Neutron Life Cycles

Question 1

Define effective multiplication factor and discuss its relationship to the state of the reactor.

Answer 1

K_eff is the ratio of the number of neutron produced in one generation by fission over the number of neutrons produced in the previous generation.

K_eff < 1 equates to a Subcritical Reactor

K_eff = 1 equates to a Critical Reactor

K_eff > 1 equates to a Supercritical Reactor

Question 2

Define critical, subcritical, and supercritical with respect to the reactor.

Answer 2

Critical is a steady state condition with K_eff = 1

Subcritical is a conditon where fewer neutrons are being produced in each successive generation (K_eff < 1). Power is lowering

Supercritical is a condition where more neutrons are being produced in each successive generation (K_eff > 1). Power is increasing.

Question 3

What are assumptions are made to simplify the neutron life cycle?

Answer 3

• All neutrons are born as fast neutrons.
• Some fast neutrons can be absorbed by fuel and cause fast fission.
• Some fast neutrons can leak out of the reactor core.
• Some fast neutrons can be resonantly captured while slowing down.
• All remaining fast neutrons become thermalized.
• Some thermal neutrons can leak out of thecore.
• Some thermal neutrons can be absorbed by non-fuel material.
• Some thermal neutrons can be absorbed by fuel and not cause fission.
• All remaining thermal neutrons are absorbed by fuel and cause thermal fission.

Question 4

Define the Fast Fission Factor - €

Answer 4

_# of neutrons born by ALL fission events_
# of neutrons born by just THERMAL fission events.

Question 5

What are some things that impact the fast fission factor - €

Answer 5

Fuel atomic density - as fuel atomic density decreases, e decreases.

Fuel pin diameter - as fuel pin diameter decreases, e decreases.

Moderation - as the ability of the moderator to slow neutrons down increases, e decreases.

The most significant effect is that of core age. As the core is operated, U-235 is depleted, decreasing the fraction of fast fissions from U-235.

Question 6

Define the Fast Non-Leakage Probability - L_f

Answer 6

Before fast neutrons begin to slow down there exists a possibility that some fast neutrons will be lost from the core due to leakage.

The fast non-leakage probability (L_f) represents that fraction of fast neutrons that do
not leak out of the core while slowing down. It is a net loss of neutrons:

L_f =
Fast neutrons that start to slow down
Fast Neutrons produced from ALL fision events.

Question 7

What influences the Fast Non-Leakage Probability Factor - L_f

Answer 7

The ability for a fast neutron to leak out of the reactor is dependent upon how far the neutron can travel and its distance from the core boundary.

Therefore, L_f is primarily a function of moderator density and effective core size.

For neutrons, the core is essentialy infinite in size. Moderator temperature has an impact: As temeprature increases, density decreases and non-leakage probability L_f decreases (more leak out).

Question 8

Define resonance escape probability factor

Answer 8

It is the fraction of neutrons that are NOT absorbed while slowing to thermal energy.

p =

Fast neutrons that become thermal
Fast neutrons that start to slow down.

Resonance absorption peaks are specific energy levels that represent vacant energy sites for a nucleus.

In the slowing down process, a fast neutron must pass through these peaks. When the neutron is in the resonance energy region, there is an increased probability of the neutron being absorbed by the non-fuel material in a resonance energy peak.

Question 9

What factors impact Resonance Escape Probability?

Answer 9

• moderator-to fuel ratio
• fuel temperature (doppler effect)
• core age

and

• fuel enrichment.

Question 10

What is the Thermal Non-Leakage Probability (L_th)?

Answer 10

L_th represents the probability that a thermal neutron will not leak out of the core.

L_th =

_# of thermal neutrons absorbed in the core_
# of fast neutrons that become thermal

It represents a net loss in the neutron population and has a typical value of 0.98.

Question 11

What is the Thermal Utilization Factor (f)?

Answer 11

It is the ratio of the number of thermal neutrons absorbed in the fuel to the number of thermal neutrons absorbed in the core.

The term core includes the fuel, moderator, fuel cladding, structural members, control rods, etc.

f=

_#thermal neutrons absorbed in the fuel_
# of thermal neutrons absorbed in the core

The thermal utilization factor is the factor that the reactor operator changes to control k_eff.

Question 12

What is the reproduction factor (n)?

Answer 12

It is the number of fast neutrons produced from fission compared to the number of thermal neutrons absorbed in the fuel.

The reproduction factor represents a net gain in neutron population and has a typical value of approximately 1.80.

n=

_# of fast neutrons produced by thermal fission events_
# of thermal neutrons absorbed in the fuel

Question 13

Define reactivity.

Answer 13

It is the measure of the departure of a reactor from criticality. Reactivity is defined as
the fractional change in neutron population per generation and is indicated by the Greek letter rho (p).

The formula is

(K_eff - 1)/K_eff

Question 14

What is Delta K_eff?

Answer 14

Delta K_eff = K_eff - 1

It is the change in reactivity from critical (1)

Question 15

What is the conversion for % Delta K / K?

Answer 15

(Delta K / K) X 100%

Question 16

What is the conversion for percent milli rho (pcm)?

Answer 16

1000 pcm = 1% Delta K/K

1 pcm = 10⁵ Delta K / K

Question 17

What is excess reactivity (p_excess)?

Answer 17

It is the reactivity associated with the excess fuel that is added to the core beyond the minimum amount necessary to achieve criticality at BOL

Question 18

What is excess multiplication factor (K_excess)?

Answer 18

It is defined as the amount by which the total installed k_eff exceeds 1.0,

and is expressed mathematically as:

K_excess = K_eff - 1

Therefore:

p_excess = K_excess / K_eff

Question 19

What is shutdown margin?

Answer 19

It is the instantaneous amount of reactivity that the core is, or can be made, subcritical from its present condition with the most reactive control rod fully withdrawn from the core at any time during the core cycle.

Question 20

What is the formula for shutdown margin?

Answer 20

SDM = (1 - K_eff) / K_eff = -p

Question 21

What is the six factor formula?

Answer 21

Question 22

What are the impacts on the six factor formula?

Answer 22