Hamiltonian description of self-consistent wave-particle dynamics in a periodic structure Frédéric André, Pierre Bernardi, Nikita M. Ryskin, Fabrice Doveil and Yves Elskens EPL, 103 2 (2013) 28004 Published online: 12 August 2013 DOI: 10.1209/0295-5075/103/28004