An energy amplifier for "clean" nuclear energy production driven by a particle beam accelerator

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DESCRIPTION

Power amplifier for the production of “clean” nuclear energy governed by a particle beam accelerator.

The present invention relates to a method for producing energy from a nuclear combustible material. The invention is also directed to a power amplifier for implementing such a method and to a power production facility incorporating such a power amplifier.

Nuclear reactors are in wide use for the production of thermal or electrical power or energy. Numerous reactor designs have been developed, leading to extensive technological studies. However, conventional reactors are not without problems. Controlling the operation or performance is generally delicate, as some accidents dramatically demonstrate. In most reactor designs, fuel material preparation involves isotopic separation, a complex and expensive process that results in proliferation risks. Proliferation risks also arise due to the fact that conventional nuclear reactors generally produce fissile plutonium. Recovery of energy from such plutonium, for example by means of a fast neutron breeder reactor, has posed many difficulties and is only marginally used. Furthermore, plutonium and other actinides, produced in non-negligible quantities in conventional reactors, are radiologically toxic and are not easily removed. Geological conservation or storage of such actinides is used, together with fission fragments, but this is clearly not a satisfactory solution.

Nuclear power today is based primarily on fissions of U²³⁵ natural, which however constitutes only about 0.7% of ordinary uranium. In the early days of the development of nuclear energy, the importance of reproducing artificial fuels from more abundant nuclear species with the help of neutron capture was noted. In particular, starting from the U²³⁸ Dominant can be played Pu²³⁹ and from natural thorium (pure isotope Th²³² ) OR²³³ easily fissionable. While the reproduction U²³⁸ - Pu²³⁹ has led to the widespread but controversial development of (fast) breeder reactors, relatively little progress has so far been made in the breeding chain Th²³² - OR²³³ .

In "Nuclear energy generation and waste transmutation using an accelerator-driven intense thermal neutron source" (Nuclear Instruments and Methods in Physics Research, 1992, Vol. A320, pages 336-367), CD Bowman et al contemplate the use of an accelerator of protons to incinerate actinide residues produced by a light water reactor (see also US Patent 5,160,696). The facility is also expected to be capable of producing energy from the thorium cycle. However, the flux of thermal neutrons in the core of the installation needs to be very high (in the range of 10¹⁶ cm^-2.s^-1) in order to achieve the transmutation of neptunium and americium. Under these conditions, the process of energy production by reproduction and fission (i.e. capture of a neutron by Th²³² leading to Pa²³³, ^ - Pa degradation²³³ in U²³³ and n-fission of U²³³) cannot be carried out in situ, but instead requires a continuous extraction of Pa²³³ relative to the neutron flux to allow for the ^ -degradation of Pa²³³ in U²³³ outside the nucleus, while limiting neutron captures by the Pa²³³, which would plague the neutron balance and lead to the production of additional actinides (at about 10¹⁶ cm^-2.s^-1 the probabilities of formation of Pa234 and U²³³ from Pa²³³ are comparable). In addition, abundant fission products must be continually extracted from the core of the facility and chemically processed. Such extractions and such chemical processing are complicated manipulations that would render the facility practically unsuitable for commercial power production applications. Furthermore, the accumulation of Pa²³³ outside the core of the installation is undesirable because it would degrade, after about 27 days, in U²³³ highly proliferating.

US Patent No. 5,037,601 discloses a critical nuclear reactor that is based on the fission of U nuclei²³³ reproduced from Th²³². Before the assembly reaches criticality, a start-up phase is carried out by means of an electron beam that generates photoneutrons.

US Patent No. 3,325,371 discloses a system for obtaining a fissile element from a fertile element contained in a fertile reproductive material that surrounds a source of spallation or division neutrons in numerous particles. Once so reproduced, the nuclear fuel is transferred to a conventional critical LWR reactor (a light water reactor).

In "Accelerator Spallation Reactors for Breeding Fissile Fuel and Transmuting Fission Products" (Nuclear Technologies in a sustainable energy system, Selected papers from an IIASA workshop, Springer-Verlag, New York, 1983, pages 203-224), a summary of state of development of accelerator spallation reactors to reproduce fissile fuel and to transmute fissile products. The article mentions a so-called project for a “Linear Accelerator Driven Reactor” (a reactor governed by a linear accelerator) in which neutrons generated by spallation would cause fission multiplication and a net power production.

To summarize the prior art, practical nuclear power reactors and fast breeders rely on a critical chain reaction that generally takes place within a sealed enclosure but many problems still arise despite several decades of extensive developments. And the previous proposal for an accelerator-governed thermal neutron scheme is currently a solution with a future. Its practical applications will be conditioned by long-term research and development, due to the extraordinarily high neutron flux and the requirement or need for chemical separation at radioactive levels of unprecedented heights.

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A primary objective of the present invention is to provide a viable alternative to conventional reactors for extracting nuclear energy, avoiding various problems encountered with such fast breeders and reactors.

Another objective of the invention is that the energy production scheme does not require continuous reprocessing of the combustible material. It is also desired that the energy production scheme be compatible with the use of thorium as the main constituent of the fuel material.

According to the invention, there is provided a method for producing energy as set forth in claim 1.

The amount by which neutrons are moderated from production to fission depends on the application. For example, neutrons could be moderated all the way to thermal energies (E_bird _ 0.025 (T / 273 ° K) eV, slightly affected by the temperature T of the medium). In other cases, such as when light water is used as a moderator, the neutrons could be allowed to reach energies of the order of several eV. Finally, in other applications, it is possible to use refrigerants that have little moderating action and therefore work with neutrons with energies of the order of 100 keV. We call such neutrons "fast neutrons", in contrast to the previous examples where they are indicated as "thermal" and "epithermal" neutrons, respectively.

In order to obtain high energy output, the average neutron flux to which the combustible material is exposed must be strong. However, there are reasons to limit the neutron flux in the method of the invention. Advantageously, the mean neutron flux is low enough to prevent neutron capture by a substantial amount of the-precursor of the fissionable element. A practical limitation is Φ <0.03 / (σ⁽²⁾τ2), in which σ, '²'and τ2 designate the neutron capture cross-section and the half-life, respectively, of the ye-precursor, so that at most 3% of the ^ -precursors capture neutrons instead of degrading in the fissile element. This condition guarantees that practically all the β-precursor nuclei are transformed into the relevant fissionable element and that the neutron balance in the enclosure is not affected by unwanted captures, thereby optimizing the energy gain.

Since the reproduction and fission process is subcritical, the effective multiplication factor k is less than 1. In order to obtain a high gain, the fissile content of the combustible material is such that the effective multiplication factor is close to 1 (typically 0.9 <k <0.98). In the case of a beam interruption, the fissile content increases due to the ^ -degradations of the ^ -precursors available, and the system can become critical. In order to avoid this, it is possible to insert control bars or the like in the enclosure. But a simpler solution is to keep the mean neutron flux low enough to limit the amount of the ^ -precursor so that the combustible material is prevented from reaching criticality in the event of beam disruption. This condition can be quantified as Φ <0.2 / (σ⁽³⁾τ2), where σ⁽³⁾ designates the total interaction cross section of the neutrons of the fissile nuclei.

Obviously, the highest value of k at which the device can really work depends on the type of protections used and on the operating stability of k due to the aforementioned effects and which in turn depend on the energy domain that is chosen for the neutrons. In general, it can be said that the above conditions allow for fast neutrons a k substantially higher than for thermal or epithermal ones.

Once the combustible material has reached equilibrium conditions, a burning phase takes place, in which the relationship between the concentrations of the fissile element and the fertile element in the combustible material is substantially stable. When in the initial fuel charge the ratio between the concentrations of the fissile element and the fertile element is substantially less than the stable value of said ratio in the burning phase, an initial reproduction phase is carried out in order to reach the stable value. During the initial reproduction phase, the intensity of the incident beam must be higher than in the burn phase.

It is also possible to use an initial fuel charge in which the ratio between the concentrations of the fissile element and the fertile element is approximately the stable value of said ratio in the burning phase. In such a case, the fissile element content of the initial fuel charge can be recovered, by means of chemical separation, from other combustible material that has been consumed in a previous and similar energy production operation. Alternatively, additional combustible material may be inserted into the enclosure during activation of the particle beam, said additional combustible material having an initial content in which the ratio between the concentrations of the fissionable element and the fertile element is substantially less than the stable value of said ratio in the burning phase, the additional combustible material being eliminated from the enclosure once the stable value of said ratio is reached, in order to use said additional fuel material as an initial fuel charge in a subsequent power production operation.

When the fertile element is Th²³² (being Pa²³³ the ^ -precursor and being U²³³ the fissile element) and the neutrons are thermal or epithermal, the mean neutron flux in the enclosure is preferably less than 1.5 x 10¹⁴ cm^-2.s^-1and the combustible material is left in the enclosure until it has been subjected to an integrated neutron flux of about 3 x 10²² cm^-2. U cores can be provided²³⁵ in the initial fuel charge, so that there is a fissile content in the fuel material before the burning phase.

When the fertile element is U²³⁸ (where Np²³⁹ the ^ -precursor and being Pu²³⁹ the fissile element) and the neutrons are also thermal or epithermal, the mean neutron flux in the enclosure is preferably less than

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10¹⁵ cm^-2 .s^-1 and the combustible material is left in the enclosure until it has been subjected to an integrated neutron flux of about 10²² cm^-2 .

The "heavy nuclei" contained in the enclosure, which interact with the particle beam to produce high-energy neutrons, can be composed of nuclei of the combustible material. In such an embodiment of the present invention, the moderating medium is water and the ratio between the values ​​occupied respectively by the water moderator and by the combustible material in the enclosure is in the range of 0.2 <V_m/ V_F <1. In particular, the moderator can be circulating water, also used to extract heat from the room. Preferably, the combustible material is then in fragmented form and forms a fluidized bed with the water moderator. The Vm / Vf ratio, and therefore the reactivity, can be easily adjusted by adjusting the flow rate of the water moderator.

Alternatively, the "heavy cores" are provided by a separate spallation target, located centrally in the enclosure and surrounded by the combustible material and moderating medium. To avoid detriment to energy production efficiency or performance, the spallation target must contain a substantial amount of a material that has a high transparency to thermal neutrons. A spallation target made of bismuth and / or lead typically meets this condition.

In the latter embodiment, a solid phase moderating medium, such as graphite, can be used. The solid-phase moderator is arranged so as to achieve substantially complete thermalization of the high-energy neutrons produced by the spallation target, for example the fuel material being composed of a plurality of fuel bodies, each encapsulated in an envelope of solid phase moderator. An important advantage of this embodiment is that the heat produced by the fissions can be removed from the enclosure by means of gaseous refrigerants, which are known to give rise to higher thermodynamic performances than liquid refrigerants.

Finally, instead of light water, a liquid metal such as lead, bismuth or a eutectic mixture of both can be used as the coolant. Due to the less moderating action of such materials, the device will then be governed by fast neutrons. Considering the considerable safety concerns associated with liquid sodium, which is almost universally chosen in fast breeder reactors, we have opted for liquid lead. Another decisive reason for choosing lead (or bismuth or a eutectic mixture of both) is the fact that these materials are high energy targets that offer excellent neutron performance and therefore the cooling material can also be the first target for the high-energy proton beam.

Although light water as a coolant is well known due to the extensive experience of PWRs, its high pressure (> 160 bars) is not without potential problems, and for example a massive loss of coolant due to a leak could lead to melting problems. . The presence of the window which must withstand such a great pressure and allow the injection of the high energy beam further complicates the problem. These problems can be greatly mitigated by reducing the temperature and therefore the operating or working pressure of the water, but at the cost of lower performance or thermodynamic efficiency, although this could still be of interest for special applications such as desalination. of water or heat production.

There are advantages to working with a liquid metallic refrigerant that has a very low vapor pressure («1mm Hg) despite the higher working or operating temperature, typically 600 ° C, with correspondingly higher thermodynamic efficiency or performance. There is no way that a major part of the coolant can get lost or leak, as long as its reservoir is strong enough and eventually double walled. The heating from the radioactivity will in practice be sufficient to keep the lead in the main reservoir or tank in its liquid form. It is then sufficient to introduce a permanent, passive, convective heat dissipation from the tank to the outside in an amount greater than the radioactive heating (a small percentage of the total thermal power). This will safely dissipate the residual power due to radioactive degradations after shutdown and will automatically and credibly eliminate all the dangers associated with an uncontrolled rise in temperature in the event of failure of the normal cooling system, with the risk of accidents due to fusion. This additional cooling system must be totally passive and involve convection cooling either with water, either with air, or with both.

The fact that the latter device provides intrinsically safe protection against accidental melting represents a significant advantage.

The incident beam particles are typically protons or deuterons provided by a linear particle accelerator or by a sector focusing cyclotron and having an energy of at least 0.5 GeV, preferably between 1 and 1.5 GeV.

According to the second aspect of the present invention, there is provided a power amplifier as set forth in claim 43.

According to another aspect of the present invention, there is provided a power production facility as set forth in claim 44.

A part of the energy production of the energy conversion means can be used to control the particle accelerator.

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The invention described here on an energy amplifier avoids the well known difficulty that nuclear reactors are plagued by insufficient reproductive power in order to use natural thorium as the main fuel under practical conditions. In order to obtain a completely self-sufficient reproduction chain reaction, the number of secondary neutrons η resulting from a captured neutron must exceed 2 for the fissile element: each time one neutron must be sacrificed to replace the fissured nucleus exiting the fertile nucleus and it needs another to continue the chain of fission. Such a fully sustained reproduction is very difficult in a reactor, since for thermal neutrons η = 2.29 for U²³³, a value very close to the minimum condition η> 2. Therefore, in a reactor a fully sustained reproduction is plagued by the problem of the quantity or inventory of neutrons. In order to guarantee both reproduction and criticality, a maximum fraction (2.29 - 2) / 2.29 = 0.126 of the neutrons can be lost due to confinement losses and captures by other materials. This is very close to the minimum value of neutron losses that can be achieved using the most careful design and moderation with heavy water, leaving little or no room for the inevitable growth of captures due for example to fission fragments and other mechanisms of the neutron absorption related to the reproduction process, which will be described in more detail below. Consequently, a conventional thorium-based thermal reactor cannot work satisfactorily in a self-sufficient cycle of Th²³² - OR²³³. The external supply of neutrons eliminates the aforementioned limitations.

Fast neutrons are in a zone in which η is significantly larger than for thermal and epithermal neutrons. Furthermore, due to the higher energies, additional neutrons are produced in each generation by different processes, such as for example fast fissions in the fertile material Th²³² and reactions (n; 2n) in the fuel and the moderator. In order to take these contributions into account, it is common to replace the parameter η by ηε, where ε is the ratio of all the neutrons produced to those of the main fissile material. In the case of fast neutrons, we expect ηε _ 2.4 θ 2.5 significantly greater than η = 2.29, but in our opinion not enough to obtain a critical long-residence reactor.

Used in conjunction with the present invention, thorium offers very important advantages over uranium-based reactors and breeders:

1) Thorium is more abundant than uranium. Most importantly, it is a pure isotope, which in principle can be fully used as fuel. Therefore, in the power amplifier, thorium is a fuel 140 times more efficient than natural uranium in a reactor in which natural uranium most often also requires an expensive and complicated isotopic enrichment.

2) The reproduction and energy production reactions used in the present scheme generate few minor actinides among the radioactive waste. Under steady state conditions, an approximately constant amount of fissile nuclei is present and is continually burned and regenerated from the bulk material. Such actinides are literally not considered to be "waste" as they constitute the much needed "seeds" for the next load of the power generation plant. In contrast, conventional reactors produce a large excess of long-lived and highly toxic actinides (the number of plutonium nuclei produced is typically 0.5 to 0.9 of the fission nuclei of U²³⁵), growing essentially indefinitely as fuel burns.

3) Of course, in both cases and for a given delivered energy, there is a comparable number of fission fragments, most of which are unstable. The toxicity of fission fragments is strong, but of a much shorter life. It degrades well below the toxicity level of a volume of natural uranium minerals for equivalent energy delivery over a period of a few hundred years, in which a safe deposit is perfectly sensitive.

4) The risk or danger of nuclear proliferation is negligible, given that the potentially strategic material, namely the U²³³, is present in the fuel as an isotopic mixture, with U²³² produced by the inevitable reactions (n, 2n) in an amount sufficient to positively "denature" uranium if chemically separated. The U isotope²³² it has a relatively short life (70 years) and its degradation products are strongly radioactive and produce great spontaneous heat making any military diversion of the material very difficult, if not impossible. Furthermore, the added toxicity due to the presence of U²³² it is not so large as to make the processing of spent fuel prohibitively expensive. This characteristic is of course lost in the "incinerators" in which the Pa²³³ is rapidly extracted and subsequently produces, by degradation, essentially U²³³ pure, pump quality. This effect is of course maximized in the case of fast neutrons that produce about 50 times more than U²³² than thermal neutrons. Fast neutrons also have the additional advantage that higher mass actinide production is totally suppressed in practice. Even the production of the lower neptunium and plutonium isotopes, such as Np²³⁷ and PU²³⁸, is practically absent (levels of less than 1 g / tonne after 100 GWat (t) day / ton). A fortiori, this applies to the higher isotopes of plutonium, americium, curium, californium, etc., which are the main source of the long-lived toxicity of ordinary nuclear reactors. In the case of thermal neutrons, plutonium isotopes are produced in very small amounts and "incinerated" so that they reach equilibrium with the fractional concentrations indicated within parentheses: Pu²³⁹ (1.03x10^-4), Pu²⁴⁰ (6.9x10^-5),

Pu²⁴² (8.8x10^-5) and PU²³⁸ (1.97x10^-4), which has the moderate lifetime of 87.7 years for α-degradation in _OR234_.

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In conclusion, the scheme is governed by the desire for simplicity and achieves the goal of creating practical nuclear energy based on the natural thorium burn-spawn cycle. The fuel remains sealed and contains a minimal and constant amount of fissile material, which results from a stable equilibrium condition or state between reproduction and fissions. The utilization of each fuel load is expected to have several years of full utilization in the power amplifier with no manipulation required. Finally, the fuel must be returned to the factory to be regenerated, removing the "poisons" due to fission fragments and recovering the chemically separated isotopes of uranium that will become the "seeds" of the next fuel load. Therefore, the replay process can continue essentially indefinitely for each installation.

The present invention differs radically from the proposals for the beam-driven or controlled "incinerators" widely described in the literature, which are expected to destroy actinides and eventually also some of the fission fragments produced by nuclear reactors. Our philosophy, on the contrary, is to strongly suppress the production of such actinides the first time. The two devices follow different design criteria and also work under very different conditions:

1) the power amplifier must work or operate with a relatively low neutron flux to guarantee the correct performance of the proposed reproduction cycle and to avoid the danger of criticality. Such a neutron flux (typically about 10¹⁴ cm^-2 s^-1 for the thermal case) it is comparable to that of ordinary nuclear reactors and for which there is already extensive technological experience in terms of materials, etc. In contrast, efficient thermal neutron-based incineration requires a neutron flux that is about two orders of magnitude higher and correspondingly higher beam energy. Equally stringent limitations apply to the fast neutron flux at which the device operates under acceptable conditions. Note that for equivalent operating conditions and, in particular, for the same burn rate, the neutron flux is approximately 33 times greater. As is well known, it simply reflects the fact that cross sections are generally smaller at higher energies. There is considerable experience with fuel rods or rods intended for fast breeders. Most of such experience can be transferred directly to our application. The thermodynamics of fuel rods allow a burn rate that is about three times that of a thermal energy amplifier, which turns out to be the limit if the limits mentioned above are calculated for this case. Then the corresponding neutron flux is about 100 times greater, that is Φ <10¹⁶ cm^-2.s^-1. At such flow, the current rod design would allow a burnout of about 100 GWat day / t.

2) Incineration of a useful quantity of actinides would be a major imposition on our inventory or quantity of neutrons and would not allow our system to operate economically. In our case, reproduction and not incineration is the main objective and determines the choice of all parameters. It is based on the Th cycle²³² - OR²³³ while in incinerators the fissions of other actinides must contribute in a main way in the generation of neutrons.

3) With a very high thermal neutron flux, a continuous on-line chemical separation is needed (with a continuous removal of the "ashes" of Th²³²), which is not required by our scheme in which the fuel remains "in situ" for the entire duration of the entire fuel cycle.

The power amplifier can be compared, in terms of its expected performance, with the long-term prospects of nuclear fusion. A fusion device based on deuterium-tritium combustion will produce about four times as many neutrons in about seven times the average energy of fissions for the same amount of energy generated. In a fusion reactor, even if there are no fission fragments, these neutrons will interact and accumulate a large amount of radioactivity on the confinement walls and surrounding equipment, posing a radiation hazard of a magnitude comparable to that of the fission fragments. Furthermore, while fission fragments are sealed within the fuel cladding, neutron contamination from a fusion power station or plant will be distributed into a number of large-scale active components dispersed over a very large volume. But, in both cases, the mass of radioactive products has a relatively short life (up to a few hundred years) and represents less of a problem compared to actinides from a thermal reactor.

Lithium is normally used to reproduce tritium. Therefore, a fusion power station or plant will essentially burn lithium and deuterium with tritium as an intermediate. The natural availability of lithium in the earth's crust is estimated to be only seven times that of thorium, and both are widely suitable for millions of years of very heavy use.

More specifically, we can compare our device to an ion beam-governed inertial fusion. Both devices need a particle accelerator, but the one for inertial fusion is much larger, complicated and expensive. The target gain for an inertia-governed fusion device, under the most optimistic assumptions, will be G = <80 100. However, this factor is liable to be substantially reduced and even to disappear since the efficiency or performance of the corresponding accelerator will be lower taking into account its much greater complexity. Therefore, the target gain for the energy amplifier concept proposed here is very likely to be close to that assumed for ion beam inertial fusion when the complexity of the latter device is fully understood and duly taken into account. . The gain of the

ES 2 129 665 T5 fast neutron version of our invention has values ​​(G = 100 v 150) that are definitely higher than expected from inertial fusion.

Finally, practical fusion devices based on magnetic confinement must be very large to guarantee efficient confinement and burning conditions. This is probably the case with inertial fusion as well, although for different reasons. Its minimum economic power or energy level is correspondingly very large, within the gigawatt range. Our device can be built with much smaller dimensions, economically deliver lower energy productions and therefore offer much greater flexibility in its use. Finally, the technology is much less sophisticated and this makes it much more suitable than fusion machines to respond to the increasing energy demands of developing countries and as an alternative to fossil fuels.

Brief description of the drawings

Fig. 1 is a graph illustrating the equilibrium concentration relationship in the case of a mixture Th²³²-OR²³³as a function of the energy of the incident neutrons.

Fig. 2 is a diagram showing various nuclear reactions that can occur starting from Th²³².

Fig. 3a is a graph showing the evolution in time of the composition of a thin initial plate of thorium exposed to a constant flux of thermal neutrons of 10¹⁴ cm^-2.s^-1.

Fig. 3b is a graph showing the evolution of the composition of a thorium plate in the presence of a fast neutron flux as a function of the integrated burn rate.

Fig. 4 is a graph similar to Fig. 3a in the case of a thorium plate initially doped with uranium "seeds".

Fig. 5a is a graph showing the normalized thermal cross section due to the accumulation of fission fragments from U fissions.²³³ in the case of Figs. 3a and 4 as a function of the integrated neutron flux.

Fig. 5b is a graph showing the fraction of neutrons captured by fission fragments as a function of integrated burning in the cases of thermal and fast neutrons.

Fig. 6 is a graph showing the expected toxicities of fission products and actinides in the power amplifier, compared to conventional pressurized water reactors.

Fig. 7 is a graph showing the evolution of the effective or efficient multiplication factor as a function of the integrated burn rate in the cases of thermal and fast neutrons.

Figs. 8a-8d are graphs showing the variations of some parameters as a function of the water / thorium volume ratio in an energy amplifier without spallation-independent target.

Fig. 9 is a schematic diagram of a power amplifier without spallation independent target.

Fig. 10a is a schematic axial sectional view of a power amplifier having an independent spallation target.

Figs. 10b and 10c are sectional views of fuel granules and spallation metal granules, respectively, used in the amplifier of Fig. 10a.

Fig. 11 is a block diagram of a LINAC proton accelerator.

Fig. 12 is a schematic diagram of an isochronous cyclotron.

Fig. 13 is a diagram showing various nuclear reactions that can occur starting from U²³⁸.

Fig. 14 is a graph similar to Fig. 3a when slightly depleted uranium is used as the starting fuel material.

Fig. 15 is a general diagram of a liquid-cooled power amplifier.

Fig. 16a is a sectional view of a fuel rod usable in the amplifier of Fig. 15. A set of such fuel rods is shown in perspective view in Fig. 16b.

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Fig. 17 is a schematic view of a fuel assembly in the form of a fluidized bed usable, for example, in the amplifier of Fig. 15.

Fig. 18 is a block diagram of an energy conversion means usable with a liquid-cooled energy amplifier.

Fig. 19 is a block diagram of an energy conversion means usable with a gas-cooled energy amplifier.

Fig. 20 is a schematic diagram of a usable energy amplifier in the case of fast neutrons.

Fig. 21 is a schematic diagram of the core of a power amplifier as shown in Fig. 20.

While the explanations of the relevant nuclear mechanism listed here are based on the best currently known experimental evidence, we do not wish to be limited by those, since other experimental data subsequently discovered may modify some details.

Thorium as a breeding fuel

A very large fission cross section for low energy neutrons is the peculiar property or characteristic of a few high Z nuclei such as U²³³ . Nuclei such as Th²³² they have a non-significant fission cross section of less than ~ 1 MeV, but can be used to reproduce fissile materials. At low energies, the (n-γ) reaction (neutron capture) is the only inelastic procedure that leads to a final (excited) nucleus with one more neutron. Instead, the child nucleus is ^ -unstable and leads, through a cascade of degradations, to a final high-Z nucleus. Therefore, the neutron capture reaction offers the possibility to "reproduce" fissile fuels from starting materials that are not fissile, in particular:

Th²³² + n Th²³³ + γ Pa²³³ + β^- OR²³³ + β^- (1)

Let us first define the relevant cross sections for the mixing of elements in the fuel rods. The ratio of the n-capture reaction σ to the fission reaction, averaged over the neutron spectrum, and the material composition is usually denoted by α and the multiplicity of neutrons by ν. Therefore the fraction of the fission and capture reactions is 1 / (1 + α) and α / (1 + α), respectively. The quantity η = ν / (1 + α) is the number of secondary neutrons that result from an interacting neutron.

Suppose that a thin plate of fertile material (Th²³²) is exposed to an intense flux Φ of neutrons. Indicating with (X₁), (X₂) and (X₃) the successive nuclei Th²³², Pa²³³ and U²³³ of the chain (1), (the γ-transition of Th²³³ to its base state and the subsequent ^ -transition to Pa²³³ neglected) the basic differential equations are:

dn1 dt = λιηι (ί) dn2 - = λιηι (t) - λ2ϋ2 (0 ^dn'= λ2ϋ2 (0 - λ₃π₃(0 dt dn4 dt = where nk (t) designates the concentration of element Xk in the combustible material (k = 1,2,3) at time t, and n4 (t) is the concentration of the fission products of X3.

In our case λ₁ = ⁽¹⁾Φ, λ2 = 1 / τ2, λ3 = [σί⁽³⁾ + σ /³⁾] Φ, where the upper index (k) means the element Xk, and τ₂ designates the half-life of element X₂ low ^ -degradation. Initially, n₂(0) = n₃(0) = 0. Catches per Pa²³³they are neglected for simplicity, at this stage, and will be considered later. Solving the differential equations and with the approximation that λ₁ «Λ₂ and λ₁ «Λ₃, we find:

ES 2 129 665 T5 n₁(t) = n₁(0) e ^λ"N₂(t) = ni (t) ^λι(1 - e ^{λ; ι}' ^λtwo n₃(t) = ni (t)^λι^λ3

1^λ3 ^{- λ}two . (e ''

Under stationary or non-dynamic conditions, n₃/ n₁ = σ,⁽¹⁾/ [σ /³⁾ + σ /³⁾], regardless of the neutron flux. Obviously, it will not be possible to irradiate the fuel uniformly; however, the fertile-fissile mixture remains stable during regime conditions, regardless of the local intensity of the neutron flux. In Fig. 1 we dotted n3 / n1 in the case of a mixture of Th²³² and U²³³ as a function of neutron energy in the wide range of 10^-5 eV up to 20 MeV. Below 1 eV, we find a constant value, n3 / n1 = 1.35 x 10^-2. Above such energy, the ratio oscillates rapidly in the resonance zone and sets at much higher values ​​in the vicinity of n₃/ n₁ »0.1 for energies corresponding to the neutron spectrum of fission. Operation without moderator and with a neutron spectrum directly from the fissions will give an equilibrium concentration of the fissile material that is approximately seven times higher than that of the alternative thermalized neutrons.

However, as we shall see, fast neutrons allow much higher burn rates and thus total fuel can be correspondingly reduced: for the same energy produced, the accumulated stocks of U²³³ they are generally comparable for both schemes.

The fact that after a period of running and under stable conditions the fissile content has a substantially constant concentration is important and should be underlined. Stability can be qualitatively verified by looking at the effect of small variations in n3 / n1: a small increase (decrease) in n3 / n1 will be corrected by higher combustion and lower reproduction which, in turn, will decrease n3 / n1 (or vice versa). But the instantaneous variations of the intensity of the beam, although they are immediately reflected in the combustion or burning regime of the fissile material, only produce new fuel after a time of the order of τ2. For example, an increase in neutron irradiation will produce an immediate reduction in n3 / n1 followed by an increase in n3 / n1 only after τ2. This is the classic delay problem in a feedback loop.

Let us now consider the intermediate element, viz. The ^ -precursor Pa²³³. In stationary conditions, n2 / n1 = σ,⁽¹⁾ Φ τ2, which implies a density of (X₂) directly proportional to the neutron flux. For this reason, the flow variations cause variations in n2 / n1 which, in turn, imply a new transition period towards the new condition or state of equilibrium. Then n3 / n1 will no longer be independent of Φ, since the instantaneous variations in the intensity of the beam, although they are reflected immediately in the burning or combustion regime of the fissile material, produce new fuel only after a time of the order of τ2 . For example, if the neutron flux is abruptly cut off, the nuclei (X2) will degrade with a rate λ2 = 1 / τ2 in (X3), leading to a final population of (X3) equal to n2 + n3. Such an increase in fissile material should not make the system critical, although the time lag is related to τ2 and long (many days) and simple corrective measures can easily be taken. Therefore, the relative relation n₂/ n₃ = (σ⁽³⁾ Φ τ₂) in which σ⁽³⁾ = σ, '³'+ σ /³⁾ should remain small, setting a limit for the neutron flux Φ.

For a less radical flux change of a step function of amplitude ΔΦ, the variations of n₃/ n₁ are correspondingly less:

σ^{(1) r}ⁿ3^(t) = ⁿ1^(t)_σ.

+ (σ⁽³⁾ ΔΦ) ^λ2 ^λ3 •(and^{- <Í3t} - e^- λ2 t) where t is calculated from the flow change and λ3 = σ⁽³⁾Φ refers to the new flow conditions. Obviously, more complex changes can be analyzed using the above formula as the sum of stage functions.

There is a second, equally relevant condition or state that limits the neutron flux. Of course, in order to achieve great reproduction, most of the Pa²³³ must survive neutron capture and rather degrade towards U²³³, which translates into the condition or state σ,⁽²⁾ Φ τ₂ «1. Inelastic cross sections for energies of E up to a few eV (less than the resonance region or zone) can be parameterized as σ (Έ) = (0.025 eV / E / ^ Σ, with the parameter Σ being collected for the relevant elements in Table 1.

Using Table 1 and n₂/ n₃ <0.2 we find Φ <1.44 x 10¹⁴ [T / (300 ° K)]^1/2 cm^-2 s^-1 for PA²³³ - OR²³³ and thermal or epithermal neutrons, corresponding to large energy yields, especially of the order of 70 MW for each ton of mass of fuel of Th²³² and reasonable temperatures. The quantity T means the temperature, in degrees Kelvin, corresponding to the average energy of the neutrons, that is, the temperature of the moderating medium when complete thermalization has taken place. Practical operating conditions

ES 2 129 665 T5 will not normally exceed this limit for Φ. For practical temperatures, the limit of the neutron flux will be: Φ <3x10¹⁴cm^-2s^-1. The condition σ ^²) Φ τ₂ «1 translates into a temperature-dependent flux of thermal neutrons, Φ« 1.05 x 10¹⁶[T / (300 ° K)]^1/2 cm^-2 s^-1, which leads to only a small percentage of playback loss for the above limit.

TABLE 1

Parameters of some nuclei below a few eV: [σ (Ε) = (0.025 eV / E / Σ]

<td>Element</td><td>Elastic, Σ barnio</td><td>Capture, Σ barnio</td><td>Fission, Σ barnio</td><td>n-multip. ν</td><td>sec / prim η</td><td>σ (γ) / σ (ί) α</td>

<td>Th²³²</td><td> 13,0</td><td> 7,48</td><td>&lt;2x10^-4</td><td></td><td></td><td></td>

<td>Pa²³³</td><td> 13,1</td><td> 40,6</td><td> - - -</td><td></td><td></td><td></td>

<td>OR²³³</td><td> 12,7</td><td> 46,2</td><td> 534</td><td> 2,52±0,03</td><td> 2,28 ±0,02</td><td> 0,105±0,007</td>

<td>OR²³⁵</td><td> 10±2</td><td> 112±110</td><td> 582±10</td><td> 2,47±0,03</td><td> 2,07±0,02</td><td> 0,192±0,007</td>

<td>OR²³⁸</td><td> 8,3±0,2</td><td> 2,75±0,04</td><td>&lt;5x10^-4</td><td></td><td></td><td></td>

<td>Pu²³⁹</td><td> 9,67±0,5</td><td> 285±13</td><td> 740±9</td><td> 2,91 ±0,04</td><td> 2,09±0,02</td><td> 0,39±0,03</td>

<td>Bi²⁰⁹</td><td> 9,37</td><td> 0,034</td><td> - - -</td><td></td><td></td><td></td>

<td>natural Pb</td><td> 13,0</td><td> 0,17</td><td> —</td><td></td><td></td><td></td>

In the case of fast neutrons, the cross sections must be integrated into the spectrum and depend to some degree on the choice of the chemical composition of the fuel (pure metal versus oxide) and the coolant. Let us first consider the already discussed consequence of the relatively long half-life of Pa²³³, that is, the significant addition of reactivity that occurs during a long stop, after the characteristic life time of degradation of Pa²³³, the concentration of U²³³ will increase by an amount asymptotically equal to the concentration of Pa²³³, essentially independent of the mode of operation of the device for a given regime of burning or equilibrium combustion. However, since now the equilibrium concentration of U²³³ is about seven times greater, its effect on reactivity will only be 1/7 of the effect of thermal neutrons. Even for a three times higher combustion or burn rate, the corresponding limit will still be 3/7 of the limit given for thermal neutrons.

Next, we consider the capture of (fast) neutrons by the intermediate elements of the reproduction process and specifically by the Pa²³³ that destroys a nascent atom of U²³³ at the price of an additional neutron. The cross section σ_α (Pa²³³) is about 43 b (b; 1b = 10^-24 cm²) at thermal energies and 1.0b for fast neutrons (E _ 10⁵ eV). Therefore, for fast neutrons, the cross section is much smaller but the flux is correspondingly greater: for a given combustion or burning regime, the loss is 0.67 times the value of thermal neutrons. Note, however, that the possibility of neutron losses is much higher for fast neutrons that have a larger ηε, and thus higher combustion or burn rates are practical; at three times the combustion or burning regime the loss is twice that set for thermal neutrons, which is quite acceptable.

Many more reactions occur due to the intense neutron flux and natural degradations. The chain of possible reactions, starting from the initial fuel Th²³², is shown in Fig. 2, in which the vertical arrows indicate neutron captures with the corresponding cross sections in barnios, (b; 1b = 10^-24cm²), the oblique arrows indicate n-fissions with the corresponding cross-sections in barnios and the horizontal arrows indicate ^ -degradations with the corresponding half-lives in minutes (m), hours (h) or days (d). The cross sections are for thermal neutrons in barnios.

The situation is complex enough to justify a computer simulation. The results are shown in Fig. 3a, in which the evolution in time of the composition of an initial thin plate of thorium exposed to a constant flux of neutrons (thermal) of 1.0 x 10 is indicated.¹⁴ cm^-2 s^-1. Can be seen the ^ -precursor Pa²³³, the mixture of isotopes of uranium and a small fraction of higher actinides, Np²³⁷ and PU²³⁸.

The last two elements are the only actual “ashes” from combustion, since uranium isotopes are the “seeds” for other uses. The full scale of the graph on the abscissa corresponds to about 10 years of continuous exposure. After a first initial phase of "reproduction" in which U²³³ until

ES 2 129 665 T5 the equilibrium relationship, a constant situation or state is set in which both fission and reproduction are taking place (combustion or burning phase). Additional elements are formed that are generally burned by neutrons and thus reach an equilibrium concentration. A significant concentration of U develops²³⁴ which has a significant probability of transforming into U²³⁵ highly fissionable. Captures are still used by the U²³³ that do not lead to fission immediately (~ 10%) to produce energy since they “reproduce” to give U²³⁵ fertile through U²³⁴. This secondary process of reproduction, which resembles reaction (1) - except that it is totally governed by neutron captures - has an additional contribution to the neutron inventory, since the transformation of U²³⁴ in U²³⁵ requires a neutron, while fission of U²³⁵ gives or gives up about 2.5 new neutrons. This isotope may not in turn achieve fission and instead capture another neutron, leading to U²³⁶. The next element to form is U²³⁷, which has a short life span (6.75 days) and degrades into Np²³⁷ which has a long life time. Another capture by neutrons and the Np²³⁷ is cremated to give PU²³⁸ which has the moderate lifetime of 87.7 years for an α-degradation to give U²³⁴. If left in the fuel for a long time, the PU²³⁸ will capture another neutron with a large cross section, thus giving Pu²³⁹ easily fissionable.

At neutron fluxes of the order of 10¹⁴ cm^-2 s^-1 these many additional stages are increasingly less likely to occur and the "ashes" remain primarily isotopes of uranium. As already noted, they have the important function of ensuring that a simple chemical separation cannot produce a significant amount of fuel for military applications. The accumulation of actinides other than the uranium “seeds” is not a problem even after several recoveries and use of seeds as shown in Fig. 4, which is the same as Fig. 3a except now the “seeds” Uranium terminals are reinjected into the new thorium fuel. In general, we expect it to be separated from uranium at each reuse cycle and stored or incinerated.

The amount of energy delivered depends linearly on the neutron flux, which is not uniform within the active volume. For this reason, it is useful to speak of an “average” exhibition_ive neutrons. The total thermal energy produced by fissions in a fuel mass M at the reproductive equilibrium and at the neutron temperature T is given by:

p = 55, 3

ZM \ z \ Z 300K V^/2\ 1Ton / \ 10¹⁴cm^-2s^-1 / \ T (^orK) /

Mwitt

As an example, setting M = 4.92 tons, &lt;l&gt;_ive = 1.50 x 10¹⁴ cm^-2 s^-1 and T = 400 ° C, we find 267 MW. If these constant conditions remain uninterrupted for two years, the integrated neutron flux of the fuel will be 9.46 x 10²¹ cm^-2, which gives a conservative figure for the allowed integrated flow. During this period, approximately 4.6% of the thorium fuel will have been burned, corresponding to a mass of about 220 kg. One ton of fuel corresponds to 2.8 million metric tons of coal. Always with fixed or stationary conditions, the amount of U²³³ fissile is of the order of 67 kg, which means that the fissile fuel reproduces completely at a rate slightly less than twice a year.

In the case of fast neutrons, the combustion or burning rate is about three times the previous one. Due to the higher energies, additional neutrons are produced with each generation by means of different processes, such as fast fission in fertile material Th²³² and reactions (n, 2n) in the fuel and the moderator. It should be noted that, in the fast neutron regime, most even-pair nuclei such as U²³², OR²³⁴, OR²³⁶, etc., exhibit a significant fission cross section. Therefore, most of these elements are converted into useful fuels. The actinide concentrations are very different with respect to the concentrations in thermal energies (Fig. 3b). While the new elements become important due to the improved channels (n, 2n) such as Pa²³¹ and U²³², the production of higher mass actinides is very strongly suppressed. Even now, the production of the lower isotopes of neptunium and plutonium, such as Np, is practically suppressed (levels below 1 g / tonne after 100 GWat (t) day / ton).²³⁷ and PU²³⁸. A fortiori, this applies to the higher isotopes of plutonium, americium, curium, californium, etc., which are the main source of long-life toxicity in ordinary nuclear reactors.

The fast neutron option also augurs a significant reduction in actinide toxicity compared to the already remarkable performance of the previous examples, provided that two problems are mastered, namely that associated with the presence of U²³² and that of Pa²³¹. The presence of a relatively large amount of U²³², which is about 50 times more abundant than thermal neutrons for comparable combustion, could of course be seen as an advantage, since it positively "denatures" the uranium making any military diversion of the material very difficult, if not impossible. As already noted, the added toxicity due to the presence of U²³² it is not so large as to make the processing of spent fuel prohibitively expensive.

The Pa²³¹ (produced at the rate of 200 g / ton of thorium fuel after 40 GWat day / ton of combustion, roughly proportional to the integrated combustion) instead represents an additional long-lived source of radiotoxicity (τ = 3.2 10⁴ years) that must be mastered. It is possible to chemically separate the Pa²³¹of spent fuel. Methods can be envisaged to eliminate it. Such an element could be introduced into a strong thermal flux and transformed into a U²³² by neutron capture and subsequent ^ -degradation. The thermal neutron capture cross section of Pa²³¹ is very large and is dominated by a large 600 ba resonance

ES 2 129 665 T5

En = 0.3eV, which means that, at a neutron flux of 2x 10¹⁴ cm^-2 s^-1, the 1 / e fold time for destruction is 96 days. A suitable device based on thermal neutrons is conceivable for this. Alternatively, if the Pa²³¹ it is simply reinjected at the next fuel load, its concentration will eventually saturate to a constant value after long combustion or burning, as a result of competitive production and incineration.

The burning or combustion of an ordinary reactor varies from 7 GWat (t) day / t of a natural uranium fuel from CANDU reactors to 30 v 50 GWat (t) day / t of PWR-enriched uranium. In the present invention, the fuel is in principle continuously renewed by means of reproduction. Therefore, in principle, final burning or combustion is determined not by fuel depletion but rather by (1) poisoning by fission fragments; (2) radiation damage to supporting structures; and (3) pressure build-up of gaseous fission fragments.

In the case of the power amplifier, as we will show later (see next paragraph), fission poisoning in the case of thermal neutrons limits the practical use of a fuel to about 50 GWat (t) day / t. Fast neutrons allow in principle much longer burning or combustion, since poisoning by fission fragments is no longer a major problem. Therefore, the fuel utilization is determined by the limitations (2) and (3). A reasonable target would then be 100 v 150 GWat day / t, corresponding to 10 v 15% of the thorium in the fuel reproduced and burned. However, the neutron flux is about 33 times higher for the same burn, given that the macroscopic cross section for fission of U²³⁵ is correspondingly less. Radiation damage becomes one of the important problems and can represent a main limitation to extend the burning or combustion beyond the indicated limit. The extensive experience accumulated in the development of fast breeders indicates that the burning or combustion objectives are realistic.

1.- Fission fragments

Combustion of an appreciable amount of fuel will produce fission fragments which in turn will have a significant effective capture cross section for thermal neutrons. This is an important question of this scheme, since it is closely related to the problem of the time during which the reaction can proceed without reprocessing. As already indicated, when compared to a nuclear reactor, in the power amplifier these effects are less relevant since now the criticality must not be maintained. An estimation of the effects due to fission fragments is an important task, since there are many nuclei and complicated chains of degradation. It is only possible to give results with numerical calculations based on cross sections and on available thermal neutron captures. Epithermal neutrons are expected to contribute only slightly, since resonances in mid-Z nuclei are generally well above these energies. It is therefore believed that these calculations can provide a reasonably accurate determination of the situation. There are three main effects to consider:

1) Fission fragments can capture some of the neutrons, thus affecting the neutron inventory and consequently the energy amplification of the block. There is a complicated interrelation between neutron captures and degradations that both lead to transformations of the hundreds of compounds that result from fission. Evolution therefore depends on the neutron flux and, more generally, on the history of the fuel. This is a well known effect in nuclear reactors. It should also be noted that the poisonous fission fragment is less important in the case of thorium in the reproductive equilibrium than, for example, in natural uranium, since the cross-section of the fuel is 2.17 times greater and therefore the number of catches for a given concentration of fission fragments is correspondingly lower. The calculation results using known cross sections are shown in Fig. 5a for reasonable neutron fluxes and with the total effective or effective cross section parameterized in the way already used in Table 1, namely ^ (E) = (0.025eV /AND)^v^]. In Fig. 5a we show a normalized thermal cross section due to accumulations of fission fragments from fissions of U²³³, as a function of the integrated flux and for a constant neutron flux of 1.0 x 10¹⁴ cm^-2 s^-1. Two curves correspond to the conditions of Fig. 3a and Fig. 4, respectively. Known degradation rates and cross-sections have been added for 1170 different nuclear fragments, taking into account evolution over time. Resonances for mid-Z nuclei from cleavage fragments generally occur at higher energies than actinides and have a lower contribution to the regime. The dependence of the fission poisoning effect grows less rapidly than linearly with the integrated irradiation Φ dt since it is in both cases saturation fission fragments (such as the well-known Xe¹³⁵ and Sm¹⁴⁹) and non-saturation.

Neutron losses due to the product Xe are well known¹³⁵ fission of high thermal cross-section. The fraction of xenon poison is dependent on the neutron flux, as it is concerned, as in the case of Pa²³³, to a balance between captures and degradations. For thermal neutrons and at reproductive equilibrium, the fraction of neutrons captured by Xe¹³⁵ is given by the expression 0.9 x 10^-19Φ / (2.1 x 10^-5+ 3.5 x 10^-18Φ) which tends to an asymptotic value of 0.028 for flows Φ&gt; 1.0 x 10¹⁴ cm^-2 s^-1. After a reactor shutdown or power reduction, xenon poisoning temporarily increases even further because Xe-producing degradations continue to occur, passing through a maximum of 10 to 12 hours after shutdown. The magnitude of this additional poisoned passenger also depends on the neutron flux. Although the loss

ES 2 129 665 T5 is not significant, a necessary reserve of reactivity, even if normally compensated by means of control devices, would represent a permanent loss of neutrons.

The same computer calculations have also been used to analyze poisoning as a function of burning or integrated combustion for conditions relevant to the case of fast neutrons. The most relevant conclusion is that the losses due to poisoning by fission fragments are much less important (Fig. 5b). Therefore, much longer burns are possible without reprocessing the fuel. For example, at a given burnout of 40 GWat day / t, the capture fraction is about 18% for thermal neutrons and only 1.4% for fast neutrons. In the latter case, the xenon-type poisoning effect is substantially absent, since there is no fission fragment core having the required characteristics in the energy domain of importance. These characteristics translate into two distinctive advantages for the fast neutron option, namely (1) in a higher burning or combustion and (2) in a higher allowed value of k, given that its variations due to the captures by the fragments of fission are now (1) independent of time and (2) much less.

2) Fission fragments are generally radioactive and produce additional heat, even if the proton beam is turned off, since they contribute about 14 MeV to the total energy emitted by fission which is (204 ± 7) MeV. Immediately after the proton beam is turned off, the power produced by this residual activity is 14/204 = 0.0686 in the steady state or steady state. Activity slowly degrades over time, roughly as t^-0,20, where t is in seconds, leading to a reduction of a factor of 10 in approximately one day. Continued cooling must of course ensure that melting does not occur. In this regard, the power amplifier does not differ substantially from a reactor.

However, the possibility exists, at least in the case of lead as a refrigerant, of extracting the heat from the fission fragments in such a way that the danger of accidental melting is totally eliminated in the event of a massive failure of the system. refrigeration.

We have taken the point of view that if a small percentage of the thermal energy produced by the power amplifier is “sacrificed” by dissipating it spontaneously by natural convection, in an amount such that it exceeds the heat of radioactivity, it is practically done accidental fusion impossible.

It is well known that a "pool" reactor is safe with respect to melt risks or dangers. This is not just due to the fact that the energy produced is modest. It is mainly because the heat produced by heating by ^ -degradation is extracted from the nucleus by natural convection. For this reason, we have explored the possibility of using natural convection in the large pool of liquid lead to extract the corresponding, but much more radioactive, degradation heat from the power amplifier. A second cooling loop, also passive, would then transfer such heat to the environment. Either water or, even better, air would be used for this secondary transfer.

Here, we focus our attention on the extraction of primary heat from the core into the pool or mass of liquid lead. Incidentally, the heat from the degradation of radioactivity will automatically ensure that the lead remains liquid. We assume a core structure made up of a large number of thin channels between the rods, each with an equivalent diameter D and a total cross-sectional area Af. The flow of coolant between the parallel rods is approximately laminar, due to the close spacing of the rods and the small driving force or convection drive. This is in contrast to forced heat extraction during power amplifier operation, in which the flow of coolant is definitely turbulent. The reason for insisting on laminar flow is not critical, but it does ensure the most efficient transfer with the minimum pressure drop across the core.

The ability to transport a thermal energy qtot out of the nucleus by convection can only be easily estimated with the help of the Poiseuille equation. The required temperature difference Δt between the top and bottom of the core to ensure heat transfer is given by

At =

[ ^96μbird

M-eAfgDCp ^ where μ_ανι,, p_bird and c_p are respectively the average viscosity, the density and the specific heat of the refrigerant fluid, g is the acceleration of gravity and β is the thermal coefficient for expansion or expansion in volume. The use of liquid lead is particularly favorable since it has a large coefficient of thermal expansion, a high density and a low viscosity and allows large temperature differences.

In order to estimate the capabilities of the method, we concentrated on a large installation with a nominal power of 2.4 GWat (t). Obviously a lower power unit would pose a simpler problem. Immediately after shutdown or shutdown, the thermal power due to delayed radioactivity is of the order of several units percent of the rated power and decreases rapidly with time. Suppose then that a maximum of qtot = 2.4 x 10 must be safely dissipated⁹ x 0.05 = 1.2 x 10⁸ wat. It is considered that the equivalent diameter of the spaces between the rods is D = 0.3 cm and that the total cross-sectional area of ​​the cooling channels, that is, the area of

ES 2 129 665 T5 flow, is A_F = 2.0 m². The temperature difference is then Δt = 244 ° C, which is very acceptable considering the exceptional nature of the event. The speed with which the liquid circulates through the nucleus is given by:

^whattot v = pepAf At which gives v = 0.168 m / s for the chosen values. At such a speed, the Reynolds number Re = 3.13 x 10³ and Poiseuille's equation can still be regarded as roughly correct. Note that while laminar flow-based calculations approximations are important, flow channel diameter and total fractional flow area critically enter the formula and considerable advantage can be achieved by relaxing in these parameters. If the flow were to become turbulent, the temperature difference would be much larger by a factor of 2-3 and a more generous cooling geometry would be required. We will leave this possibility or choice for the detailed design of a specific device.

The bottom line is that natural convection can be used to extract residual heat from even a large power amplifier core in the 1 GWat (e) domain.

3) Long-lived radioactivity is a major problem, although much less relevant than in the case of actinides. The time evolution of the fragments after arrest and separation is shown in Fig. 6, in which the predicted toxicities of the fission fragments and actinides are indicated as a function of time, for an equivalent delivery or supply. of energy. In the case of actinides, we have included all relevant elements (except permanent uranium seeds) at their “incineration” saturation level. If normalized to uranium ores for equivalent energy delivery or supply, its relative toxicity will decrease inversely proportional to the number of recycles. It can be seen that after about 300 years the toxicity content is lower than that of natural uranium minerals for an equivalent energy supply and becomes totally negligible a few hundred years later.

In practice, in order to maintain a constant behavior during the use of the fuel, some neutron absorbing elements could be initially introduced which either were progressively removed or burned to give less absorbent elements during the combustion process. In any case, such evolution is not a problem, since it occurs over a very long period of time and only decreases the reactivity of the system.

2.- A thorium-based reactor?

As noted, thorium, as a nuclear fuel, has considerable advantages when compared to uranium. However, the realization of a classical reactor based on the complete reproduction of thorium presents serious difficulties, which will be briefly illustrated, and which justify the greater complexity of an external neutron source according to the present invention.

In a reactor, the neutron flux is fully supported by the neutron multiplication process, which is governed or determined by fission. A key parameter is the effective multiplication factor, Keff, the ratio of neutrons at the end of a generation to the starting number of this generation. It is evident that for a critical reactor, Keff = 1. We can separate the effects due to neutron leakage and introduce the corresponding parameter K. = K_eff/ P, which is the parameter that would apply to an identical (homogeneous) lattice arrangement in which the dimensions are large enough to make the 1 - P neutron leakage probability negligibly small. Clearly, K. must be significantly greater than 1 in order to allow criticality to be achieved with a sufficiently small lattice volume. The characteristic of K. it does not depend on the geometric dimension of the device, which refers to P: the excess of K. with respect to unity represents the possibility of fractional neutron losses due, for example, to leaks .

In the case of theoretically pure natural uranium and graphite, the maximum possible value of K. is ~ 1.1, whereas when heavy water (D2O) is used as moderator, also with natural uranium, higher K. constants can be achieved, which are close to 1.3. As is well known, this leaves enough latitude for losses due to leakage and absorption by impurities and fission fragments to realize practical devices. However, for a thorium-based device the situation is not so favorable.

The value of K. is directly related to the concentration of fissile material. While for natural uranium the relevant concentration is that of U²³⁵ which is fixed and known (0.71%), in the case of thorium that reproduces U²³³ the equilibrium concentration of the latter material depends on the previous intensity and the history of the local neutron flux. As noted, under constant conditions and after a suitable period of time, such a concentration reaches an equilibrium level at which U²³³ fission is balanced by the amount of U²³³ reproduced from Th²³². Such equilibrium concentration also depends on the energy spectrum of the captured neutrons which, in turn, is related to the basic geometry of the lattice. Besides U²³³, several other isotopes of uranium and other actinides are inevitably formed with a variety of time constants, which eventually also reach an equilibrium level. They also contribute both to neutron captures and to multiplication with fissions and to a lesser extent with reactions (n, 2n).

ES 2 129 665 T5

Among the best neutron moderators are “reactor grade” heavy water (D2O + 0.14% H2O), beryllium, water (H2O), and graphite. More generally, a large number of moderators can be used and various choices are available, this being of course application dependent and dictated by the requirements or needs of the specific design. The moderator must be sufficient to reduce the energy of the fission neutrons, since, as indicated, at lower energies the amount of U²³³ required to achieve reproductive equilibrium is less.

Several practical lattice geometries have been evaluated, with fuel bodies of several different shapes and dimensions (such as fuel spheres or fuel rods), adequately spaced and evenly distributed in a substantially continuous moderating medium, an evaluation that has been performed with methods calculations in which the best of the underlying nuclear physics knowledge has been used. The relevant parameters are the radius r of the rods or spheres and the ratio ρ of fuel volumes with respect to the moderator. Results can be expressed in terms of iso-K curves. as a function of the variables r and p. A clear optimum emerges for a wide appropriate choice of these parameters. The starting fuel can be in various chemical forms, for example metal, oxide or carbide. The resulting values ​​of K. for the optimal choices of r and ρ have been evaluated and are given in Table 2.

TABLE 2

Properties of some reactor infinite lattice geometries

<td>Initial fuel composition</td><td>Moderator composition</td><td>Fuel geometry</td><td>Maximum reactivity (theor.)</td>

<td>Pure thorium</td><td>Graphite</td><td>Spheres, bars</td><td>K. = 1.07</td>

<td>Pure thorium</td><td>Water</td><td>Spheres, bars</td><td>K. = 1.07</td>

<td>Pure thorium</td><td>Beryllium</td><td>Spheres, bars</td><td>K. = 1.36</td>

<td>Pure thorium</td><td>Beryllium +⁶Li</td><td>Spheres, bars</td><td>K. = 1.08</td>

<td>Pure thorium</td><td>Heavy water</td><td>Spheres, bars</td><td>K. = 1.10</td>

Results are given for graphite, beryllium, water (H2O), and reactor grade heavy water (D2O). A special case concerns beryllium, which has a significant cross section for the reaction (n, 2n) and therefore acts effectively as a neutron multiplier. However, interactions with fission neutrons also produce⁶Li by means of the Be (n, α) reaction which has a cross section for thermal neutrons (0.025 eV) of 940 barniums and which reaches saturation very quickly, compensating for the advantages of the (n, 2n) reaction. Furthermore, the neutron captures of the⁶Li produce a large amount of tritium which is radioactive and must be disposed of.

The values ​​of K. include only the contributions to the captures in the moderators and are given for a mixture of Th²³² - OR²³³ in the reproduction balance. Additional catches should be added, with a corresponding loss of reactivity:

1) Captures by intermediate element Pa²³³ whose concentration is proportional to the neutron flux. For Φ = 10¹⁴ cm^-2 s^-1 we find AK = -5.3 x 10^-2.

2) Captures in the fast-saturating fission fragments of Xe¹³⁵ and Sm¹⁴⁹, which are slowly dependent on neutron flux. For Φ = 10¹⁴ cm^-2 s^-1 we find AK. = -2.0 x 10^-2.

3) Captures by the higher isotopes of uranium U²³⁴, OR²³⁵, OR²³⁶ and U²³⁸, generated by multiple neutron captures. Its concentration depends on how long the fuel has been used. Note that chemical separation cannot separate them from the main fuel U²³³ and that both fission and catches contribute, with opposite signs, to reactivity. For relatively long integrated neutron exposure

Φ dt&gt; 3 x 10²² cm^-2 at which the concentrations reach approximately saturation, the contribution is AK = -5.0 x 10^-2.

The highest value of K. for the optimal choice of the parameters and including only the effects (1) and (2) is typically in the range of 1.01 v 1.03, that is, too small to determine the criticality for a system. finite in size and once other sources of captures due to impurities (slowly saturating and unsaturating fission fragments) are taken into account. It should be noted that K. is also significantly reduced by effect (3), that is, the accumulation of uranium isotopes higher than U²³³ whenever we want to make efficient use of fuel without isotopic enriched.

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Therefore, under realistic conditions, a thorium flaring reactor can hardly reach criticality with full replication requirements. This is the reason why, according to the present invention, the addition of an external neutron source is critical to provide the practical operability of thorium-related nuclear energy.

According to the present invention, there is no criticality. However, the effective or efficient multiplication factor needs to be high to achieve a high gain. It has already been observed that the condition σ, '²'Φ τ2 «1, which limits the neutron flux, causes an efficient production of U²³³. It will further be noted that this condition also minimizes the effect (1) discussed above, thereby guaranteeing a reasonably high reactivity. Of course, minimizing effect (1) appears to be a severe criterion for limiting neutron flux. In practice, the neutron flux Φ should be a maximum of 0.03 / (σ,⁽²⁾τ2), that is, it must be such that at most 3% of the Pa nuclei²³³ absorb a neutron instead of degrading into U²³³.

In the case of fast neutrons, εη is larger but not high enough to make a conservative reactor design. For example, the excess reactivity, K. = 1.2, is substantially lower than that of a thermal reactor with natural uranium, which is somewhat a limiting case for practical use, for which K. = 1, Four.

The external supply of neutrons

The external supply of neutrons eliminates the aforementioned limitations. It can be done, for example, by means of a high-energy, high-intensity proton accelerator, the beam of which hits a heavy metal target located in the central area of ​​the enclosure. Although the initial sample of the low energy neutrons is provided by the impact of the beam on the target, the main multiplication of this sample is generated naturally by the fissions in the fuel elements. For N1 carriers in the first generation injected by the external neutron source, there will be Nn = N1 k^n-1 carriers in generation n^to, where k is the effective multiplication factor or criticality factor already defined. Of course, in order to avoid criticality, k &lt;1. The total number of neutrons produced is then:

n =. Neither

Ntot = Ni Σ k^n-1 = Ni (1 + k + k² + k³ + ...) = n = 1 1 - k with an improvement factor of 1 / (1 - k). The criticality factor has already been decomposed as k = P K., where K. refers to an infinite lattice and P to the probability that a neutron will not escape and therefore react in the fuel. Note that criticality (k = 1) is easily avoided since, as already noted for a thorium K reproductive device. ~ 1.0. On the other hand, k must be large to get good multiplication. We therefore need a neutron retention geometry, especially a large value for P, to ensure that the probability of further fissions remains large and that the cascade of an incoming neutron continues for several generations.

We begin our consideration, as before, in the case of thermal neutrons. The case of fast neutrons will also be discussed later.

The practical examples indicate that a value of k within the range of 0.9v 0.95 is optimal, corresponding to a total number of neutrons in the moderator-fuel that is 10 v 20 times the number injected by the target. Clearly, the success of the scheme depends on the healthy development of the nuclear cascade, which has the maximum production in the range of energies that goes from thermal energies to a few MeV. The relevant parameter is the fission rate or regime, which guarantees the continuation of the cascade with newly produced neutrons and is the main source of energy production. The neutron yield from high-energy protons on a massive target made of high-Z material - demonstrated by practical sources of spallation - is very large. For example, a possible choice of target dimensions and composition - described later - will lead to an average neutron yield of about 42 neutrons for every 1.5 GeV incident proton. Therefore, the fraction of the beam energy required to produce a neutron with the help of the high-energy cascade alone is of the order of ε_η = 35 MeV. The subsequent multiplication of neutrons in the cascade, due to fissions, is important since it further reduces the energy “cost” of a neutron as a function of the energy of the incident proton beam by the multiplicative factor (1 - k), taking it to as low as 1.75 v 3.5 MeV / n. It is admitted that the choice of this fringe for k is rather conservative and that perhaps even higher gains can be maintained in a well-designed device. For comparison, the fission energy yield is about e_F = 190 MeV (includes fission fragment βdegradations, but excludes neutrinos).

The energy gain of the energy amplifier is indicated by G and is defined as the ratio between the total energy produced in the device and the energy deposited by the high energy beam. In order to give a first estimate of G, it must be taken into account that under conditions of equilibrium and an infinite lattice, approximately 0.40 of all neutrons produce fissions, the rest being dedicated to reproduction or to be captured in the moderator. , to fission fragments, etc. Therefore, the net energy gain of the device is roughly given by G = 190 MeV / (35 MeV) x 0.4 x 1 / (1 - k) = 2.17 / (1 - k) and will generally fall between G = 22 and G = 43. Even far from criticality the energy gain is considerable. Suppose for example that the efficiency or efficiency of the conversion of heat into electricity, using a high temperature gas turbine, is 0.45. The electric energy

ES 2 129 665 T5 produced will then be 10.2 (20.4) times the energy deposited by the high energy beam for k = 0.9 (0.95). There is an abundance of electrical energy produced, in excess of that necessary to operate the accelerator.

The neutron conservation equation refers directly and on very general bases to the achievable gain G and the relationship Γ = nloss / n0, in which nloss (“loss” = loss) is the number of neutrons that escape or are absorbed by something other than the actinide fuel mixture, and n0 is the number of neutrons absorbed by the actinide fuel mixture, i.e.

G =

The parameters a and b are functions of ν, the multiplicity of fission neutrons, and of α, the ratio of cross-sections of (n, γ) and fission, weighted by the fraction fi of atoms of all actinides in the fuel and averaged by the neutron energy spectrum (the subscript i indicates each actinide and the bar above the cross sections σ represents a value averaged over the relevant neutron spectrum):

α =

Σζσ (η, γ)¹

Σϋσ *.

a = b = ε · 1 ε_η 1 + α

Note that when the device becomes critical (G = ^), r_crit = a. Therefore, in a first approximation, a ~ k - 1. The contribution to Γ due to the beam is given by the second term b / G. The exemplified figures, appropriate for a practical device working with thermal and epithermal neutrons, are a = 0.070 and b = 2.52. The computer models used to determine a and b take into account the true energy spectrum of neutrons and the dependence of cross sections on energy, which is particularly difficult in the resonance zone. Using a high neutron saving design, it will be able to achieve, in the absence of fission fragment poisoning, Γ₀ »0.08. Γ₀ represents the contribution to Γ of any neutron losses from fission fragment captures, i.e. leakage, moderator captures, fuel coating, spallation target if used, etc. The margin ΔΓ = Γ - Γ₀ it is large when the system tolerates a relatively large amount of fission products. The negative value of ΛΓ ^ = Γ ^ - Γ₀ ensures that the power amplifier never becomes critical. But, under the same conditions and at the gain G = 20, already quite practical, we find ΛΓ = 0.116, which provides a considerable reactivity capacity. For a gain of G = 40, ΔΓ = 0.053. Therefore Γ should be kept reasonably small in order to ensure maximum profit. The design of the device is therefore governed primarily by the neutron economy.

The payoff for minimizing Γ0 is a higher energy gain and a broader capacity for catches due to fission fragments, which in turn means a longer lifetime without extraction. The (normalized) cross section for fission fragments Σ ^ »is given in Fig. 5 previously described. A good estimate after an integrated flow of 10²² cm^-2 is Σ ^ »= 1.6 barnios, from which we calculate a contribution ΔΓ = 0.106. Obviously, shorter exposures and / or lower earnings will improve the ΔΓ margin.

The accumulation of fission fragments has a direct influence on the gain, unless it is corrected by decreasing it during the early phases by introducing a variable amount of neutron absorption by other means. These extra neutrons do not necessarily have to be wasted on the control rods. They could be used for example to reproduce new fuel for another use.

Of course, there are also other reasons that suggest the operation of the thermal neutron regime with relatively small values ​​of k, especially its relatively large variations due to degradation mechanisms after stoppage or energy variations (Pa²³² and Xe¹³⁵ ) so that sufficient margin is left regarding criticality hazard.

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However, the same type of considerations could suggest a much higher gain for a fast neutron scheme, in which an operating point or operation in the vicinity of k = 0.980 is an optimum operating point, corresponding to an energy gain of the interval G = 100 v 150. A first reason for this choice arises from the much larger value of ηε = 2.5, which implies&gt; 0.20. On the other hand, the poisoning by fission is much lower and grows linearly with combustion or burning, amounting to about ΔΓ = 0.03 after 100 GWat day / t. The effect of Xe¹³⁵, which depends on the flow, is absent and the variation of k, which depends on time, due to degradations of Pa²³³, is seven times less for a given combustion or burning regime. All these considerations suggest that k = 0.98 is very appropriate for a fast neutron environment. Furthermore, the captures by fission fragments are typically more than an order of magnitude smaller than in the case of thermal neutrons for the same combustion or burning. Many of the considerations given above for thermal neutrons are no longer relevant now. The value of k is of course extremely constant during the combustion or burning period, as exemplified in Fig. 7. In this particular case, the operation has been started with a concentration of U²³³ slightly less than the optimal reproduction balance and a perfect cancellation has been achieved between the slightly decreasing effect of fission catches and the rise due to the increase in U²³³reproduced.

In order to tune the power amplifier to the desired constant value of k, we must introduce an appropriate destination for excess neutrons, which are typically on the order of all neutrons produced. It is therefore necessary to determine what use is intended to be made of them, such as for example (1) reproducing new fuel, (2) incineration of unwanted waste or eventually (3) their absorption in "control rods". This choice would then define how the criticality parameter will be tuned to the desired value, dissipating excess criticality.

In the present application, we will assume that the extra criticality must essentially be deployed to reproduce additional fuel. The excess of neutrons is of the order of 10% of the total quantity or inventory, once the effects of higher actinides and captures by the moderator have been taken into account. These neutrons can conveniently be captured in a fertile zone of pure thorium, in the form of oxide ThO2 or of metallic thorium, arranged at the periphery of the nucleus. Contrary to the main nucleus, in which the Th²³² and the U²³³ have essentially the same macroscopic cross sections, all neutrons here contribute to the reproduction of U²³³. This will remain so, at least as long as the accumulation of U²³³ produces a concentration that is much less than the equilibrium concentration in the vicinity of 0.10. Therefore, it is expected to accumulate in the reproducer approximately 20% of the U²³³ which is reproduced by the nucleus.

The high energy beam

The success of the scheme is therefore based on the injection of a large number of neutrons from the outside. This is achieved with the help of a high-energy beam - typically protons - that initiates a neutron-rich nuclear cascade that is capable of producing neutrons at a small energy cost, especially a small ε._η Two alternatives are possible. In the first alternative the beam is fired directly into the moderator-fuel mixture. Alternatively, a dedicated target can be used to absorb the beam and produce the neutrons. Such a target must also be as transparent as possible to low-energy neutrons, so as not to affect neutron multiplication due to fissions.

A computer simulation with the Monte Carlo method has been performed on a practical geometry, using a specially written waterfall evolution program. They represent a very realistic simulation since the relevant cross sections are well known and entered into the calculations. Therefore, they are a valid guide to optimize the geometry of the device.

1. The fuel moderator as a high-energy target

The possibility of sending the beam over the same fuel-moderator mixture is considered first, since it has the obvious advantage of simplicity. The spallation process provides neutrons in greater multiplicity for heavy nuclei than for light nuclei which should be preferred to moderate neutrons. Furthermore, thorium has a large, high-energy cross-section for fission with a large multiplicity of neutrons. It is therefore evident that in order to have copious neutron production by the cascade, the fractional or fractional amount of moderation material must be as low as possible.

Typically, a 1.5 GeV proton striking a large thorium block will produce on average about 70 neutrons, corresponding to ε_η - 21 MeV. This efficiency is approximately linearly dependent on energy, leading to an almost constant value for ε_η. For example, at 800 MeV we find ε_η - 26 MeV. However, the same 1.5 GeV proton, impacting for example on water or graphite, will provide on average only 5.0 v 5.5 neutrons. The moderator-fuel medium composed of finely subdivided elements will provide an intermediate neutron regime, largely independent of the details of the lattice geometry. Indicating with Vm and Vf the relative fractions of volume occupied by the moderator and by the fuel, the approximate yields for the water-thorium mixture are given by the expression (valid in the interval V_m &lt;2 V_F): ε_η (MeV) _ 21.89 + 4.55 V_m/ V_F y ^ (MeV) - 26.82 + 5.29 V_m/ V_F for 1.5 GeV and 800 MeV, respectively. We observe that up to V_m &lt;V_F the value of ε_η it is not very different from the value of pure thorium. It is this happy circumstance that the present invention aims to exploit.

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Very similar results are found for ε_η with various low Z-thorium moderator mixtures, provided that for different materials, 1 and 2, the volumes Vm, 1 and Vm, 2 are compared as a function of equal geometric lengths of nuclear collision Lint: Vm, 1 = Vm, 2 (Lint, 2 / Lint, 1)³. In contrast, the moderation power, defined as the mean logarithmic loss of neutron energy - that is, the change in lethargy - per unit length, decreases very rapidly as A of the moderation nucleus increases much more rapidly than the length geometric of the nuclear collision, as illustrated in Table 3.

TABLE 3

Some Properties of Some Pure Moderators for Thermal Neutrons and High Energy Protons (HE)

<td>Moderator</td><td>Density g / cm²</td><td>HE nuclear interaction length, cm</td><td>Neutron moderation length, cm</td><td>Moderation power, cm^-1</td>

<td>Water</td><td> 1,0</td><td> 84,9</td><td> 5,74</td><td> 1,53</td>

<td>Heavy water</td><td> 1,1</td><td> 77,2</td><td> 10,93</td><td> 0,37</td>

<td>Beryllium</td><td> 1,85</td><td> 40,6</td><td> 10,0</td><td> 0,125</td>

<td>Graphite</td><td> 1,80</td><td> 47,9</td><td> 19,7</td><td> 0,064</td>

As a consequence, for most moderators such as for example graphite, the requirements of effective or efficient moderation and an efficient neutron cascade cannot be satisfied simultaneously for a common value of Vm / Vf. The important exception is water, since hydrogen is extremely efficient at moderating neutrons. However, in order to make it possible to use hydrogen as a moderating element, we must also ensure that the fraction of neutrons captured by the well-known radioactive capture process (n, γ) is small enough, taking into account the severe requirements taxes on the quantity or inventory of neutrons. We recall that a fully thermalizing water moderator equal to that used, for example, in normal PWRs, will easily capture as much as 1/5 of all neutrons, a loss that is clearly incompatible with the present scheme.

We have identified an alternative system in which the water maintains a small neutron capture rate while the other parameters, that is, ε_η and the equilibrium ratio of the fissile material in the reproduction equilibrium n3 / n1, both have acceptable values, as long as the neutron energy remains significantly higher than thermalization with the help of undermoderation. In practice this is obtained by choosing 0.2 V_F &lt;V_m &lt;V_F, as required by the high energy cascade. In other words, such undermoderation in a water lattice simultaneously fulfills both requirements of (1) - efficient neutron production by the high energy beam and of (2) - low neutron capture during moderation. Furthermore, the resulting spectrum of neutron energy with energies significantly higher than thermal has other useful characteristics: (1) the reactivity K. is increased by the presence of a significant contribution due to high energy fissions in Th²³³, OR²³⁴ and U²³⁶; and (2) the neutron losses in Pa are reduced²³³, Xe¹³⁵ and the fuel coating. Finally, the reproduction performance is not impaired: however there will be an increase in the corresponding fraction of neutron captures by thorium, due to the resonance region, which requires a corresponding and significantly higher concentration of U²³³, n3 / n1, in the reproduction balance.

The parameter dependence for an infinite lattice consisting of water and thorium is given in Figs. 8a-8d. The results are substantially independent of temperature (they have been calculated for pressurized water at 300 ° C) and of the shape of the fuel elements (spheres, rods of radius r) and of their characteristic dimension r. They are given for average performances in the range 4.0 mm &lt;r &lt;2.0 cm and remain within this range at ± 5%. Fig. 8a shows the concentration of U²³³ in the reproduction balance as a function of the Vm / Vf ratio. Fig. 8b shows the excess reactivity K. -1 again as a function of the Vm / Vf ratio. The contribution due to neutron absorptions by the moderator and all actinides at their expected or predicted equilibrium concentration are included. The individual or separate contribution of the different components in the reproductive equilibrium to the fission and capture regimes (n, γ) is shown in Fig. 8c and Fig. 8d, respectively. It is observed from Fig. 8d that the probability of radiation capture in the water moderator has become small or even negligible for Vm / Vf &lt;1. The typical conditions for Vm / Vf = 0.4 and Vm / Vf = 0 , 8 are listed in Table 4. As already indicated, the concentrations of U, Pa and Np used are always those corresponding to a very long exposure without isotopic separation, which corresponds to conditions of asymptotic equilibrium. Note however that the net effects on K. of the elements with A&gt; 234 are extraordinarily small, since the effects of the captures are almost completely compensated by the neutrons produced by the fissions. The net neutron balance per generation is, in fact, substantially equal to zero, 0.0323 x 2.49 - 0.0841 = -0.00353 for Vm / Vf = 0.8 and 0.0375 x 2.49 - 0.0900 = + 0.00259 for Vm / Vf = 0.4.

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The water must also be abundant enough to also perform the important function of extracting heat from the fuel-moderator block. The heat extraction is finally fixed by the well known "burning" or "combustion" condition that limits the energy that can be extracted from a given surface. In practice, operating or operating conditions must be kept many times below this limit. In a water-deficient arrangement, this problem can be solved with an appropriately large liquid contact surface, such as for example with cooling fins in the fuel liner.

The above figures are for an infinitely large device. Controlling neutron losses due to leakage is largely a matter of cost. In order to improve confinement, a reflector can be added, although this is not a necessity. As a general rule, in a power amplifier designed for optimized cost, these losses are likely to lead to a criticality factor k = (0.97 v 0.95) K .. Once the inevitable losses in the fuel coating, by xenon and other poisonous fragments, etc. are added, the final value of k is likely to be only slightly less than unity, so that the system is slightly subcritical.

TABLE 4

Typical parameters of an infinite geometry submoderated with water

<td>Fuel elements, shape</td><td colspan="2">sphere, cylinder</td><td>sphere, cylinder</td>

<td>Fuel elements, radio, r</td><td></td><td>4mm v 2cm</td><td>4mm v 2cm</td>

<td>Vm / Vf</td><td></td><td> 0,4</td><td> 0,8</td>

<td>Average density (g / cm³)</td><td></td><td> 8,67</td><td> 6,96</td>

<td>Equilibrium concentration of U²³³ (1.3x10 units^-2)</td><td></td><td> 1,725</td><td> 1,291</td>

<td>Longitudinal confinement of the cascade (95%) (1.5 GeV beam), m</td><td></td><td> 1,11</td><td> 1,34</td>

<td>Cascade radial confinement (95%), m</td><td></td><td> 0,505</td><td> 0,62</td>

<td>εη, MeV</td><td></td><td> 23,5</td><td> 25,2</td>

<td>K. - 1</td><td></td><td> 0,088</td><td> 0,060</td>

<td>Screenshots in the moderator:</td><td>-H2O</td><td> 0,00528</td><td> 0,0216</td>

<td>Captures in fuel:</td><td>-Th232</td><td> 0,405</td><td> 0,407</td>

<td></td><td>_-OR233</td><td> 0,0473</td><td> 0,0458</td>

<td></td><td>-Pa233</td><td> 0,0152</td><td> 0,0159</td>

<td></td><td>_-OR234</td><td> 0,0584</td><td> 0,0585</td>

<td></td><td>_-OR235</td><td> 0,00715</td><td> 0,00635</td>

<td></td><td>_-OR236</td><td> 0,0231</td><td> 0,0176</td>

<td></td><td>-Np²³⁷</td><td> 0,00134</td><td> 0,00163</td>

<td>Fissures in fuel:</td><td>-Th232</td><td> 0,0415</td><td> 0,0237</td>

<td></td><td>_-OR233</td><td> 0,351</td><td> 0,365</td>

<td></td><td>-Pa233</td><td> 0,00027</td><td> 0,00016</td>

<td></td><td>_-OR234</td><td> 0,0123</td><td> 0,00529</td>

<td></td><td>_-OR235</td><td> 0,0209</td><td> 0,0251</td>

<td></td><td>_-OR236</td><td> 0,00428</td><td> 0,00196</td>

<td></td><td>_-Np²³⁷</td><td> 0,00009</td><td> 0,00004</td>

The confinement of the cascade due to the proton beam must also be guaranteed. Fortunately, this generally leads to dimensions that are comparable to those required by the previously defined requirements for neutron confinement. Suppose the beam collides with an infinite fuel-moderator block. We define, somewhat arbitrarily, as "produced" neutrons all neutrons in the cascade induced by protons as soon as their energy falls below 1 MeV. They obviously act as the seed for a continuous cascade that is produced by the multiplication process already discussed.

The confinement of 95% of the "produced" neutrons is guaranteed longitudinally and radially at depths in meters that are parameterized as 0.863 + 0.577 Vm / Vf - 0.0366 (Vm / Vf)² and 0.431 + 0.223 Vm / Vf - 0.0188 (Vm / Vf)²respectively. The size of the precipitation is only slightly less than 800 MeV. Therefore, the entire waterfall can be conveniently confined or contained in a cubic enclosure of, say, at least one meter on each side.

A conceptual diagram of the target geometry is shown in Fig. 9. The moderator-fuel assembly is schematically indicated by 1. Some of the produced neutrons undergo redispersion and actually emerge in the rearward cone as seen from the point of beam impact on target. In order to minimize this effect, the beam must penetrate about 15-20 cm through a hole 2 adapted to the relatively small size of the beam.

ES 2 129 665 T5

The proton beam traveling through a tube 4 under vacuum has to penetrate the energy amplifier through a thick window 3. This is not a problem as long as the window is relatively close to the moderator-fuel block (~ 30- 40 cm, depending on its thickness), since the few interactions that occur in it continue to propagate their secondaries through the block and have a comparable neutron yield. However, some additional precautions must be employed in shielding against neutrons escaping from the power amplifier enclosure through the beam tube. This is done with the help of a long input collimator 5.

Finally, the interactions initiated by the high-energy proton beam cause the nuclei and atoms within the enclosure to decompose. Nuclear decay produces a series of nuclei, most of which are radioactive. The main effect of atomic decomposition is the hydrolysis of the water moderator. Both effects have been considered in detail and turn out to be produced at a very acceptable level.

two. A separate high energy target

In some cases, such as a bulkier and less efficient moderator (graphite), the neutrons must be supplied by a separate or spallation-independent target. The target preferably occupies the central part of the device to ensure the highest solid angle of use. The target material must be as permeable as possible to low-energy neutrons that can be redispersed from the moderator and the fuel. For this reason, we can base ourselves, in its design, on the experience obtained for neutron spallation sources.

Several possible geometries can be envisaged. The size of the target area (typically a cylinder with a radius of 30 cm and a length of 1 m) must be optimized to contain or confine the largest fraction of the high-energy cascade but to allow evaporation neutrons to emerge or escape. . The average energy of such neutrons is of the order of a few MeV. The simplest geometry is a homogeneous volume rich in heavy material, typically natural lead or bismuth or a (eutectic) mixture of both. The choice of the Pb-Bi mixture, instead of pure Pb or other materials such as tungsten or uranium, is justified by the main requirement - already mentioned - that the target must be as transparent as possible to low energy neutrons. Of course, in the inventory of practical nuclei with high Z only the Bi²⁰⁹, the Pb²⁰⁶ and the Pb²⁰⁸, exhibit or have a negligibly small capture cross section (&lt;0.03 barnium for a neutron energy of 0.025 eV) for thermal and epithermal neutrons. While natural bismuth is a pure isotope, lead is a mixture of many isotopes and its capture cross section is dominated by Pb²⁰⁸ (&lt;0.70 barniums for a neutron energy of 0.025 eV) which has an abundance of 22.6%. Optionally, isotopic separation could be used to remove this more dangerous isotope.

In the cascade development we can ideally distinguish two phases: a first phase in which the high-energy particle produces several secondaries and a neutron multiplication phase due to inelastic collisions of a high-Z medium. In more sophisticated designs, these two phases could be carried out with separately optimized materials. For the sake of simplicity we have taken a single uniform volume. We expect a neutron yield of about 42 neutrons per incident 1.5 GeV proton. Therefore, the energy required to produce each neutron is ε_η »35 MeV, significantly higher than the ε value_η »21 MeV in the case of thorium.

In practice, the target must be liquid, since both Pb and Bi have very low thermal conductivity and it is necessary to rely on convection to extract the heat produced by nuclear interactions. Fortunately, the melting point of Pb is 327 ° C and that of Bi 271 ° C. Pb and Bi can be mixed in a eutectic mixture that has an even lower melting point. From the point of view of neutron transparency, Bi is of course highly preferable. However, it also has some disadvantages. When solidifying, it expands by 3.3% of the volume and is highly corrosive. Neutron captures lead to Bi²¹⁰ (radius-E) and this is a ^ -emitter of a degradation half-life of 5 days in Po²¹⁰ that it is an α-emitter with a half-life of 134 days and that it is very toxic and difficult to contain or confine. However, these problems can be solved but require rigorous confinement of the molten metal. The best containment materials for liquid Bi or Pb are chromium steels. Mass transfers, which become significant at high temperatures, around 550 ° C, can be controlled by adding small amounts (a few hundred ppm) of zirconium and magnesium to the liquid metal.

We therefore see that both the target and the fuel will be contained or confined in sealed elements of similar design but with different content, for example rods or spheres or other suitable geometric shapes. The same refrigeration circuit can then be used to remove heat from both units. The simplest case is that of gas cooling (helium, CO2, etc.), since then the probability of interactions of the high-energy cascade in it, as well as the probability of neutron absorption, are negligible. The blank elements will then be periodically removed and reconditioned in the same way as fuel. The structure of the fuel element assembly must be able to withstand the volume changes of the target material upon melting.

A conceptual diagram of the target geometry is shown in Figs. 10a-c. For reasons of accuracy the alternative of gas cooling is shown. The density of helium, CO2, and other suitable high-temperature but compressed gaseous refrigerants is small enough to allow the proton beam to travel safely through them. Consequently, the beam window 11 into the throttle vacuum may

ES 2 129 665 T5 be conveniently installed outside the enclosure 10. The "cold" gaseous refrigerant circulates as indicated by the arrows in Fig. 10a: it is introduced into the enclosure 10 through an inlet 9 located in the upper part of the enclosure and then circulates down between the enclosure wall and a thermal shield 12 in the form of a skirt that surrounds the fertile core 13; At the bottom of the enclosure, the refrigerant gas is diverted upwards so that it travels through the fertile core 13 and the target area 14 before exiting through exit 15. In the illustrated embodiment, the inlet 9 and outlet 15 are coaxial and are separated from each other by a tube formed by an upper extension of the heat shield 12. The beam reaches the target area through a recessed area 16, filled by the refrigerant gas. Both the fertile core zone 13 and the spallation target zone 14 are made up of a suitable number of fuel elements, shown in Figs. 10b and 10c. We have chosen fuel granules in the examples: they are sealed by a suitable coating 19 (Zircalloy, steel or other suitable material with low neutron absorption and good mechanical properties). The refrigerant gas circulates through the interstices between the granules, which ensures a significant heat exchange surface.

(1) In zone 14 of the blank, there is no moderation medium and the liquefied metal 20, either Pb, or Bi, or the eutectic mixture of both, fills as much as possible the available space and leaves a small space 21 for solid-to-liquid expansion (Fig. 10c). Note that the 58% Bi-Pb eutectic mixture already melts at 125 ° C and does not show appreciable shrinkage on solidification.

(2) In the fuel-moderator zone 13, the spheres are constituted by a central fuel core 22, surrounded by a graphite moderator 23 (Fig. 10b).

Perforated panels (not illustrated) are used to contain the granules in the fertile core zone 13 and to separate the target zone 14 from the fertile core zone 13, while allowing gas circulation.

Careful work must be done on the geometry to make the coolant travel along (curved) paths that are not capable of allowing a significant fraction of the proton beam to miss its target. The proton beam travels through a tube 18 under vacuum to window 11. A thick collimator 17 is necessary to reduce the flux of neutrons escaping through the beam hole.

As in the case of the target fuel moderator, the structural material used to confine the liquid metal participates in the high energy cascade. Fortunately, however, the behavior of materials such as Zircalloy, steel, etc., with respect to high-energy protons is not as different as that of thorium, as is the case with the water moderator. For example, if the target is made of solid zirconia, we anticipate ε_η »70 MeV. Therefore, although a relatively large fraction of the weight of the target is structural material, only modest effects on ε are expected._η.

High-energy beam interactions will produce large numbers of different nuclei due to spallation and other inelastic nuclear collisions. Most of these products are radioactive and must be confined like fission products. Fortunately, the quantity of these products is relatively modest when compared to fission products. The presence of a relatively large and non-fissionable target in the center of the fuel moderator medium with its own accumulation of reaction products inevitably reduces the reactivity of the system. A first order estimate of the effect gives Δk = - (1.0 v 2.0) x10^-2. Although the container parameters depend on the application, a significant additional loss of reactivity must be taken into account.

In conclusion, an independent or separate target leads to a significant reduction in neutron yield (due to the poorer performances of Pb and Bi when compared to Th) and to a significant reduction in reactivity due to additional neutron captures in the non-fertile materials. However, this opens the way to the possibility of using various moderators, such as for example graphite, and therefore of operating the device at higher temperatures than is possible with water. Higher temperatures make it possible to increase the efficiency of the conversion into electricity and consequently to at least partially compensate for such drawbacks. In conclusion, the efficient use of the fuel-moderator material, as a direct high-energy target, implies that the neutrons remain under-moderate. These neutrons of substantially higher energies than thermal have the disadvantage of requiring a much higher concentration of fissile material at equilibrium. In the case of water, which has a very high moderating power, we indicate a compromise situation in which the concentration of fissile is only slightly higher than in the thermal case and the efficiency of the target is high. Of course, other schemes with less efficient means of moderation or no moderator are possible, but at the expense of a much larger quantity of fissile material.

In the alternative case that the target has a different topology from that of the fuel-moderator medium, the high neutron yield and neutron transparency must be guaranteed at all relevant energies, for the target, the corresponding cooling medium and the equipment. corresponding physical confinement. The gaseous refrigerant has the interesting characteristic that it is substantially transparent to neutrons. Of course other liquid media are possible. Since they do not have to moderate neutrons within the high energy target, the many refrigerants already used in fast neutron reactors can be identified, the choice largely depending, including of course, on the specific application.

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The high-energy particle accelerator

The purpose of the accelerator is to produce as efficiently as possible the largest possible number of secondary neutrons per collision between the beam and a solid target. As already indicated, there is great independence between the energy and the nature of the incoming beam. For example, using a deuteron beam instead of a proton beam will improve the neutron yield by about 10%. In the following, for the sake of simplicity, protons are chosen. The energy of the incoming protons is not critical and any value over a wide range, below several hundred MeV, gives comparable performance and a neutron yield proportional to the energy of the beam. The accelerator must also be energy efficient, that is to say that the beam must carry the largest possible fraction of the energy required to actuate or govern it.

The accelerated average current (“ave”) iave, once its kinetic energy T is set, is proportional to the power or energy Pbeam required by the beam (“beam”), which in turn is related to the power or energy P delivered by the power amplifier and the gain G:

ⁱbird

P (Mwatt) GT (GeV) mA beam ^P

G

For the typical parameters G = 40, T = 0.8 GeV and P = 250 MW, we find iave = 7.18 mA and Pbeam = 6.25 MW. Smaller devices will require correspondingly less accelerated current. Accelerators of characteristics close to those required here have been widely used for research purposes and, with the existing experience in this field, there is no reason to consider their construction or operation particularly delicate or complicated. Therefore it can be very brief. There are several possible technical choices in throttle design. Two possible schemes will be briefly outlined.

1.- The LINAC accelerator.

The accelerator chain is shown schematically in Fig. 11. It is composed of a proton source and a pre-injector 31, followed by a pre-accelerator 32 which could be for example an RFQ (Radio Frequency Quadrupole). The RFQ will bring the energy of the beam to about 2 MeV and will be followed by an intermediate acceleration structure 33 which could be for example a DTL (impulse tube linac) or another structure with similar performance. At the exit of the DTL the beam, which at this moment has about 25 MeV, is profiled by a collimator 34 (in order to minimize the losses of the beam at high energy) before entering the main acceleration section 35. Such a LINAC main section can be normal or superconducting:

1) In the case of non-superconducting acceleration cavities, the relevant figure refers to the energy dissipated in the cavity (in the absence of a beam). There is an advantage to pulsing the accelerator for periods longer than the cavity fill time (typically ~ 50 μδ) since at high currents the energy delivered to the beam greatly exceeds that dissipated in the acceleration cavities. For example, for a maximum peak current of 180 mA (which seems very acceptable, since there is no restriction on emittance), corresponding to a peak power or energy of 150 MW at 0.80 GeV, the energy dissipated in the copper of cavities is only about 50 MW. The average power or energy is of course less and is controlled by the throttle duty cycle. For example, if the indicated current of iave = 7.18 mA is required, the accelerator will be pulsed by means of modulators 37 at a rate of a few hundred pulses / s so that it will pulse 4.4% of the time. . The corresponding average dissipation in the cavities will be about 2.3 MW. The (average) energy gain is 1.5 MeV / m, which leads to a rather long structure. Optionally, since the magnetic stiffness of the beam is relatively modest, 180 ° bending elements could be inserted along the length of the structure to fold it into smaller longitudinal dimensions. RF sources 38 (clistrons) typically have an efficiency or efficiency of 70%. Several such units with appropriate cleavers feed the multitude of cavity units. An overall beam current efficiency of 50% is a reasonable figure.

2) Superconducting cavities for particle accelerators have been developed and could be used for the present application. The advantage of superconductivity is a higher (peak) gradient (&gt; 6.0 MeV / m, even higher gradients can be achieved with pulsed superconducting cavities; the final limit is probably in the vicinity of 20 v 30 MeV / m), This results in an accelerator of approximately 1/3 of the length and an overall better current-to-beam efficiency, which will be in the vicinity of 60%. However, the complexity of operating a superconducting device - at least in the current state of the art - is somewhat greater and it is quite possible that, in simpler cases, it may be excessively complicated. However, the benefits or advantages of superconductivity for this application should be emphasized and simplicity of operation can be achieved in the not too distant future with more R&amp;D work.

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In all versions with LINAC, transverse focusing must be guaranteed over the entire length of the throttle and this is easily done with the help of tetrapole doublets. Matching or matching of the beam to the target is accomplished by means of the final focusing tetrapole lenses and beam transport 36. Particular care must be taken in limiting beam losses that cause activation of the throttle structure. The accelerator complex could in principle feed more than one power amplifier. This can easily be done with pulsed electric or magnetic deflectors or deflectors in sync with the LINAC followed by classic septum magnets and beam transport elements that deliver separate and independent pulses in close succession to different targets.

2.- The isochronous cyclotron

Such circular machines are capable of accelerating smaller but quite significant currents typically up to about 10 mA. When compared to LINAC they have the advantages of smaller size and, for some configurations, lower cost. Particularly interesting is the possibility of an FFAG (fixed field alternation gradient) accelerator or a sector focus cyclotron, in applications where the beam power does not exceed several MW and for beam energies less than 1 GeV. The limitation of the main current in a circular machine is due to the effects of transverse space charges and occurs at low energies. This is the reason why it is proposed to use the circular machine only after the beam has been accelerated to a substantial energy (for example with a lower LINAC and up to a value in the range of 50 v 200 MeV, depending on the needs of the machine. final accelerated current), according to the diagram in Fig. 12. As in the case of a LINAC illustrated above, it is composed of a source and a proton pre-injector 41, followed by a pre-throttle 42 which could be for example an RFQ (radio frequency tetrapole). The RFQ will accelerate the beam to about 2 MeV and will be followed by the intermediate acceleration structure 43 which could be for example a DTL (Impulse Tube Linac) structure. At the exit of the DTL the beam is approximately 25 MeV and is profiled by means of a collimator 44 before entering a third acceleration section 45 which brings the energy of the beam to the value required by the injection of FFAG. The FFAG is composed of several sector magnet units 46 with a strong focus gradient arranged in a circular geometry. The beam circulates through a chamber 47 under vacuum in the air gaps of the magnets. The number of such sectors depends on the energy: for energies of 800 MeV about 8 v 10 sectors are typical. The space that remains available between these sectors can be conveniently used to insert RF acceleration cavities 48 and the injection and extraction channels 49. The cavities 48, as well as the other acceleration units 42, 43, 45, are activated by suitable RF sources 51. The particles are isochronous and RF works at a constant frequency, accelerating a continuous beam.

The extraction of the beam with respect to the FFAG is a delicate operation, since it has to be done with high performance or efficiency to avoid the activation of the accelerator components.

Throttle power consumption mainly refers to (large) magnets and RF. The efficiency or performance of the present RF is very comparable to that previously discussed in a LINAC. The power consumption of the magnet can be kept at a reasonable level (1v2 MW) by means of a conservative coil design. Alternatively, a "super-ferrous" magnet, in which the coil is made superconductive, offers the potential for significant energy savings.

In Figs. 11 and 12, the power supply of the particle accelerators is shown coming from the network. Of course, once equilibrium conditions are reached, it is more appropriate to use a part of the plant's energy production to drive or govern the throttle.

The initial fuel charge

In order to work with significant gain, the device must contain a reasonable amount of material that is fissile for thermal neutrons. The simplest solution consists of starting or starting with only thorium or a compound thereof as a combustible material and carrying out an initial phase of reproduction, in which the intensity of the beam is greater, until the equilibrium quantity of U is formed.²³³. Although conceptually simple, it is very difficult to do this in practice and the problem of how to "prime the pump" needs more attention, even if it must be done only once in the lifetime of each specific application. We can indicate the following alternatives:

1) U may occur²³³ by inserting, into the moderator, some additional thorium early in the fuel life of a similar but already operational device. The excess neutrons, intended to provide the possibility of capture by fission fragments later in the life of the fuel, can be dedicated to the reproduction of new fuel. Although such a possibility is not practical in a thermal environment, given that the neutron inventory is marginal, as already mentioned, in the case of fast neutrons there is a fairly significant possibility of additional reactivity and about 10% of all neutrons could used, for example, to reproduce some of U²³³ fresh or new from a fertile area of ​​Th²³²pure surrounding the central core. The fast nature of neutrons could be preserved, since the large equilibrium concentration = 0.1 of U²³² guarantees that for small concentrations of U²³²reproduced in a relatively large mass of initial thorium there is only little or no burning or combustion, but only reproduction. In this way, it should be possible to reproduce approximately 20% excess U²³² with respect to burning in the central core of high concentration. In practice, this

ES 2 129 665 T5 allows, for the parameter chosen later in this note, a doubling time of the available fuel of approximately every 8/10 years, without relying on “start-up” processes (see below) based on U²³² enriched or with excess PU²³⁹ and PU²⁴¹ from spent fuel or military applications. A doubling time of the installed power of the power amplifier of about 8/10 years seems perfectly a suitable growth regime, naturally after an initial number of installations with different fuels have been put into operation. Much higher yields can be achieved by sacrificing energy production, increasing beam power and correspondingly reducing gain with replay captures. It is important that the added material is used primarily for reproduction. Hence the fractional density of U²³³ it must be at all times well below the equilibrium level for fixed or stationary reproduction. This implies that chemical purification is required to produce new fuel rods for the new power plant or facility.

2) U could be used²³⁵ as initial fissile fuel instead of U²³³. Natural uranium has the considerable drawback that the unavoidable captures of U²³⁸ they lead to a significant accumulation of plutonium and lower actinides. Therefore it is preferable to use U²³⁵ highly enriched. This fuel can either be dissolved directly in the fuel or be contained in some auxiliary elements, which will be removed after start-up. The properties of U²³⁵ are very similar to those of the U²³³ and an initial weight load of about 90% of the equilibrium level will be sufficient to ensure a smooth transition between the start-up fuel and the self-sustaining cycle Th²³²-OR²³³. Note that this process should be followed only once in the history of each facility. Plutonium could also be used, but it involves the production of higher actinides and is not recommended, at least if the philosophy behind the present application is to be followed.

Once equilibrium conditions have been reached, combustion can begin. This phase can take a very long time (several years), the limit being the "poisoning" of the rods by fission products and the consumption of a major fraction of thorium-based fuel.

When the thorium charge has been used sufficiently and the fission fragment catches have reached the maximum acceptable level, a regeneration of the fuel is recommended. This must be done in a specialized center. Fuel is chemically separated. The uranium fuel is recovered while the other products (mostly fission fragments) are removed. Such fuel is then used to prepare new thorium rods, in order to skip the initial breeding phase for the next filling and limit actinide storage. Initial fuel replication should only occur once in the history of each power plant.

A power amplifier based on reproduction from natural uranium

A major advantage of the present invention is the ability to burn thorium under conditions that are substantially free of higher actinide residues and especially plutonium. However, natural or depleted uranium can also be used instead of thorium. Uranium has a similar replication reaction, in which U²³⁸ becomes Pu²³⁹ with Np²³⁹ as ^ -precursor:

OR²³⁸ + n U²³⁹ + γ Np²³⁹ + β&gt; Pu²³⁹ + β- (2)

Using the basic reproduction equations indicated above and the experimental data in Table 1, we find, for the mixture of U²³⁸ - Pu²³⁹ at reproductive equilibrium, the remarkably small number of n3 / n1 = 2.85x 10^-3. This means that under constant regime conditions, the reaction can be sustained indefinitely by Pu²³⁹ in equilibrium at the small concentration of 2.85 kg / ton of uranium. We note that this inventory or quantity is much less than the quantity of plutonium required in an ordinary fast breeder reactor and that no manipulation of the plutonium is required since it is reproduced "in situ" from U²³⁸.

When compared to a reactor, the present energy-amplified burn-reproduce process uses the dominant isotope U²³⁸ instead of the fissionable U²³⁵ naturally present or enriched, leading to much better utilization of the combustible material. Of course, the present constant rate of reproduction is impossible in a reactor, since it refers only to a subcritical condition or state governed by the beam. A fraction of the U²³⁵ naturally present can conveniently act as a "starter". It is quickly burned and replaced by a smaller amount of Pu²³⁹ highly fissionable.

As in the case of thorium, a large number of different nuclei can be produced by multiple neutron captures and eventually degradations. They are illustrated in Fig. 13. The total time dependence of an initially somewhat depleted uranium fuel is given in Fig. 14. A fraction of the U²³⁵ naturally present has been preserved since it can conveniently act as a natural "starter". It can be seen that when compared with the corresponding case of thorium (Fig. 3a) there is a much higher production of higher actinides, but that their concentration remains at a constant value due to the high “incineration” capacity of the scheme. From the concentrations, one can calculate α = 1.694, which is slightly higher than in the case of a mixture of Th²³²- OR²³³when we have α = 1,223. Therefore the value (averaged over the white) of η = ν / (1 + α) gives the number of secondary neutrons that result from an interaction of a neutron and is slightly smaller (for example 1.8 versus 1.13), which is detrimental but not unacceptable regarding the gain. They in turn have a larger cross section

ES 2 129 665 T5 capture and more significantly affect the quantity or inventory of neutrons. It should also be noted that the effects of fission fragments are now more important, since the "reproduction" cross section is less by a factor of about two. Therefore, the performance of uranium is slightly worse than that of thorium: a lower profit is expected and more frequent reprocessing is required in order to eliminate “poisoning” by fission fragments, but not more frequently than in an ordinary nuclear reactor. .

As in the case of thorium, if the neutron flux is abruptly cut off there is an increase in criticality, due to the fact that all the nuclei of Np²³⁹ will demote to Pu²³⁹, leading to an increase in the final population of Pu²³⁹. Such an increase in fissile material should not make the system critical. This condition, as already indicated, determines a limit for the flux of thermal neutrons of Φ &lt;9.84 x 10¹⁴ [T / (300 ° K)]^1/2cm^-2 s^-1 for the U²³⁸ - Pu²³⁹ (which is less demanding than the corresponding limit for Th²³² - OR²³³ which was Φ &lt;1.44 x 10¹⁴ [T / (300 ° K)]^1/2cm^-2 s^-1). For practical temperatures, the limit for the neutron flux will be Φ &lt;2 x 10¹⁵cm^-2s^-1. However, being the lifetime of the Np²³⁹ less than that of Pa²³³, the burn phase is obtained somewhat more quickly (days instead of weeks).

The target and fuel-moderator configurations described for thorium are also applicable to the case of (depleted) uranium. In particular, we have verified that both schemes of the fuel-moderator as a high energy target (moderation with sub-moderate water) and the configuration with an independent target can easily be extended to the present case.

An illustrative beam-driven, liquid-cooled power amplifier with no separate or independent target

This illustrative case exploits the characteristics of undermoderation with water already described above. The main parameters of the scheme are given in Table 4. The typical thermal power that can be produced more easily in this way is of the order of 200 MW. In order to ensure sufficient cooling of the fuel, especially for higher power, the choice V is more appropriate._m/ V_F ~ 0.8. Once neutron leaks and other losses in the fuel cladding, etc. are taken into account, the system will be subcritical with k = 0.92t0.95, corresponding to an energy gain G = 33 t 50. Therefore , a good design value is G = 40. The beam current at T = 800 MeV is then iave = 6.25 mA and Pbeam = 5.0 MW. Both a LINAC and an accelerator from FFAG can easily meet such requirements.

Extensive experience with pressurized water reactors (PWRs) can be used for heat removal. Of course, other alternatives can also be used, such as the boiling water mode, the choice being determined by the type of application.

The operating pressure of the device (PWR) is of the order of 154 bar corresponding to an inlet temperature of 291 ° C and an outlet temperature of 322 ° C. The refrigerant flow for the nominal power production of 200 MWt is 1.1 m³/ s. The required coolant transfer area within the fuel core is approximately 300 m². Such a surface is provided even without cooling fins by means of cylindrical fuel rods 2.5 (2.0) cm in diameter or smaller and a fuel mass of at least 21.4 (17.1) tons.

The general arrangement is shown in Fig. 15. It is composed of two separate main parts, the final beam transport and the main power amplifier assembly. The proton beam, which travels in a vacuum from the accelerator, is focused or concentrated by means of the magnetic tetrapole lenses 52, 53 and 54 and is deflected or deflected by 90 degrees with the help of the bending magnets 55 and 56 . It is introduced into the pressurized chamber 62 through a long inlet collimator 57, which has a pressure retention window 58 at its upper end. Various beam observing devices 60 are used to follow the path of the beam. A heavy 59 shielding floor ensures safety against radiation. Neutrons from the moderating fuel assembly can escape through the beam tube. This loss is considerably reduced by the collimator 57. The narrow neutron beam that recedes through the collimator is collected in a reserve 61 of the beam since, contrary to the proton beam, such a neutron beam remains undeviated by part of the magnet 56 of bent.

Energy is extracted with the help of the pressurized water contained in the main enclosure 62. The cooling fluid enters through an inlet nozzle 63 and exits through an outlet nozzle 64. It passes first between the interior walls of the main container 62 and the core support drum 65. Its flow is smoothed by the flow skirt 66 and enters the inner volume of the core support drum 65 in order to reach the fuel assembly 67 from below. It runs through the many channels of the fuel assembly, efficiently extracting the heat produced therein, and exits through an outlet port 64a arranged in the support drum 65 above the fuel assembly 67, communicating the outlet port with the outlet nozzle 64.

The upper part of the main enclosure houses a support structure 68, fuel handling equipment 69, and various control rods 70, primarily for use to securely secure, in the non-critical condition, the fuel after it has been cut. or turn off the beam. The need for such a device is mainly due to the fact that the U²³³ fissile accumulates after unemployment due to degradation of Pa²³³. During operation, these control rods can also be conveniently used to modify the neutron multiplication parameter k and therefore the gain of the power amplifier.

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Several different fuel assemblies can be used. Note that almost infinite variations are possible in the fuel-moderator configurations. Two such schemes, largely inspired by reactor designs, are indicated in the following:

1) A fuel assembly is schematically shown in Figs. 16a-b. The fuel is composed of metallic thorium fuel elements 74 stacked to form fuel rods 75 and lined with a thin sheet 73 of Zircalloy to prevent corrosion (Fig. 16a). Each rod has an end cap 71 with a spring 72 to retain or hold the fuel elements 74. The fuel rods are grouped into subsets 76 that constitute rigid units for easy handling (Fig. 16b). Note that the metallic fuel elements 74 could be replaced by granules of ThO2, ThC2, or other chemically stable thorium compounds.

2) We mentioned the advantageous possibility of ThO2-based fuel and spherical fuel pellets in a fluidized bed configuration. A fluidized bed is a bed in which a fluid circulates upward through a bed of solid particles which are then supported or fluidized but not carried or bound. The bed is in a state of turbulence and the solid particles are in constant motion, resulting in good mixing and excellent heat transfer characteristics. A typical design (Fig. 17) is constituted by an outer container 80 (for example to be placed inside the support drum 65 of Fig. 15), which houses a cylindrical container 81 having a bottom 82 of perforated plate strong enough to support the weight of the entire fuel load, and a flared top 83. The perforations must be such that they prevent the fuel from falling through, but they must allow the flow of the coolant without too great a pressure drop. The top 83 is flared to reduce the flow rate and prevent fuel elements from escaping from the top. The cooling fluid (water) enters the container 80 through a lower inlet 85 and exits through an upper outlet 86. The fuel elements are simple small spherical granules 84 that may be coated by a coating or, if ThO2 is used, they may not be lined. Abrasion problems can arise and should be addressed as they may affect the design of the primary cooling loop or circuit and require that the scorched radioactive fuel be recovered safely. The maximum compaction of the fuel in the collapsed or resting state corresponds to the random compaction of a very large number of spheres and has a porosity (free volume filled with water / total volume) at ~ 0.40, corresponding to V_m/ V_F ~ 0.666. However, the liquid flow will increase the porosity and therefore Vm / Vf. Control of reactivity k can be easily achieved without control rods, simply by varying the flow rate of coolant within the fluidization band and hence the fuel-moderator ratio Vm / Vf. This considerably simplifies the design of the pressure chamber. The simplicity of the fuel loading is also evident, since the continuous loading and unloading of the fuel is possible through small openings arranged in the wall of the container.

The use of the heat produced is, of course, dependent on the application. However, the heated and pressurized water from the enclosure must be retained in a closed circuit and extracted for later use by means of a normal heat exchanger. In the most obvious application of the device, one or more turbines have to be operated, as shown schematically in Fig. 18. The water that passes through the power amplifier 91 is pressurized by the device 92 and circulates with the help of the pump 93. A heat exchanger 94 is used to transform the water from another circuit or loop into steam that drives the turbine. or to the turbines 95. A condenser 96 and another pump 97 close the circuit.

Common practice indicates that such an arrangement, widely used in power generation plants, can lead to a conversion efficiency to electricity slightly greater than 30%. Thus about 60 MW of electricity can be produced with the exemplified parameters given above.

An illustrative beam-driven, gas-cooled power amplifier with a separate or independent target

This illustrative case exploits the characteristics of a separate high energy target, described above. Gas is preferred as a refrigerant since, as already noted, it is substantially transparent to both the incoming high-energy beam and neutrons. Following the usual practice of nuclear reactors and other similar applications, the best gas choices are helium or CO2 (pressurized) (or their mixture) due to their excellent thermodynamic properties and the absence of corrosive effects. As an example, we will focus on pressurized helium - due to its high heat transfer, low pressure drop, high sonic velocity, and neutrality to metals and graphite - but our considerations will apply to other gases as well. The moderation medium, taking into account its performance at high temperatures, has been chosen to be graphite. Of course, many different lattice geometries are possible: we will describe in detail the one based on spherical units, called "granules", each constituted by a central nucleus of combustible material (metallic thorium or a thorium compound) 22 of Fig. 10b surrounded by a graphite envelope 23. An optimization of the relevant parameters (reactivity, concentration of U²³³, etc.) carried out according to the general lines of the previous example of moderation with water indicates that Vm / Vf should be in the range of 10v20 for optimal performance, especially K. = 1.04 and n3 / n1 = 1.7 x 10^-2. The ratio of the diameters of the spheres of the external moderator and the fuel core is then (Vm / V_F + 1)^1/3 = 2.22 v 2.75. There is great freedom in choosing the outer diameters of the "granules", typically on the order of several centimeters. The porosity of the fuel-moderator volume is

ES 2 129 665 T5 that of a set of a very large number of spheres compacted randomly, to ~ 0.39. Of course, the empty spaces are traversed by the refrigerant gas and do not appreciably influence the neutrons.

The geometry of the fuel-moderator and the target closely follows that already described with reference to Figs. 10a-c. The white "granules" are spheres filled with Bi-Pb or pure Bi metallic, liquefied by the energy carried by the beam during operation. A specially recessed area allows the beam to penetrate deep into the interaction volume. Special grates or other form of mechanical separators ensure that granules of different kinds cannot mix. Appropriate mechanisms allow new granules to be introduced or removed from the volume. Several stop control rods must penetrate the set of granules and do so through several graphite tubes, which of course also participate in moderation.

The present "atomic heater" can be used for a number of practical applications where high temperatures are required, up to about 1000 ° C and sometimes higher. We are concentrating on a closed-loop, gaseous helium turbine-based scheme, largely inspired by closed-loop, fossil fuel-driven power production facilities. Following extensive experience in such devices, the typical thermal power that can be more easily produced in this way is up to the order of 200 MWt. A flow chart, as a general example giving the main design data of a direct helium cycle, is shown in Fig.

19. Of course, different ways of arranging the machines are possible. Helium compressed to about 58 ata (1 ata = 101.3 kPa) enters the energy amplifier 101 at a temperature of 435 ° C and exits at 710 ° C with an estimated pressure drop across the energy amplifier of ~ 2 ties. The gas flow is of the order of 200 kg / s. It delivers its energy through two cascading turbines 102 and 103. It is necessary to use heat resistant material only for the high temperature turbine 102. An expansion ratio in the turbine of 2.5 to 3 offers good design conditions and a small number of stages (2). At the outlet of the second turbine 103 the gas has a temperature of 470 ° C and a pressure of 26 ata and enters a recuperator 104 to further reduce its temperature to 150 ° C. With the help of a cooler 105, the temperature of the gas is lowered to 38 ° C (25 ata) and enters a two-stage compressor 106 and 107 with an additional cooler 108 between the two units. At the compressor outlet (120 ° C, 60 ata) the gas is preheated in the recuperator to 435 ° C (58 ata) and closes the circuit by entering the power amplifier 101.

Adequate control 109 is provided to ensure consistent performance over a wide power range. Fill supplies 110 and 111 are used to fill the gas leaks from external tank 112. The total efficiency at full load is of the order of 40%. Some 80 MW of electricity can thus be produced by means of the generator 113 governed by the turbines 102, 103, with the exemplified parameters given above.

An illustrative beam-driven, lead-cooled power amplifier working with fast neutrons

This illustrative case gives an example of the possibilities of the fast neutron environment. The extensive study of such a device carried out in the previous chapters shows that it has remarkable characteristics and that it can overcome several of the limitations of the previous examples. With reference to the previous example of the water-cooled power amplifier, which is largely based on the well-mastered technique of PWRs, a non-moderating refrigerant should be chosen. In view of the considerable safety concerns associated with liquid sodium, which is almost universally chosen in fast breeder reactors, we have opted for liquid lead, for which there is little experience so far, other than with a small reactor developed in the field. the former Soviet Union and the use in the USA of a fairly similar metal, bismuth, as a cooling agent.

Its boiling point is 1740 ° C, safely above any foreseeable operating temperature. Its melting point, 327 ° C for the pure metal, can be lowered to 125 ° C with an equal eutectic mixture of lead and bismuth. Its density is high (~ 10 g / cm³) and its fluidity and thermal capacity are quite good. At high temperature, it has some corrosive properties that can be resolved with appropriate additives. Its vapor pressure is also very low, reaching 1 mm Hg only at 973 ° C.

Another overwhelming reason to choose lead (or bismuth or a eutectic mixture of both) is the fact that these materials offer excellent neutron performance as high-energy targets and therefore the cooling material can also be the first target. for the high-energy proton beam.

A second important difference from the present illustrative example, when compared to the previous cases, is that the neutron flux and the corresponding radiation damage are now a hundred times greater. This is a well known problem in fast breeder reactors and has apparently been solved for at least flaring or combustion on the order of 100 GWat (t) day / ton.

The reasons for accepting these additional changes are in our view overwhelming considering the considerable performance improvement, especially (1) higher gain (G ~ 100v150), (2) higher maximum power or energy density (160 MWat (t) / ton (Th)) and (3) an extended combustion (&gt; 100 GWat (t) day / ton (Th)).

As already illustrated above, the higher gain is due both to a more efficient configuration of the high energy target and to a higher practical value of the neutron multiplication factor k. The higher energy density arises from the higher allowable neutron flux which, in turn, is related to the low neutron capture rate of Pa²³³ (which, as is well known, suppresses the formation of the U²³³ fissile) and

ES 2 129 665 T5 with much smaller variations in k after stopping due to degradations in Pa²³³ for a given burning or combustion regime. Finally, a longer integrated burnout is made possible due to the low rate of capture by fast neutron fission fragments and is limited by the mechanical survivability of the fuel elements.

In practice, a 20 MWat (20 mA at 1 GeV) proton beam accelerated by a cyclotron will be sufficient to drive a compact power amplifier at the ~ GWat level._and. Integrated fuel burn can extend beyond 100 GWat day / ton, being limited by the mechanical survivability of the fuel elements. Due to the high or higher operating temperature (&gt; 600 ° C) of the lead refrigerant, a thermodynamic efficiency of the order of 42% can be safely assumed. Therefore, the nominal thermal power is 2.4 GWat (t). The mass of fuel is of the order of 15 tons in the form of a ThO2-UO2 mixture that fills thin stainless steel bars or rods, in a configuration similar to those already described in Fig. 16a and Fig. 16b. The "seeds" of U²³³ (at the equilibrium concentration of 10% thorium) they then have a weight of 1.5 tons.

The fast neutron option has a higher neutron yield and lower poisoning-related losses due to fission fragments and higher uranium isotopes. Therefore, it can reproduce U²³³ fissile in excess of that which is normally regenerated through the main reproductive process that is creating new U²³³ exactly at the rate at which U burns²³³ in the fuel. In this way, it will be able to reproduce approximately 20% excess U²³³ with respect to burning in the central core, of high concentration. In practice, this allows a doubling time of the available fuel every 8/10 years or so, without relying on U-based “start-up” processes.²³⁵ enriched or in excess of Pu²³⁹ and Pu²⁴¹ from spent fuel or military applications. A doubling time of the installed power below ten years seems a very suitable growth regime, naturally after having started several initial installations with different fuels.

Neutron cross-sections (n, γ) for fast neutrons are much smaller for both fission fragments and several of the newly produced uranium, protactinium, and neptunium isotopes. Actinide concentrations are very different from thermal neutron concentrations and should be illustrated:

(1) Two new elements become important due to the improved channels (n, 2n), namely Pa²³¹ and U²³². The presence of a relatively large amount of U²³² (τ = 70 years), which is approximately 50 times more abundant for a comparable burn, can be seen as an advantage since it positively "denatures" the mined uranium, helping to combat military diversions of the material. The added toxicity, due to the presence of U²³², is not so large as to make the processing of spent fuel prohibitively expensive. The Pa²³¹ represents a long-lived source of additional radiotoxicity (τ = 3.3 10⁴ years) that must be mastered. It is possible to chemically separate the Pa²³¹ of spent fuel. Methods can be envisaged to transform it into U²³²by neutron capture and subsequent ^ -degradation.

(2) The production of higher mass actinides is strongly suppressed, especially from Np²³⁷ and PU²³⁸, at levels below 1 g / tonne after 100 GW (t) day / ton. The higher isotopes of plutonium, americium, curium, californium, etc., are well below these levels, with corresponding beneficial effects on the toxicity of the actinides produced. The almost total absence of higher actinides has a tremendous consequence in solving the problem of long-term storage of spent fuel, provided that two problems are mastered, namely that associated with the presence of U²³² and that of Pa²³¹.

A small percentage of all neutron absorptions will occur in the refrigerant; It is important to evaluate the effects of the daughter nuclei both in terms of neutron capture and in terms of radiotoxicity. It may be important to note that natural lead has already been used as a practical reactor coolant.

Natural lead is made up of several isotopes, Pb²⁰⁸ (52.4%), Pb²⁰⁶ (24.1%), Pb²⁰⁷ (22.1%) and Pb²⁰⁴ (1.4%). If the target is ideally constituted by Pb²⁰⁸ pure, a neutron capture will produce Pb²⁰⁹ that rapidly (t1 / 2 = 3.25 hours) degrades into stable Bi²⁰⁹ which will remain as a eutectic mixture with the target material. (N, 2n) type reactions occur at a level that is a low percentage of captures and create Pb²⁰⁷, also stable. Both daughter nuclei are stable elements and excellent target material. A naturally leaded target will produce an appreciable amount of Pb²⁰⁵ from captures of Pb²⁰⁴ and at a lower level from (n, 2n) of Pb²⁰⁶. This element has a long life (t1 / 2 = 1.52 10⁷ years) and degrades in Tl²⁰⁵ stable by electron capture and no γ-ray emission. The neutron capture properties of Pb²⁰⁵ are unknown and therefore it is impossible to estimate the possibility of other transformations. Finally, the Pb²⁰³ from (n, 2n) of Pb²⁰⁴ has a short life (t1 / 2 = 51.8 hours) and degrades into Tl²⁰³ stable by electron capture. Reactions of the type (n, p) transform the isotopes of Pb into the corresponding isotopes of thallium (Tl²⁰⁸, Tl²⁰⁷, Tl²⁰⁸ and Tl²⁰⁴) that are ^ -degraded all rapidly to give Pb nuclei again. We observe that, in general, there could be an important advantage in the use of Pb²⁰⁸ isotopically enriched metallic as a coolant.

The situation is more complex in the case of a bismuth target. Neutron captures lead to Bi²¹⁰short-lived that degrades (t1 / 2 = 5.0 days) in Po²¹⁰ which, in turn, degrades with t1 / 2 = 138 days to Pb²⁰⁶ stable. However, there is an isomeric state Bi²¹⁰ long-lived (t1 / 2 = 3 10⁶ years), also excited by neutron capture, which is degraded by α-degradation to Tl²⁰⁶ (RaE) short-lived, which in turn is ^ -degraded into

ES 2 129 665 T5

Pb²⁰⁶ stable. Reactions of the type (n, 2n) would produce the Bi²⁰⁸ long-lived (t_1/2 = 3,58 10⁵ years), ending in Pb²⁰⁸stable through internal conversion. Thus, a bismuth moderator can present significant radiotoxicity issues that must be further examined before such material is seriously considered as a target.

Additional fragments are produced by the spallation processes due to the high energy beam. The toxicity problem should also be investigated, although it is assumed that no major problems should arise. The effects due to neutron capture on such added impurities are generally considered to be small and will be neglected at this level.

The principle design of a lead-cooled, fast neutron power amplifier is shown in Fig. 20. The incident beam 115 of protons is directed by bending magnets 116 and collides, through a tube 125 of beam, over core 121. Molten lead includes a zone 123 that is brought to a high temperature by the released heat of reaction. After passing through a heat exchanger 120, the molten lead enters the low-temperature zone 122 and is recirculated by means of a pump 119 to re-enter the high-temperature zone through a feed-through screen 124. The installation is enclosed in a double-walled container 117 which is covered by a lid 118. Radioactive heat in the event of accidental failure of the main cooling system is extracted from the main core by convection currents 126 and released into the atmosphere through a convection system in contact with molten lead (not shown).

The core of the power amplifier, schematically illustrated in Fig. 21, having for example a cylindrical geometry, is subdivided into five separate zones. The innermost zone 127 is simply filled with molten lead and acts as a high-energy target for the incident beam. The next zone 128 is the main core, filled with the appropriate fuel rod / rod geometry, containing the fuel in oxide form clad by thin stainless steel walls. The geometry of these bars is similar to that already described in the case of the water-moderated power amplifier (Fig. 16a and Fig. 16b). There is considerable experience with fuel rods or rods intended for fast breeders. Most of such experience can be transferred directly to our application. The main parameters of a typical fast breeder fuel rod are shown in Table 5. Its design can be perfectly adapted to our application. The thermodynamics of fuel rods allow a burning or combustion rate that is about three times that of an example with thermal neutrons. The corresponding neutron flux is then approximately a factor of 100 greater, that is Φ = 10¹⁶ cm^-2 s^-1. At such a flow, the design of the normal rods would allow a burning or combustion of about 100 GW day / t.

After a buffer zone 129 only filled with molten lead, we have the spawning zone 130, made up of a rod / rod structure similar to that of the core except that (1) the rods / rods are filled with initially pure thorium and (2 ) there is little or no burning or combustion and therefore the cooling needs are much more modest. We anticipate that the amount of U²³³ produced in the breeder is approximately 20% of the amount burned in the nucleus.

TABLE 5

Main parameters of a typical fuel rod

<td>Material</td><td>UO2, PuO2, (ThO2)</td><td></td>

<td>Diameter of fuel granules</td><td> 6,0</td><td>mm</td>

<td>Coating thickness</td><td> 0,35</td><td>mm</td>

<td>Coating type</td><td>SS16Cr13Ni</td><td></td>

<td>Diffusion density</td><td>0.80 v 0.85</td><td></td>

<td>Linear power of the bars</td><td> 450</td><td>W / cm</td>

<td>Nominal fuel power (ThO2 + reproduction), ρ</td><td> 160</td><td>kW / kg</td>

<td>Gap between fuel pellets and liner</td><td> 80,0</td><td>μm</td>

<td>Average maximum temperature of coating hot spots</td><td> 700</td><td>° C</td>

<td>Burned</td><td> &gt;100</td><td>GW day / t</td>

<td>Duration of an element at 100 GW day / t</td><td>2 years</td><td>to 85% useful.</td>