Dose Course Book

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5.2
Boltzmann linear transport equations
for photon field radiation transport
Particle conservation book keeping:
{ {
3
att
j , , , , ' ', ,
' 1
d
0 source term
net number attenuation
through surface secondary particle production
"Gauss divergence theorem"
d d d d d
j E j j E j j j E j
j
V E
N E E Q
Ω Ω Ω
Ω
Ω Ω Φ σ Φ σ Φ Ω
′ ′ →
=
≡


′ ′ = − ⋅∇ − + +

∑ ∫ ∫ ∫ uur
142443 14243
14444244443
dV


 
 
 
 

14444444444444244444444444443
0 ≡
3
att
1 , , 1 , , 1 , , ' 1 ', , 1
' 1
3
att
2, , 2, , 2, , ' 2 ', , 2
' 1
3
att
3, , 3 , , 3 , , ' 3 ', , 3
' 1
d d
d d
d d
E E E j j E
jE
E E E j j E
jE
E E E j j E
jE
E Q
E Q
E Q
Ω Ω Ω Ω
Ω
Ω Ω Ω Ω
Ω
Ω Ω Ω Ω
Ω
Ω Φ σ Φ σ Φ Ω
Ω Φ σ Φ σ Φ Ω
Ω Φ σ Φ σ Φ Ω
′ ′ →
=
′ ′ →
=
′ ′ →
=
′ ′
⋅∇ + = +
′ ′ ⋅∇ + = +
′ ′ ⋅∇ + = +
∑∫ ∫
∑∫ ∫
∑∫ ∫
uur
uur
uur
j =1 photons
j =2 electrons
j =3 positrons
5