PIC simulations of magnetized curved shocks
Plasma shocks form between two spatially uniform collision-less plasmas that collide at a large enough speed. Unlike their counterparts in a collisional medium, shocks in collision-less plasma can not be mediated by binary collisions between particles. The absence of binary collisions implies in turn that separate particle populations can form that move through each other. A net current develops if the plasma's electrons and ions move in different directions and it yields the growth of electromagnetic fields. These fields can grow to an amplitude that is large enough to thermalize plasma and to mediate a shock. The properties of the electromagnetic fields in the shock transition layer can vary drastically with the plasma's bulk parameters, e.g. its background magnetic field direction and amplitude and/or the collision speed. Collision-less plasma shocks can thus come in many forms. Most previous PIC simulation studies have addressed unmagnetized and magnetized planar shocks in uniform plasma and these shocks are well-understood. Such studies can be performed in one spatial dimension or in a relatively small two-dimensional simulation box. The increasing performance of supercomputers permits us to study shocks in increasingly large two-dimensional domains. It is now possible to resolve a spatial interval that is large enough to contain curved shocks or shocks in non-uniform plasma. This opens up the possibility to study the stability of non-planar and non-uniform shocks from first principles. It is also possible to study the stability of shocks against blobs or other structures in the inflowing upstream plasma, which is not yet well-understood. I will study with PIC simulations the shocks, which form when the thermal pressure jump between a circular dense plasma and a dilute ambient magnetized plasma accelerates parts of the dense plasma to a speed at which shocks form. By introducing a spatially uniform and unidirectional magnetic field that points along one of the resolved spatial directions, it is possible to study simultaneously the evolution of perpendicular and parallel shocks and shocks with intermediate angles. I will compare the simulation results with the results from laser-plasma experiments performed by my collaborators. I also intend to study the interaction of a stable shock with density- and magnetic field irregularities in the upstream medium and the penetration of such structures through the shock. The results obtained from the latter studies might potentially be relevant for the Earth's bow shock, which forms between the solar wind and the Earth's magneto-sheath. The solar wind plasma can have a variable plasma density and the direction and strength of the magnetic field can change drastically. Modeling a shock with the large size and low curvature of the Earth's bow shock in a two-dimensional PIC simulation is impossible. However, PIC simulations may shed light on some aspects of the shock reaction to a non-uniform upstream medium. Such an aspect might the the localized penetration of a plasma blob through the magnetized shock.