Nonlinear collective effects in photon–photon and photon–plasma interactions

We consider strong-field effects in laboratory and astrophysical plasmas and high intensity laser and cavity systems, related to quantum electrodynamical (QED) photon–photon scattering. Current state-of-the-art laser facilities are close to reaching energy scales at which laboratory astrophysics will become possible. In such high energy density laboratory astrophysical systems, quantum electrodynamics will play a crucial role in the dynamics of plasmas and indeed the vacuum itself. Developments such as the free electron laser may also give a means for exploring remote violent events such as supernovae in a laboratory environment. At the same time, superconducting cavities have steadily increased their quality factors, and quantum non-demolition measurements are capable of retrieving information from systems consisting of a few photons. Thus, not only will QED effects such as elastic photon–photon scattering be important in laboratory experiments, it may also be directly measurable in cavity experiments. Here we describe the implications of collective interactions between photons and photonplasma systems. We give an overview of strong field vacuum effects, as formulated through the Heisenberg–Euler Lagrangian. Based on the dispersion relation for a single test photon travelling in a slowly varying background electromagnetic field, a set of equations describing the nonlinear propagation of an electromagnetic pulse on a radiation-plasma is derived. The stability of the governing equations is discussed, and it is shown using numerical methods that electromagnetic pulses may collapse and split into pulse trains, as well as be trapped in a relativistic electron hole. Effects, such as the generation of novel electromagnetic modes, introduced by QED in pair plasmas is described. Applications to laser-plasma systems and astrophysical environments are discussed.