Avalanche proton-boron fusion based on elastic nuclear collisions

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
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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
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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
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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).
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