Open MCFlowMace opened 6 months ago
The Kassiopeia implementation in https://github.com/KATRIN-Experiment/Kassiopeia/blob/c07cbb354be937e26f8a2ce11973639d9f327a64/Kassiopeia/Trajectories/Source/KSTrajTermDrift.cxx#L48 is in agreement with the Kassiopeia paper [Daniel Furse et al 2017 New J. Phys. 19 053012] (see screenshot below).
I can reproduce the implemented CRESana formular given that equation 12.55 [Section "Particle Drift in Nonuniform, Static Magnetic Fields, p.589, 3rd edition] in Jackson is correct. I verified relativistic cyclotron frequency and cyclotron radius seperately.
The only reference in Kassiopeia paper is to the original Northrop paper (Screenshot reference list Kassiopeia paper) The corresponding Northrop paper discusses only the non-relativistic case The relativistic case is discussed in a different paper. https://journals.aps.org/pr/pdf/10.1103/PhysRev.117.215
The Grad-B drift velocity is incorrect: https://github.com/MCFlowMace/CRESana/blob/905d542d533e554f35b246b5c8bd9dedd6bce06b/cresana/cyclotronphysics.py#L109-L112
I added the factor
sqrt(gamma)
because only then I ended up with good agreement to Kassiopeia. Following the equations from literature this factor should not be there. From Jackson one can extract this equation for example: One can show that this is equivalent to the used value in the code (minus thesqrt(gamma
) by using The version in Jackson is also equivalent to the one in this original publication about the guiding center approximation https://agupubs.onlinelibrary.wiley.com/doi/10.1029/RG001i003p00283 One only has to pay attention to not get confused in the comparison because both Northrop and Jackson use CGS units and therefore they have an additional factor1/c
in their definition of the cyclotron frequency that we usually do not have.It is odd that using the factor
sqrt(gamma)
gave good agreement because it should clearly not be there according to literature. I tried to find out what is going on in the Kassiopeias source and the relevant code seems to be here https://github.com/KATRIN-Experiment/Kassiopeia/blob/c07cbb354be937e26f8a2ce11973639d9f327a64/Kassiopeia/Trajectories/Source/KSTrajTermDrift.cxx#L48 and I assume that the term for the grad-B drift is only the part withtTransMomentum2
. The part2. * tLongMomentum2
has to be the contribution from the curvature drift. If I interpret the variables correctly this results in an equation likev=v_J*2*gamma/(1+gamma)
wherev_J
would be the drift velocity out of Jackson. At the tritium endpoint we have gamma=1.036 and in this case by coincidence it is approximatelysqrt(gamma)=2*gamma/(1+gamma)=1.018
. This looks like Kassiopeia has indeed this factor wrong and usingsqrt(gamma)
makes the drift velocity agree to Kassiopeia by coincidence.To me it seems like Kassiopeia is wrong here and that the factor
sqrt(gamma)
should be removed on our end. Before opening an issue in Kassiopeia I would like to have someone else look at this and confirm my suspicion.