  Many experiments and devices in physics use static magnetic fields to guide
charged particles from a source onto a detector, and we ask the innocent
question: What is the distribution of particle intensity over the detector
surface? One should think that the solution to this seemingly simple problem is
well known. We show that, even for uniform guide fields, this is not the case
and present analytical point spread functions (PSF) for magnetic transport that
deviate strongly from previous results. The "magnetic" PSF shows unexpected
singularities, which were recently also observed experimentally, and which make
detector response very sensitive to minute changes of position, field
amplitude, or particle energy. In the field of low-energy particle physics,
these singularities may become a source of error in modern high precision
experiments, or may be used for instrument tests, for instance in neutrino mass
retardation spectrometers.
