We show analytically and through three-dimensional particle-in-cell simulations that nonlinear wakefields driven by Laguerre-Gaussian laser pulses can lead to hollow electron self-injection and positron acceleration. We find that higher order lasers can drive donut shaped blowout wakefields with strong positron accelerating gradients comparable to those of a spherical bubble. Corresponding positron focusing forces can be more than an order of magnitude stronger than electron focusing forces in a spherical bubble. Required laser intensities and energies to reach the nonlinear donut shaped blowout are within state-of-the-art experimental conditions.

The properties of four-wave interaction via the nonlinear quantum vacuum is investigated. The effect of the quantum vacuum is to generate photons with new frequencies and wave vectors, due to elastic photon-photon scattering. An expression for the number of generated photons is derived, and using state-of-the-art laser data it is found that the number of photons can reach detectable levels. In particular, the prospect of using the high-repetition Astra Gemini system at the Rutherford Appleton Laboratory is discussed. The problem of noise sources is reviewed, and it is found that the noise level can be reduced well below the signal level. Thus, detection of elastic photon-photon scattering may for the first time be achieved.

We study theoretically the exchange of angular momentum between electromagnetic and electrostatic waves in a plasma, due to the stimulated Raman and Brillouin backscattering processes. Angular momentum states for plasmon and phonon fields are introduced for the first time. We demonstrate that these states can be excited by nonlinear wave mixing, associated with the scattering processes. This could be relevant for plasma diagnostics, both in laboratory and in space. Nonlinearly coupled paraxial equations and instability growth rates are derived.

The inverse Faraday effect is usually associated with circularly polarized radiation; here, we show that it can also occur for linearly polarized radiation. The quasistatic axial magnetic field generated by a laser propagating in plasma can be calculated by considering both the spin and the orbital angular momenta of the laser pulse. A net spin is present when the radiation is circularly polarized and a net orbital angular momentum is present if there is any deviation from perfect rotational symmetry. The orbital angular momentum gives an additional contribution to the axial magnetic field that can enhance or reduce the effect usually attributed to circular polarization and strongly depends on the intensity profile of the Laguerre-Gaussian modes involving the azimuthal and radial mode numbers.