. Krasa, A. Szydlowsky, G. Bertuccio, Y. Shi, A. Mangione, J. Prokupek, A. Malinowska, E. Krousky, J. Ullschmied, L. Laska, M. Kucharik, and G. Korn, Phys. Rev. X 4, 031030 (2014). 6 D. Margarone, A. Picciotto, A. Velyhan, J. Krasa, M. Kucharik, A. Mangione, A. Szydlowsky, A. Malinowska, G. Bertuccio, Y. Shi, M. Crivellari, J. Ullschmied, P. Bellutti, and G. Korn, Plasma Phys. Controlled Fusion 57, 014030 (2015). 7 H. Hora, P. Lalousis, L. Giuffrida, D. Margarone, G. Korn, S. Eliezer, G. H. Miley, S. Moustaizis, and G. Mourou, SPIE Proc. 9515, 951518 (2015). 8 H. Hora, G. Korn, L. Giuffrida, D. Margarone, A. Picciotto, J. Krasa, K. Jungwirth, J. Ullschmied, P. Lalousis, S. Eliezer, G. H. Miley, S. Moustaizis, and G. Mourou, Laser Part. Beams 33, 607 (2015). 9 P. Lalousis, H. Hora, and S. Moustaizis, Laser Part. Beams 32, 409 (2014). 10 H. Hora, Phys. Fluids 12, 182 (1969). 11 G. Mourou, C. P. J. Barty, and M. D. Perry, Phys. Today 51(1), 22 (1998). 12 H. Hora, J. Badziak, M. N. Read, Y.-T. Li, T.-J. Liang, Y. Cang, H. Liu, Z.-M. Sheng, J. Zhang, F. Osman, G. H. Miley, W. Zhang, X. He, H. Peng, S. Glowacz, S. Jablonski, J. Wolowski, Z. Skladanowski, K. Jungwirth, K. Rohlena, and J. Ullschmied, Phys. Plasmas 14, 072701 (2007). 13 H. Hora, P. Lalousis, S. Moustaizis, I. F€ oldes, G. H. Miley, X. Yang, X. T. He, S. Eliezer, and J. M. Martinez-Val, in IAEA Proceedings Fusion Energy, San Diego, October 2012 (IAEA, Vienna, 2013), Paper No. IFE/ P6-03, p. 8. 14 L. D. Landau and E. M. Lifshitz, Mechanics, 2nd ed. (Pergamon Press, 1962), p. 17. 15 W. M. Nevins and R. Swain, Nucl. Fusion 40, 865 (2000). 16 H. Hora, P. Lalousis, and S. Eliezer, Phys. Rev. Lett. 53, 1650 (1984). Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 121.216.144.135 On: Mon, 16 May 2016 17:44:41
© Copyright 2026 Paperzz