1010-1011 / 2239
Fermi-Eyges theory for pencil beam propagation
in slab media
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
/ 2
1
1
/ 3
i
i
i i
i i
hT
kh S
i
r r
h
hT
kh S
θ θ
Σ
θ θ
θ
Σ
−
= +
+
−
= +
+
+
θ
θ
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
:
Utrecht 2016
(
)
{
}
1
1
2
2
2
1
1
1
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
r r h r
h
hT
kh S
i
θ
θ
Σ
−
−
−
−
−
−
= +
+
+
+
−
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
Σ Σ
=
−
+
h
1
h
2
h
3
h
i
θ
r
Mix of Hogstrom and Brahme/Lax papers