Reactor Physics Flashcards by Marissa Zweig

WhTs the best moderator to fuel ratio for water?

2:1

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Why is water a good moderator?

Largest slowing down power due to small mass and large scattering xs, but it has a large thermal absorption xs

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How are leakage and dimension related?

The larger the medium the less leakage. For an infinite medium you can assume no leakage.for a sphere leakage increases as r^2 and fission increases as r^3

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What is the conversion or breeding ratio?

The average number of fissile atoms produced in a reactor per fuel atom consumed either by fission or absorption

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What does it mean when a reactor breeds?

More fuel is produced than consumed, measured by breeding gain g

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What values of eta allow a reactor to breed?

Much larger than 2. Note that eta increases with energy, so breeding reactors are often fast reactors

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why do heavy nuclei not make good moderators?

take a large number of collisions to slow down since they have larger inelastic scattering cross sections

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reaction rate

phi Sigma = nvN sigma

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mean free path

average distance a neutron travels between collisions d = 1/Sigma_t

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neutron lethargy

ln(E_0/E) where E_0 is 10 MeV

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gain in lethargy

ln (E/E’) = 1 + alpha/(1-alpha)ln(alpha)

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neutron generation lifetime

l = n(t)/L(t)

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two factor formula

f eta = (nu Sigma_f^F)/(Sigma_a^F + Sigma_a^other)

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six factor formula

fast fission factor - thermal + fast neutrons/thermal neutrons

resonance escape probability

thermal neutron utilization factor

thermal neutron reproduction factor

fast neutron non leakage probability

thermal neutron non leakage probability

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what causes reactivity feedback caused by?

doppler broadening of resonances, changes in moderator density and temperature, changes in fission product inventory, changes due to core expansion

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probability of decay between t and (t + dt)

p(t)dt = lambda e^{-lambda t} dt

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binding energy

c^2[Nm_n + Zm_p - M_nucleus(A, Z)] in words strong nuclear force - surface tension binding + spin pairing + shell binding - coulomb repulsion

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mass excess

[M_at(Z, N) - A]c^2

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simple reactor power formula

P = epsilon_f R_f V = epsilon_f Sigma_f phi V

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macroscopic cross section

Sigma = N sigma

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Reaction Rate

R = phi Sigma = n v N sigma

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intensity

I = I_0 e^{-Sigma_t x}

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mean free path

lambda = 1 / Sigma_t

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first collision probability

p(x)dx = Sigma_t e^{-Sigma_t x}

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probability of uncollided flight

P = e^{- Sigma_t x}

thermal disadvantage factor

PhiMod_th/ PhiFuel_th

in hour equation

rho_0 = sl/(sl + 1) + 1/(sl +1) SUM((s beta_i)/(s + lambda_i))

general solution of in hour equation

phi(t) = A_1 e^{s_1t} + A_2 e^{s_2t} rho = 0, s1 = 0; rho goes to 1, s1 goes to infinity; rho goes to -infinity, s1 goes to -lambda

measure of reactivity in dollars

rho/beta

reactor period

T = 1/s1

prompt jump approximation

P1/P2 approx (beta - rho_2)/(beta - rho_1)

what will power look like after a long enough time?

P_2(t) = e^{-omega1 t}

Fick's Law

J(r) = -D(r) del phi(r)

partial current J+

J+ = 1/4 phi(x) - 1/2D dphi/dx

when is the diffusion equation not valid?

1. near boundaries where material properties change dramatically over the distance of several mean paths 2. near localized sources 3. in strongly absorbing media

fixed source diffusion equation

non multiplying medium with external source. -D d^2phi(x)/dx^2 + Sigma_a phi(x) = S_ext(x)

eigenvalue problem diffusion equation

multiplying medium, no external source, homogeneous equation -D d^2phi(x)/dx^2 + Sigma_a phi(x) = 1/k nu Sigma_f phi(x) d^2phi(x)/dx^2 + B^2 phi(x) = 0 where B^2 = B^2_m/k

what is the finite flux boundary condition?

as x goes to infinity, flux stays finite.

solutions for 1d slab diffusion

1. C1 e^{-kx} + C2e^{kx} 2. C1 cosh (kx) + C2sinh(kx), k^2 <0 3. C1 + C2x, k=0 4. C1cos(kx) + C2sin(kx), k^2>0

Macroscopic cross section

probability per unit path length that a neutron will have a collision of a certain type. cm^-1

critical energy for fission reaction

minimum energy necessary to be supplied to a nucleus in order to deform the nucleus to a point where it can begin to split in two

products of a fission reaction that will be released up to a minute after

fission fragments, prompt neutrons, prompt gamma rays, delayed neutrons, delayed gamma rays, neutrinos

what's the sequence of the life history of a neutron chart

P_FNL, p, P_TNL, P_AF, P_F

what are two assumptions in the six factor formula?

1. two energy regions 2. neutrons emitted per fission is the same for both energy regions

heterogeneous thermal utilization factor

f = (Sigma_a V Phi)^F / [(Sigma_a V Phi)^F + (Sigma_a V Phi)^M]

thermal disadvantage factor

ratio of average thermal flux in moderator to average thermal neutron flux in fuel

thermal utilization factor, homogeneous

Sigma_a^F/(Sigma_a^F + Sigma_a^M)

which thermal utilization factor is larger, homogeneous or heterogeneous?

it depends on moderator to fuel ratio. if moderator volume is larger than fuel volume, the hetrogeneous factor will be smaller.

what is ell in the in hour equation?

prompt neutron lifetime,

what is beta in the in hour equation?

beta - delayed neutron fraction,

what is lambda in the in hour equation?

lambda - decay constant for delayed neutron precursors;

what is rho in the in hour equation?

rho - reactivity (k-1)/k,

what is s in the in hour equation?

s - reactor frequency and inverse reactor period.

what is a vacuum boundary condition mean?

incoming partial current is 0

what does a reflected boundary condition mean?

net current 0

what does an interface boundary condition mean?

current and flux are equal across boundary

what does a source condition mean?

lim as J goes to 0 = S/2

what is a symmetry boundary condition?

J(0) =0

what nuclide has highest binding energy per nucleon

Fe-56

what is the average binding energy per nucleon

8 MeV

Finding xs in 1/v region

sigma(E) = sigma(E') E'/E

fast fission factor

epsilon fast neutrons at all energies / fast neutrons at thermal energies

resonance escape probability

p, number of neutrons that reach thermal energies / number of fast neutrons that start to slow down

thermal utilization factor

f number of thermal neutrons absorbed in fuel / number of thermal neutrons absorbed in all material

thermal reproduction factor

eta number of fast neutrons produced by thermal fission / number of thermal neutrons absorbed in nuclear fuel

Multigroup Diffusion Matrix form

M phi = 1/k F phi

removal cross section

Sigma_R,i = Sigma_t,i - Sigma, s, i to i

criticality condition

B_g^2 = (nu Sigma_f - Sigma_a)/D = B_m^2

important neutron poison

xe-135

why is xe-135 particularly terrible?

1. its concentration can change dramatically over hours 2. the thermal absorption cross section is > 10^6