Spin tracking of moving muons

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I have a number of questions about spin tracking of moving particles (muons particularly).

To set up the questions, a few words about our experimental environment: We have a polarized (of course:-) muon beam travelling in vacuum through a set of magnetic fields, and coming to rest in a target, also immersed in a magnetic field. We need to track the muon spin, and apply spin dependent muon decay. During transport, we use the G4Mag_SpinEqRhs equations, and see the spin precessing correctly (we think). We use G4DecayWithSpin, and see the proper distribution of muon decays around the muon spin direction. I'm currently using both 4.9.1 and 4.9.2 on Linux machines. So far so good.

Here are some of the issues that I don't quite understand:

1) If I understand correctly, the units of the evolution equation have d\vec{s}/dx = (1/\beta)(d\vec{s}/dt). The dominant term on the RHS in the BMT spin evolution for low energy muons is the \vec{s} \cross \vec{B} term, which has no problem as \beta->0. But, because we multiply by a number that diverges (1/\beta) in the stopping limit, we in principle could have a big problem with inaccurate evolution. Practically, given the way Geant4 handles the energy loss, should I be worried about this? Do we ever end up in a condition where 1/\beta gets big enough to be a problem? If so, is there any good way to deal with this?

2) In some of the EqRhs equation classes, the EvaluatRhsGivenB term includes the statements:

   dydx[6] = dydx[8] = 0.;//not used
   // Lab Time of flight
   dydx[7] = inverse_velocity;

for example, G4EqEMFieldWithSpin. But others, particularly the G4Mag_SpinEqRhs that I need, has instead

   // Initialise the values of dydx that we do not update.
   dydx[6] = dydx[7] = dydx[8] = 0.0;

Is the difference meaningful? I definitely need the lab TOF to have the right value.

3) In another experiment, we have higher momentum muons and also electric fields. All else being correct, I should be able to use G4EqEMFieldWithSpin to evolve the spin in these fields. But I think there's a problem with the implementation in G4EqEMFieldWithSpin::EvaluateRhsGivenB: the BMT equation has a term of the form \vec{s} \cross (\vec{\beta} \cross \vec{E}), but the implementation of the spin evolution in this class is identical to that of G4Mag_SpinEqRhs. Is this intentional (am I missing something), or an oversight (ie. bug)?