Four factor formula

The four-factor formula describes how the multiplication factor of an infinitely extended homogeneous thermal nuclear reactor results from four parameters. ${\displaystyle k_{\infty }}$

formula

${\displaystyle k_{\infty }=\eta \,\varepsilon \,p\,f}$

meaning

→ Main article: Multiplication factor

The multiplication factor is the number of neutrons in a given generation divided by the number of neutrons in the previous generation.

The underlying model of the reactor is greatly simplified:

• The reactor is assumed to be infinitely large, i.e. H. the actually occurring seepage or leakage losses (neutron losses through the surface of the reactor to the outside) are neglected. The effective multiplication factor of a finitely large homogeneous reactor is therefore always smaller than . ${\displaystyle k_{\mathrm {eff} }}$ ${\displaystyle k_{\infty }}$
• The reactor is assumed to be a homogeneous mixture of all of its materials. A real reactor is almost always constructed heterogeneously from nuclear fuel, structural material and moderator / coolant. Depending on the structure, this can decrease or increase compared to the homogeneous case. ${\displaystyle k_{\infty }}$

Explanation of the four factors

symbol	Surname	meaning	formula	Typical value
${\displaystyle \eta }$	Generation factor	Average number of fission neutrons per absorbed in the nuclear fuel neutron. This number is less than the neutron yield per fission, because there are also absorptions in the fuel that do not lead to fission. is the cross section for fission, the cross section for absorption. ${\displaystyle \nu }$ ${\displaystyle \sigma _{f}}$ ${\displaystyle \sigma _{a}}$	${\displaystyle \eta =\nu {\frac {\sigma _{f}}{\sigma _{a}}}}$ ${\displaystyle \nu \approx 2{,}43}$for 235 U	1.3
${\displaystyle \varepsilon }$	Fast splitting factor	${\displaystyle {\frac {\text{Zahl der Kernspaltungen}}{\text{Zahl der durch thermische Neutronen induzierten Kernspaltungen}}}}$ The fast fission factor takes into account that fast neutrons can also cause nuclear fission.		1.03
${\displaystyle p}$	Moderation success or Resonance transmission probability	Some neutrons are absorbed during thermalization (cooling) by the moderator, the structural material or (especially) by neutron capture in the resonances of the uranium-238. is the fraction of neutrons that reach the thermal energy without being lost through such absorption. ${\displaystyle p}$		0.89
${\displaystyle f}$	thermal utilization factor	${\displaystyle {\frac {\text{vom Brennstoff absorbierte thermische Neutronen}}{\text{insgesamt absorbierte thermische Neutronen}}}}$ Thermal neutrons can also be absorbed by the moderator or other non-fissile material ( parasitic absorption ). is the macroscopic cross section for absorption of a thermal neutron in the fuel, the one for absorption somewhere in the material. ${\displaystyle \Sigma _{aF}}$ ${\displaystyle \Sigma _{a}}$	${\displaystyle f=\Sigma _{aF}/\Sigma _{a}}$	0.88

literature

• A. Ziegler, H.-J. Allelein (Hrsg.): Reaktortechnik : Physical-technical basics . 2nd edition, Springer-Vieweg, Berlin, Heidelberg 2013, ISBN 978-3-642-33845-8

Web links

• anonymous: nuclear power plant. July 5, 2007, accessed March 25, 2011 . 
• M. Hietschold: Nuclear Energy. (PDF) In: Kerne_Elementarteilchen (lecture WS 2010/2011) [1] . February 15, 2011, pp. 78–81 , accessed on March 25, 2011 (slides under [2] ; see also KP_ET_1.pdf to KP_ET_14.pdf (corresponding slides accordingly)).