Reactor Physics

Question 1

Two principle interaction mechanisms between neutrons and nuclei

Answer 1

Potential scattering and compound nucleus formation

Question 2

Potential scattering collisions are elastic, what does this mean

Answer 2

KE and momentum are conserved

Question 3

What is potential scattering

Answer 3

Potential scattering is a process in which the incident neutron is bounced or scattered off the
nucleus.

Question 4

What is compound nucleus formation and what does it result in

Answer 4

compound nucleus formation starts with the absorption of the incident neutron into the original nucleus to form a compound nucleus. The compound nucleus will be in an excited state and will decay immediately, emitting either a particle or gamma
-radiation (high energy photons) or both. It is the product of decay that distinguishes different types of compound nucleus interaction.

Question 5

What happens in a capture interaction

Answer 5

The compound nucleus decays to its ground state by the emission of gamma radiation only, and obviously the mass number of the nucleus has increased by 1

Demoted as a (n, gamma) reaction

Question 6

What happens in inelastic scattering interaction

Answer 6

The compound nucleus decays by emitting a neutron. If the nucleus is still in an excited state, it decays to its ground state by emission of gamma radiation.

KE is not conserved in this interaction as some of the KE of the incident neutron is transformed to gamma radiation.

Question 7

What happens in compound elastic scattering

Answer 7

The excited compound nucleus emits a neutron and immediately returns to ground state, so KE is conserved. Therefore identical to potential scattering in its consequences. Together they’re known as elastic scattering

Question 8

What happens in a fission interaction

Answer 8

Some of the heaviest elements will have their excited nucleuses each by splitting into two intermediate nuclei of unequal mass plus
a few neutrons.
Most associated nucleus for this is U-235

Question 9

Difference between fissionable and fissile

Answer 9

Fissile means they undergo fission with low energy neutrons where as fissionable need over a threshold incident energy (given in eV)

Question 10

What’s more common, symmetrical or asymmetrical fission

Answer 10

Asymmetrical

Question 11

What can be emitted in a fission reaction

Answer 11

Two fission fragments, between zero and five neutrons, beta particles (electron/positron) gamma radiation, neutrinos and energy.

Question 12

How to find energy released in a fission reaction

Answer 12

Compare the total binding energy of the products

Question 13

What amounts for t(e vast majority of energy released in a fission reaction

Answer 13

The KE of the fission products which quickly gets turned into heat.

Question 14

What is the purpose of the moderator

Answer 14

a material included in the reactor specifically to slow the neutrons down to energies at which fission reactions are more favourable.

Question 15

What’s the only source of energy that can’t be recovered in a fission reaction

Answer 15

The energy associated with the neutrinos

Question 16

Unit of cross section

Answer 16

Barns (10^-28 m^2)

Question 17

Factors that dictate the effective cross section that a nucleus presents a neutron

Answer 17

• the type of target (the individual element)
• the type of “bullet” (the neutron’s energy)
• the type of reaction under consideration

Question 18

Reaction rate equation (number of events per second per unit volume)

Answer 18

R = phi sigma N

Phi is neutron flux - neutron density times average neutron speed

Sigma is the microscopic cross section

N is the number of atoms (nuclei) per unit volume

Question 19

Equation for macroscopic cross section

Answer 19

Sigma N

Sigma is microscopic cross section

N is number of nuclei per unit volume

Question 20

How to find total cross section

Answer 20

Sum all the individual interaction’s cross section: • the elastic scattering cross-section
• the inelastic scattering cross-section
• the capture cross-section
• the fission cross-section (which is, of course, zero for all non-fissionable isotopes)

Question 21

What’s the scattering cross section

Answer 21

the sum of the elastic and inelastic scattering cross-sections

Question 22

What’s the absorption cross section

Answer 22

sum of the capture and fission cross-sections

Question 23

What are fast neutrons

Answer 23

Neutrons are released in fission reactions with energies of about 2 MeV.

Question 24

What’s a thermal neutron and how many to find the eV value that qualifies one as thermal

Answer 24

A neutron in thermal equilibrium with its surroundings

Multiply the temperature in K by the ratio k/e

k Boltzmann const
e elementary charge

Question 25

What is a fertile isotope

Answer 25

Isotopes which can be transmuted (changed) into fissile isotopes are termed fertile

Question 26

What is a fast reactor

Answer 26

A reactor with no moderation

Question 27

Equation for multiplication factor k for a fast neutron cycle

Answer 27

k = eta f L n eta (weird n) number of neutrons emitted per neutron absorbed f utilisation (the fraction of neutrons that are captured which are captured by the fuel) L leakage (the probability of a neutron not leaking) n number of neutrons initially

Question 28

What is the fast fission factor epsilon

Answer 28

The probability a beauty on will cause fission is U-238 before they have been slowed down

Question 29

Equation for multiplication factor for thermal reactor neutron cycle

Answer 29

k = epsilon Lf p Lt f eta Therefore for 0 leakage, infinite multiplication factor is know as the ‘four factor formula’

Question 30

What is the critical mass

Answer 30

The size of reactor where the multiplication factor is equal to 1, so neutron population is constant

Question 31

What is a supercritical mass

Answer 31

When the reactor is of a size where k is greater than 1 and thus the neutron population is increasing

Question 32

What is a subcritical mass

Answer 32

When the reactor is of a size where k is less than 1 so the neutron population is decreasing.

Question 33

What does j repr sent in fick’s law?

Answer 33

Neutron current density

Question 34

What does mu bar represent in diffusion coefficient equation

Answer 34

the mean cosine of the angle of scattering

Question 35

What’s the general equation for the rate at which the neutron density changes

Answer 35

dn/dt = S + P - A + R S is the independent source rate, the rate at which neutrons are produced within the unit volume by means other than fission (e.g. from isotopes which decay by neutron emission). P is the net rate at which neutrons are produced through fission per unit volume A is the rate at which neutrons are absorbed (through capture but not fission reactions) per unit volume R is the net rate at which neutrons diffuse into the unit volume

Question 36

How is the one group neutron diffusion equation altered for steady state conditions

Answer 36

dn/ dt = 0

Question 37

How is the one group neutron diffusion equation altered for source free conditions

Answer 37

S = 0

Question 38

How is the one group neutron diffusion equation altered for a non multiplying medium

Answer 38

Mu = 0

Question 39

Form of general solution for 2nd ODE for real, distinct roots

Answer 39

Let r1 and r2 be solutions to auxiliary equation y = Ae^(r1 x) + Be^(r2 x)

Question 40

Form of general solution for 2nd ODE for complex roots

Answer 40

Let r1 +- r2 i be solutions to auxiliary equation y = Ae^(r1 x) cos(r2 x) + Be^(r1 x)sin(r2 x) Exponential with imaginary power can also be expressed as cos + isin form

Question 41

Form of general solution for 2nd ODE for repeated roots

Answer 41

Let r be the solution to auxiliary equation y = Ae^(r x) + Bxe^(r x)

Question 42

Form of solution to SHM equation x.. = -w^2 x

Answer 42

X = Asin(wt) + Bcos(wt)

Question 43

Is there is symmetry in the geometry of the reactor/ where the origin of the coordinate system is, what terms must be eliminated from GS

Answer 43

Sin terms (only cosine terms remain)

Question 44

What do you plug into the one group neutron diffusion equation (with laplacian geometry plugged in, to help find general solution.

Answer 44

Phi (flux) = X(x)Y(y)Z(z) for a coordinate system where flux depends on the x, y, and z coordinates ETC So basically a product of the coordinates who flux is a function of

Question 45

What does ‘one group’ refer to

Answer 45

It identifies the fact that all neutrons have been assumed to have constant energy

Question 46

What do form factors represent

Answer 46

The ratio of the maximum power density to the average power density in the core. Same as the ratio of the max flux to average neutron flux in the core.

Question 47

What is better, low or high form factor

Answer 47

Lower as that indicated a better, more even power distribution in the reactor

Question 48

How does a reflector reduce a reactors form factor

Answer 48

By surrounding the core with a reflector, a material with a high neutron scattering cross-section, so that leaking neutrons tend to be reflected back into the core. Materials which are good moderators also make good reflectors, and so it is usual for the moderator and reflector to be the same in a given reactor design. a reflector improves neutron economy (fewer neutrons are lost) it reduces the critical mass of fuel required

Question 49

What is the material buckling Bm equation

Answer 49

Bm^2 = (η-1)Σa / D

Question 50

What is the dispersion equation

Answer 50

The equation relating frequency ω and the wave number k

Question 51

What is the group velocity

Answer 51

The speed at which a group of waves travels, not just how fast a particular crest of a wave moves Given by partially differentiating ω wrt to k

Question 52

What is the condition for zero dispersion

Answer 52

The wave speed c (ω/k) is the same as the group velocity cg (δω/δk)