Eur. Phys. J. D (2014) 68: 178
https://doi.org/10.1140/epjd/e2014-50153-0

Regular Article

Phase space dynamics after the breaking of a relativistic Langmuir wave in a thermal plasma^*

¹ Department of Physics “Enrico Fermi”, University of Pisa, 56127 Pisa, Italy
² National Institute of Optics, National Research Council (CNR/INO), 56127 Pisa, Italy
³ QuBS, Japan Atomic Energy Agency, 1-8-7 Umemidai, Kizugawa, 619-0215 Kyoto, Japan

^a e-mail: pegoraro@df.unipi.it

Received: 27 February 2014
Received in final form: 17 April 2014
Published online: 27 June 2014

Abstract

The relativistic Vlasov equation is integrated numerically in an Eulerian framework in order to investigate the phase space development of the wavebreak of a relativistic Langmuir wave in a thermal plasma. Relativistic kinematic and beam loading effects lead to a “differential retardation” in the time required by the electrons to evolve in phase space, the largest momentum electrons taking the longest time. This leads to the formation of a long lasting spike in momentum space at the wavebreak position that propagates with a velocity close to the speed of light and to an extremely steep density change in coordinate space.