# Particle-in-cell modeling for near-surface cusp confinement of micro-scale plasma (Past)

Magnetic cusp confinement of plasma at conducting surfaces involves interactions between a highly divergent magnetic field, ions, electrons, neutral particles, and the pre-sheath and sheath conditions that develop along the surface boundary. Large plasma devices have benefitted greatly by using permanent magnet cusps for bulk plasma confinement for both terrestrial and space applications; however, the magnetic cusp confinement mechanisms and the associated plasma dynamics very near the conducting surface are poorly understood. This lack of understanding has prevented researchers of micro-scale discharges from fully realizing the benefits of cusp confinement and control at smaller scales, and has also prevented the optimization of larger discharges.

We develop a computational model that properly treats the behavior of plasma very near the wall for a cusp confined plasma. The model will also serve as a tool to reveal important plasma mechanisms in the cusp region and will aid in the development of analytical description of particle motion in this region due to particle drifts, collisions, and electric field. The computational model employs the iterative Monte-Carlo (MC) method, tracking super-particles of different species (high energy primary electrons, ions, and plasma electrons) separately. In the model, particles are moved in electric and magnetic fields while they are weighted to the computational grid at every time-step. Once all the particles are tracked, the electric potential and field are updated using the densities computed from the last particle tracking subroutine. These calculations are repeated until the electric potential converges to a solution. This model can be considered as a simplified version of a particle-in-cell (PIC) model commonly used for kinetic simulation of plasma, as the electric field is computed asynchronously with particle tracking instead of being updated while the particles are tracked.

This model will be extended to a hybrid model treating ions and plasma electrons as fluids, and will be used as a tool to design an efficient micro-scale discharge. The model will use a magnetic field aligned mesh to minimize the numerical diffusion that takes place when the mesh is not aligned with the magnetic field.