Numerical modeling of plasmas often demands a kinetic approach to handle extreme nonlinearities, wave-particle interactions and other non-Maxwellian phenomena. Mathematically this requires the ab initio solution of the relativistic Vlasov-Boltzmann equation for the plasma constituents together with the appropriate Maxwell equations for the electromagnetic fields. State of the art three dimensional PIC simulations involve 1012 particles on 105 cores on modern supercomputers and have become an indispensable tool for exploring the complex physics behind laser-based particle beam and radiation sources.
Recently a complementary modeling paradigm has been established – mesh-free plasma simulation – in which fast summation techniques replace the solution of the field equations on the mesh. The key innovation behind this development is the hierarchical tree algorithm, a rapid O(N log N) technique for evaluating mutual (Coulomb) forces due to an ensemble of charged particles, permitting hi-fidelity simulation of certain collective and collisional plasma phenomena in a variety of physical settings and geometries.
Recent studies performed at the Jülich Supercomputing Centre on the development and application of the above two paradigms will be presented, including electron and ion acceleration with high-intensity, few-cycle lasers, QED-induced opacity of multi-petawatt laser beams interacting with solid targets, and fully kinetic treatments of the Kelvin-Helmholtz and Weibel filamentation instabilities in magnetized plasmas.
Dr. Paul Gibbon is currently working at the Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany as a Head of Computational Science Division. He specializes on computational plasma physics, laser-based particle and radiation sources. Dr. Gibbon is associate professor at Centre for Mathematical Plasma Astrophysics in Leuven, Belgium. He has more than 30 years of experience in Petawatt laser-plasma interactions, Laser acceleration of particles, Femtosecond light sources (XUV, X-, γ-ray), Ultra-strong magnetic fields, Nonlinear wave propagation, Strongly coupled plasmas and Tokamak edge physics.