Effects of the extraction voltage on the beam divergence for a H$^−$ ion source

Negative hydrogen (H$^−$) ion sources have a wide range of applications. The general requirement for these H$^−$ ion sources is to produce intense H$^−$ ion beams with good beam optics. The purpose of this paper is to clarify the effects of the beam extraction voltage on the beam divergence angle by three-dimensional Particle-in-Cell (PIC) modeling. Perveance matching has been studied for a wide range of the extraction voltage with the model geometry of a Linac4 H$^−$ ion source. The extracted H$^−$ beam divergence angle is evaluated for extraction voltages ranging from 7 to 14 kV by using the Keio-BFX PIC code. The results show divergence minima in the range of 9.2–11.5 kV for the case without surface H$^−$ production, which correspond to experimental results. The dependence of divergence on the extraction voltage is explained by the change of the shape of the meniscus. In particular, a flat meniscus corresponds to low beam divergence, and particles extracted through the center of the meniscus have a lower divergence than particles extracted near the Plasma Electrode.