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Weibel instability turns out to be the a ubiquitous phenomenon in High-Energy Density environments, ranging from astrophysical sources, e.g., gamma-ray bursts, to laboratory experiments involving laser-produced plasmas. Relativistic particles (electrons) radiate in the Weibel-produced magnetic fields in the Jitter regime. Conventionally, in this regime, the particle deflections are considered to be smaller than the relativistic beaming angle of 1/$\gamma$ ($\gamma$ being the Lorentz factor of an emitting particle) and the particle distribution is assumed to be isotropic. This is a relatively idealized situation as far as lab experiments are concerned. We relax the assumption of the isotropy of radiating particle distribution and present the extension of the jitter theory amenable for comparisons with experimental data., Comment: Proceedings of International Conference on HEDP/HEDLA-08

It has recently been realized that the Weibel instability plays a major role in the formation and dynamics of astrophysical shocks of gamma-ray bursts and supernovae. Thanks to technological advances in the recent years, experimental studies of the Weibel instability are now possible in laser-plasma interaction devices. We, thus, have a unique opportunity to model and study astrophysical conditions in laboratory experiments — a key goal of the Laboratory Astrophysics program. Here we briefly review the theory of strong non-magnetized collisionless GRB and SN shocks, emphasizing the crucial role of the Weibel instability and discuss the properties of radiation emitted by (isotropic) electrons moving through the Weibel-generated magnetic fields, which is referred to as the jitter radiation. We demonstrate that the jitter radiation field is anisotropic with respect to the direction of the Weibel current filaments and that its spectral and polarization characteristics are determined by microphysical plasma parameters. We stress that the spectral analysis can be used for accurate diagnostics of the plasma conditions in laboratory experiments and in astrophysical GRB and SN shocks.