Relation of the runaway avalanche threshold to momentum space topology

The underlying physics responsible for the formation of an avalanche instability due to the generation of secondary electrons is studied. A careful examination of the momentum space topology of the runaway electron population is carried out with an eye toward identifying how qualitative changes in the momentum space of the runaway electrons is correlated with the avalanche threshold. It is found that the avalanche threshold is tied to the merger of an O and X point in the momentum space of the primary runaway electron population. Such a change of the momentum space topology is shown to be accurately described by a simple analytic model, thus providing a powerful means of determining the avalanche threshold for a range of model assumptions. (paper)