ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: choose a unique for each particle upon emission. We assume the field changes on a length scale , where λ is a model parameter, and at the beginning of each time step we calculate the timescale for the particle to experience a significant change in :where z is a random number between 0 and 1. If is less than the time for a particle to leave a zone or end the grid time step, the magnetic “scattering” action is selected, the particle position and energy are updated, and a new field direction is chosen at random. The re-orientation preserves energy and the magnitude of the momentum in the cmf. This is reasonable because these discrete scatters are standing in for smoother and more gradual field gradients. However, it also leads, on average, to energy losses in the center-of-explosion frame, which decrease thermalization efficiency. This can be thought of as the particles transferring their energy to the bulk kinetic energy of the ejecta rather than the thermal background. It is a small effect. The propagation of a particle along field lines depends on total velocity and Particles are emitted on the grid with a random direction defined by the unit vector , so μ is . In the case of radial fields, μ evolves to preserve the magnetic adiabatic invariant . This evolution encourages outward motion. Inward-moving particles encounter ever-stronger fields, and decrease their inward velocity in response, eventually “mirroring” off the field and beginning to travel outward. Particles streaming outward move into weaker magnetic fields, so their pitch angle increases and they stream out even faster. We include magnetic beaming and mirroring only for radial fields, where changes to the pitch angle facilitate particle escape and can be meaningful for thermalization. Particles in toroidal fields are confined to one region of velocity space; changes in their pitch angle cannot promote outward motion and so cannot affect thermalization. While particles in random fields could experience beaming and mirroring, they may also undergo pitch angle scattering—interactions with small fluctuations in the field that can change pitch angle, and would act to isotropize μ , counter to beaming and mirroring. We assume the two effects balance out, and hold pitch angle constant for particles in random and toroidal fields. A.3.2. Fission Fragment Transport As discussed in Section 2.2 , at late times, fission fragments may have Larmor radii comparable to the magnetic field coherence length. This could affect the transport, especially for disordered fields, where field lines in close proximity may have very different orientations. In such a system, the guiding center approximation breaks down, and the motion of the particle must be resolved. We estimate the importance of this effect by modeling fission fragment transport in a tangled field as a random walk of the fragment itself (as opposed to its guiding center). In this simple scheme, fission fragments travel in straight lines and