Week 2: Neutron Kinetics

Question 1

What is the definition of Decay Constant?

Answer 1

Probability of decay per unit time - denoted as lambda

Question 2

What is the definition of delayed neutron fraction? How does this relate to Beta bar?

Answer 2

Delayed neutron fraction (denoted as Beta) is the number of delayed neutrons/fission over the number of neutrons (prompt + delayed)/fission.

Beta bar is the weighted average of the betas of all precursor nuclei.

Question 3

What is the definition of Beta effective?

Answer 3

Beta effective is the fraction of fission neutrons released as delayed neutrons.
Delayed neutrons are born too slow to fission U-238, so they are less important to the neutron life cycle.

Question 4

What is the definition of Reactor Period?

Answer 4

The length of time required to change reactor power (or neutron density) by a factor of e - denoted as tau.

Question 5

What is the birth energy of a prompt neutron? A delayed neutron?

Answer 5

Prompt - 2 MeV, can fission with U-238
Delayed - 0.5 MeV, cannot fission with U-238

Question 6

What is an average Beta effective for BOL? EOL?

Answer 6

BOL - 0.0065
EOL - 0.005

Question 7

What is the startup rate after shutdown?

Answer 7

-1/3 dpm; tied to decay of Br-87 as the longest lived delayed neutron precursor

Question 8

What is the definition of average precursor decay constant? What are some typical values?

Answer 8

The weighted average of the decay constants of all the precursors in the core at a given time - denoted as lambda bar.
Rapid up - 0.2
Slow up - 0.1
Steady-State - 0.077
Rapid down - 0.0124

Question 9

What is the reactor power as a function of time/startup rate?

Answer 9

P(t) = P_0 * 10^(SUR*t)

Question 10

What is the steady-state startup rate equation?

Answer 10

SUR = 26.06*((lambda barr * rho)/(Beta effective - rho))

Question 11

What is the transient startup rate equation?

Answer 11

SUR = 26.06*((lambda barr * rho + rho_dot)/(Beta effective - rho))
rho_dot is the reactivity addition rate