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The studies on Accelerator-Driven Systems (ADSs) have renewed the interest in the theoretical and computational evaluation of the main integral parameters characterizing subcritical systems (e.g., reactivity, effective delayed neutron fraction

The studies on Accelerator-Driven Systems (ADSs) have renewed the interest in the theoretical and computational evaluation of the main integral parameters characterizing subcritical systems (e.g., reactivity, effective delayed neutron fraction, and mean neutron generation time [

Let us take as

If the perturbation is assumed to be equal to the delayed neutrons fission operator

The effectiveness of delayed neutrons is normally obtained by one of the following two relationships:

Furthermore,

As shown in the previous section,

Analogously,

as introduced in the previous section, the classical

the relationship

The following

It can be seen that, besides the approximation on the delayed neutron spectrum and on the total fission spectrum, (

On the basis of the theory outlined in the previous section, (

On the basis of (

The GUINEVERE system, shown in Figure _{235}. The fuel matrix has the following volumetric fractions: Uranium 17%, Stainless Steel 16%, Lead 60% and Air 7%. The zone Air + SS Sheet has the following volumetric fractions: Stainless Steel 93% and Air 7%. The RZ system is a simplified schematization of the GUINEVERE start-up (at critical) configuration (after start-up the central zone is replaced by the beam tube of the deuteron accelerator delivering, in continuous or pulsed mode, 14 MeV neutrons by deuterium-tritium reactions).

Simplified RZ model of the GUINEVERE start-up (at critical) configuration. Dimensions, not in scale, are given in cm.

ERANOS transport calculations are performed with 49 energy groups (see the appendix), P_{0} transport approximation, and angular quadrature S_{4} (module BISTRO [

Delayed neutron data

Family | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Sum |
---|---|---|---|---|---|---|---|---|---|

U_{235} | 0.00055 | 0.00245 | 0.00162 | 0.00326 | 0.00509 | 0.00152 | 0.00142 | 0.00039 | 0.01630 |

U_{238} | 0.00039 | 0.00484 | 0.00174 | 0.00637 | 0.01367 | 0.00921 | 0.00595 | 0.00433 | 0.04650 |

The following

Synthesis of the results.

Case | Equation | _{p} | _{p}/k | ||
---|---|---|---|---|---|

(a) | ( | 723 | |||

(b) | ( | 1.01955 | |||

(c) | (^{+} | 1.01955 | |||

(d) | ( | 1.02149 | |||

(e) | (^{+} | 1.02149 | |||

(f) | (_{p} | 1.01402 | |||

(g) | (_{p}/k | 732 | |||

(h) | (_{p}) | 732 | |||

(i) | ( | 731 |

The 49 energy group scheme.

Upper energy (eV) | Group # | Upper energy (eV) | Group # | Upper energy (eV) | Group # | Upper energy (eV) | Group # |
---|---|---|---|---|---|---|---|

1 | 14 | 27 | 40 | ||||

2 | 15 | 28 | 41 | ||||

3 | 16 | 29 | 42 | ||||

4 | 17 | 30 | 43 | ||||

5 | 18 | 31 | 44 | ||||

6 | 19 | 32 | 45 | ||||

7 | 20 | 33 | 46 | ||||

8 | 21 | 34 | 47 | ||||

9 | 22 | 35 | 48 | ||||

10 | 23 | 36 | 49 | ||||

11 | 24 | 37 | |||||

12 | 25 | 38 | |||||

13 | 26 | 39 |

Total fission spectrum

Case (a) is the classical

Case (g), representing the approach used by Monte Carlo calculations, provides exactly the same value as in case (h), that is, the last term in (

Actually, the differences between

Total and prompt fluxes, together with spectral differences

When evaluating

Following the perturbation theory approach, a rigorous relationship may be established between the

Both theoretical and numerical results confirm the effectiveness of the

The 49 energy group structure, presented in Table