493 / 1245
Fermi-Eyges theory for pencil beam propagation
in media (incl slab media)
Warsaw 2017
5
Fermi-Eyges theory describes the broadening of a pencil beam due to
multiple
scattering
along its path. The result is Gaussian distributions of the electrons
characterized by:
2
2
1
2
1
1
2
2
2
1
1
1
/ 2
1
1
/ 3
1
2
1
2
/ 4
1
3
i
i
i i
i i
i
i
i
i
i
i
i i
i
i
i
i
i
i
i i
i i
hT
kh S
i
r r
h
hT
kh S
i
r r h r
h
hT
kh S
i
2
2
- Mean square of scattering angle:
- Mean radius-angle covariance:
- Mean square of radius:
r
r
In a stack of slabs one gets, after slab
i
:
where
thickness of stack
scattering power of stack
stopping power of stack
1
a scaling constant to increase with depth (Brahme-Lax)
i
i
i
i i
h
i
T
i
S
i
kh S
i
i
k
T
h
1
h
2
h
3
h
i
r
Mix of Hogstrom and Brahme/Lax papers