Limit on stably trapped particle fluxes in planetary magnetospheres
Bibliographic record
Abstract
We reexamine the Kennel‐Petschek concept of self‐limitation of stably trapped particle fluxes in a planetary magnetosphere. In contrast to the original Kennel‐Petschek formulation, we carry out a fully relativistic analysis. In addition, we replace the wave reflection criterion in the Kennel‐Petschek theory by the condition that the limit on the stably trapped particle flux is attained in the steady state condition of marginal stability when electromagnetic waves generated at the magnetic equator acquire a specified gain over a given convective growth length. We derive relativistic formulae for the limiting electron integral and differential fluxes for a general planetary radiation belt at a given L shell. The formulae depend explicitly on the spectral index and pitch angle index of the assumed particle distribution and on the ratio of the electron gyrofrequency to the electron plasma frequency. We compare the theoretical limits on the trapped flux with observed energetic electron fluxes at Earth, Jupiter, and Uranus.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".