How Does the Delayed Neutron Fraction Influence Reactor Kinetics?

[oksuz_]

Hi

Point kinetics equation with one-group delayed neutrons,

dn/dt= ((ρ-β)/∧)n+λC

dC/dt= (β/Λ)n - λC

When a reactor in steady-state operation, derivative terms would be zero. From second equation,
C/n= β/λΛ is found. For given β=0.0065, λ=0.08 and Λ=0.0001, the ratio of the steady state delayed neutron concentration to the total neutron is found about 812.5. So, what I do not understand is that the delayed neutrons is just a small fraction of the total neutrons (around 1%). How come the ratio becomes 812.5 ? Am I missing something?

Thank you ..

 

[mathman]

http://www.nuclear-power.net/nuclear-power/fission/delayed-neutrons/

Above may help.

 

[oksuz_]

Thank you for reply. However, I had already checked this source before I wrote this question. It gives the delayed neutron fractions for the six groups but does not answer my question.

 

[Astronuc]

Hi

Point kinetics equation with one-group delayed neutrons,

dn/dt= ((ρ-β)/∧)n+λC

dC/dt= (β/Λ)n - λC

When a reactor in steady-state operation, derivative terms would be zero. From second equation,
C/n= β/λΛ is found. For given β=0.0065, λ=0.08 and Λ=0.0001, the ratio of the steady state delayed neutron concentration to the total neutron is found about 812.5. So, what I do not understand is that the delayed neutrons is just a small fraction of the total neutrons (around 1%). How come the ratio becomes 812.5 ? Am I missing something?

Thank you ..

Looking at the coefficients in the second equation, (β/Λ) = 65 as compared to λ=0.08, which simply means that the rate of change of C is more greatly affected by the neutron flux than by the delayed neutron fraction of the population.

 

[rpp]

This is an interesting problem to think about. Since the number of fraction of delayed neutrons produced by fission is fairly small (~0.65%), you would expect that the ratio of delayed precursors to the number of neutrons would be fairly small also. The difference is in the lifetimes of the neutrons and the delayed precursor. A neutron is going to have a lifetime on the order of 0.0001 sec, while the delayed precursor can have a lifetime of up to 55 seconds.

While there are many more neutrons produced by fission, the delayed neutrons stay in the system much longer. Therefore, if you take a snapshot in time, there are many more precursors in the system than there are neutrons.