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The Vlasov-Poisson equations describe the evolution of a collisionless plasma, represented through a probability density function (PDF) that self-interacts via an electrostatic force. One of the main difficulties in numerically solving this system is the severe time-step restriction that arises from parts of the PDF associated with moderate-to-large velocities. The dominant approach in the plasma physics community for removing these time-step restrictions is the so-called particle-in-cell (PIC) method, which discretizes the distribution function into a set of macro-particles, while the electric field is represented on a mesh. Several alternatives to this approach exist, including fully Lagrangian, fully Eulerian, and so-called semi-Lagrangian methods. The focus of this work is the semi-Lagrangian approach, which begins with a grid-based Eulerian representation of both the PDF and the electric field, then evolves the PDF via Lagrangian dynamics, and finally projects this evolved field back onto the original Eulerian mesh. In particular, we develop in this work a method that discretizes the 1+1 Vlasov-Poisson system via a high-order discontinuous Galerkin (DG) method in phase space, and an operator split, semi-Lagrangian method in time. Second-order accuracy in time is relatively easy to achieve via Strang operator splitting. With additional work, using higher-order splitting and a higher-order method of characteristics, we also demonstrate how to push this scheme to fourth-order accuracy in time. We show how to resolve all of the Lagrangian dynamics in such a way that mass is exactly conserved, positivity is maintained, and high-order accuracy is achieved. The Poisson equation is solved to high-order via the smallest stencil local discontinuous Galerkin (LDG) approach. We test the proposed scheme on several standard test cases., Comment: 48 pages, 13 figures

We describe the problem of regular small telemetry losses incurred during coherency mode transitions in Cassini’s telecommunication. The project did not originally plan any corrective steps for avoiding these data losses, because of 1) the disparity between the small durations of the transitions (1-2 min) and large playback capability losses (15 min) needed for bracketing the transition time spans and 2) the unpredictable content of data downlinking during the transitions. However, as the intense science data return from the tour began, it became apparent that the impact of these small losses can sometimes be significant. We provide two examples of the impact on Radar-dedicated Titan flybys. In general, the impacts are larger for high-rate data and for data acquired during a targeted flyby of Titan and other icy satellites. Although the content of data during a transition for every downlink pass is unpredictable, we are certain that some important data will be lost on downlink passes dedicated to transmit the flyby data and it does not matter what part of the data will be hit by the transitions. We collected more than 200 days of data from Cassini tour operations between June 2004 and February 2005 to analyze the distributions of the start time and duration of the transitions. We found that the occurrence of a transition can be predicted within a 5-min window, with 95 percent confidence. Given that, it is possible to eliminate the data losses by pausing playback at the beginning of a transition for 5 minutes and resuming playback after transition completion. We briefly describe three operational fixes as to how to implement the playback pause, with the pros and cons for each method. Finally, we report the results of the method chosen by the project and implemented on the spacecraft for several Titan and icy satellites flybys between September and October, 2005.