Starting from first principles the physics of radiation reaction for strong laser fields interacting with electrons and positrons is revisited. With the help of a Wigner formulation of QED a derivation of a system of molecular dynamical (MD) equations of motion with a new radiation reaction term and spin is given. The new equations obtained are delay equations which promise to be void of the problems encountered with the LAD theory.
Laser driven ion wave breaking acceleration (IWBA) in a plasma wake field is investigated with the help of particle-in-cell (PIC) simulations and theoretical methods. IWBA operates in relativistic self-transparent plasma for laser intensities in the range of 10<sup>20</sup>-10<sup>23</sup>W/cm<sup>2</sup>. When propagating a laser pulse in a transparent plasma, a co-moving cold ion wave is produced due to ion oscillation. When driven strongly, the oscillation is nonlinear and eventually breaks. Then a fraction of ions is self-injected into the laser driven wake. The wakefield is square-wave like and sensitive to the injected ions. After an injection, the wake weakens and then there is no further injection. This leads to a superior ion pulse with peaked energy spectra; in particular in realistic three-dimensional (3D) geometry, the injection occurs localized close to the laser axis producing highly directed bunches.
The Extreme Light Infrastructure project ELI<sup>1</sup> is aiming at laser intensities up to 10<sup>26</sup> W/cm<sup>2</sup>. At such high
intensities novel aspects of laser-matter and laser-vacuum interaction have to be considered.<sup>2</sup> In particular,
cascades of electrons, positrons, and photons may arise that are capable of absorbing the laser energy efficiently.
In the present paper we report about first simulations of cascading in strong laser fields.
Results of 2DMonte-Carlo simulations of development of QED cascades in intense uniformly rotating electric field
are presented. We consider cascades produced by initially slow electrons. It is shown that under such conditions
stable cascade development starts at field strength of the order of 1% of the QED critical field 5 × 10<sup>29</sup>W/cm<sup>2</sup>.
The cascade yield is growing exponentially in time. Several characteristics of cascade, including average energy of
particles and their mean free path times are computed. Our results are in good agreement with recent estimations
[A. M. Fedotov et al., PRL 105, 080402 (2010)].