PENELOPE 2003 - OECD Nuclear Energy Agency

Appendix C
Electron/positron transport in
electromagnetic fields
In this appendix, we consider the transport of electrons/positrons in static external
electromagnetic (EM) fields, in vacuum and in condensed media. We assume that, in
the region where particles move, there is an electric field E and a magnetic field B,
which are set up by external sources and do not vary with time. For practical purposes,
we also consider that both E and B are continuous functions of the position vector r.
The interactions with the medium will be described by means of penelope. In each
individual interaction event, the electron/positron loses a discrete amount of kinetic
energy and changes its direction of motion. In the absence of EM fields, the electron
travels freely between consecutive interaction events, i.e. following a straight trajectory
segment at constant speed. To simulate electron transport with static external EM
fields, we assume that the interaction properties of electrons with the medium are not
substantially affected by the field. Consequently, to account for the effect of the EM
field, we only need to consider that along each “free flight” the electron is driven by the
EM force. With a proper selection of the simulation parameters (i.e. the energy loss and
angular cutoff values), trajectory segments may have macroscopic lengths. Therefore, in
material media it is appropriate to consider the macroscopic EM fields D and H rather
than the microscopic fields E and B.
It should be noted that, under the action of an electric field, the kinetic energy of the
electron can vary substantially along a single trajectory segment. This conflicts with
one of the basic assumptions in penelope, namely that the energy of the particle stays
practically constant along the segment. In practice, however, we can always limit the
maximum segment length by means of the parameter s max . Then, the effect of the EM
field can be treated independently of that of the interactions with the medium. In other
words, for simulation purposes, we only need an efficient method to generate particle
trajectories in the EM field in vacuum. It is also important to recall that strong electric
fields in material media accelerate unbound charged particles, even when they are at
rest (i.e. electrons are never absorbed, simulated tracks can only terminate when they