Electron collection and thermionic emission from a spherical dust grain in the space-charge limited regime
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Bibliographic record
Abstract
The collection and emission of electrons from a spherical body in the Space-Charge Limited (SCL) regime are investigated. When a Virtual Cathode (VC) in the potential profile around the body is present, the barrier in the effective potential energy of electrons is assumed to be located near the position of the minimum of the VC potential, for both collected and emitted electrons. This assumption is confirmed to be reasonable in the case of a double Yukawa potential profile and allows the SCL cross-section for electron collection and the emitted electron’s trapped-passing boundary to be written in a simple way. An expression for the collection current for Maxwellian electrons is derived and is shown to recover the classical Orbital Motion Limited (OML) theory when the VC vanishes. Using the same assumptions, an expression for the thermionic emission current in the SCL regime is also obtained and comparisons with the OML+ theory are made. Finally, an expression for the dust electric charge in the SCL regime is derived and shown to give drastically different results when compared to the commonly used formula (obtained from a Yukawa potential profile). Consequences in the framework of dust in tokamak plasmas are discussed.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it