The classical nonlinear laser-plasma interaction theory is corrected. Giventhe effects of vacuum polarization (induced by extreme laser) as nonlinearmedia response, one-dimensional wave equations of a monochromatic laser fieldare derived from the Heisenberg-Euler Lagrangian density and a derivativecorrection with the first order quantum electrodynamic (QED) effects. A moresuitable model to formulate the interactions of extreme laser andhigh-energy-density plasma is developed. In the results, the enhanced effect ofvacuum polarization will be discussed and shown.
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