PENELOPE 2003 - OECD Nuclear Energy Agency

C.2. Exact tracking in homogeneous magnetic fields 231
with [see eqs. (C.16) and (C.31)]
and
(∆v) E = s Z 0e [E 0 − β 2 0(E 0·ˆv 0 )ˆv 0 ]
m e c γ 0 β 0
(∆v) B = [cos(sω/v 0 ) − 1] v 0⊥ + sin(sω/v 0 )( ˆω×v 0⊥ ).
(C.37)
(C.38)
In our implementation of this tracking algorithm, the allowed step lengths s are
limited by the following constraints [see eqs. (C.19) and (C.20)]
|E(r(s)) − E(r 0 )|
|E(r 0 )|
< δ E ≪ 1,
|B(r(s)) − B(r 0 )|
|B(r 0 )|
< δ B ≪ 1 (C.39)
and
∣ E(s) − E ∣∣∣∣ 0
< δ
∣
E ≪ 1,
E 0
∣
∣(∆v) E + (∆v) B
∣ ∣∣
v 0
< δ v ≪ 1. (C.40)
The algorithm is robust, i.e. the accuracy of the generated trajectories increases when
the δ-parameters are reduced. In many practical cases, a good compromise between
accuracy and simulation speed is obtained by setting δ E = δ B = δ E = δ v = 0.02.
Notice that, in the case of a uniform magnetic field, the tracking algorithm is now
exact, irrespective of the step length.
This tracking algorithm has been implemented in the subroutine package penfield,
which is devised to work linked to penelope and pengeom. To simulate radiation
transport in a given field/material configuration, the user must provide the steering
main program as well as specific routines that define the EM field (see the examples and
comments in the source file PENFIELD.F).