Lecture 6

Question 1

Under steady state conditions, neutron conservation requires that

Answer 1

(neutrons leaking) + (neutrons absorbed) = (source neutrons emitted) + (fission neutrons produced)

Question 2

The neutron diffusion equation is

Answer 2

Question 3

Fick’s approximation is

Answer 3

relating the current to the flux so that

Question 4

D =

Answer 4

Question 5

Diffusion equation for uniform, non-multiplying system

Answer 5

Question 6

diffusion area =

Answer 6

L²=D/Σ_a

Question 7

Differential equation for source-free, plane geometry

Answer 7

Question 8

general solution of

Answer 8

Question 9

Boundary conditions for a source-free example in semi-infinite plane geometry

Answer 9

Question 10

For a uniform source in plane geometry, φ_h =

Answer 10

Question 11

For a uniform source in plane geometry, φ_p =

Answer 11

Question 12

boundary conditions for uniform source in plane geometry

Answer 12

Question 13

cosh(x)=

Answer 13

Question 14

sinh(x) =

Answer 14

Question 15

Answer 15

Question 16

The vacuum boundary condition

Answer 16

Question 17

The vacuum boundary condition 2/3λ is the ______, at which point the flux is _____.

Answer 17

extrapolation distance, zero

Question 18

If the solution is symmetric about x=0 such that the _________ is zero, then we may solve the problem only for _____, and bc becomes

Answer 18

net number of neutrons crossing the plane, x>0, dφ(0)/dx=0

Question 19

For a surface source

Answer 19

s’’

Question 20

albedo eqn

Answer 20

α = (1-2D/L)/(1+2DL) or

Question 21

Flux for surface source

Answer 21

Question 22

Diffusion theory requires continuity of ______, ______, and _____ at interface conditions.

Answer 22

flux, normal component of current,

Question 23

If there is a localized source along the interface, the diffusion equation becomes

Answer 23

Question 24

For a point source, s_p =

Answer 24

Question 25

Neutron diffusion eqn in sperical geometry

Answer 25

Question 26

Find current equation for point source

J_r =

Answer 26

Question 27

For a point source, φ(r) =

Answer 27

Question 28

Find φ_h for spherical geometry with uniform source

Answer 28

Question 29

Find φ_p for spherical geometry with uniform source

Answer 29

Question 30

Boundary and interface conditions for a uniform sphere in non-multiplying medium

Answer 30

Question 31

Diffusion theory is valid for situations where neutrons ______ with a _____ distribution. And if the neutron distibution is changing _____ in space.

Answer 31

travel in all directions, uniform, gradually

Question 32

Diffusion theory leads to significant errors for saptial distributions of neutrons near _____ and at ______.

Answer 32

boundaries, materials with sharply different properties

Question 33

In reactor lattices consisting of fuel, coolant, moderators, and other materials, we use diffusion theory to examine the _____ distribution of neutrons only after taking appropriate _____ over the lattice cells.

Answer 33

global, averages

Question 34

Diffusion length, L, in terms of r

Answer 34

Question 35

Diffusion length in terms of λ and c

Answer 35

Question 36

The uncollided flux drops off as _____ while total flux drops of as ____

Answer 36

1/r², 1/r

Question 37

root mean square idstance between birth and first collision

Answer 37

Question 38

For the diffusion equation to give reasonable accuracy, ____ of the neutron populatin at a point can remain uncollided

Answer 38

only a small fraction

Question 39

material buckling (B²) equation

Answer 39

Question 40

Geometric buckling equation

B²=

Answer 40

Question 41

In a reactor, the flux level becomes _____ when it is critical

Answer 41

infinite

Question 42

For a fixed source, the flux level __________ with increasing k_∞

Answer 42

increases

Question 43

laplacian in cartesian coordinates

Answer 43

Question 44

Laplacian in cylindrical coordinates

Answer 44

Question 45

Laplacian in spherical coordinates

Answer 45