The radial spread of charged particles emitted from a point source in a magnetic field is a potential source of systematic error for any experiment where magnetic fields guide charged particles to detectors with finite size. Assuming uniform probabil
ity as a function of the phase along the particles helical trajectory, an analytic solution for the radial probability distribution function follows which applies to experiments in which particles are generated throughout a volume that spans a sufficient length along the axis of a homogeneous magnetic field. This approach leads to the same result as a different derivation given by Dubbers et al. But the constant phase approximation does not strictly apply to finite source volumes or fixed positions, which lead to local maxima in the radial distribution of emitted particles at the plane of the detector. A simple method is given to calculate such distributions, then the effect is demonstrated with data from a $^{207}$Bi electron-conversion source in the superconducting solenoid magnet spectrometer of the Ultracold Neutron facility at the Los Alamos Neutron Science Center. Potential future applications of this effect are discussed.
It is generally accepted that the main cause of ultracold neutron (UCN) losses in storage traps is the upscattering to the thermal energy range by hydrogen adsorbed on the surface of the trap walls. However, the data on which this conclusion is based
are poor and contradictory. Here, we report a measurement, performed at the Los Alamos National Laboratory UCN source, of the average energy of the flux of upscattered neutrons after the interaction of UCN with hydrogen bound in semicrystalline polymer PMP (tradename TPX), [C$_{6}$H$_{12}$]$_n$. Our analysis, performed with the MCNP code based on the application of the neutron scattering law to UCN upscattered by bound hydrogen in semicrystalline polyethylene, [C$_{2}$H$_{4}$]$_n$, leads us to a flux average energy value of 26$pm3$ meV in contradiction with previously reported experimental values of 10 to 13 meV and in agreement with the theoretical models of neutron heating implemented in the MCNP code.
