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γ

γγ

γ

γ

γ

σ

q q

t

+ =Φ+Φ∇⋅Ω

!

ˆ

(

)

e

e

ee

e

R

e e

t

e

q q q

S

E

+ + =Φ

−Φ+Φ∇⋅Ω

γ

σ

!

ˆ

Photons:

Electrons:

(

)

ξ

η

µ

, , ˆ

Ω

unit direction vector

(

)

Ω Φ

ˆ, ,

,

Er

e

!

γ

photon/electron angular fluence

(

)

zyxr

, ,

!

position vector

energy

E

particle sources

q

Linear Boltzmann transport equations

total cross-section

t

σ

( )

ErS

R

,

!

stopping power

Grid-based LBTE solver