Critical assessment of the applicability of the Child-Langmuir law to plasma ion source extraction systems

Applicability of the classical one-dimensional and the recently developed multi-dimensional Child-Langmuir laws to plasma ion source extraction systems is studied. Experiments with a filament-driven multicusp ion source using a simplified extraction system, and comprehensive simulations with two different software packages, suggest that ion beams, which are typically assumed to be space charge or Child-Langmuir limited, are actually divergence-limited. In addition, it was observed that the dynamic plasma meniscus and geometric effects of the extraction system have a greater impact on the ion beam behavior than the effects predicted by the multi-dimensional Child-Langmuir law. Nevertheless, it was found that ion beams produced by the ion source exhibit space charge limited behavior, the beam current scaling with the extraction voltage as $I\propto V^{3/2}$, provided that the entire beam is measured and its divergence is kept small and constant for each extraction voltage. This implies that the applicability of the Child-Langmuir law on a specific extraction system cannot be resolved by a straightforward voltage sweep and beam current measurement but instead, the plasma parameters must be adjusted for each extraction voltage. By shifting the focus from the Child-Langmuir limited framework to the divergence-limited framework, a clearer interpretation of the beam current -- voltage characteristics of extraction systems can be achieved. This shift in perspective may also lead to the development of new design paradigms that can further enhance the performance of plasma ion source extraction systems.