Tunable Fermi acceleration in a nondissipative driven magnetic billiard

Some dynamical properties for an oval billiard with a scatterer in its interior are studied. The dynamics consists of a classical particle colliding between an inner circle and an external boundary given by an oval, elliptical, or circle shapes, exploring for the first time some natural generalizations. The billiard is indeed a generalization of the annular billiard, which is of strong interest for understanding marginally unstable periodic orbits and their role in the boundary between regular and chaotic regions in both classical and quantum (including experimental) systems. For the oval billiard, which has a mixed phase space, the presence of an obstacle is an interesting addition. We demonstrate, with details, how to obtain the equations of the mapping, and the changes in the phase space are discussed. We study the linear stability of some fixed points and show both analytically and numerically the occurrence of direct and inverse parabolic bifurcations. Lyapunov exponents and generalized bifurcation diagrams are obtained. Moreover, histograms of the number of successive iterations for orbits that stay in a cusp are studied. These histograms are shown to be scaling invariant when changing the radius of the scatterer, and they have a power law slope around -3. The results here can be generalized to other kinds of external boundaries.

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Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

Costa

Dettmann

Oliveira

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Critical Velocity for the Onset of Fast Fermi Acceleration

Lubchenko

Savin

2022

Int. J. Bifurcation Chaos

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One of the well-known effects in nonlinear science is Fermi acceleration that is the unlimited growth of the velocity of a particle when it collides with oscillating walls. It is rather common for time-dependent billiard-like systems in which a particle moves inside a closed oscillating boundary and elastically collides with it. But if the oscillations are weak, more complex effects may arise in the system. Earlier one of these effects was shown for time-dependent stadium-like billiards. In the case of a weak boundary oscillation the particle’s velocity grows if its initial value is greater than a certain critical value and tends to the limit otherwise. We consider the dynamics of a particle moving between two planar and harmonically corrugated walls and colliding elastically with them. We tried to find a similar effect and revealed that the ensemble-averaged velocity grows rapidly if the initial velocity is larger than some critical value. Otherwise, the ensemble-averaged velocity grows much slower and the velocities of all particles tend to become equal. We numerically estimated the band of the oscillation amplitude in which this effect exists and illustrated the dependence of the behavior of the critical initial velocity on various parameters.

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Tunable Fermi acceleration in a nondissipative driven magnetic billiard

Cited by 2 publications

References 26 publications

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

Critical Velocity for the Onset of Fast Fermi Acceleration

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