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Prelims > Reactor Physics > Flashcards

Reactor Physics Flashcards

1
Q

WhTs the best moderator to fuel ratio for water?

A

2:1

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2
Q

Why is water a good moderator?

A

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

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3
Q

How are leakage and dimension related?

A

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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4
Q

What is the conversion or breeding ratio?

A

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

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5
Q

What does it mean when a reactor breeds?

A

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

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6
Q

What values of eta allow a reactor to breed?

A

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

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7
Q

why do heavy nuclei not make good moderators?

A

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

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8
Q

reaction rate

A

phi Sigma = nvN sigma

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9
Q

mean free path

A

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

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10
Q

neutron lethargy

A

ln(E_0/E) where E_0 is 10 MeV

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11
Q

gain in lethargy

A

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

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12
Q

neutron generation lifetime

A

l = n(t)/L(t)

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13
Q

two factor formula

A

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

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14
Q

six factor formula

A

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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15
Q

what causes reactivity feedback caused by?

A

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

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16
Q

probability of decay between t and (t + dt)

A

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

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17
Q

binding energy

A

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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18
Q

mass excess

A

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

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19
Q

simple reactor power formula

A

P = epsilon_f R_f V = epsilon_f Sigma_f phi V

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20
Q

macroscopic cross section

A

Sigma = N sigma

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21
Q

Reaction Rate

A

R = phi Sigma = n v N sigma

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22
Q

intensity

A

I = I_0 e^{-Sigma_t x}

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23
Q

mean free path

A

lambda = 1 / Sigma_t

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24
Q

first collision probability

A

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

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25
Q

probability of uncollided flight

A

P = e^{- Sigma_t x}

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26
Q

thermal disadvantage factor

A

PhiMod_th/ PhiFuel_th

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27
Q

in hour equation

A

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

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28
Q

general solution of in hour equation

A

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

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29
Q

measure of reactivity in dollars

A

rho/beta

30
Q

reactor period

A

T = 1/s1

31
Q

prompt jump approximation

A

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

32
Q

what will power look like after a long enough time?

A

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

33
Q

Fick’s Law

A

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

34
Q

partial current J+

A

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

35
Q

when is the diffusion equation not valid?

A
  1. near boundaries where material properties change dramatically over the distance of several mean paths
  2. near localized sources
  3. in strongly absorbing media
36
Q

fixed source diffusion equation

A

non multiplying medium with external source.

-D d^2phi(x)/dx^2 + Sigma_a phi(x) = S_ext(x)

37
Q

eigenvalue problem diffusion equation

A

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

38
Q

what is the finite flux boundary condition?

A

as x goes to infinity, flux stays finite.

39
Q

solutions for 1d slab diffusion

A
  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
40
Q

Macroscopic cross section

A

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

41
Q

critical energy for fission reaction

A

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

42
Q

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

A

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

43
Q

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

A

P_FNL, p, P_TNL, P_AF, P_F

44
Q

what are two assumptions in the six factor formula?

A
  1. two energy regions 2. neutrons emitted per fission is the same for both energy regions
45
Q

heterogeneous thermal utilization factor

A

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

46
Q

thermal disadvantage factor

A

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

47
Q

thermal utilization factor, homogeneous

A

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

48
Q

which thermal utilization factor is larger, homogeneous or heterogeneous?

A

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

49
Q

what is ell in the in hour equation?

A

prompt neutron lifetime,

50
Q

what is beta in the in hour equation?

A

beta - delayed neutron fraction,

51
Q

what is lambda in the in hour equation?

A

lambda - decay constant for delayed neutron precursors;

52
Q

what is rho in the in hour equation?

A

rho - reactivity (k-1)/k,

53
Q

what is s in the in hour equation?

A

s - reactor frequency and inverse reactor period.

54
Q

what is a vacuum boundary condition mean?

A

incoming partial current is 0

55
Q

what does a reflected boundary condition mean?

A

net current 0

56
Q

what does an interface boundary condition mean?

A

current and flux are equal across boundary

57
Q

what does a source condition mean?

A

lim as J goes to 0 = S/2

58
Q

what is a symmetry boundary condition?

A

J(0) =0

59
Q

what nuclide has highest binding energy per nucleon

A

Fe-56

60
Q

what is the average binding energy per nucleon

A

8 MeV

61
Q

Finding xs in 1/v region

A

sigma(E) = sigma(E’) E’/E

62
Q

fast fission factor

A

epsilon

fast neutrons at all energies / fast neutrons at thermal energies

63
Q

resonance escape probability

A

p,

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

64
Q

thermal utilization factor

A

f

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

65
Q

thermal reproduction factor

A

eta

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

66
Q

Multigroup Diffusion Matrix form

A

M phi = 1/k F phi

67
Q

removal cross section

A

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

68
Q

criticality condition

A

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

69
Q

important neutron poison

A

xe-135

70
Q

why is xe-135 particularly terrible?

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

Prelims (4 decks)

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