Lecture 6 Flashcards

1
Q

Under steady state conditions, neutron conservation requires that

A

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

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2
Q

The neutron diffusion equation is

A
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3
Q

Fick’s approximation is

A

relating the current to the flux so that

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4
Q

D =

A
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5
Q

Diffusion equation for uniform, non-multiplying system

A
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6
Q

diffusion area =

A

L2=D/Σa

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7
Q

Differential equation for source-free, plane geometry

A
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8
Q

general solution of

A
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9
Q

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

A
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10
Q

For a uniform source in plane geometry, φh =

A
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11
Q

For a uniform source in plane geometry, φp =

A
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12
Q

boundary conditions for uniform source in plane geometry

A
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13
Q

cosh(x)=

A
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14
Q

sinh(x) =

A
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15
Q
A
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16
Q

The vacuum boundary condition

A
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17
Q

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

A

extrapolation distance, zero

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18
Q

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

A

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

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19
Q

For a surface source

20
Q

albedo eqn

A

α = (1-2D/L)/(1+2DL) or

21
Q

Flux for surface source

22
Q

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

A

flux, normal component of current,

23
Q

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

24
Q

For a point source, sp =

25
Neutron diffusion eqn in sperical geometry
26
Find current equation for point source Jr =
27
For a point source, φ(r) =
28
Find φh for spherical geometry with uniform source
29
Find φp for spherical geometry with uniform source
30
Boundary and interface conditions for a uniform sphere in non-multiplying medium
31
Diffusion theory is valid for situations where neutrons ______ with a _____ distribution. And if the neutron distibution is changing _____ in space.
travel in all directions, uniform, gradually
32
Diffusion theory leads to significant errors for saptial distributions of neutrons near _____ and at \_\_\_\_\_\_.
boundaries, materials with sharply different properties
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.
global, averages
34
Diffusion length, L, in terms of r
35
Diffusion length in terms of λ and c
36
The uncollided flux drops off as _____ while total flux drops of as \_\_\_\_
1/r2, 1/r
37
root mean square idstance between birth and first collision
38
For the diffusion equation to give reasonable accuracy, ____ of the neutron populatin at a point can remain uncollided
only a small fraction
39
material buckling (B2) equation
40
Geometric buckling equation B2=
41
In a reactor, the flux level becomes _____ when it is critical
infinite
42
For a fixed source, the flux level __________ with increasing k
increases
43
laplacian in cartesian coordinates
44
Laplacian in cylindrical coordinates
45
Laplacian in spherical coordinates