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Comments on: “Neutron driven fusion” [Phys. Lett. A 334 (2005) 42]
Physics Letters A 342 (2005) 196–197 www.elsevier.com/locate/pla
Comments on: “Neutron driven fusion” [Phys. Lett. A 334 (2005) 42] S. Atzeni Dipartimento di Energetica, Università di Roma “La Sapienza” and INFM, Roma, Italy Received 22 March 2005; accepted 5 May 2005 Available online 1 June 2005 Communicated by F. Porcelli
Abstract It is shown that the scheme suggested by R.L. Liboff [Phys. Lett. A 334 (2005) 42] cannot lead to significant energy production by fusion reactions. A modest energy release (less than 1% of the value claimed by Liboff) is obtained from the reaction n + 6 Li → T + 4 He + 4.78 MeV, while fusion reactions only occur at negligible rate. 2005 Elsevier B.V. All rights reserved. PACS: 25.70.Jj; 28.52.-s Keywords: Controlled fusion reactions; Neutron reactions
Controlled fusion reactions may provide a nearly inexhaustible and possibly relatively cheap energy source, with modest environmental impact. The two main routes followed to achieve this goal aim at igniting thermonuclear fusion reactions in magnetically confined [1,2] or inertially confined [3,4] hightemperature deuterium–tritium plasmas. In a recent Letter [5], Liboff has proposed a new concept, where reactions are triggered by a flux of fission neutrons. Unfortunately, the conclusions reached by Liboff are affected by serious flaws. Indeed (i) the
DOI of original article: 10.1016/j.physleta.2004.10.077. E-mail address: [email protected] (S. Atzeni). 0375-9601/$ – see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2005.05.047
power released by the proposed device is at least 100 times smaller than the value computed in Ref. [5]; (ii) this power is in any case essentially released by the reaction n + 6 Li → T + 4 He + 4.78 MeV,
(1)
while fusion reactions only occur at negligible rate. The active portion of the system considered by Liboff essentially consists of many thin layers of lithiumdeuteride layers crystals. The device is invested by an intense neutron flux, extracted by a fission reactor. The fission neutrons (with initial energy about 2 MeV), thermalize in the device and then react with lithium, through the reaction (1), which is just the reaction foreseen for tritium breeding in DT fusion reactors.
S. Atzeni / Physics Letters A 342 (2005) 196–197
According to Liboff, a fraction of the tritons produced by reaction (1) react with deuterons, releasing additional energy. An upper estimate for the energy released by reactions (1) in the device is obtained by assuming that all incoming neutrons are contained within the device, thermalize without any loss, and react. Let J0 = I0 S be the incoming neutron current (neutrons per unit time), where S is the area of the device normal to the neutron flux and I0 is the neutron flux. The maximum released power is Pmax = J0 Q, where Q = 4.78 MeV is the reaction yield. With the parameters of Ref. [5], I0 = 1014 cm−2 s−1 and S = 100 cm2 , one has Pmax = 7.65 kW. This is to be compared with P 1 MW, computed in Ref. [5]. The source of this large difference lies in an erroneous use of the concept of cross-section in Ref. [5]. Indeed a particle beam of intensity I is attenuated in a path dx by an amount dI = −I nσ dx = −I Σ dx, where σ is the microscopic cross-section, n is the density of the target nuclei, and Σ = σ n is the macroscopic cross-section. If Σ is constant, then the current of fast particles (which is J0 at x = 0) decreases with x as J = J0 exp(−Σx), and the rate of reactions in the space 0 x x is dN/dt = J0 − J = J0 (1 − exp(−Σx)). For small Σx one has dN/dt = J0 Σx = J0 nσ x, while for large Σx one has dN/dt J0 , meaning that all incoming particles (neutrons in our case) react. With the parameters of Ref. [5], Σx = 70, and then an upper limit to the reaction rate is J0 as computed above. Liboff, instead, inappropriately used the expression dN/dt = J0 Σx, yielding dN/dt 70J0 . Liboff correctly states that most neutrons thermalize rapidly and in a distance smaller than the size of its proposed device. However, its proof is not correct, and should be replaced by the following. According to basic neutron slowing down theory [6,7], when neutrons are slowed down by elastic collisions with nuclei of mass number A > 1, the average logarithmic energy decrement per collision E (2) E − E (where E and E − E are the energies of the neutron before and after the collision, respectively) is constant, ξ = 1 + (α ln α)/(1 − α), with α = [(A − 1)/(A + 1)]2 . ξ = ln
197
The number of collisions required to slow a 2 MeV fission neutron down to the thermal energy of 0.025 eV is then ncoll = ln(2 × 106 /0.025)/ξ = 18.2/ξ . For scattering in deuterium, ξ = 0.75 and ncoll = 25, in 3 He ξ = 0.634 and ncoll = 28.7. These figures have to be compared with the value 0.3 computed in Ref. [5]. The average distance between the neutron source and the point of thermalization can be computed from the Fermi-age theory [6,7]. For low-Z materials one obtains 13–30 cm. The energetic tritons released by reaction (1) can in principle fuse with other light nuclei, and in particular with deuterons through the DT reaction. However, the cross-section for Coulomb scattering is much larger than the fusion cross-section, and it has been shown (see, e.g., Ref. [8]) that the probability of a fusion reaction prior to thermalization is extremely small. The bounces of tritons between the surfaces of the layers, mentioned in Ref. [5], can increase triton confinement, but cannot increase the reaction rate. In conclusion, a neutron flux cannot drive the production of an appreciable amount of fusion energy in a device like that described by Liboff in Ref. [5]. Some energy production does occur in the layers of the device containing lithium, due to reaction (1). This mechanism is well known and is indeed accounted for in the conceptual designs of the tritium producing blankets [3,4,9] of thermonuclear reactors based on the DT reaction.
References [1] E. Teller (Ed.), Fusion, vol. 1, Academic Press, New York, 1981. [2] J. Wesson, Tokamak, third ed., Oxford Univ. Press, Oxford, 2004. [3] S. Atzeni, J. Meyer-ter-Vehn, The Physics of Inertial Fusion, Oxford Univ. Press, Oxford, 2004. [4] Energy from Inertial Fusion, International Atomic Energy Agency, Vienna, 1995. [5] R.L. Liboff, Phys. Lett. A 334 (2005) 42. [6] S. Glasstone, A. Sesonske, Nuclear Reactor Engineering, Van Nostrand–Reinhold, New York, 1967. [7] A. Weinberg, E. Wigner, The Physical Theory of Neutron Chain Reactors, University of Chicago, 1958. [8] R.F. Post, Rev. Mod. Phys. 28 (1956) 388. [9] R.W. Conn, Magnetic fusion reactors, in Ref. [1], p. 193.
Comments on: “Neutron driven fusion” [Phys. Lett. A 334 (2005) 42] S. Atzeni Dipartimento di Energetica, Università di Roma “La Sapienza” and INFM, Roma, Italy Received 22 March 2005; accepted 5 May 2005 Available online 1 June 2005 Communicated by F. Porcelli
Abstract It is shown that the scheme suggested by R.L. Liboff [Phys. Lett. A 334 (2005) 42] cannot lead to significant energy production by fusion reactions. A modest energy release (less than 1% of the value claimed by Liboff) is obtained from the reaction n + 6 Li → T + 4 He + 4.78 MeV, while fusion reactions only occur at negligible rate. 2005 Elsevier B.V. All rights reserved. PACS: 25.70.Jj; 28.52.-s Keywords: Controlled fusion reactions; Neutron reactions
Controlled fusion reactions may provide a nearly inexhaustible and possibly relatively cheap energy source, with modest environmental impact. The two main routes followed to achieve this goal aim at igniting thermonuclear fusion reactions in magnetically confined [1,2] or inertially confined [3,4] hightemperature deuterium–tritium plasmas. In a recent Letter [5], Liboff has proposed a new concept, where reactions are triggered by a flux of fission neutrons. Unfortunately, the conclusions reached by Liboff are affected by serious flaws. Indeed (i) the
DOI of original article: 10.1016/j.physleta.2004.10.077. E-mail address: [email protected] (S. Atzeni). 0375-9601/$ – see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2005.05.047
power released by the proposed device is at least 100 times smaller than the value computed in Ref. [5]; (ii) this power is in any case essentially released by the reaction n + 6 Li → T + 4 He + 4.78 MeV,
(1)
while fusion reactions only occur at negligible rate. The active portion of the system considered by Liboff essentially consists of many thin layers of lithiumdeuteride layers crystals. The device is invested by an intense neutron flux, extracted by a fission reactor. The fission neutrons (with initial energy about 2 MeV), thermalize in the device and then react with lithium, through the reaction (1), which is just the reaction foreseen for tritium breeding in DT fusion reactors.
S. Atzeni / Physics Letters A 342 (2005) 196–197
According to Liboff, a fraction of the tritons produced by reaction (1) react with deuterons, releasing additional energy. An upper estimate for the energy released by reactions (1) in the device is obtained by assuming that all incoming neutrons are contained within the device, thermalize without any loss, and react. Let J0 = I0 S be the incoming neutron current (neutrons per unit time), where S is the area of the device normal to the neutron flux and I0 is the neutron flux. The maximum released power is Pmax = J0 Q, where Q = 4.78 MeV is the reaction yield. With the parameters of Ref. [5], I0 = 1014 cm−2 s−1 and S = 100 cm2 , one has Pmax = 7.65 kW. This is to be compared with P 1 MW, computed in Ref. [5]. The source of this large difference lies in an erroneous use of the concept of cross-section in Ref. [5]. Indeed a particle beam of intensity I is attenuated in a path dx by an amount dI = −I nσ dx = −I Σ dx, where σ is the microscopic cross-section, n is the density of the target nuclei, and Σ = σ n is the macroscopic cross-section. If Σ is constant, then the current of fast particles (which is J0 at x = 0) decreases with x as J = J0 exp(−Σx), and the rate of reactions in the space 0 x x is dN/dt = J0 − J = J0 (1 − exp(−Σx)). For small Σx one has dN/dt = J0 Σx = J0 nσ x, while for large Σx one has dN/dt J0 , meaning that all incoming particles (neutrons in our case) react. With the parameters of Ref. [5], Σx = 70, and then an upper limit to the reaction rate is J0 as computed above. Liboff, instead, inappropriately used the expression dN/dt = J0 Σx, yielding dN/dt 70J0 . Liboff correctly states that most neutrons thermalize rapidly and in a distance smaller than the size of its proposed device. However, its proof is not correct, and should be replaced by the following. According to basic neutron slowing down theory [6,7], when neutrons are slowed down by elastic collisions with nuclei of mass number A > 1, the average logarithmic energy decrement per collision E (2) E − E (where E and E − E are the energies of the neutron before and after the collision, respectively) is constant, ξ = 1 + (α ln α)/(1 − α), with α = [(A − 1)/(A + 1)]2 . ξ = ln
197
The number of collisions required to slow a 2 MeV fission neutron down to the thermal energy of 0.025 eV is then ncoll = ln(2 × 106 /0.025)/ξ = 18.2/ξ . For scattering in deuterium, ξ = 0.75 and ncoll = 25, in 3 He ξ = 0.634 and ncoll = 28.7. These figures have to be compared with the value 0.3 computed in Ref. [5]. The average distance between the neutron source and the point of thermalization can be computed from the Fermi-age theory [6,7]. For low-Z materials one obtains 13–30 cm. The energetic tritons released by reaction (1) can in principle fuse with other light nuclei, and in particular with deuterons through the DT reaction. However, the cross-section for Coulomb scattering is much larger than the fusion cross-section, and it has been shown (see, e.g., Ref. [8]) that the probability of a fusion reaction prior to thermalization is extremely small. The bounces of tritons between the surfaces of the layers, mentioned in Ref. [5], can increase triton confinement, but cannot increase the reaction rate. In conclusion, a neutron flux cannot drive the production of an appreciable amount of fusion energy in a device like that described by Liboff in Ref. [5]. Some energy production does occur in the layers of the device containing lithium, due to reaction (1). This mechanism is well known and is indeed accounted for in the conceptual designs of the tritium producing blankets [3,4,9] of thermonuclear reactors based on the DT reaction.
References [1] E. Teller (Ed.), Fusion, vol. 1, Academic Press, New York, 1981. [2] J. Wesson, Tokamak, third ed., Oxford Univ. Press, Oxford, 2004. [3] S. Atzeni, J. Meyer-ter-Vehn, The Physics of Inertial Fusion, Oxford Univ. Press, Oxford, 2004. [4] Energy from Inertial Fusion, International Atomic Energy Agency, Vienna, 1995. [5] R.L. Liboff, Phys. Lett. A 334 (2005) 42. [6] S. Glasstone, A. Sesonske, Nuclear Reactor Engineering, Van Nostrand–Reinhold, New York, 1967. [7] A. Weinberg, E. Wigner, The Physical Theory of Neutron Chain Reactors, University of Chicago, 1958. [8] R.F. Post, Rev. Mod. Phys. 28 (1956) 388. [9] R.W. Conn, Magnetic fusion reactors, in Ref. [1], p. 193.