The Intense Radiation Gas

– We present a new dispersion relation for photons that are nonlinearly interacting with a radiation gas of arbitrary intensity due to photon–photon scattering. It is found that the photon phase velocity decreases with increasing radiation intensity, it and attains a minimum value in the limit of super-intense fields. By using Hamilton's ray equations, a self-consistent kinetic theory for interacting photons is formulated. The interaction between an electromagnetic pulse and the radiation gas is shown to produce pulse self-compression and nonlinear saturation. Implications of our new results are discussed. In classical electrodynamics photons are indifferent to each other in vacuum, while in quantum electrodynamics (QED) photons can interact via virtual electron–positron pairs, giving rise to vacuum photon–photon scattering [1]. This is commonly expressed using a series expansion (in the field strength) of the Heisenberg–Euler Lagrangian, yielding nonlinear corrections to Maxwell's vacuum equations. These corrections give rise to single particle effects (some of which are highly speculative), such as closed photon paths [2], vacuum birefringence [3–5], photon splitting [4] and lensing effects in a strong magnetic field [6, 7], and coherent effects, such as the self-focusing of beams [8] or the formation of light bullets [9]. Moreover, as an example of a collective effect, the QED photon self-energy will change the refractive index of a radiation gas [10–12], which can result in, e.g., Cherenkov emissions in a radiation gas [13]. Recently, it has been shown that nonlinear vacuum corrections cause photonic collapse in a radiation gas [14]. The phenomena of photonic collapse in two space-dimension has been confirmed by computer simulation studies [15]. As indicated in Ref. [15], the increase in intensity will show no upper bound as the collapse has begun, and will eventually surpass the Schwinger field ∼ 10 16 V/cm 2. Even as dispersive corrections are added [16–18], with resulting pulse splitting, the field intensities within the collapse region may still reach values well above the ones allowed by the approximate Heisenberg–Euler formalism. Thus, this raises the critical question of how far the predictions of the approximate Heisenberg–Euler Lagrangian can be c EDP Sciences