Non-linear interaction of laser light with vacuum: contributions to the energy density and pressure in presence of an intense magnetic field

Recent simulations show that very large electric and magnetic fields near the kilo Tesla strength will likely be generated by ultra-intense lasers at existing facilities over distances of hundreds microns in underdense plasmas. Stronger ones are even expected future although some technical dificulties must overcome. In addition, it has been shown vacuum exhibits a peculiar non-linear behaviour presence high field strengths. this work we interested analysis thermodynamical contributions to energy density pressure when radiation interacts with an external field. Using Euler-Heisenberg formalism regime weak i.e. smaller than critical Quantum Electrodynamics values, evaluate these magnitudes analyze highly anisotropic find. Our implications for photon-photon scattering astrophysically magnetized systems far outside their surface where matter effects increasingly negligible.