The mother of all F ring simulations

There was a paper published recently on new observations of the F ring. The F ring is a very dynamic narrow ring a bit outside of Saturn's main rings. The main reason it is so dynamic is that it has two moons that orbit near it, Prometheus and Pandora. I have done some of my own work on the F ring because it is a fun system to simulate. I started with simulations that included just Prometheus. Putting Prometheus on an eccentric orbit alone is challenging because it forces the simulation to use a fairly large cell size. The cell needs to have dimensions such that the full cell drifts past Prometheus in one orbit of the moon so that the perturbations on the two edges match and wrapping doesn't create a discontinuity.

If you only have Prometheus though, you create a ring that is perfectly periodic and the real F ring isn't. To break this, you need to include Pandora. The problem is, if you include Pandora you lose any chance to have a small cell. Prometheus and Pandora are not in a mean motion resonance so to have proper boundaries, the simulation has to be global. This means that it needs to go all the way around Saturn. A few years ago I spent some computer time doing a global F ring simulation with Prometheus and Pandora, both on eccentric orbits.

The movie shows an initially uniform ring getting kicks from the moons. The kicks from Prometheus are larger than those from Pandora because of size and proximity. It shows how collisions in the compression regions lead to negative diffusion and cause the ring material to move into a tight core. It also shows fairly complex structures forming.

While significant, this simulation has three significant limitations. First, the radial extent of the particles is too small. Second, the F ring is circular when in reality the ring is eccentric. Third, there is no self-gravity between the ring particles. I have tried at times to address different parts of this. In fact, I ran an eccentric ring simulation for a while. However, the guiding center coordinates we normally use do not handle this properly and I got an artificial precession of the rings relative to the moons. Now I am giving it another shot and trying to run what you might call the mother of all F ring simulations. First, I spread out the particle distribution a fair bit. It is now a Gaussian that covers roughly 100 km radially. Second, I'm using an extended form of the guiding center coordinates that Glen Stewart derived as they should handle the eccentric ring properly. Third, everything is self-gravitating. Even the moons are normal particles having normal gravity and collisions.

This simulation has 50 million particles in it. The down side of doing that with full self-gravity is that even though I am doing it across 12 machines and 96 cores, it is taking about 1.5 days to complete an orbit. At that rate, it will complete about two synodic periods in a year. From earlier work I know that I need 3-4 synodic periods before the system will get out of the transient state. Maybe I need to ask someone for some faster computers. :)