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arXiv · 2610.07281

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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Matheus Rolim Sales, Leonardo Costa de Souza, Ricardo Luiz Viana, Edson Denis Leonel, Iberê Luiz Caldas. 2026-10-05. Adiabatic confinement and escape in an open billiard. https://arxiv.org/abs/2610.07281

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