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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.

To evaluate the extraction capabilities of ion optics and promote the generation of highly collimated ion beams for propulsion, the properties of the upstream sheath of the ion optics and how those properties relate to the beam divergence are investigated numerically and theoretically. The characteristics of the beam divergence at different grid parameters are studied from the behaviors of the impingement current and divergence angle obtained by simulations. Additionally, the simulations indicate the existence of an optimal structure for the upstream sheath of the ion optics, one that corresponds to a moderate focusing effect and a relatively small divergence angle. The plasma densities at the dividing points of different sheath structures are then derived with the matching model of the ion optics and the Child–Langmuir law, coupled with semi-empirical approaches based on the simulation results. According to the theoretical analyses, the range of existence of the most-desirable sheath structure depends on the strength of the penetration of the extraction field, the voltage between the grid apertures, and the distance between the upstream surfaces of the grids. Also, sensitivity analyses are performed with the numerical partial derivatives of the models to investigate how the grid parameters affect the sheath structures. The plasma densities at the dividing points generally vary synchronously with the changes of grid parameters, but the ranges of variations are different. Consequently, the desirable sheath structure and operating conditions of the ion optics can be achieved by correctly adjusting the grid parameters.

Space-charge effects limit the beam-extraction capability of the ion optics and thus hindering the miniaturization and other performance improvements of ion thrusters. This paper numerically studies the space-charge effects in ion optics using hybrid and full particle-in-cell (PIC) simulations and proposes a modified Child-Langmuir (CL) law. As the injected current increases, the parallel-plane electrode system which corresponds to the classical CL law will reach an unstable and oscillatory state, while the ion optics system remains stable because the electrons from the bulk plasma will compensate for the space-charge effects. Furthermore, the radial expansion of ion beam and the loss of ions on the grids can counteract the space-charge effects when the injected current increases. In general, the space-charge effects in ion optics are self-consistently adjusted by the compensating electrons and the variation of the beam radius. Accordingly, we identify a region in ion optics where generally no electrons exist to exclude the influence of electron compensation, and then we modify the CL law of this region by taking into account the effect of the change in the beam radius. We validate the modified CL law and demonstrate its effectiveness in predicting the operating points of the ion optics, such as the perveance-limit point.