Bibliographic record
Abstract
Abstract An exact formula for the limit of the safety factor q at a magnetic axis is derived for the general up-down asymmetric plasma equilibria possessing axial symmetry, generalizing Bellan’s formula for the up-down symmetric ones. New exact axisymmetric plasma equilibria depending on arbitrary parameters α , ξ , b kn , z kn , where k = 1, ⋯, M , n = 1⋯, N , are constructed ( α ≠ 0 is a scaling parameter), which are up-down asymmetric in general. The equilibria are not force-free if ξ ≠ 0 and satisfy Beltrami equation if ξ = 0. For some values of ξ the magnetic field and electric current fluxes have isolated invariant toroidal magnetic rings, for another ξ they have invariant spheroids (blobs) and for some values of ξ both invariant toroidal rings and spheroids (blobs). A generalization of the Chandrasekhar – Fermi – Prendergast magnetostatic model of a magnetic star is presented where plasma velocity V ( x ) is non-zero.
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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 | 0.000 | 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.163 | 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".