For this purpose, I have ported the PWFA into Python for testing new numerical algorithms and different physics models. Some of the ideas I’ve been considering are

**Speed-Limited Particle-In-Cell (SLPIC)**, a mathematical interpretation of the Vlasov equation by University of Colorado researchers, Greg Werner and John Cary. Here, particles will not be allowed to go past a specified “speed limit”, effectively modifying the plasma oscillation for those particularly fast particles. While this method has been proven to be useful for static simulations (for example, simulations of plasma sheath potential), I am interested in whether this method can be useful for eliminating the high-frequency plasma oscillation in dynamic simulations such as my FRC turbulence simulations.**Sparse Grid Techniques for Particle-in-Cell Schemes**, an implementation of some mathematical techniques in PIC simulations by L.F. Ricketson and A.J. Cerfon. This will allow for lower requirements for grid resolution and decrease particle noise, which will allow for more efficient simulations.**Phase-space re-mapping of marker particles**, an idea that came up in discussions during the Wei-Li Lee Gyrokinetic Symposium and was first explored by Y. Cheng and S. Parker, known as “coarse graining phase-space”. In long-running non-linear simulations, marker particles can and will move off of flux-surfaces, and an initially uniformly loaded distribution of marker particles may evolve into an extremely non-uniformly loaded distribution of marker particles, drastically changing the statistical signal-to-noise ratio in regions of interest. By calculating the physical distribution function (whether*f*or*df*), simulations can re-load marker particles in a more statistically relevant distribution through interpolation of that physical distribution function to the marker distribution. This will have the added benefit of allowing the testing of numerical convergence of the number of marker particles, in addition to timestep and grid resolution, at any simulation timestep which has the saved distribution function.**Gyrokinetic Electrons Fully Kinetic Ions (GeFI)**, a physics model by University of California, Irvine researcher, Liu Chen et al. The GeFI model is meant for simulations in the regime where the relevant timescales are between the ion-gyrofrequency and the much higher electron-gyrofrequency. If we were interested in lower frequencies, we could just use the usual gyrokinetic ion model instead. For my FRC simulations where the ions are hot and the magnetic field is weak, this GeFi model can be extremely important.**Asynchronous particle evolution**, a computational approach by Yuri Omelchenko. The main gist of the idea is that particles are not pushed by a finite constant time step but are instead pushed by a finite change in the distribution instead. That is, instead of constant Δt, a Δt is found for each particle based on a constant Δf from the Vlasov equation. Particles are asynchronously pushed but are synchronized for finding the field whenever needed. I honestly believe this is the future of computational work.