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PreprintCC BY 4.0arXiv

Adiabatic confinement and escape in an open billiard

  • Matheus Rolim Sales
  • Leonardo Costa de Souza
  • Ricardo Luiz Viana
  • Edson Denis Leonel
  • Iberê Luiz Caldas
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Abstract

We introduce a stationary, field-free billiard that reproduces the adiabatic confinement mechanism of a magnetic mirror through boundary geometry alone. Rapid transverse reflections generate an approximately conserved action that plays the role of the magnetic moment, producing an effective longitudinal barrier and a nominal loss cone for escape. For the half-width profile considered here, confinement is controlled by a competition between mirror strength and adiabaticity: shortening the profile increases the mirror ratio but also reduces the accuracy of the adiabatic approximation. As a result, the escaping fraction is nonmonotonic and confinement is strongest at an intermediate profile length. We characterize the associated phase-space structure, escape-time statistics, and escape basins, revealing long-lived transient motion and a strong sensitivity of the final escape direction to the initial condition that persists as the uncertainty in the initial condition is reduced.

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Cite

BibTeXRIS
BibTeX
@misc{sales2026adiabatic,
  title = {{Adiabatic confinement and escape in an open billiard}},
  author = {Matheus Rolim Sales and Leonardo Costa de Souza and Ricardo Luiz Viana and Edson Denis Leonel and Iberê Luiz Caldas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07281},
  eprint = {2610.07281},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07281},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Adiabatic confinement and escape in an open billiard
AU  - Matheus Rolim Sales
AU  - Leonardo Costa de Souza
AU  - Ricardo Luiz Viana
AU  - Edson Denis Leonel
AU  - Iberê Luiz Caldas
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07281
UR  - https://arxiv.org/abs/2610.07281
AB  - We introduce a stationary, field-free billiard that reproduces the adiabatic confinement mechanism of a magnetic mirror through boundary geometry alone. Rapid transverse reflections generate an approximately conserved action that plays the role of the magnetic moment, producing an effective longitudinal barrier and a nominal loss cone for escape. For the half-width profile considered here, confinement is controlled by a competition between mirror strength and adiabaticity: shortening the profile increases the mirror ratio but also reduces the accuracy of the adiabatic approximation. As a result, the escaping fraction is nonmonotonic and confinement is strongest at an intermediate profile length. We characterize the associated phase-space structure, escape-time statistics, and escape basins, revealing long-lived transient motion and a strong sensitivity of the final escape direction to the initial condition that persists as the uncertainty in the initial condition is reduced.
ER  -