PENELOPE 2003 - OECD Nuclear Energy Agency

4.4. Generation of random tracks 147
stages of the particle history (such as its initial state, the crossing of an interface or the
effective absorption after slowing down). The trajectory of the particle between a pair
of successive events is straight and will be referred to as a “segment”. We keep the term
“step” to designate the portion of a track between two hard events, which consists of
two segments and a hinge (when mixed simulation is effective).
Simulation with penelope is controlled by the constants C 1 and C 2 [see eq. (4.85)]
and the cutoff energies W cc and W cr . Hereafter, these four quantities will be referred
to as simulation parameters. The parameter C 1 , which determines the mean free path
between hard elastic events, should be small enough to ensure reliable simulation
results. penelope admits values of C 1 from 0 (detailed simulation) up to 0.2, which
corresponds to a mean angular deflection 〈θ〉 ∼ 37 deg after a steplength λ (h)
el . The
simulation parameter C 2 gives the maximum average fractional energy loss in a single
step and it is effective only at high energies. From the discussion in section 4.3, it is
clear that C 2 should also be small. penelope allows values of C 2 between zero and 0.2.
The cutoff energies W cc and W cr mainly influence the simulated energy distributions.
The simulation speeds up by using larger cutoff energies, but if these are too large
the simulated distributions may be somewhat distorted. In practice, simulated energy
distributions are found to be quite insensitive to the adopted values of W cc and W cr
when these are less than the bin width used to tally the energy distributions. Thus, the
desired energy resolution determines the maximum allowed cutoff energies.
λ (h)
el
The combined effect of all soft elastic and stopping interactions in a step is simulated
as a single artificial event or hinge, in which the particle changes its direction
of movement and loses energy. When W cc is less than the lowest oscillator resonance
energy, the simulation of inelastic collisions becomes purely detailed, i.e. inelastic collisions
do not contribute to the soft stopping power. On the other hand, the simulation
of bremsstrahlung emission is only possible by means of a mixed scheme, because of
the divergence of the DCS at W = 0 [see eq. (3.131)]. To test the accuracy of mixed
algorithms, and also in studies of low-energy electron and positron transport (with, say,
E < 100 keV), it may be convenient to perform strictly detailed simulations (see below).
For this purpose, penelope allows the user to switch off the emission of soft
bremsstrahlung photons with energy less than 10 eV. This option is activated when the
W cr value selected by the user is negative, in which case the program sets W cr = 10 eV,
disregards soft bremsstrahlung events and simulates hard events (with W > 10 eV) in
a detailed way. The generation of the angular deflection in artificial events is discontinued
when the simulation of elastic and inelastic scattering becomes detailed (i.e. when
λ (h)
el = λ el , W cc = 0).
As indicated above, the length of the steps generated by penelope is always less than
s max , an upper bound selected by the user. The simulation code limits the step length
by placing delta interactions along the particle track. These are fictitious interactions
that do not alter the state of the particle. Their only effect is to interrupt the sequence
of simulation operations, which requires altering the values of inner control variables to
permit resuming the simulation in a consistent way. The use of bounded step lengths
is necessary to account for the energy dependence of the DCSs for soft interactions.