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3.6 Fringe Fields
Real magnets have fringe fields, and G4beamline makes an attempt to model them. The model is based
on that in Cosy Infinity [13], and uses Enge functions with six parameters {𝑎! … 𝑎! }:
𝑧 − 𝑧!"#!
𝑠 = 𝑓𝑟𝑖𝑛𝑔𝑒𝐹𝑎𝑐𝑡𝑜𝑟 ∗
𝑎𝑝𝑒𝑟𝑡𝑢𝑟𝑒
𝑖𝑓 𝑠 < −4 𝐸𝑛𝑔𝑒 𝑠 = 1
𝑖𝑓 𝑠 > 4 𝐸𝑛𝑔𝑒 𝑠 = 0
𝐸𝑛𝑔𝑒 𝑠 = 1/(1 + exp 𝑎! + 𝑎! 𝑠 + 𝑎! 𝑠 ! + 𝑎! 𝑠 ! + 𝑎! 𝑠 ! + 𝑎! 𝑠 ! )
Both genericbend and genericquad have reasonable default values for these parameters. The commandline can set fringeFactor and fringe=’𝑎! , 𝑎! , 𝑎! , 𝑎! , 𝑎! , 𝑎! ’ (all must be real numbers). The user must
ensure that the parameter values result in a smooth Enge function with correct limiting behavior.
3.7 Stepping and Hard Edges
If your simulation has hard-edge fields, then beware of the interaction between the stepping during
tracking and these hard edges. In particular, tiny changes in track parameters can have much larger
effects on the tracking, because one more or fewer steps occurred in the field region. This can also occur
for the edges of physical components, as one more or fewer steps occur inside a material. The effects
can be minimized by setting maxStep to a small value (e.g. 1 mm), and by ensuring that every hard-edge
field corresponds to a geometrical boundary (e.g. don’t use openAperture=1).
Usually this is not a big problem, as the effects normally are both small and inherent in the monte-carlo
method. This can be bothersome when making a detailed comparison with some other code or an
analytic result.
3.8 Radiative Decays
Decaying particles can always emit an extra gamma (or more than one), which is called a “radiative
decay”. It is not generally realized how frequently this occurs, or how important it can be in some cases
(generally backgrounds). For a multi-TeV muon facility, the radiative muon decays3 produce an intense
gamma beam parallel to the muon beam; for gamma energies above 1 GeV it can be comparable in
number to the muon decays, with gamma energies up to hundreds of GeV – this is a background above
and beyond that of the decay electrons, and cannot be ignored.
The Geant4 Decay process does not include radiative decays. The MuonDecayWithSpin process does
include them, and can be enabled on the physics command by setting spinTracking=1 (works even with
unpolarized muons).
3
The PDG booklet lists the branching ratio for radiative muon decay as 1.4%, with a note stating this is for gammas with
energies above 10 MeV. For a TeV-scale muon beam, gammas of much lower energy get boosted to multi-GeV energies; the
branching ratio for them is about 25% when using MuonDecayWithSpin.
1/10/14 TJR
G4beamline User’s Guide
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