Transmutations of nuclear waste in accelerator-driven subcritical systems

Applied Energy 75 (2003) 97–117 www.elsevier.com/locate/apenergy

Transmutations of nuclear waste in acceleratordriven subcritical systems Stefan Taczanowski* Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy al. Mickiewicza 30, Cracow 30 059, Poland Accepted 24 December 2002

Abstract The physical preconditionings of transmutations are analysed. It has been suggested that one of the most viable incineration concepts is a symbiotic nuclear-energy system, consisting of a transmuter and a number of co-operating light-water reactors (LWRs). Closing of the fuel cycle is not easily achievable, since the minor actinides (MAs), unavoidably then produced in significant quantities, show disadvantageous safety properties (positive void reactivity coefficients). Accelerator-driven subcritical systems (ADSSs), distinct by their remoteness from super prompt criticality, have been attracting more and more attention. The superiority of subcritical ones is shown by comparing their behaviours in the case of a rapid reactivity insertion that brings no risk, in contrast to the fast critical ones. Finally, research problems and difficulties are mentioned. Any form of closed fuel cycle cannot avoid dealing with large quantities of radioactive materials. Yet, a definitive elimination of actinides, with the use of the enormous released energy, is worth this price. Summarising, the concept of nuclear transmutations in accelerator-driven subcritical systems significantly heightens the safety of nuclear-power systems. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: Nuclear transmutations; Actinides; Radwaste; Accelerator-driven subcritical systems

* Corresponding author. Fax: +48-12-34-00-10. E-mail address: [email protected] (S. Taczanowski). 0306-2619/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0306-2619(03)00023-0

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1. Introduction 1.1. Global energy problems The constant growth in material consumption (with energy in first place) of humankind as a whole is an unquestionable fact. Also, the forecasted exhaustion of cheap organic fuels (oil and gas) one day, though it is difficult to predict. Yet some signs exist—a radical increase in the prices of energy carriers [1] could be seen already in 1999/2000. In regard to the growth of electricity demand, the demographic aspect enhances the gravity of the question. Since, at present, nearly one third of the world’s population lives outside electrified areas, within the next quarter of century the number of electricity consumers will double. Calmed by often spectacular energy savings in modern electronics (per device), one neglects its avalanche expansion in numbers (e.g. of the mobile phones). The estimated power capacity required to satisfy the demand of electricity alone in information processing in Western Europe already exceeds 40 GVA [2,3]. The related demand for power is surprisingly high mainly as a result of a very particular load of electronic equipment characterised by the 3rd and further uneven harmonics, generated in alternate-todirect current converters. Besides, many households in the world are going to be equipped with faxes, modems, PCs, mobile phones, heat pumps, (de)humidifiers, air conditioners, etc. In addition, one should expect the transfer of still larger quantities of information over larger distances as well as the emergence of the electric vehicle— see the regulations of California [4] imposing this deployment. Such additional demand can reach tens of TWhs in Europe in 20 years, while the night-load [5] levelising the daily power demand has advantages for utilities and distribution companies. Having all the above in mind, one can anticipate a global permanent increase in the electricity consumption. Such demand must not be met with organic fuels, that threaten with unforeseeable consequences of the further heightening of CO2 concentration in the atmosphere (Kyoto Protocol). The opinion that a deployment of renewables to meet this demand is very desirable does not give rise to any doubts. Unfortunately, the present quite important share (about 1/5) of hydroenergy in the world electricity production cannot be significantly increased. In turn, the possibilities of other renewables (e.g. solar and wind), because of their low power densities and practical/low availablility limitations are insufficient. Therefore, the only option which is simultaneously meaningful and has a potential to increase fast is nuclear energy. 1.2. Problems of nuclear energy Unfortunately, nuclear energy provokes considerable social objections originating from the subjective perception of potential risk associated with nuclear power. These are:
Contingency of uncontrolled supercriticality in extreme accidents.
Highly radioactive, long-lived nuclear waste.

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(1) An intuitive measure of safety is the distance of the system state from the super prompt criticality [6]. In this state, any control of the system is impossible because of the rapidity of the power increase that excludes any intervention. This remoteness of a critical system from the super prompt criticality is determined by nature’s bounty—the delayed neutrons, by their effective fraction
eff specific for each composition of nuclides in the given system. A safety margin larger than
eff is thinkable, but can occur solely in subcritical systems that can operate in a steady state provided an external neutron source is continuously filling the above margin i.e. the neutron deficit in each generation. (2) High radiotoxicity of nuclear spent fuel is the reason why finding a way for its neutralisation has become a necessary condition for the social acceptance of nuclear power. Meanwhile the problem is aggravating. At the world’s current levels of deployment of nuclear energy (ca. 350 GWel installed civilian capacity), the yearly global yield of spent fuel is about 10,000 metric tonnes, whereas the global inventory of civilian spent nuclear fuel (including the reprocessed fraction) amounts to over 200,000 t [7] that contain nearly 4000 tonnes of fissile nuclides. The amount of actinide waste of military origin (mainly either depleted or weakly burned-up uranium from dedicated reactors supplying weapons-grade Pu) may even triple this quantity [8]. The global problem of waste has not been resolved until now in an indisputable way. Spent nuclear fuel at present is stored either at the plant or in interim engineered installations. Up to now, a disposal in geological formations is assumed to be the main way of final solution of the problem. The properties of the repository (its construction and position) should guarantee the retention of radioactive substances during millions of years, which should be sufficient for natural decay even of the longest-lived radioisotopes of the waste. Just the time scale of the necessary efficient functioning of such disposal disqualifies engineered solutions giving rise to a need for disposal in geological formations. This not inexpensive concept assumes drilling of adequate caverns several hundred metres deep in seismically stable, impermeable geological structures, for the secular storage of specially designed containers with nuclear waste. Since this option does not signify a physical destruction of the fissile materials, a permanent safeguarding of the disposal in order to prevent its use (secret or open) as a plutonium mine must be foreseen. The danger posed by such an amount of high-level waste containing thousands of tonnes of fissile nuclides has been recognised. But to the author’s mind, the most important aspect is the enormous energy content of the actinides, (200 MeV/1 atom 2500 MWt yr/1 ton) which is equal to 81020 J in the world yearly as spent fuel, i.e. more than twice the total world’s annual energy consumption. Moreover, the energy contained in the global (civilian only) inventory (= to 21022 J) is equal to the consumption of energy (at the present rate) in all forms by the whole of humankind during 50 years. To bury such an enormous amount of energy would be really deplorable. One should consider it as a duty of present generations not only to protect future generations from the thinkable harmful influence of the waste being left to them, but still more to assure for them its future use as a precious energy source. When sharing this view, any irreversible disposal of actinides becomes deeply unjustified, while it is rational to work out a technology of safe utilisation of this waste.

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Therefore, a desirable way of solving this question is fuel recycling, first of all since the open uranium fuel cycle utilises a mere  1% of fission energy contained in the mined uranium. Only fissioning is the means of getting rid of radiotoxic actinides, since other nuclear reactions with exchange of only several nucleons leave the nucleus to remain an actinide one. In turn, a major part of the fission products are short-lived or stable. A partially closed fuel cycle has been realised on an industrial scale in France and the UK as the recovery of plutonium from the spent fuel for the mixed oxide (UO2+PuO2), i.e. Mixed Oxides (MOX) fuel. Social acceptance of nuclear energy can be facilitated by the possibility of definitive destruction of nuclear waste, thus adding an important social value to this research. The development of the concept of nuclear power including the idea of nuclear transmutations is a major step for this to occur.

2. Physical precondition The trajectories of generation and decays of actinides in the (only at present) U-Pu nuclear-fuel cycle are illustrated in the Fig. 1. This figure shows that the exploitation of a nuclear fuel is coupled with a variety of processes generating significant quantities of many nuclides. It is so, since many of them instead of fissioning are transmuted into heavier Minor Actinides (MAs) as a result of successive neutron captures. Quantitatively, this is described in Table 1 based upon Refs [9,10]. On the basis of Table 1, one can state that ca. 7% of the fissioned mass is transmuted into long-lived fission products (LLFP). The amounts of transplutonic MAs: (Am and Cm) in the MOX spent fuel are much higher than in the uranium one, while the fraction of uneven (i.e. fissile) Pu isotopes is lower. The content of Am and Cm still increases with further burn-up (approaching 10% of the fissioned Pu). Therefore, the full recycling of Pu in LWRs, i.e. in thermal spectra, unavoidably leads—in addition to the Pu degradation—to the transmutation of its significant

Fig. 1. Main trajectories of nuclear transformations in the U–Pu nuclear-fuel cycle [6].

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S. Taczanowski / Applied Energy 75 (2003) 97–117 Table 1 Average composition of spent nuclear fuel (main radionuclides/1GWel.year) Fission productsb

Actinides Nuclide

235

U U 238 U 237 Np 238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 241 Am 242m Am 243 Am 244 Cm 245 Cm 236

a

T1/2 (a)

7.0.108 2.3.107 4.5.109 2.1.106 88 2.4.104 6600 14 3.8.105 430 141 7370 18 8500

Mass (kg)

Nuclide

U(235U)

MOXa

280 120 2.8 104 15 6 (2%) 170 (57%) 70 (23%) 40 (13%) 15 (5%) 7 0.1 3 0.7 0.1

50 20 2.7 104 10 25 (3.5%) 350 (47.5%) 200 (27%) 80 (11%) 80 (11%) 30 0.2 25 15 3

85

Kr Sr 137 Cs 151 Sm 79 Se 93 Zr 99 Tc 107 Pd 126 Sn 129 I 135 Cs 90

T1/2 (year)

Mass (kg)

Isotope fraction (%)

10.8 29 30 93 6.5.104 1.5.106 2.1.105 6.5.106 1.0.105 1.6.107 2.106

0.4 14 32 0.3 0.2 23 25 7 1 6 10

10 20 100 16 31 75 14

Approximate values. U.

b 235

part into highly radiotoxic nuclides (Table 2) which makes it less convenient as a fuel (Table 3). The data in Table 2 indicate that in the case of MOX spent fuel actinides are the main source of radiotoxicity from the beginning, whereas for uranium fuel, they become so after the partial decay of 90Sr and 137Cs. One can see (Table 3) that the MAs are distinct by a minute fraction of the delayed neutrons. The next question is: what neutron spectrum is suitable for the Table 2 Committed effective doses (CED) of selected nuclides when ingested by adults [11] Actinide 235

U U 238 U 237 Np 238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 241 Am 242m Am 243 Am 244 Cm 245 Cm 236

CED (Sv kg1) 3.8 110 0.5 2.8.103 1.5.108 5.7.105 2.1.106 1.9.107 3.5.104 2.6.107 7.3.107 1.5.106 3.7.108 1.3.106

Fission product 85

Kr Sr 137 Cs 151 Sm 79 Se 93 Zr 99 Tc 107 Pd 129 I 135 Cs 90

CED (Sv kg1) – 1.4.108 4.3.107 9.2.105 102 90 4.102 0.7 7.102 95

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Table 3 Approximate values of the fission parameters: delayed neutron fraction b, number of neutrons per fission n and per absorption  of selected actinides /based ENDF/B-VI, JENDL-3/ Nuclide

232

Th U 235 U 238 U 237 Np 238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 241 Am 242m Am 243 Am 244 Cm 245 Cm 246 Cm 233

a


(%)

2.4a 0.4 0.7 1.7a 0.4a 0.14a 0.26 0.30a 0.55 0.65a 0.12a 0.18 0.23a 0.13 0.16 0.24a

 (thermal spectr.)

2.2a 2.5 2.42 2.6a 3.0a 3.1a 2.88 3.0a 2.9 3.0a 3.4a 3.3 3.5a 3.3 3.6 3.7a

 0.025 eV

Fasta

0 2.29 2.07 0 0 0 2.12 0 2.17 0 0.02 2.93 0 0 3.12 0

0.11 2.34 2.08 0.13 0.82 2.06 2.63 1.38 2.70 1.13 0.56 3.22 0.68 1.34 3.33 1.07

Fission neutron spectrum.

most efficient transmutation? First, we should look at  (Fig. 2) and the crosssections of the actinides (Figs. 3 and 4). Figs. 3 and 4 show: (1) the striking prevalence of capture over fission processes for the thermal spectrum; (2) the advantage of the fast spectrum is paid with minute values of cross-sections that in turn draws behind a need for higher nuclide inventories. On this basis, one can state that the present common preference of hard spectra is justified, though in some cases, e.g. for Pu incineration without fissile regeneration, a soft spectrum may prove more advantageous. Finally, it should be remembered that the rate of actinide transmutation, i.e. by fissioning, has a wellfixed intensity (per energy unit). Thus its rate per power unit is nearly constant and the yield is directly determined by the size, i.e. the power, of the device. As concerns transmutations of LLFP, the process though possible in principle (Fig. 5) is neither effective, nor advantageous as it worsens the neutron balance. Thus, the energy poor incineration of the relatively less toxic LLFP is not recommended. At this point, one should mention an alternative to the U-Pu fuel cycle, i.e. the Th-U cycle (Fig. 6). Fig. 6 suggests that the generation of Pu and first of all of transplutonics in the Th-U cycle is very minute. Another important question, that must be addressed here regards the problem of proliferation. Some actinide properties, which are significant in view of the possible use as nuclear explosives, are collected in Table 4. But first of all one must not forget that there is no way to incinerate spent nuclear fuel without its reprocessing. There is no possibility of destroying completely nuclear

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Fig. 2. Parameter (E) of some nuclides vs. energy and the neutron spectrum
(E) in a Pb-cooled system [6].

Fig. 3. Transmutation related neutron cross-sections of selected actinides.

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Fig. 4. Probability of fissioning of selected actinides after absorption of a (thermal or fast) neutron.

Fig. 5. Example of fission-product transmutations (129I).

Fig. 6. Main trajectories of nuclear transformations in the Th–U fuel cycle.

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S. Taczanowski / Applied Energy 75 (2003) 97–117 Table 4 Significant parameters of actinides (specific heating,  dose rate, spontaneous fission neutrons, etc.) Nuclide

Specific heating (W/kg)

 Dose rate Spontaneous fission mSv [m2/ (kg h)] Yield Dose rate [n/(kg s)] [mSv m2/ (kg h1)]

Pa 4.104 1.6.108 – U (.06%232U) 0.2 1.2.102 0.6 237 Np+233Pa – 6 0.2 238 Pu 6.102 12 3.6.106 239 Pu 2 3 20 240 Pu 7 2.5 1.6.106 241 Pu 30 – 3 242 Pu 0.1 – 2.3.106 241 Am 120 1.2.103 2.5.103 242m Am+242Cm 15+4.102 4.102+5.102 6.104+8.107 243 Am 8 80 8.102 242 Cm 1.1.105 1.5.105 2.2.1010 244 Cm 3.103 1 1.3.1010 245 Cm 6 40 1.2.105 246 Cm 10 20 1.108 233

–

233

a

– <0.1 – <0.1 – <0.1 – 0.8 – 2.2.102 1.3.102 – 1

Neutron yield from (,n) in H2O

Bare critical massa (kg)

Dose rate Yield [n/(kg s1)] [mSv m2/ (kg h1)] – 2.104 2.103 7.107 2.105 8.105 – 1.104 1.5.107 5.107 7.105 1.5.1010 4.108 8.105 1.5.106

– – 0.7 – – – – 0.1 0.5 – 1.5.102 4 – <0.1

k1 <0.5 1715.5 6062.7 109.7 1010.1 3637 1213 5585.3 7560 179.1 150209 350 2127 129.2 4041

Range.

waste. The realistic aim is to carry out the recycling in a way preventing a diversion of processed fissile materials. The ambivalence of the properties of 238Pu, Am and Cm is worthy of notice. Spontaneous fission neutron yield, heat release and gamma activity make MA a very troublesome material for nuclear explosives. Alpha heating, of many hundred watts, corresponding to critical masses, disintegrates the chemical explosive; spontaneous fission neutrons provoke a predetonation that significantly reduces the energy of the explosion and—more important—make even small amounts of MA easily detectable, whereas large ones are sometimes deadly (e.g. 233Pa, Cm)—if handled unprotected. In connection with the Th-U cycle, a diversion also faces difficulties. The tremendous heating of 233Pa (40W/g) hinders chemical separations of even small quantities of this isotope, thus imposing, say, yearlong cooling times. Meanwhile, a chain stemming from 232U and emitting very penetrating gamma radiation (208Tl, Eg=2.6 MeV) develops with the time constant 2.7 years (228Th). On the other hand, all these effects make MA inconvenient materials for the fuel too, requiring remote handling during all fabrication and transport. More important is to hinder the misuse of recycled Pu. A significant ‘‘contamination’’ of Pu can be done when associating Pu with 237Np. This mixture, subject to a neutron flux, results in a higher content of 238Pu in the final composition, due to the

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reaction (n,). The very high heat release of this isotope ( 0.6 kW/kg) makes Pu containing above 5–7% of 238Pu hardly suitable for military purposes [12]. Thus it seems that closing of the fuel cycle does not provide more proliferation problems as those in the acknowledged and used technology of the MOX fuel cycle. Finally, the decades long experience of many thousand tons of spent fuel reprocessed in the UK and France indicates that reliable Pu accountancy, safeguarding and diversion prevention are possible.

3. Proposed conceptual solutions In general, two primary objectives of transmutations can be considered: (1) Incineration of actinides and if possible, of other radwaste. (2) In addition to current exoergic actinide destruction, a supply of fuel for further (future) use. A number of options of power systems with transmutation unit have been proposed, principally due to different assumptions of primary objectives. One can aim either at a more farsighted objective of designing a self-sustaining nuclear power system, with a closed fuel cycle or confine oneself to the development of technology of incineration of nuclear waste (the global amount of which will continue to grow for a half century). The example (see Fig. 7) of a symbiotic system, LWRs—transmuter, illustrates an option recommended here while leaving open the alternatives of

Fig. 7. Symbiotic nuclear power system (U–Pu cycle) with accelerator-driven subcritical unit (LEU—low enriched uranium, SLFP—short lived fission products).

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material flows and their quantitative estimations. That choice has been made in the belief that assisting the present mature and economically competitive nuclear-power technology to close the fuel cycle has most chances of the being realised in the foreseeable future. Another reason results from the French studies indicating a successful admixing of sole 237Np to the regular LWR fuel [13]. Instead, already small fractions (2.5%) of Am and a mere 0.25% of Cm heighten the  and neutron background respectively by two orders of magnitude, thus making the increase of the fabrication costs—if for the whole power system—unacceptable. In a symbiotic system, two extreme variants can be noted: (1) Conservative—waste-incinerating system (e.g. stored Pu and MA) without regeneration of fissile nuclides; (2) Optimistic—self-sustaining nuclear power system (more precisely, assuming a replenishment of incinerated actinides in the system with natural or depleted uranium or thorium) and restrained to use only self-generated fissile materials (except of the initial inventory). Between these extremes, there are plenty of intermediate options. There are several concepts of devices for transmutations, mostly of a hard spectrum as, e.g. the pool-type reactors cooled with liquid Pb or Pb–Bi eutectics, descending from Russian submarine propulsion units [14]. The advantage of this solution is that it excludes a core melt. However, fast water-cooled systems, as based upon the most common technology, deserve mentioning [15]. Qualitatively, the principal material flow is as follows: the LWRs can be supplied with both types of fuel—the LEU or the MOX. In spent fuel recycling, U and Pu are separated first, then the MAs from the rest, i.e. from the fission products. In thermal spectra, Pu can be recycled at most twice because of the incineration of fissile isotopes 239Pu and 241Pu. Therefore, the Pu must be regularly ‘‘refreshed’’ in a harder spectrum, in the transmuting unit together with other MAs, namely Am and Cm. The regenerated Pu returns as a MOX fuel associated with Np to the LWRs. This optimistic picture is unfortunately darkened by the threat of positive void reactivity coefficients (due to a spectrum hardening as a result of moderator dilatation) [16]. (This is caused by the relation and shape of fission and capture cross-sections of MA that, with spectrum hardening, favour the former process). According to some authors [9], in thermal systems the fraction of recycled Pu in the inventory of actinides to be transmuted should not exceed 12%, whereas that of MAs is even 5%. Thus, for safety reasons, the asymptotic compositions of incinerated actinides should be well known and their reactivity coefficients reliably checked. This composition, however, depends on many factors (see Section 4 and the Appendix) that cannot be determined at present. Though a decisive choice among particular concepts would be premature, there are good grounds for doubts if the equilibrium actinide compositions can have safe reactivity coefficients at the neutron balance assuring criticality. Therefore, it may be expected that the whole transmutation process will not be licensed in critical reactors and one has to look for other

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solutions. In other words, the use of subcritical systems may prove indispensable. Hence arose the concept of using accelerator-driven systems (ADSS) for both the neutralisation of nuclear waste and power production.

4. Properties of subcritical systems The fundamental advantage of subcritical systems is their significantly higher level of safety of operation, due to a much larger distance of the system from the super prompt criticality, as shown in Fig. 8 [6]. This feature is an essential difference as compared with typical nuclear reactors, routinely operating in a critical state. It is so, since the negative reactivity of subcritical systems i.e. their, larger distance (by one order of magnitude) from the superprompt criticality practically excludes the latter. The advantage of the higher safety of subcritical systems over those critical ones is illustrated by a computer simulation (Fig. 9) of their behaviours [17] in the case of a fast reactivity ramp insertion. In computer simulations, usually a ramp insertion is assumed (expressed in dollars per second i.e. in
/s) during 10–20 ms [18]. It may correspond to an extreme event, e.g. to a rod ejection from the system, what in critical systems leads in a few milliseconds to superprompt criticality, in turn, drawing behind an increase in power by several orders of magnitude. This effect fructifies with the rapid adiabatic heating of

Fig. 8. Safety margins of critical and subcritical systems.

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Fig. 9. Power excursion in critical and subcritical systems following a reactivity ramp insertion (insertion time=15 ms; fast systems: subcritical, keff=0.975, shut-off time-constant=1 ms, critical,
=0.33%, d/ dt=200 $/s, Doppler reactivity coefficient=3106/K, neutron lifetime=5107 s; thermal critical system:
=0.5%, dr/dt=120 $/s, D.r.coef.=2105/K, n.l.time=104 s; [18,19,14]).

the fuel, i.e. with an increase in its temperature, that brings Doppler broadening of the resonance lines of the neutron with violent damping of the flux in the system. This negative feedback is, however, quickly (within milliseconds) overcompensated by the continued growth (until the completion of the rod ejection) in the neutron multiplication coefficient. Finally, the process is finished with a successive damping of power and its (momentary) stabilisation at a much higher level. With these rather drastic assumptions, the energy release in a fast system is enormous; damage of the fuel will occur as a result of the temperature increase by about 2000 K. In turn, thermal critical systems, where the Doppler reactivity coefficients are larger (due to the greater significance of the resonance regions for softer spectra), demonstrate a much milder power jump. Yet, since the neutron lifetimes are several hundred times longer and the enthalpy of the system larger, which significantly delays the action of negative feedback, the power growth continues long after the end of the reactivity insertion. Yet, finally, a much lower temperature increase (here ca. 400 K) is expected in thermal systems. One should also consider what happens in critical systems on a longer time-scale i.e. after the sequence pictured in the Fig. 9, when a mechanical intervention in the system occurs (i.e. after ca. 0.1s in fast systems [20], and several tenths of a second in thermal ones). First of all, the above-mentioned momentary power stabilisation is

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not seen, since the system remains supercritical, though not prompt. This signifies, that when lacking intervention, (e.g. no scram rods insertion), a further (albeit relatively slow) increase in power takes place with a subsequent rise in the temperature of the coolant/moderator. Therefore, independently of any deliberate actions in both LWRs and liquid-metal fast-breeder reactors (LMFBR), another negative feedback effect emerges. It follows the ‘‘dilution’’ of the coolant/moderator (resulting from dilatation) that attenuates the neutron slowing-down process in thermal systems and enhances the neutron leakage mainly from the fast ones. This mechanism finally makes both systems subcritical and thus automatically shuts them down. But, in subcritical systems, the same circumstances do not result in any hazard. Here, the power increase following the reactivity insertion amounts to a mere several dozen per cent, while the temperature rises only by a few degrees: the quick beam shut-off brings the power down to a fraction of the initial value within milliseconds (Fig. 9). The still-being-released delayed neutrons, enhanced by a factor proportional to (1keff)1, are the source of the remaining power. If necessary, a fast shutoff of this component is achieved when significantly reducing the above factor due to the insertion of absorption rods, which are otherwise indispensable for safety reasons and used for routine shut-downs of the system. Based on the above considerations, one can conclude that subcritical systems promise significantly safer utilisation of transplutonics as a fuel (in spite of their disadvantageous properties) and thus open the way to a practical closed fuel cycle. As could be concluded from all the above, though nuclear fusion could be the external neutron source for a subcritical system (e.g. [21]), a more promising source is the target bombarded by protons accelerated to an energy of ca. 1 GeV. The present rebirth of interest in the transmutations has been conditioned by the significant progress in accelerator technology permitting us to expect sufficient target currents and thus neutron yields in order to achieve reasonable reaction rates. The primary interaction of hadrons with the above mentioned energy and a heavy nucleus initiates an intranuclear cascade generating a number of high-energy particles, mainly nucleons (i.e. first of all neutrons) and less often pions or light nuclei— deuterons, alphas, tritons, etc. [22]. The remaining excited nucleus evaporates further neutrons (not contained in the Coulomb barrier), first in a pre-equilibrium and then in an equilibrium state. Even fissions of nuclei routinely considered as not fissible (e.g. of Pb, in view of its very high fission threshold) can occur. The energy of the original proton, and also of the secondary particles, is sufficient to produce similar processes in the other nuclei hit in the target, thus creating an internuclear cascade. The final number of generated neutrons (preceding the fission-chain reaction) per 1 GeV proton in the heavy metal (but not fissible) target, e.g. Pb, is about 30. The use of the accelerator should also facilitate and improve the safety of the system, by enabling us to achieve a very fast shut-off with the beam switch-off. This, obviously for safety reasons, does not signify a resignation of the scram rods. A question may appear, as to whether a direct transmutation with the accelerator beam can perform the task. We presume 1 GeV protons, 10 mA i.e.  6.1016 p/s !  2.1024 p/a )  0.8 kg/a (fissions/proton). Thus, the effect of the beam alone is

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insufficient and the use of not only secondary processes in the target (intra- and inter-nuclear cascades), but of a whole neutron multiplication chain is necessary, i.e. a subcritical system. Most designs of subcritical devices for transmutations use fast neutrons, e.g. those cooled with liquid Pb (Fig. 10 a) [23], though there are also proposals for thermal systems (using molten-salt fuel) [24]. Fast water-cooled systems (Fig. 10b) deserve mentioning too [25]. A pressurised or boiling calandria type system (e.g. CANDUlike but with a vertical axis, and no moderator between tubes) with a hard spectrum has several advantages: namely the easiness of refuelling and fuel shuffling—a key point when the objective is transmuting and uniform incineration is impossible; the mature water-based technology; well-mastered material problems; and there is no need for an expensive vessel. 4.1. Selected research problems Nuclear transmutations in accelerator-driven systems sometimes do not comply with present understanding. First of all, their multidisciplinary and applied character should be emphasized. Unfortunately, a comprehensive description of all these fields would exceed the scope of this study. Thus, not forgetting that the system properties are decided at lower energies (i.e. < 20 MeV), where over 99% of total energy and  99.9% of transmuting neutrons are released, one should recognise the priority of reactor physics. As regards safety, though a subcriticality of the system relaxes the respective requirements (namely, only slightly negative values of reactivity coefficients are desirable), a thorough check of them is necessary. It has to be done in a wide palette of material compositions and spectra. Another objective is not only to keep the

Fig. 10. Schemes of accelerator-driven subcritical assemblies for transmutations.

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neutron multiplication factor keff below a certain value recognised as a safe, but also to maintain a quasi-steady keff over the whole fuel campaign. Such a stabilisation of keff in subcritical systems would allow for keeping the energy gain of the system constant, that is desirable in order to have always the optimal load on the accelerator. In cases of a difficult neutron balance, instead of the use of burnable poisons the actinide inventory in the system should have the asymptotic composition. An example of such evaluations (see also the method described in the Appendix) is shown in Fig. 11. On the other hand, since fissile incineration and breeding are not uniform in space and time, an adequate shuffling of the fuel within the assembly may prove indispensable requiring, in turn, an elaboration of a respective shuffling procedure. The information about the composition of the recycled fuel is important also for radiochemists charged with the development of partitioning methods on an industrial scale, without which a closed fuel cycle would remain out of the question. The fair agreement of the results obtained here with those given in Refs. [23,24] is satisfying, when remembering that, in the present calculations, the unknown details could not be corroborated. Besides, the advantages of the Th-U cycle lying ca. 3 orders of magnitude lower in Pu content and with much less transplutonics are quantitatively shown. Any construction decision must be preceded by detailed studies. Moreover, the requirements regarding reliability and accuracy of information for a future industrial design worth hundreds of millions of dollars must exceed those in most other scientific research. In the field of neutronic problems, the validation of computation tools—codes and nuclear data by appropriate experiments is necessary, particularly for nuclide production and energy release, shielding (at high energies); neutronics of

Fig. 11. Examples of equilibrium actinide compositions.

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subcritical systems. A need for such validation is confirmed by the still insufficient accuracy ( 10%) of some neutronic calculations [26,27]. The hitherto noticeable lack of motivation for research upon subcritical systems can explain why all their properties are as yet not thoroughly known. For instance, weakly-coupled subcritical systems deserve more investigation [28–30]. Research should be based upon the expectation of achieving much higher system powers, without heightening keff, i.e. without affecting the safety of the system. A lowering in the current demanded for an unchanged power of the system, down to the level achievable with the use of a cyclotron, would be a true success. The use of a much more expensive linac could be avoided when replacing it with an isochronous cyclotron. (The maximum feasible cyclotron currents seem to be limited to values only slightly exceeding  10 mA, because of space-charge effects). A need for flexibility in fuel composition (there are options of homo-and-heterogeneous recycling) requires the necessity for separating all actinides (mutually) and from fission products. Meanwhile, the chemical affinity of lanthanides and MA makes these processes difficult with classical chemical methods. Thus, one needs to apply more sophisticated ways, e.g. pyrometallurgy and electrorefining. Yet, the assumption that separation processes can be carried out at exactly 100% efficiency is over-optimistic. Separation factors, though well exceeding 0.99 (even values as high as 0.9995 are quoted in the pertinent bibliography) still do not assure null concentrations in the depleted fractions. Thus one can expect the final reduction of actinide waste by more than two orders of magnitude, but not to zero. Specialists in accelerator technology still are facing the task of assuring a sufficient reliability of the device, high efficiency and adequate shaping of the beam of the required high power (> 10 MW). There has been developed a technology of generating 1 GeV proton beams of intensity up to 100 mA (as a military research spinoff), but there is no experience as yet regarding an uninterrupted operation of such a device: this is an indispensable ability for all elements of any power system. The existing research accelerators, though generally very reliable, lack current stability (frequent beam trips), i.e. a fault absolutely inadmissible for electricity production. Finally, not all the pertinent material science problems (e.g., corrosion) in the presence of additional (from high-energy hadrons) radiation have been resolved.

5. Conclusions It would be an illusion to expect that subcritical systems can be free from all the drawbacks of critical ones. Nevertheless, the problems sketched herewith can be overcome, and since they are not fundamental questions only technological ones, their solutions should come gradually with technological maturity. In the most important aspect—safety—the remoteness of subcritical systems from superprompt criticality is pointed out as the essential advantage of the subcritical systems over critical ones. A superiority of the former ones is shown by comparing their behaviour in the case of a rapid reactivity insertion, that entails no risk, in contrast to the fast critical ones.

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The symbiotic character of the proposed nuclear-energy system composed of an accelerator-driven subcritical assembly and existing LWRs, does not lead to a revolutionary turning point in the development of nuclear energy by pretending to be able to replace all the present power plants. The ADSS applied for transmutations of actinide waste thus associated with energy production, seem to be the most attractive emerging option for nuclear power. While incinerating the most toxic long-lived actinide waste, this concept can efficiently shorten the duration of the related hazard. The fissioning of materials that could not be licensed in critical systems (i.e. transplutonics) makes this operation safe in subcritical assemblies, thus promising to achieve a closed fuel cycle. Moreover, it must emphasized that radical abatement of actinides, i.e. of the main source of heat, thus leaving in the remaining waste practically only LLFP, facilitates and reduces the cost and scale of the waste disposal in geological repositories. The concept of accelerator-driven subcritical systems for transmutations should help in the deployment of nuclear energy, as being just a technology with less environmental impact and a positive social undertone.

Acknowledgements This study has been sponsored by the Polish State Committee for Scientific Research. The assistance of Mr. W. Pohorecki with the computations is gratefully appreciated.

Appendix Fast simple evaluation of actinide equilibrium compositions in transmutation systems A knowledge of the equilibrium state is important since the system unavoidably approaches it in the course of the transmutation process, and so prediction of the system properties (e.g. reactivity coefficients) are essential. The respective lengthy calculations following the fuel evolution during incineration, e.g. [25], can be radically shortened when a reasonable guess of the asymptotic composition is made, thus being a starting point for the transmutation evaluations. The walk in the phase space lies in adapting actinide concentrations that balance all the production and destruction processes of each actinide for each desired external supply or removal (Fig. 12) [31], while maintaining the criticality of the system. The savings in computation expense are due to: (1) the initial composition is much closer to the asymptotic one than e.g. the spent fuel to be incinerated; (2) the walk towards the equilibrium is short; and (3) it does not require time-evolution calculations. It should be noted that the balance of nuclear processes (reactions and decays) alone is not possible for all actinides without an external supply, since some of them, being raw materials for production of others, cannot be generated from the latter. Literally, the condition of uninterrupted flow of materials can be realized solely in

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molten-salt systems, where a constant reprocessing of fluid fuel is carried out, yet a channel-type system (e.g. like CANDU), where the refuelling is done on-line, the assumption of continuous material flow is acceptable. This approach is simplified, nevertheless its accuracy seems sufficient, as can be seen in Fig. 12, where the equilibrium actinide compositions in transmutation systems are compared [23,24]. A The balance j n0 ðA z /due to zero/ of the nuclide Z X in j-th iteration step towards the asymptotic composition is obtained: j

PðA Þ ¼ lðAþ4 Þ l j nðAþ4 Þ þ lðA Þ l
j nðA Þ Z Z1 Z1 Zþ2 Zþ2 h < F ðn; ÞðA1 Þ > j nðA1 Þ þ < F ðn;3nÞðAþ1 Þ > j nðAþ1 Þ Z Z Z Z þ ij þ < F ðn;3nÞðAþ2 Þ >j nðAþ2 Þ N Z

ð1Þ

Z

jDðA Þ ¼ lðA Þ j nðA Þ þ < Fð t  s ÞðA Þ > j nðA Þ j N  IðA Þ j nðA Þ Z Z Z Z Z Z Z

ð2Þ

j 0

ð3Þ

n ðA Þ ¼ j PðA Þ  j DðA Þ Z

Z

Z

The number of neutrons jN in the system, determined by the assumed energy release W and mean fission energy Qf, is (l designates walk over A and Z of all actinides):

A  =number Fig. 12. Model of the transmutation balance of the nuclide A Z X where: Z =nuclide index; nðA ZÞ of atoms of this A nuclide in the system;
=neutron flux; < >=integration over neutron energy system volume; <
r Z > =reaction rate/per atom/ of cross-section s; l=decay   A  constant; l,l
=branching ratios of the respective decays; t- s=transmutation cross-section; I A Z N Z =rate of supply or removal A  of the nuclide Z .

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jN ¼ W=

X l

< F fðA Þ Qf > j nðA Þ Z Z



ð4Þ

All components of expressions (1)–(4) are known either from nuclear data, or from transport calculations, whereas the amount of nuclide A Z X in the consecutive, j+1 step is: 2 3 j PðA Þ  j DðA Þ Z jþ1 Z 5 jnðA Þ nðA Þ ¼ 41 þ ð5Þ Z Z j j max PðA Þ ; DðA Þ Z Z where, e.g. c=0.2. The present approach, though simplified (e.g. confinement to the most important nuclides and reactions, no fission product evolutions; integral reaction rates instead of local ones) is a fast way of reliably estimating the actinide composition in the given circumstances.

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