2. BASIC POWER NUCLEAR REACTOR DESIGNS

The main types of nuclear power reactors are shown in Table III. They are categorized by the material used to moderate the neutrons generated in nuclear fission and the coolants used for the transport of heat.

Pressurized Water Reactor (PWR): Primary water pressurized to about 160 bar act as both the moderator and the coolant. The fuel is up to 5% enriched uranium dioxide in Zircaloy tubes. The primary water heats water in a secondary circuit to produce steam. The reactor is housed in a containment building. The thermal efficiency is about 32%.

Boiling water Reactor (BWR): It is essentially a PWR without the steam generator and the secondary circuit. Water at a pressure of about 70 bar is pumped through the core and, since it is at a lower pressure compared to the PWR, steam is generated in the primary circuit. About 10% of the water is converted to steam and goes to the steam turbine. After condensing it is pressurized and returned to the coolant. The power density of a BWR is about half that of a PWR with lower temperature and pressure, but the efficiency is similar.

CANadian DeUterium Reactor (CANDU): Heavy water is used as both the moderator and the coolant with natural uranium oxide in Zircaloy tubes as the fuel. The fuel tubes pass through a tank of heavy water. Heavy water is pumped through the fuel tubes at about 90 bar pressure and then to a steam generator as in a PWR. The power density is about 1/10th of that of a PWR.

High Temperature Gas-cooled Reactor (HTGR): These are graphite moderated, helium cooled reactors. The fuel is a coated particle to contain the fission products. Water has been used in the secondary circuit to generate steam. Recently a direct cycle (single loop) gas turbine concept has been developed.

Liquid Metal Fast Reactor (LMFR): Liquid metal transports heat very efficiently and only lightly moderates the neutrons from fission. LMFRs consequently need more fissile material to keep the chain reaction going. The core may also contain fertile material to produce new fuel. Since they can breed fuel, they are also known as breeder reactors. Sodium has been used as the most common form of liquid metal for these reactors. Enriched uranium and Plutonium dioxide and metals have been used as fuel. They operate at a much lower pressure compared to the common light water reactors.

Other Reactor Types: There are two reactor types developed and built only in the UK, Magnox and AGR, which are still operating. Magnox is a carbon-dioxide cooled (at about 20 bar pressure), graphite moderated reactor. It has natural uranium fuel in a Magnesium alloy cladding. Overall thermal efficiency is about 30%. The AGR, Advanced Gas Cooled Reactor, is a gas-cooled reactor with graphite moderation and carbon-dioxide as the coolant at a pressure of about 40 bar. The fuel is 3% enriched uranium-dioxide and clad in Stainless Steel. Its thermal efficiency is about 40%. It is a unique UK design. Similarly, the Graphite Moderated Boiling Water Reactor (RBMK) is an older Russian design and built only in the former Soviet Union. The RBMK core is an assembly of graphite blocks through which runs the pressure tubes containing the fuel. Water is pumped through these tubes where it boils to steam. The fuel is 2% enriched uranium dioxide in Zircaloy tubes.

An older concept that is receiving new attention is the Molten Salt Reactor (MSR), which can generate energy and at the same time considerably burn the long — lived radioactive wastes. It is a circulating, molten salt homogeneous reactor. The fuel is a mixture of fluorides of Li-7, Be, Th, and U-233, U-235 or Pu-239 fissile material. Graphite is used as moderator although some moderation is achieved by the Li, Be and F used in the fuel. Heat is transferred from the fuel leaving the core by an intermediate heat exchanger. Fuel processing is an integral part of the reactor operation. The fuel and the fuel composition can be changed without shutting down the reactor. One 8 MWt Molten Salt Reactor Experiment (MSRE) facility was operated for four years at Oak Ridge, USA, from 1965 — 69.

This work would not have been possible without the dedicated effort of many diploma and Ph. D. students, contributing in various ways. The financial support of the Deutsche Forschungsgemeinschaft and the BMBF is greatfully acknowledged.

(a) Continuous beta and gamma spectra

The detailed decay data required to construct a complex decay scheme that is correct, and the difficulties experienced in obtaining the discrete decay data of short-lived fission products represent considerable challenges when producing decay-data files for decay-heat summation calculations. However, the OSIRIS and ISOLDE facilities have been used in tandem to address the problem of recommending adequate decay data for such nuclides (Rudstam et al, 1990). Radionuclides of interest with high p— decay rates and sufficiently significant fission yields have been studied, focusing on nuclides with half-lives in the range from a fraction of a second to 1 hour.

The gamma-ray measurements were carried out by means of a low-resolution detection system (NaI(Tl)) and a high-resolution Ge(Li) detector. Mass-separated beams from OSIRIS impinged on an aluminised Mylar tape located directly in front of the NaI(Tl) spectrometer, which was well characterised up to an energy of 4.5 MeV (an extrapolation process was adopted for higher energies, although there is considerable doubt about the accuracy of this approach). These samples could also be monitored by the Ge(Li) detector. A large range of fission products was simultaneously released from the target-ion source, and the resulting mass-separated beam contained several isobars (also non-isobaric nuclides formed through the delayed-neutron emission from isobar components).

The cyclic procedure involved a background measurement, sample collection, waiting period, and sample measurement in a chosen manner that allowed a particular component to be favourably studied and quantified. This process was repeated several hundred times for each nuclide of interest in order to generate good statistics.

The number of decays of each fission-product nuclide was determined by means of the Ge(Li) detector, using the most prominent gamma rays. Pulse spectra measured by the NaI(Tl) detector can be defined by the following equation:

j I Dupi

i

where Nj is the number of counts in energy channel j for experiment k, Dki is the number of decays of component i during experiment k, and Pj is the pulse spectrum of component i. This equation is a linear combination of contributions from

components i for each channel j. Hence, with k equations, Pj can be solved exactly for k = i, and can be determined by the least squares method for k > i. Individual pulse spectra (Pj) can be converted to gamma-ray spectra from the response function of the spectrometer. Integration produces the mean gamma energy per decay, and the mean number of gamma rays per decay. The overall uncertainties are quantified in terms of three components: statistics (number of counts), uncertainties in the absolute branching ratios (sometimes large), and the absolute calibration of the two spectrometers.

Beta spectra were measured in a similar manner on the OSIRIS and ISOLDE facilities, using high-purity Ge and Si(Li) detectors. Both sets of spectra can be used to check the validity of the recommended decay schemes constructed from detailed gamma-ray measurements. Examples are given in Figs. 23 — 25 of a number of important fission-product nuclides that have complex decay schemes. Whenever possible, the gamma-ray data have been compared with equivalent decay data from the ENSDF files (see Section 5.5.1); the regular “shortfall” of the ENSDF solid line in many of the figures demonstrates the inadequacies in these discrete decay-data

files (particularly with respect to high-energy gamma rays). This observation underlines the assessment of Hardy et al (1977) concerning the incomplete nature of complex decay schemes derived from gamma-ray measurements (pandemonium). Rudstam et al (1990) and Johansson et al (1994) have generated an extremely important set of mean-energy data for fission-product nuclides that contribute ~70% of the beta decay heat for short irradiations, and between 60% and 25% for long irradiations followed by cooling times of 0 to 1000 sec. These radionuclides have a similar impact as major contributors to the gamma decay heat at short cooling times. Examples of the resulting data for a limited set of these nuclides are given in Table 10. The mean beta and gamma data for over 100 nuclides determined by this method have been incorporated into many of the decay-data files used for decay-heat calculations in order to address the problem of recommending suitable data for those nuclides with high-energy p — decay and incomplete decay schemes. Such gross adjustments to the mean energies may result in the creation of inconsistencies with the discrete spectral data.

The OSIRIS on-line mass separator has also been used to prepare sources of short­lived fission products for the measurement of their half-lives and delayed-neutron branching fractions by means of a neutron counter and beta detector (Rudstam et al, 1993). Over 60 radionuclides in the mass range 70 to 150 have been studied, and the branching fractions for a significant number of these nuclides were reported for the

first time. Improved half-lives were determined for many of these radionuclides, including 84Ge, 84As, 85As, 86As, 87As, 133Sn, 134Sn, 135Sb, 136Sb, 137Te, 138I, 147Ba, 148Cs,

District heating is residential and commercial building heating. District heating systems use hot water or steam in the temperature range of 70 — 150 C with steam — water and water-water heat exchangers as needed. Usually steam is extracted from low pressure turbines in the nuclear power plant to provide the base heating load and steam from the high pressure turbine is used for the peak heat demand. Development of a heat distribution system is required but, due to heat losses in the heat distribution system, the source must be nearby, usually within a few kilometres at most. The longest known delivery distance is 24 km in Slovakia. Also, the demand for heat fluctuates with the season, being very high in cold winters and low in summer, and the source must be able to accommodate this fluctuation.

District heating has been used in some countries for decades. District heating networks exist in Bulgaria, Czech Republic, Hungary, Slovakia, Belarus, Russia and Ukraine. Denmark, Finland, Sweden, and Switzerland also have developed heating networks. The power capacity of heat networks is estimated to be about 600 — 1200

MWt in large cities and 10 -50 MWt in small communities2. At present nuclear district heating appears to be most promising in countries which already have heat distribution networks.

The concern of leakage of radioactivity into the heating network has been taken care of by intermediate heat transfer loops operating at higher pressures than the steam loop from the turbines, and by constant monitoring. The safe and reliable operation of several district heating networks (e. g., in Bulgaria, Hungary, Slovakia, Russia, Ukraine and Switzerland) has proved their effectiveness.

Table VI from IAEA Tecdoc 1056 (1998), as improved in ref 2, shows the world experience of nuclear reactors in commercial district heating. Out of these 46 reactors, only two in China and Russia were used for the sole purpose of district heating. Over twenty plants in Russia and the Bruce CANDU plants in Canada were used for electricity generation and to provide heat for both process heat and district heating. Steam from Bruce A plant was used for the heavy water production plant and for the nearby agricultural and industrial complex. One also notes that of the many existing and proposed designs of nuclear power systems for district heating, the majority are based on the use of water reactor technology.

TABLE VI. OPERATING NUCLEAR REACTORS WITH HEAT APPLICATIONS* [6] [7] [8]

The market potential for district heating has been estimated2 to be between 340GWt and 7600GWt. Table VI shows that nuclear power provides only about 4.4 GWt. Since there are various sources for heat such as oil, coal and natural gas, unless nuclear power is economical in the open market, it cannot make a big dent in commercialising nuclear district heating. The scaling effect is also important for nuclear district heating as it is more expensive at lower power. At 500 MWt and above the nuclear option shows good chances to be competitive even at higher discount rates2. Perhaps as nuclear power receives more acceptance from the public and nuclear electricity becomes competitive with other sources of electricity, nuclear district heating will also become more common.

The RIPL-2 library is close to completion, with public release expected in July 2002. Users of reaction codes will benefit considerably from the gener­ation of a complete and consistent set of starting parameters to give sensible results for cross sections and spectra. However, RIPL-2 should be further ex­tended and continuously updated in order to retain the relevance and value of the library to the users. At the recent co-ordination meeting in Vienna, December 2001, the CRP participants discussed possible improvements of the current project and formulated recommendations for further activities. These finding are summarized below:

• RIPL-2 provides valid sets of parameters for spherical and near-spherical nuclei. On the other hand, data for the deformed nuclei are scarce and less accurate. In particular there is a need for more Coupled-Channels potentials and 7-ray strength functions for the deformed nuclei.

• Special techniques should be applied for the determination of parame­ters for nuclei far from the stability line for which there are usually no experimental data available. These nuclei are important for ADS and astrophysics.

• New experimental data from the recently initiated projects (HINDAS and N-TOF at CERN) should become available within a year or two, offering possibilities for testing RIPL-2 parameters. The same is true for the SNS facility at Oak Ridge at a somewhat longer time scale.

• RIPL-2 library should be complemented with a set of routines for the calculation of certain input parameters (such as level densities, binding energies, 7-strength functions, etc.) in order to facilitate user access to the database and to avoid misuse of the parameters.

• More attention should be dedicated to the use of microscopic models for producing parameters. Parameters related to the fission channel contained in RIPL-2 need more accurate analysis and improvement.

• The problem of collective enhancement of level densities should be addressed in more detail in order to provide a reliable prescription for calculating level densities in deformed nuclei. The latter are often needed for ADS and new reactor concepts. [3]

• Use of the results obtained in heavy ion induced reactions could be helpful in determining model parameters, especially for nuclei far from the stability line.

• Medical applications require charged particle reactions, which could be better represented in the parameter library.

3 Participants

The following scientists contributed to the RIPL-2 library: T. Belgya (IIS — CCR, Budapest, Hungary), O. Bersillon (Bruyres-le-Chtel, France), R. Capote (NCEADNC, Havana, Cuba), T. Fukahori (JAERI, Tokai-mura, Japan),

S. Goriely (Univ. of Brussels, Belgium), M. Herman (IAEA, Vienna, Aus­tria), A. V. Ignatyuk (IPPE, Obninsk, Russia), S. Kailas (Bhabha, Trombay — Mumbai, India), A. Koning (Petten, Holland), P. Oblozinsk (BNL, Brookhaven, USA), V. Plujko (Univ. of Kiev, Ukraine), P. G. Young (LANL, Los Alamos, USA), Ge Zhigang (CNDC, Beijing, China).

References

[1] J. J. M. Verbaarschot, H. A. Weidenmueller, and M. R. Zirnbauer, Phys. Rep. 129, 367 (1985).

[2] H. Feshbach, A. Kerman, and S. Koonin, Ann. Phys. 125, 429 (1980).

[3] T. Tamura, T. Udagawa, and H. Lenske, Phys. Rev. C26, 379 (1982).

[4] H. Nishioka, J. J. M. Verbaarschot, H. A. Weidenmiiller, and S. Yoshida, Ann. Phys. 172, 67 (1986).

[5] Handbook for calculations of nuclear reaction data: reference input pa­rameter library (International Atomic Energy Agency, Vienna, Austria, 1998, http://www-nds. iaea. or. at/ripl), No. IAEA-TECDOC-1034.

[6] P. Moller, J. R. Nix, W. D. Myers, and W. J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995).

[7] G. Audi and A. H. Wapstra, Nucl. Phys. A595, 409 (1995).

[8] J. Duflo and A. Zuker, Phys. Rev. C52, 23 (1995).

[9] S. Sukhoruchkin, Z. N. Soroko, and V. V. Deriglazov, in Low Energy Neutrons Physics, Tables of Neutron Resonance Parameters, edited by

H. Schopper (Springer-Verlag, Darmstadt, 2000), Vol. 16B.

[10] A. Koning and J. Delaroche, to be published (2002).

[11] S. Goriely, F. Tondeur, and J. Pearson, At. Data Nucl. Data Tables 77, 311 (2001).

[12] M. Avrigeanu and V. Avrigeanu, Comput. Phys. Commun. 112, 191 (1998).

[13] S. S. Dietrich and B. L. Berman, At. Data and Nucl. Data Tables 38, 199 (1988).

[14] Liu Jianfeng and Su Zongdi, Chinese J. Nucl. Phys. 17, 336 (1995).

[15] P. Van Isacker et al., Phys. Rev. C45, R13 (1992).

[16] S. Goriely, Phys. Lett. B436, 10 (1998).

[17] F.-K. Thielemann and M. Arnould, in Conf. on Nuclear Data for Sci­ence and Technology, Antwerp, 6-10 September, 1982, edited by K. Bockhoff (Reidel, Dordrecht, The Netherlands, 1983), p. 762.

[18] S. Goriely and E. Khan, Nucl. Phys. A submitted for publication (2002).

[19] E. Khan et al., Nucl. Phys. A694, 103 (2001).

[20] G. Smirenkin, Report INDC(CCP)-359, IAEA, Vienna (unpublished).

[21] A. J. Sierk, BARMOM, no.967 ed., National Energy Software Center (Argonne National Laboratory, IL60439).

[22] A. Mamdouh, J. Pearson, M. Rayet, and F. Tondeur, Nucl. Phys. A679, 337 (2001).

The International Nuclear Information System (INIS) is a co-operative, decentralised information system which contains bibliographical information on the peaceful uses of nuclear science and technology, as well as on economic, environmental and health aspects of nuclear and other energy sources. An entry into the INIS data base consists of several pieces of information: title of publication, author(s) and reference citation, an abstract, if available, and sets of descriptors, plus some information on the origin and availability of the published information. Searches of the data base can be made either by bibliographic information (author, reference) or by keywords (to be found in title, abstract or descriptors). The information is provided by INIS Liaison Officers in several international organisations as well as to the IAEA Member States, who also have the right to disseminate that information within their restricted areas (as laid down in agreements).

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The dismantling of a nuclear installation requires the cutting and segmenting of equipment and structures with varying sizes, dimensions, and materials. To assume a final decision it is necessary to take into account the acceptance specification of the national disposal site, where these wastes will be sent. In the USA, for example, some plants have disposed the entire reactor vessel, without any fine cutting. In other countries the vessel shall be segmented, generally with remote control techniques under water.

The conditions under which the cutting operations are carried out depend on the location and space of the working area, on the qualification and experiences of the personnel, on the available tools and technologies as well as on the environmental conditions under which the operations will be performed: under water, in the air, under radioactive radiation, under contaminated atmosphere, etc.

There is a great diversity in existing cutting tools, which are useful and available under industrial conditions or in the R&D phase, each tool having its own performances, conditions and field of application.

The following techniques are presently available:

• thermal cutting

• hydraulic cutting

• laser cutting

• mechanical dismantling

• microwave spalling

• explosive cutting

When choosing cutting techniques the following factors should be taken into account:

• the technique (tool) should be used in practice, so that experience exists and a safety in furnish, spare parts and handling is available

• the technique (tool) should only generate a minimum of secondary waste, e. g. dust, particles, smokes, aerosols with controlled dispersion, liquid effluents

• low risk of contamination for personnel on site

• the technique (tool) has to be compatible to the working-environment.

In thermal cutting techniques, the solid material is melted and then blown away. Since molten states of material are present, the net amount of force needed is much smaller than for the techniques which use strain energy. Hence the contribution of mechanical force is only a minor part of thermal cutting processes.

It is possible to subdivide the thermal cutting techniques, according to the type of heat source, in:

• gas processes

• arc processes

• plasma arc processes

• a composition of the above processes

The energy density of the heat source increases from the gas flame over the arc and the plasma arc to the laser beam.

The abrasive water jet cutting technique is based on the application of plain water jets. Abrasive particles are accelerated by a high speed water jet and cause the removal of the material. Instead of an erosion process as in case of plain water jets, abrasive water jets cut by micro-chipping the material by the sharp-edged particles. When using the correct abrasive material, which has to be harder than the work piece material, any material can be cut — metals as well as ceramics, glass and concrete. With abrasive water jets, severance cutting as well as gouging, is possible. To generate abrasive water jets two different methods are currently available. The abrasive can be added to a plain water jet in a special mixing head (injection jet), or a premixed and pressurised abrasive water suspension can be released to the nozzle to form the abrasive jet (suspension jet). Sharp-edged mineral particles such as silicon sand, corundum or garnet sand are used as abrasives. The increasing number of cutting applications has helped the abrasive water suspension jet (AWSJ) to become more important despite the high consumption of water and abrasives.

The last groups of techniques are the mechanical cutting techniques. A limited list of such techniques is reported below as an example of the available alternatives to be optimized on a case by case basis:

• Grinder

• Hacksaw and Guillotine Saw

• Shears

• Milling Cutters and Orbital Cutters

• Knurl Tube Cutter (rotary disk knife or cutting wheel or plumber’s pipe cutter)

• Diamond Saws and Cables

Electromagnetic transitions are a reliable tool to study the structure of nu­clear systems, because of the weakness of the electromagnetic interaction compared to the strong one. Such transitions, however, cannot be calcu­lated by the techniques developed so far, because the transition operators contain besides spin operators and operators treated in chapter 3.1 also a plane wave in one of the particle coordinates measured from the center-of — mass, for details see [25].

A possibility is to expand the plane wave in a power series, keeping only the lowest orders, which is the so-called long wavelength limit, and then pro­ceed along the lines of chapter 3.1, as given in [26]. This procedure allows to describe radiative capture reactions quite well, see e. g. [27], however, in (e, Є)- or (e, Є ^-reactions the momentum transfer is usually much too large for this approximation to be a reasonable one. Therefore, we are not allowed
to make the long wavelength approximation, when describing electron scat­tering experiments. In order to illustrate the essential points, we follow [28] and strip the various electromagnetic transition operators, see [25], of all its parts, which can be treated by the methods described so far and consider in the following only the essential spatial part in a multipole expansion

Wj (LM )= jb(kr’j )Ylm (rj) (3.27)

where jb(kr) is a spherical Bessel function [15] and rj denotes the coordinate of the particle j with respect to the center-of-mass. Expanding the plane wave into spherical harmonics [20] we convert the operator Wj (LM) into

Wj(LM) = —^ f УсМ(к)еік’г^к (3.28)

It is now straightforward to define matrix elements analogous to eq. (3.4)

J ds1 …dsN-1 exp(— £ q,, (p К ■ v)

z

Yim (Qn)

n=1

with Qo = r’p(j) being the coordinate of the interacting particle, after the permutation P has been applied. The generating integral eq. (3.8) is easily generalized to

I(a1b1 . ..azbz) =

z

Q**’s*’s*’ + anbn ■ Qn + *kQo

**’ n=1

yielding by expansion again the expression (3.9). Now the generating integral I can be calculated directly and comparing like terms we find the desired integrals Г. Following along the lines of eqs. (3.10 — 3.12) we find

with the relation

Qo = ^ Wot . (3.32)

A

The integral is solved in the usual way by completing squares. Since the function e-z is holomorphic the path of integration can be chosen arbitrarily, yielding

(3.33)

Expanding the square in the exponent, we find a result analogous to eq. (3.13)

П exp((Trara/araara/6ra6ra/)exp(-^araara/6^)exp(-^araara/6^,) • (3.34)

with the abbreviation

All the exponents in eq. (3.34) are again expanded in a power series. For the terms (br • k)dr eq. (3.5) is used, yielding

final result.

Z z ngnnf ++lnn/ +knn’ L, i dr

E П П,№ ,! <-i)’w+w ■ id — ЬС^,У^Лк)

(3.37)

The summations run over all possible combinations of gnn’, hnn> ,knn’ ,dr, and er with the former being non-negative integers fulfilling now the relations

In’ dnf + ^ ^ (gnnf + hnnf + knn’ + gn’n + hn’n + kn’n) (3.38a)

n

ffln’ = en’ + ^(hnn’ hn’ n + kn’n knn’) (3.38b)

n

-dr < er < dr (3.38c)

Introducing Ln = ln — dn and Mn = mn — en reduces eqs. (3.38) to eqs. (3.16) and hence can be solved as before. What remains to be done is to determine all combinations (dn, en) for given (ln, nn). Since g, h and k are non-negative, dn is restricted to

0 < dn < ln n = 1,…,z (3.39)

and an obvious solution of eqs. (3.38) is

Summing eqs. (3.38a) and (3.38b) over n1 yields two other equations, re­stricting the choice for dn and en :

‘У ^ ln’ У ^ dn’ + 2 У ‘Xgnn’ + hnn’ + knn’) (3.41a)

n’ n’ nn’

mn’ = en’ (3.41b)

To solve eqs. (3.38) we now start from the solution (3.40) and look for all combinations of en’, which fulfill eq. (3.38c) and (3.41b). For each such combination (dnen) we solve (3.38a) and (3.38b) like eqs. (3.16) and then start with a new dn combination till all combinations (d1,d2,…dz) є (0, ) ®—®(0,…,lz) have been tried. Some further conditions allow to

restrict the choice of (dn, en) combinations appreciably, e. g. from eq. (3.41a) we deduce that the sum of all dn is even (odd) if the sum ln is even (odd).

What remains to be done is to integrate over the angles of the vector k according to eq. (3.28) leading to integrals of the form

Because of the above condition these integrals are always real. By combining successively two spherical harmonics to one [20], the integrals can be reduced to Clebsch-Gordan coefficients and trivial factors yielding

z — i

E П (ds esPs-lfis-lPsfis)(ds0ps-l0Ps0)

Pi,—,Pz-l s=2

■ (dzezPz-ifiz-iL — M)(dz0pz-i0|L0) (3.43)

where p1 = d1,p1 = e1 and ps = es + fis-1,s = 2,…z — 1. The symmetry properties of the Clebsch-Gordan coefficients lead to the following conditions for a non-vanishing T

dj + L = even j

and

With this expression we have now a complete prescription how to calculate matrix elements of electromagnetic transition operators, like eq. (3.42). Ad­ditional differential operators can be treated as described in chapter 3.1. An extension to meson-exchange-currents is given in [29].

In summary, all matrix elements, be it overlap, or potential, or electromag­netic transitions ones, can be calculated by using the methods described in this chapter, provided the radial dependencies are in the form of Gaussian, positive and negative powers in r, solid spherical harmonic, powers of the differential operator, and plane waves. Since combinations of these depen­dencies are possible, a wide variety of operators can be treated, so that the above restriction is no practical restriction. In addition it is possible to deal with special operators, like the relativistic kinetic energy Jp2 + m2 and find analytic expressions for arbitrary number of clusters [30].

Mass distributions are normally obtained from measurements, but models can be used to fill gaps that are too large for linear interpolation. A variable number of

Gaussian functions can be used to represent the mass distributions of different fission reactions and neutron energies, from Th to Es (Z = 90-99) and for excitation energies < 20 MeV (e. g., Figs. 9 and 10). Thus, the sum of 2 to 5 Gaussian functions can be fitted to the experimental chain yield data [Y(A)] of products from the fission of these nuclei, using the method of least squares. The Gaussian functions can then be characterised against mathematical functions of the atomic numbers (ZF), mass numbers (Af), and excitation energies (E*) of the fissioning nuclei. Reciprocal variance weighting is used in both types of calculation, and the resulting functions provide a means of determining complete mass distributions for fissioning nuclei.

The central Gaussian curve is not needed to represent chain yields from spontaneous fission reactions (SF), in agreement with experimental observations that show the valley yields from spontaneous fission to be more than an order-of-magnitude less than those from thermal-neutron induced fission reactions. Furthermore, one Gaussian curve per peak can be adopted to represent the chain-yield data reasonably well for both 14 MeV neutron-induced fission and thermal-neutron induced fission of the heavier actinides (ZF > 94). Other modifications can be made to improve the chain-yield representations: for example, fission of heavier actinides — modify the peak Gaussian functions to include an exponential drop in Y(A) for AH < 130 and in the complementary range for the light peak (these modified peak functions are then renormalized to achieve a 200% sum for all yields).

Equations have also been developed to calculate the uncertainties in fission yields obtained from these model estimates. Uncertainties in the calculated yields can be estimated from the following empirical equation proposed for the percentage uncertainty (PER):

PER = (25) exp{-0.25[lnY(A)]}

with an estimated range of uncertainty of Y(A)/(l + PER/100) to Y(A)(l + PER/100).

Most experimental chain yields fall within the estimated range of uncertainties, implying that most of the calculated chain yields should be reliable.

Many of the measured chain yields have fine structure that cannot be fully reproduced by summing smooth Gaussian functions (Figs. 9 and 10), although complementary single Gaussian curves can represent the experimental data reasonably well for high excitation energies and ZF > 94. Thus, an empirical multi­Gaussian model has been successfully developed to calculate the chain yields [Y(A)] of fission reactions, with a nuclear charge [ZF ] from 90 to 99 and excitation energy E* < 20 MeV. There are many other features of these mass distribution curves that will not be considered in any further detail within this review.

A A

Fig. 9. Various Gaussian curves fitted to mass distributions of fission processes: thermal-neutron fission of 239Pu, 242mAm and 249Cf, and spontaneous fission of 252Cf

A lot of work has been done around the world to improve the existing reactor designs. The large base of experience with the current nuclear plants has been used to guide development of the new designs on the basis of User Requirements Documents (URDs) such as the Electric Power Research Institute URD5 and the European Utility Requirements6. Common goals are simplification, larger margins to limit system challenges, longer grace periods for response to emergency situations, high availability, competitive economics and compliance with internationally recognized safety objectives. The new designs are also incorporating features to meet more stringent safety objectives by improving severe accident prevention and mitigation.

Several of these designs have reached a high degree of maturity, and some have been certified by nuclear regulatory authorities. Some are entering a design optimization phase to reduce capital cost. Many of the new design features have been tested to demonstrate technological readiness.

The full spectrum of these advanced nuclear power plants covers different types of reactors with different coolants. They are referred to as evolutionary or innovative designs. An evolutionary design is a design that achieves improvements over existing designs through small to moderate modifications with a strong emphasis on maintaining proven design features to minimize technological risks. It requires at most engineering and confirmatory testing. An innovative design is one, which incorporates radical conceptual changes in design approaches or system configuration in comparison with existing practices. They could have new types of coolant, moderator or fuel. Consequently, substantial R&D, and feasibility tests are required, and a prototype or demonstration plant may be necessary to bring the concept to commercial maturity. Figure 3 gives a relative standing of efforts and costs needed for development of advanced reactors7.

Fig.3 Relative indication of cost of development of advanced reactor designs

For new plants, the basis for achieving high performance is also being laid down during the design phase8. These include design for on-line maintenance and short outages. Many other aspects such as better man-machine interface using computers and improved information displays, and better operator qualification and simulator training, which have been applied at current plants, will contribute to high performance of future plants. The advanced designs also desire plant lifetimes of 60 years.

A new terminology is being used for the advanced reactors. Bill Magwood first introduced this from the US Department of Energy9 and is shown in Table IV, which also describes the evolution of reactor designs. First generation reactors (Generation I) were those introduced early in the prototype stage of nuclear power. Generation II reactors were the commercial PWR, BWR, HWR, and WWER reactors built in the 70s and 80s. Generation III are the evolutionary advanced reactors. These could be divided into two categories: (1) those whose designs have been completed such as AP600/1000, SWR 1000, and the EPR, and (2) those which have been built such as ABWR, System 80+, KSNP. The next generation or Generation IV reactors are those designs that are beyond the current advanced designs and are “revolutionary” in nature. However, no Generation IV reactors have been built or even demonstrated, and so from a utility perspective, we may think of the next generation reactors as those just beyond the near term deployment designs. In other words, those are reactors that still need demonstration or some significant tests before commercial operation.