Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Abstract

Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables velocity and time. The system is characterized by a control parameter $\epsilon$ and experiences a transition from integrable ($\epsilon =0$) to non integrable ($\epsilon \ne 0$). For small values of $\epsilon$, the phase space shows a mixed structure where periodic islands, chaotic seas and invariant tori coexist. As the parameter $\epsilon$ increases and reaches a critical value ${\epsilon }_c$ all invariant tori are destroyed and the chaotic sea spreads over the phase space leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space. For large $\epsilon$, the survival probability decays exponentially when it turns into a slower decay as the control parameter $\epsilon$ is reduced. The slower decay is related to trapping dynamics, slowing the Fermi Acceleration, i.e., unbounded growth of the velocity

arXiv comment9 pages, 7 figures

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• Leaking from the phase space of the Riemann-Liouville fractional standard map
• Statistical investigation and thermal properties for a 1-D impact system with dissipation
• Transition from normal to ballistic diffusion in a one-dimensional impact system
• Normal and anomalous diffusion in a bouncing ball over an irregular surface
• A dynamical survey of the trans-Neptunian region II.: On the nature of chaotic diffusion
• Diffusion and escape times in the open-leaky standard map
• Stochastic Web Map: Survival probability and escape frequency
• Controlling synchronization in coupled area-preserving maps using stickiness