Effects of the extraction voltage applied by the puller-electrode on the H$^−$ extraction in the Linac4 negative ion source

In order to understand the H$^−$ extraction mechanism and investigate the effect of the extraction voltage applied by the puller-electrode on the H$^−$ extraction in the Linac4 negative ion source, we are developing a 2D3V-PIC (two dimensions in the real space and three dimensions in the velocity space, Particle in Cell) model with volume produced H$^−$ ions. It is shown that how to take the magnetic filter field direction is important for the 2D modeling to take into account the important 3D effect of electron $E \times B$ drift. It is also shown that the meniscus formation is not symmetric due to the electron $E \times B$ drift in the extraction region and the divergence of the H$^−$ beam is asymmetric. In order to make more quantitative comparison of the extracted H$^−$ and electron currents with the experiments and 3D modeling, further improvements, especially the electron loss along the magnetic filter field line will be needed