Reactor Physics Flashcards
Two principle interaction mechanisms between neutrons and nuclei
Potential scattering and compound nucleus formation
Potential scattering collisions are elastic, what does this mean
KE and momentum are conserved
What is potential scattering
Potential scattering is a process in which the incident neutron is bounced or scattered off the
nucleus.
What is compound nucleus formation and what does it result in
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.
What happens in a capture interaction
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
What happens in inelastic scattering interaction
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.
What happens in compound elastic scattering
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
What happens in a fission interaction
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
Difference between fissionable and fissile
Fissile means they undergo fission with low energy neutrons where as fissionable need over a threshold incident energy (given in eV)
What’s more common, symmetrical or asymmetrical fission
Asymmetrical
What can be emitted in a fission reaction
Two fission fragments, between zero and five neutrons, beta particles (electron/positron) gamma radiation, neutrinos and energy.
How to find energy released in a fission reaction
Compare the total binding energy of the products
What amounts for t(e vast majority of energy released in a fission reaction
The KE of the fission products which quickly gets turned into heat.
What is the purpose of the moderator
a material included in the reactor specifically to slow the neutrons down to energies at which fission reactions are more favourable.
What’s the only source of energy that can’t be recovered in a fission reaction
The energy associated with the neutrinos
Unit of cross section
Barns (10^-28 m^2)
Factors that dictate the effective cross section that a nucleus presents a neutron
- the type of target (the individual element)
- the type of “bullet” (the neutron’s energy)
- the type of reaction under consideration
Reaction rate equation (number of events per second per unit volume)
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
Equation for macroscopic cross section
Sigma N
Sigma is microscopic cross section
N is number of nuclei per unit volume
How to find total cross section
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)
What’s the scattering cross section
the sum of the elastic and inelastic scattering cross-sections
What’s the absorption cross section
sum of the capture and fission cross-sections
What are fast neutrons
Neutrons are released in fission reactions with energies of about 2 MeV.
What’s a thermal neutron and how many to find the eV value that qualifies one as thermal
A neutron in thermal equilibrium with its surroundings
Multiply the temperature in K by the ratio k/e
k Boltzmann const
e elementary charge
What is a fertile isotope
Isotopes which can be transmuted (changed) into fissile isotopes are termed fertile
What is a fast reactor
A reactor with no moderation
Equation for multiplication factor k for a fast neutron cycle
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
What is the fast fission factor epsilon
The probability a beauty on will cause fission is U-238 before they have been slowed down
Equation for multiplication factor for thermal reactor neutron cycle
k = epsilon Lf p Lt f eta
Therefore for 0 leakage, infinite multiplication factor is know as the ‘four factor formula’
What is the critical mass
The size of reactor where the multiplication factor is equal to 1, so neutron population is constant
What is a supercritical mass
When the reactor is of a size where k is greater than 1 and thus the neutron population is increasing
What is a subcritical mass
When the reactor is of a size where k is less than 1 so the neutron population is decreasing.
What does j repr sent in fick’s law?
Neutron current density
What does mu bar represent in diffusion coefficient equation
the mean cosine of the angle of scattering
What’s the general equation for the rate at which the neutron density changes
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
How is the one group neutron diffusion equation altered for steady state conditions
dn/ dt = 0
How is the one group neutron diffusion equation altered for source free conditions
S = 0
How is the one group neutron diffusion equation altered for a non multiplying medium
Mu = 0
Form of general solution for 2nd ODE for real, distinct roots
Let r1 and r2 be solutions to auxiliary equation
y = Ae^(r1 x) + Be^(r2 x)
Form of general solution for 2nd ODE for complex roots
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
Form of general solution for 2nd ODE for repeated roots
Let r be the solution to auxiliary equation
y = Ae^(r x) + Bxe^(r x)
Form of solution to SHM equation x.. = -w^2 x
X = Asin(wt) + Bcos(wt)
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
Sin terms (only cosine terms remain)
What do you plug into the one group neutron diffusion equation (with laplacian geometry plugged in, to help find general solution.
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
What does ‘one group’ refer to
It identifies the fact that all neutrons have been assumed to have constant energy
What do form factors represent
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.
What is better, low or high form factor
Lower as that indicated a better, more even power distribution in the reactor
How does a reflector reduce a reactors form factor
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
What is the material buckling Bm equation
Bm^2 = (η-1)Σa / D
What is the dispersion equation
The equation relating frequency ω and the wave number k
What is the group velocity
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
What is the condition for zero dispersion
The wave speed c (ω/k) is the same as the group velocity cg (δω/δk)
