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The effects of radiation reaction (RR) have been studied extensively by usingthe ultraintense laser interacts with the counter-propagating relativisticelectron. At the laser intensity at the order of $10^{23}$ W/cm$^2$, theeffects of RR are significant in a few laser period for a relativisticelectron. However, the laser at such intensity is tightly focused and the laserenergy is usually assumed to be fixed. Then, the signal of RR and energyconservation cannot be guaranteed. To assess the effects of RR in a tightlyfocused laser pulse and the evolution of the laser energy, we simulate thisinteraction with a beam of $10^9$ electrons by means of Particle-in-Cell (PIC)method. We observed that the effects of RR are suppressed due to theponderomotive force and accompanied by a non-negligible amount of laser fieldenergy reduction. This is due to the ponderomotive force that prevents theelectrons from approaching the center of the laser pulse and leads to theinteraction at weaker field region. At the same time, the laser energy isabsorbed through ponderomotive acceleration. Thus, the kinetic energy of theelectron beam has to be carefully selected such that the effects of RR becomeobvious.

The Suppression of Radiation Reaction and Laser Field Depletion in Laser-Electron beam interaction