Perturbation theory based solution of the pitch-angle dependent cosmic ray diffusion equation
Bibliographic record
Abstract
The motion of cosmic rays and energetic particles in general is described via transport equations. If a pitch-angle dependent description is desired, a Fokker-Planck equation provides the basis for exploring the particle motion. To date, no exact and pure analytical solution to the two-dimensional cosmic ray Fokker-Planck equation has been found. Previous attempts are either solutions of the pitch-angle averaged equation or the space integrated equation. Of course, numerical calculations can easily be performed but those are not very useful in astrophysical applications. In the current paper we employ perturbation theory in order to solve the cosmic ray Fokker-Planck equation. Corrections up to fourth-order to the eigenvalues and second-order eigenfunctions are computed. Our results are compared with previous solutions. Furthermore, we discuss applications such as estimating higher order correlations occurring in analytical treatments of perpendicular transport.
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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) | 0.000 | 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 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".