THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e<sup>±</sup> PAIR BEAMS
Bibliographic record
Abstract
ABSTRACT The annihilation of TeV photons from extragalactic TeV sources and the extragalactic background light produces ultrarelativistic beams, which are subject to powerful plasma instabilities that sap their kinetic energy. Here we study the linear phase of the plasma instabilities that these pair beams drive. To this end, we calculate the linear growth rate of the beam-plasma and oblique instability in the electrostatic approximation in both the reactive and kinetic regimes, assuming a Maxwell–Jüttner distribution for the pair beam. We reproduce the well-known reactive and kinetic growth rates for both the beam-plasma and oblique mode. We demonstrate for the oblique instability that there is a broad spectrum of unstable modes that grow at the maximum rate for a wide range of beam temperatures and wave-vector orientations relative to the beam. We also delineate the conditions for applicability for the reactive and kinetic regimes and find that the beam-plasma mode transitions to the reactive regime at a lower Lorentz factor than the oblique mode due to a combination of their different scalings and the anisotropy of the velocity dispersions. Applying these results to the ultrarelativistic beams from TeV blazars, we confirm that these beams are unstable to both the kinetic oblique mode and the reactive beam-plasma mode. These results are important in understanding how powerful plasma instabilities may sap the energy of the ultrarelativistic beams as they propagate through intergalactic space.
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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 | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".