Numerical and theoretical modeling of the sheath upstream of ion optics: sheath structure transition and its effect on the beam divergence
Haolin Li, Xuchu Yuan, Jinyuan Yang, Anbang Sun
Abstract
Abstract The grasp of the sheath characteristics is fundamental to evaluate the extraction capabilities of ion optics and accommodate the wide application of ion sources. A one-dimensional theoretical model is developed to investigate the sheath upstream of ion optics as well as the matching relation between the ion optics and plasma, by simplifying and decomposing the Poisson’s equation at the outer surface and centerline of the grid aperture. The one-dimensional model is validated by 2D3V hybrid simulations which are also applied to visualize the sheath structure and ion beam divergence. With the increase of plasma density, it is found that the upstream sheath will transform gradually into a sheath near the plate electrode at first and then enter the screen aperture with a sheath edge approximately paralleling to the meniscus. Accordingly, the structure of the upstream sheath can be classified into four kinds which correspond to different beam divergence. The structure transition of the upstream sheath reflects the interaction between the extraction field and plasma, and the ion optics is considered to work at the matching point when the plasma is relatively balanced with the extraction field. Around the matching point, a small beam divergence angle can be achieved without the occurrence of over-perveance. Then a matching model is proposed based on the characteristics of the potential distribution at the matching point. It is verified to be effective of the model for quickly analyzing the ion beam divergence characteristics and determining an ideal operating range of the ion optics.