Sawtooth events are large and periodic substorms, explosive reconfigurations of the nightside magnetosphere, during which the magnetic field is first stretched away from Earth and then snaps back quickly towards Earth on a 2-3 hour cadence. This usually occurs during magnetic storms, or at least during strong driving conditions from the solar wind.
There is a series of numerical modeling papers that find that ionospheric outflow is likely responsible for both the repeated nature and the large magnitude of the substorms within a sawtooth event interval. The claim is that the initial substorm drives significant outflow from the nightside auroral region, which then mass-loads the tail magnetic field, preventing small-scale reconnection, until the tail reaches some catastrophic level of stretching and the whole tail reconnects at once. This big substorm then causes a big burst of nightside auroral zone ionospheric outflow, continuing the cycle.
Lund et al.  challenge this interpretation. By carefully analyzing satellite observations of ions in the magnetotail during two sawtooth event intervals, they conclude that the ions they see are from the dayside cusp, a region which is not influenced by nightside substorm activity. In fact, they find no evidence of enhanced outflow from the nightside auroral zone.
So, if you picture Earth as your head, this study suggests that it is the outflow from your forehead that matters most for controlling the dynamics of sawtooth oscillations.
Two other related papers that lay the groundwork for this challenge are those by Yu and Ridley  and Liao et al. , one numerical and one observational, that also question the role of the nightside auroral zone as a controlling factor in sawtooth events. The Lund et al.  study demonstrates that the ions near the nightside reconnection site are indeed from the dayside cusp and not the nightside auroral zone, at least for the events they examined.
Citation: Lund, E. J., Nowrouzi, N., Kistler, L. M., Cai, X., & Frey, H. U. . On the role of ionospheric ions in sawtooth events. Journal of Geophysical Research: Space Physics, 123. https://doi.org/10.1002/2017JA024378
—Mike Liemohn, Editor-in-Chief, JGR: Space Physics