On the breaking of a plasma wave in a thermal plasma: I. The structure   of the density singularity
  The structure of the singularity that is formed in a relativistically large amplitude plasma wave close to the wavebreaking limit is found by using a simple waterbag electron distribution function. The electron density distribution in the breaking wave has a typical "peakon" form. The maximum value of the electric field in a thermal breaking plasma is obtained and compared to the cold plasma limit. The results of computer simulations for different initial electron distribution functions are in agreement with the theoretical conclusions. 
Sergei V. Bulanov, Timur Zh. Esirkepov, Masaki Kando, James K. Koga,   Alexander S. Pirozhkov, Tatsufumi Nakamura, Stepan S....
physics.plasm-ph