Date:
Wed, 22/03/201711:45-13:00
Location:
Danciger B building, Seminar room
Lecturer: Prof. Vered Rom-Kedar
Affiliation: Department of Computer Science
and Applied Mathematics,
Weizmann Institute of Science
Abstract:
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 when particles are allowed to enter and exit them through a small hole [5]. The implications of this mechanism on equilibration of energy in slow-fast systems will be discussed [6].
[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 exponential accelerators, PRL 106, 074101, 2011.
[3] V.Gelfreich, V. Rom-Kedar and D. Turaev, "Fermi acceleration and adiabatic invariants for non-autonomous billiards", Chaos 22, 033116 (2012); (21 pages).
[4] V. Gelfreich, V. Rom-Kedar, D. Turaev Oscillating mushrooms: adiabatic theory for a non-ergodic system , 2014, Journal of Physics A : Mathematical and Theoretical, Volume 47 (Number 39). Article number 395101 . ISSN 1751-8113
[5] Leaky Fermi Accelerators, K. Shah, V. Gelfreich, V. Rom-Kedar, D. Turaev, Phys. Rev. E 91, 062920 (2015).
[6] Equilibration of energy in slow-fast systems, K. Shah, V. Gelfreich, D. Turaev, V. Rom-Kedar, in preparation (2017).
Affiliation: Department of Computer Science
and Applied Mathematics,
Weizmann Institute of Science
Abstract:
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 when particles are allowed to enter and exit them through a small hole [5]. The implications of this mechanism on equilibration of energy in slow-fast systems will be discussed [6].
[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 exponential accelerators, PRL 106, 074101, 2011.
[3] V.Gelfreich, V. Rom-Kedar and D. Turaev, "Fermi acceleration and adiabatic invariants for non-autonomous billiards", Chaos 22, 033116 (2012); (21 pages).
[4] V. Gelfreich, V. Rom-Kedar, D. Turaev Oscillating mushrooms: adiabatic theory for a non-ergodic system , 2014, Journal of Physics A : Mathematical and Theoretical, Volume 47 (Number 39). Article number 395101 . ISSN 1751-8113
[5] Leaky Fermi Accelerators, K. Shah, V. Gelfreich, V. Rom-Kedar, D. Turaev, Phys. Rev. E 91, 062920 (2015).
[6] Equilibration of energy in slow-fast systems, K. Shah, V. Gelfreich, D. Turaev, V. Rom-Kedar, in preparation (2017).