Experimental verification of the space charge law for ion beams from a plasma ion source

Rautenbach, W.L.

doi:10.1016/0029-554x(61)90126-4

Cited by 21 publications

(6 citation statements)

References 10 publications

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“…It is this variation in the shape of the meniscus that results in the various beam shapes that are observed. 26 In this paper, we shall concentrate on spherical and cylindrical symmetry but the reasoning in both cases can be extended to planar diodes, where the extraction field is so as to be equal to the sheath voltage for a flat sheath and the electrodes are designed to accommodate a parallel beam. In addition, focus will be on positive ion extraction.…”

Section: A Statement Of the Problemmentioning

confidence: 99%

Generalization of the Langmuir–Blodgett laws for a nonzero potential gradient

2005

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The Langmuir-Blodgett laws for cylindrical and spherical diodes and the Child-Langmuir law for planar diodes repose on the assumption that the electric field at the emission surface is zero. In the case of ion beam extraction from a plasma, the Langmuir-Blodgett relations are the typical tools of study, however, their use under the above assumption can lead to significant error in the beam distribution functions. This is because the potential gradient at the sheath/beam interface is nonzero and attains, in most practical ion beam extractors, some hundreds of kilovolts per meter. In this paper generalizations to the standard analysis of the spherical and cylindrical diodes to incorporate this difference in boundary condition are presented and the results are compared to the familiar Langmuir-Blodgett relation.

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Section: A Statement Of the Problemmentioning

confidence: 99%

Generalization of the Langmuir–Blodgett laws for a nonzero potential gradient

2005

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“…This is justified experimentally in the literature by observing the evolution of beam form as a function of extraction voltage or extracted current. 12 As the extraction orifice is circular in our experiment, the flow of particles in the extractor can be thought of as a cone of current flowing between two concentric spheres. A solution to the Child law under the assumption of current flow between concentric spheres was given by Langmuir and Blodgett.…”

Section: Extraction From a Plasmamentioning

confidence: 99%

“…The changing shape of the plasma meniscus leads to three different beam forms. 12 Assuming zero ion temperature, a sufficiently concave meniscus results in a convergent beam and a sufficiently convex meniscus produces a divergent beam. At some point between being convergent and divergent, the plasma meniscus is such that the extracted beam is parallel ͑Fig.…”

Section: B Angular Divergencementioning

confidence: 99%

Comparison between experiment and two simulation strategies for the extraction of focused ion beams

Sutherland

Keller

Irzyk

et al. 2004

Review of Scientific Instruments

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Computer simulation codes for the extraction of ion beams have been used for over three decades. Here we describe medium current extraction ͑ϳ1 mA͒ from a high density plasma source (Ͼ10 12 cm Ϫ3) with a three electrode extraction system and compare the extracted current and the angular divergence with the results of two computer simulation programs. The first is called PBgun and is a commercially available ray tracing code; the second, called simulation d'extraction de faisceaux d'ions ͑SEFI͒ uses a particle-in-cell code to simulate the plasma and ion beam. It is the purpose of this article to ascertain whether these codes can adequately model the plasma/beam interface and hence successfully predict the extracted current and beam form across a broad range of extraction parameters. We found that SEFI could accurately predict the function of extracted current versus extraction voltage and that PBgun gave accurate simulations when the current or current density could be specified near the meniscus. Also for a thin plasma aperture and a fixed current at the meniscus, PBgun gave roughly 60% of the functional dependence of the extracted current on the extraction voltage and the other 40% on variations in the plasma pre-sheath. Both codes had some error from beam crossing near the axis which changed the amount of meniscus curvature predicted.

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“…Despite of there being more than 100 years since the original CL law was first published, it is still commonly cited and used in publications and textbooks relating to accelerator and ion source physics [5,6]. To the authors' knowledge the applicability of the CL law (of type I ∝ kV 3/2 , where k is a constant) to extraction of ion beams from plasma ion sources was first studied by Rautenbach in 1960s, who found it to be 'basically correct' and went on to state that 'it should be true for all plasma ion sources' [7]. Since then the CL law has been widely accepted and adopted by the ion source community.…”

Section: Introductionmentioning

confidence: 99%

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

Kosonen

Kalvas

Toivanen

et al. 2023

Plasma Sources Sci. Technol.

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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.

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Experimental verification of the space charge law for ion beams from a plasma ion source

Cited by 21 publications

References 10 publications

Generalization of the Langmuir–Blodgett laws for a nonzero potential gradient

Generalization of the Langmuir–Blodgett laws for a nonzero potential gradient

Comparison between experiment and two simulation strategies for the extraction of focused ion beams

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

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