The macroscopic stability, transport and RF wave propagation mechanisms determining the performance of magnetic confinement fusion reactors are highly nonlinear, and interact over a wide range of temporal and spatial scales. A sound approach to study these mechanisms computationally is to separately develop codes describing the phenomena at each given length and time scale, and then couple them in a self-consistent way.
In my group, we develop fast, high order solvers to compute plasma equilibria in magnetic fusion experiments (stellarators, tokamak, spherical torus). These solvers need to be fast, so the computational time is mostly spent on the expensive parts of the simulations (i.e. MHD stability, RF wave propagation and microturbulence simulations). The equilibrium solvers also need to be accurate, so errors in the calculated equilibrium do not propagate to other elements of the simulations.
In order to satisfy the speed and accuracy requirements, we use integral equation methods to construct our solvers. We collaborate with Leslie Greengard's and Mike O'Neil's research group on these topics.

In high intensity cyclotrons, the self electric force due to the charges of the accelerated particles is strong enough that it can have a significant effect on the particle dynamics during the accelerating phase. As a result, as the beam of charged particles rotates around the cyclotron and gets accelerated, it can also spiral on itself (see figure on the left) or even break up because of this self electric field. Understanding these mechanisms is crucial if one wants to design efficient cyclotrons capable of producing clean intense beams.
In my research group, we use continuum kinetic theory for nonneutral plasmas to develop models and design numerical methods that yield new analytic insight into these phenomena and have the potential to significantly accelerate existing simulation codes.
As an alternative and complementary approach, we also investigate noise reduction strategies to improve the speed and accuracy of Particle-in-Cell (PIC) codes, which are the current codes of choice for the beam dynamics community. Presently, we are particularly interested in the potential gains obtained by combining the PIC scheme with sparse grids approaches.

For the analysis and interpretation of experimental results and the design of new experiments, it is important to account for uncertainties, such as measurement errors, or fabrication uncertainties, and identify how these uncertainties propagate and impact the physics and engineering quantities of interest.
In my group, we develop multi-fidelity methods for uncertainty quantification, currently applied to the analysis of turbulent transport and energetic particle confinement in magnetic confinement fusion experiments. For this work, we collaborate with Benjamin Peherstorfer and Di Qi.

I am interested in a variety of other problems in physics and engineering for which methods of applied mathematics and high performance computing can help improve the accuracy and/or reduce the computational time of large scale simulations. For example, I am collaborating with Jiehang Zhang and Yue Shi (NYU Physics) for the simulation of ion crystal formation and stability in linear Paul traps for quantum computing applications.
I also work with Guillaume Le Bars, Joaquim Loizu, Stefano Alberti, and Jean-Philippe Hogge (EPFL) on the electron dynamics in gyrotron guns.
Finally, I am interested in listening to any idea you might want to suggest or discuss with me. Feel free to contact me!