Can the Effective Potential of a Linear Quadrupole be Extended to Values of the Mathieu Parameter <b><i>q</i></b> Up to 0.90?
Bibliographic record
Abstract
The motion of ions in a linear quadrupole is usually described by solutions to the Mathieu equation. A simplifying approximation to this theory that is widely used for low values of the Mathieu parameters a and q describes ion motion in an effective potential. In this work, we have calculated the effective potential for any q from displacements of calculated ion trajectories caused by a dipole DC electric field. It is assumed that the dipole DC electric field at the center of the displaced trajectory is countered by an "effective" electric field. For all q values, the effective electric field is found to increase linearly with the distance from the center of the quadrupole. The trapping forces probed in this way increase continuously with q up to the first stability region boundary at q=0.908. The well depth (D) at any q can be described by D = q[V(rf)/c], where c=3.955±0.005, very similar to the standard effective potential model with c=4.000.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".