Numerical and theoretical modeling of the sheath upstream of ion optics: sheath structure transition and its effect on the beam divergence

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.

On the space-charge effects in the beam extraction process of ion thrusters: the roles of compensating electrons and changing beam radius

“…Assuming n i is the ion density, the positive ion CL sheath described by equation ( 2) is a space-charge layer where the contribution of the electrons in the sheath is negligible compared with the ions [7,27]. However, depending on the plasma properties and grid parameters, the upstream sheath of the ion optics can take on different structures [18], which means that the electrons will penetrate in the ion sheath against the retarding electric field of the sheath and compensate for the space-charge effects. Accordingly, there is a need for further research on the space-charge effects in ion optics considering the compensation effects.…”

“…Here we set four simulation cases: #1 represents the parallel-plane electrodes system with the ion injection only; #2 is the parallel-plane electrodes system where both ions and electrons are injected; #3 represents the ion optics system where both ions and electrons are injected and equation ( 4) is used in the regions upstream of SG and downstream of AG; #4 is similar to #3 but equation ( 4) is used in the upstream and downstream regions of AG. Note that the electrons from the bulk plasma are forcibly prevented from entering the region behind z = 0 in #3 with such a setup, while #4 is a more realistic case [18]. The cases with the injection of electrons are simulated with the hybrid model introduced in section 2.…”

“…The classical CL law provides a reliable description of the space-charge effects of the simplest 1D scene, but it has been continually extended to accommodate more and more extensive practical applications [11], such as the considerations of the finite injection velocities of particles [12], radio-frequency biased electrodes [13], coaxial cylindrical or concentric spherical diodes [14,15], two-or three-dimensional scene [16,17], etc. However, the space-charge effects in ion optics still lack investigation and understanding due to the difficulties in the experimental measurement and theoretical modeling of it [2,18]. Previous studies have made some attempts to build a reliable model for evaluating the space-charge effects in ion optics.…”

“…The CL law is essentially a mathematical description of the CL sheath, but earlier experimental and numerical studies demonstrated that the properties of the sheath in the ion optics show significant differences from that of the sheath in a planeparallel electrode system [18,25,27]. In the ion optics, the beam divergence and the structure of the sheath are typically determined by the plasma properties and the grid parameters [18], which leads to the space charge distribution in the CL sheath not being constant and having no analytic solution yet. For example, the CL sheath thickness l e , which is also considered to be the effective ion acceleration length [2], is not constant when the plasma parameters change [18,28].…”

“…In the ion optics, the beam divergence and the structure of the sheath are typically determined by the plasma properties and the grid parameters [18], which leads to the space charge distribution in the CL sheath not being constant and having no analytic solution yet. For example, the CL sheath thickness l e , which is also considered to be the effective ion acceleration length [2], is not constant when the plasma parameters change [18,28]. Besides, the space-charge effects exist in multiple directions of the ion beam, leading to the complex ion dynamics in the CL sheath and changeable sheath structure.…”