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Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances
1Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany. alx_it@yahoo.com
Chaos (Woodbury, N.Y.)
|July 5, 2012
Summary
Moving boundaries in a slowly rotating rectangular billiard can cause particle acceleration. Resonance phenomena disrupt adiabatic invariance, leading to unlimited particle energy gain.
Area of Science:
- Classical mechanics
- Dynamical systems theory
- Nonlinear dynamics
Background:
- Billiard systems model complex dynamics.
- Adiabatic invariance is crucial in conservative systems.
- Slowly evolving systems can exhibit resonant phenomena.
Purpose of the Study:
- Investigate particle dynamics in a rotating rectangular billiard with moving boundaries.
- Analyze the impact of resonance conditions on particle behavior.
- Examine the breakdown of adiabatic invariance.
Main Methods:
- Canonical perturbation theory applied to a slowly rotating system.
- Analysis of resonance conditions and their implications.
- Study of scattering and capture phenomena.
Main Results:
- Resonance conditions are identified during slow evolution.
- Scattering and capture into resonance are observed.
- Breakdown of adiabatic invariance leads to particle acceleration.
Conclusions:
- Moving boundaries in rotating billiards can induce resonance.
- Resonance phenomena are key to unlimited particle acceleration.
- Adiabatic invariance is not preserved under these conditions.
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