The geometry of a problem is described in the Cell cards; cells are volumes delimited by surfaces; these volumes may or may not be filled with materials. But before seeing how to define cells, let us see how Surface cards are defined.

MCNP has a wide choice of surface types to describe cells; however, here we will just present the surface types that we will use for our reactor examples. A Surface card consists in a surface number, a special keyword indicating the type of the surface, and parameters for that keyword. Table

5.2 lists these surfaces and their parameters.

Thick-target neutron yields are, evidently, of great interest for hybrid reactor designs. As mentioned above, most measurements resort to a measure of the number of neutrons exiting from a large piece of material. The recent measurements of Hilscher et al. [110] use a large, gadolinium loaded, liquid scintillator. Such detectors allow an event by event measurement of the neutron multiplicity, with a very high detection efficiency. However, the

neutron energy is not measured and the detection efficiency does depend on the neutron energies, especially above 10 MeV. In the Hilscher work an average neutron detection efficiency of 0.85 was assumed.

Independently of the difficulties mentioned above for making a direct comparison between these measurements and the results of a calculation, it is not trivial to define an optimal size for the target. If the target is too small, the initial cascade may not be contained. This is exemplified in figure 6.8 which shows that the multiplicity measured[40] depends on the length and diameter of the target. It is possible to find a target thickness and diameter such that the multiplicity saturates. However, this does not guarantee that the measured multiplicity will be exactly the number of neutrons emitted per incident particle. This is due to two opposite effects: (a) neutrons may be absorbed in the target, even after being reflected from the detector, and (b) neutron multiplication may already be effective in the target. Lead targets should be largely immune from both effects, although Hilscher et al. find that, using a very pure lead target, as compared with

1.22 GeV p + Pb

their standard one, the neutron multiplicity is increased by approximately 2.5%. Figure 6.9 shows the ‘asymptotic’ results obtained by Hilscher et al. Uranium, on the other hand, is a multiplying medium whose кж can be estimated from equation (3.75) and table 3.2, with a value of v = 2.3: k1nat = 0.29 corresponding to a total multiplication in an infinite medium of 1/(1 — 0.29) = 1.4. This effect is probably responsible for the much higher neutron multiplicities observed with uranium as compared with lead, as can be seen by comparing figures 6.9 and 6.10. Another difficulty in interpreting the data, in view of an application to accelerator driven systems, is that the energy of the neutrons and thus their ‘importance’[41] is not known. Therefore, the results of direct thick-target multiplicity measure­ments should not be taken as source data to be input into a neutron propa­gation code, but rather as benchmarks for selecting valid INC calculations. Such calculations have been done by Hilscher et alJ who find that, as a very good agreement between their measured value for their lead target and a HERMES calculation is obtained, the same calculation yields

30.5 n/p reaction/GeV for a target 100 cm long and 150 cm in diameter.

The Truex process uses a neutral organophosphorus bidendate extractant: n- octyl-phenyl-di-isobutyl-carbamoylmethyl-phosphine-oxide (CMPO). CMPO displays both high and low affinities for actinides(III) and lanthanides(III) at high and low nitric acid concentrations respectively. It is, then, relatively easy to obtain an An-Ln (actinide-lanthanide) mixture by the succession of extracting and stripping steps. The separation of An from Ln can then be done by selective complexing agents like DTPA (diethylenetriamino — pentaacetic acid) which seems to make more stable complexes with Ans than with Lns.

The Diamex process

The Diamex process uses malonamide extractants, the only one practically tested being di-methyl-dibutyltetradecylmalonamide (DMDBTDMA) which has very attractive properties as actinide extractant, with comparatively small technological wastes. The Diamex process has to be followed by an additional step to separate Ans from Lns.

More recently, Bowman [133] has proposed using a molten salt subcritical reactor for plutonium incineration with the principal aim of preventing its use for nuclear proliferation. The reactor would have the following characteristics:

• Thermal power: 750 Mwt.

• Molten salt fuel with NaF-ZrF4 carrier, fission fragments and plutonium fluorides.

• Thermal flux: 2 x 1014n/cm2/s.

• Moderator: graphite.

• ks = 0.96.

The reactor is fed with a mixture of fission fragments, zirconium and plutonium fluorides obtained through fluorization of the spent fuels and extraction by sublimation of the uranium hexafluoride. The yearly input would be 300 kg of plutonium and minor actinides, 1200 kg of fission products and zirconium cladding.[57] The output would be 65 kg of plutonium

and minor actinides, 1435 kg of fission products and carrier salt.

Following Bowman, the advantages of such a system would be:

• No weapons plutonium or other weapons materials in repository.

• Possibility of underground criticality in repository eliminated.

• 80% of fission energy recovered before waste emplacement.

• Instant irreversible elimination of weapons potential upon entry into transmuter.

The emphasis is clearly put on the prevention of uncontrolled military use of the plutonium in spent fuels. One TIER reactor would be associated with every 3000 MWt reactor, thereby eliminating the need for radioactive material transportation.

Further incineration of the remaining plutonium and minor actinides would require more elaborate chemical processing in order to separate

fission fragments. Special reactors would be devoted to the second stage of incineration. In this case, however, transportation would again be necessary, but with no risk of weapons materials smuggling.

The Unit 4 reactor was to be shut down for routine maintenance on 25 April 1986. It was decided to take advantage of this shutdown to determine whether, in the event of a loss of station power, the slowing turbine could provide enough electrical power to operate the emergency equipment and the core cooling water circulating pumps, until the diesel emergency power supply became operative. The aim of this test was to determine whether cooling of the core could continue to be ensured in the event of a loss of power.[64]

This type of test had been run during a previous shutdown period, but the results had been inconclusive, so it was decided to repeat it. Unfortunately, this test, which was considered essentially to concern the non-nuclear part of the power plant, was carried out without a proper exchange of information and coordination between the team in charge of the test and the personnel in charge of the operation and safety of the nuclear reactor. Therefore, inadequate safety precautions were included in the test programme and the operating personnel were not alerted to the nuclear safety implications of the electrical test and its potential danger.

The planned programme called for shutting off the reactor’s emergency core cooling system (ECCS), which provides water for cooling the core in an emergency. Although subsequent events were not greatly affected by this, the exclusion of this system for the whole duration of the test reflected a lax attitude towards the implementation of safety procedures.

As the shutdown proceeded, the reactor was operating at about half power when the electrical load dispatcher refused to allow further shutdown, as the power was needed for the grid. In accordance with the planned test programme, about an hour later the ECCS was switched off while the reactor continued to operate at half power. It was not until about 23:00 hr on 25 April that the grid controller agreed to a further reduction in power.

For this test, the reactor should have been stabilized at about 1000 MWth prior to shutdown, but due to operational error the power fell to about 30 MWth, where the positive void coefficient became dominant. The operators then tried to raise the power to 700-1000 MWth by switching off the automatic regulators and freeing all the control rods manually. It was only at about 01:00 hr on 26 April that the reactor was stabilized at about 200 MWth.

Although there was a standard operating order that a minimum of 30 control rods was necessary to retain reactor control, in the test only six to eight control rods were actually used. Many of the control rods were with­drawn to compensate for the build-up of xenon which acted as an absorber of neutrons and reduced power. This meant that if there were a power surge, about 20 s would be required to lower the control rods and shut the reactor down. In spite of this, it was decided to continue the test programme.

There was an increase in coolant flow and a resulting drop in steam pressure. The automatic trip, which would have shut down the reactor when the steam pressure was low, had been circumvented. In order to main­tain power the operators had to withdraw nearly all the remaining control rods. The reactor became very unstable and the operators had to make adjustments every few seconds trying to maintain constant power.

At about this time, the operators reduced the flow of feedwater, pre­sumably to maintain the steam pressure. Simultaneously, the pumps that were powered by the slowing turbine were providing less cooling water to the reactor. The loss of cooling water exaggerated the unstable condition of the reactor by increasing steam production in the cooling channels (posi­tive void coefficient), and the operators could not prevent an overwhelming power surge, estimated to be 100 times the nominal power output.

The sudden increase in heat production ruptured part of the fuel and small hot fuel particles, reacting with water, caused a steam explosion, which destroyed the reactor core. A second explosion added to the destruction two to three seconds later. While it is not known for certain what caused the explosions, it is postulated that the first was a steam/hot fuel explosion, and that hydrogen may have played a role in the second.

The present annual rate of anthropic emission of CO2 amounts to 6 Gtons of carbon. It appears that about 3 Gtons are reabsorbed into the ocean. There­fore about 3 Gtons contribute to increasing the CO2 concentration in the

atmosphere. Climatic models [25, 26] show that atmospheric concentration stabilization of CO2 can be stabilized only if anthropic emissions are reduced below 3 Gtons. Figures 2.3 and 2.4 illustrate this.

Figure 2.3 shows that emission rates much below the present value are required to obtain a stabilization of the CO2 concentration. Examination of figure 2.4 shows that this stabilization will take a long time to be established. For example, in the S450 case (stabilization of the concentration at 450ppmv) the stabilization occurs only after year 2075, although the emissions decrease as soon as 2020. For the S750 case the corresponding dates are 2200 and 2070 respectively.

Slab reactor. The diffusion equation reduces to a one-dimensional equation

where we have used a single absorption cross-section Xa, independent of x, and a plane neutron source at position x = 0. At the boundaries x = ±a/2, we require ‘(x = ±a/2, t) = 0. It is, therefore, convenient to use a Fourier development of ‘ and S,

with Bn = ш/a (n = 1,3,…). The coefficients An(t) are obtained by solving the equations

If S = 0, the solution is

A„0) =An(0) exp (^1 — 1 — B £avt.

For кж < 1 + B^(D/St) = 1 + (7r2D/a2Sa) all terms vanish exponentially. For кж > 1 + (7r2D/a2Sa), the first term, and possibly some other low order ones, increases exponentially. The reactor becomes critical for ki = 1 + (7r2D/a2Sa); in this case A1(t) becomes time independent, while higher order terms decrease exponentially. Therefore, the neutron flux distri­bution becomes time independent and is a solution of the time-independent diffusion equation

2

Ddx1 ‘(x, t) + ‘(x, t)^a(ki — 1)= 0

j2 2

d к

dX2 ‘(x, 0+^2 ‘(x, t) =0

which has the form

kx

‘(x) = A1 cos —.

Simple solutions are also obtained for spherical and cylindrical reactors.

Spherical reactor. For spherically symmetric systems the time-independent diffusion equation reads

IA (r2 d’ r2 dr dr

(3.36)

R being the radius of the reactor. The solution satisfying the boundary con­ditions is

(3.37)

(3.38)

Cylindrical reactor. Similarly, for infinite cylindrical systems

г d(r d)+B'(r)=0

whose solution is

‘(r) = AJ0(Br),

with J0 the ordinary Bessel function of order 0. J0(BR) = 0. This condition is fulfilled for a number of values, the smallest being BR = 2.405.

As seen from equation (6.11), the number of secondary neutrons is kN0/(1 — k). Each of these neutrons is produced by a fission (we disregard (n, xn) reactions), which itself produces v neutrons. Thus, the number of secondary fissions in the system is kN0/v(1 — k). Since each fission releases about 0.18 GeV energy,[28] the thermal energy produced in the medium will be 0.18kN0/v(1 — k). This energy has to be compared with the energy of the incident protons Ep to define an energy gain of the system:

G — v(1 — k)Ep — T~—k ■ (4:3)

The CERN FEAT experiment [122] gave a constant value of G0k — 3, for incident proton energies larger than 1 GeV and for a uranium target.

The proton beam is produced with a finite efficiency which is the product of the thermodynamic efficiency for producing electricity from heat (typically 40% in foreseen reactors^) by the acceleration efficiency. For high intensity accelerators, most of the power is used for the high-frequency cavities, at variance with low-intensity accelerators where most of the power is spent in the magnetic devices. High intensities, therefore, are expected to allow 40% efficiencies (see Appendix III) [2, 76]. Finally, the total efficiency for proton acceleration is expected to be in the vicinity of 0.16. This leads to a minimum value of the multiplication factor for obtaining a positive energy production (ignition), km — 0.68. For a value k — 0.98 a net energy gain of 16 is achieved.

The previous reactor is very simple; a more realistic configuration consists of replacing the homogeneous core by a core with fuel rods in a moderator. Each rod has a radius of 0.5 cm. The core will then be filled by a square lattice. In order to satisfy the moderator/fuel volume ratio, the side of each square is 1.98 cm. Of course, it is not possible to describe each small cell. But it is possible to define a lattice (hexagonal or hexahedra). One has to define a mesh (the hexahedra or the hexagon) and two universes: a universe is either a lattice or a collection of cells; it defines different ‘geometry levels’ (somewhat like Russian dolls).

Heterogeneous core c

c Exterior c

1 0 1:-2:3 imp:n=0 c

c Iron tank c

2 1 -7.87 -1 2 -3 (4:-5:6) imp:n=1 c

c Lead reflector c

3 2 -10.34 -4 5 -6 (10:-11:12) imp:n=1 c

c Core c

4 0 -10 11 -12 imp:n=1 fill=1

5 0 21 -22 23 -24 imp:n=1 u=1 fill=2 lat=1 63-1. 30 imp:n=1 u=2

7 4 -10. -30 imp:n=1 u=2

c tank/reflector surfaces

1 cz 155

2 pz -155

3 pz 155

4 cz 150

5 pz -150

6 pz 150

c reflector/core surfaces

10 cz 100

11 pz -100

12 pz 100

c square mesh

21 px -0.99

22 px 0.99

23 py -0.99

24 py 0.99 c

30 cz 0.5 c Material

m1 26000.55c 1 $ Iron of the tank

m2 82000.50c 1 $ Lead of the reflector

m4 92235.60c 0.0135 92238.60c

0.9865 & 8016.60c 2. $ 235U(1.357)+238U(98.657)+1 O2

m3 1001.60c 2. 8016.60c 1. $ 6 H2O + 1 O2 (of the fuel)

sdef pos 000 erg 2.5 kcode 1000 1 10 150 totnu

The geometry is shown in figure 5.5. In this example, the core is a cylinder filled with universe 1 (cell 4, the fill card = 1). This universe is defined in cell 5 (u = 1). Cell 5 is filled with universe 2 (fill = 2) with a hexahedron lattice (lat = 1); the hexahedral mesh is defined by the planes 21 to 24. Universe 2 is defined as cells 6 and 7 (u = 2).

The keff of the heterogeneous reactor is keff = 1.050 ± 0.001, which is higher because the flux is slightly more thermal (self-shielding of uranium capture) than in the homogeneous case.

The requirements for a high-proton-intensity accelerator connected to an ADSR can be summarized as follows:

those for power reactors. Another event specific to accelerators is the occurrence of short-duration trips where the beam is lost. If the duration of a trip exceeds the time it takes for the subcritical system to reach thermal equilibrium after an input power variation (temperature relaxation time) the ADSR structures will be submitted to thermal stress and, thus, increased fatigue. The reduction of the frequency and duration of trips is therefore an important request for high-intensity accelerators.

• The energy efficiency of the accelerator complex should be reasonably high.