Radiation from non-linear Weibel plasma modes

This Review is concerned with summarizing known properties of the linear and non-linear Weibel instabilities including radiation from particles constrained by non-linear waves. In view of the purported importance of the Weibel instability for astrophysical objects (such as AGNs and relativistic jets) and for which only the emitted radiation field is available to help determine the existence of such Weibel modes, it seems appropriate to discuss the extent to which such modes are relevant. The first observation is that only for gyrotropic particle distribution functions (where the gyrotropy is perpendicular to the wave direction) can one have decoupled longitudinal and transverse linear Weibel modes that exist over a continuum of wavenumbers. For any asymmetry, no matter how small, the longitudinal and transverse linear modes are coupled and the continuum of wavenumbers collapses to isolated wavenumbers allowing Weibel modes as is determined both analytically and also with numerical simulations. This isolation of the wavenumbers suggests that any Weibel-like modes are non-linear and so a discussion of transverse non-linear Weibel modes is then given. Within the framework of such non-linear modes the emitted radiation of charged particles constrained by such modes is discussed. The spectrum of the emitted radiation tends to be concentrated in an emission cone centered on the direction of propagation of the soliton-like structure; the frequency spectrum tends to have emission at the highest frequencies allowed by the total emitted power limitations suggesting gamma-ray emission is dominantly prevalent. The polarization tends to be dominated by the parallel component of emission and has the electric vectors plane polarized. These basic properties of the emission spectra are the only components related to the underlying Weibel non-linear mode that are at all observable and can be used to indicate the appropriateness of such Weibel modes in the physical description of the astrophysical objects in question.