Open Collections

Exponential Fermi accelerators in closed and open geometries and on energy equilibration

Banff International Research Station for Mathematical Innovation and Discovery

In 1949, Fermi proposed a mechanism for the heating of particles in cosmic rays. He suggested that on average, charged particles gain energy from collisions with moving magnetic mirrors since they hit the mirrors more frequently with heads on collisions. Fermi, Ulam and their followers modeled this problem by studying the energy gain of particles moving in billiards with slowly moving boundaries. Until 2010 several examples of such oscillating billiards leading to power- law growth of the particles averaged energy were studied. In 2010 we constructed an oscillating billiard which produces exponential in time growth of the particles energy [1]. The novel mechanism which leads to such an exponential growth is robust and may be extended to arbitrary dimension. Moreover, the exponential rate of the energy gain may be predicted by utilizing adiabatic theory and probabilistic models [2,3]. The extension of these results to billiards with mixed phase space leads to the development of adiabatic theory for non-ergodic systems [4]. Finally, such accelerators lead to a faster energy gain in open systems, when particles are allowed to enter and exit them through a small hole [5]. The implications of this mechanism on transport in extended systems [6] and on equilibration of energy in closed systems like springy billiards will be discussed [7]. These are joint works, mainly with with K. Shah, V. Gelfreich and D. Turaev [1-5],[7] and [6] is with M. Pinkovezky and T. Gilbert: [1] K. Shah, D. Turaev and V. Rom-Kedar, Exponential energy growth in a Fermi accelerator, Phys. Rev. E 81, 056205, 2010. [2] V. Gelfreich, V. Rom-Kedar, K. Shah, D. Turaev, Robust expo- nential accelerators, PRL 106, 074101, 2011.

Mathematics; Dynamical systems and ergodic theory; Probability theory and stochastic processes; Dynamical systems

video/mp4

Author affiliation: Weizmann Institute

2019-04-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69396

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/