Radiation from Small-Scale Magnetic Field Turbulence: Implications for Gamma-Ray Bursts and Laboratory Astrophysical Plasmas

Relativistic charged particles moving within regions of small-scale magnetic field turbulence radiate as they undergo transverse accelerations reflective of the magnetic field variation along the particle's path. For a particle of Lorentz factor (gamma), relativistic beaming concentrates the bulk of the particle's emission within a small angle 1/(gamma) from the particle's forward direction. Synchrotron radiation is produced when large-scale magnetic fields cause the charged particles to gyrate, with the resulting radiation spectrum being primarily determined by the intermittent sweep of the relativistic beaming cone past the direction to the observer. In small-scale magnetic field turbulence, magnetic fields may be locally strong but varies over sufficiently small scales that the particle's emission is more consistently oriented towards a particular direction. Consequently, deflection effects cease to dominate the observed spectrum and the standard synchrotron model no longer applies. In this dissertation, we focus on the strong jitter radiation regime, in which the field varies over sufficiently short scales that the particle is never substantially deviated from a straight line path and an observer in the particle's forward direction receives consistently strong radiation over many correlation lengths of the magnetic field. We develop the general jitter radiation solutions for such a case and demonstrate that the resulting radiation spectrum differs notably from the synchtrotron spectrum and depends directly on the spectral distribution of the magnetic field encountered by the particle. The Weibel-like filamentation instability generates small-scale magnetic field turbulence through current filamentation in counterstreaming particle populations, such as may be found at or near propagating shock fronts, in outflow from regions of magnetic reconnection, or from a variety of other scenarios producing an anisotropic particle velocity distribution. The current filamentation produces an anisotropy in magnetic field distribution that causes the jitter radiation spectrum to be sensitive to the radiating particle's orientation with respect to the filamentation axis. Because the spectrum observed from any given direction will be dominated by emission from particle's moving along that particular line-of-sight, this results in a natural angular dependence of the jitter radiation spectrum. We explore the implications of jitter radiation's spectral sensitivity to the field anisotropy produced by the Weibel-like filamentation instability to relevant astrophysical and laboratory plasma scenarios. We calculate the jitter radiation spectra that may be produced in a high-energy density laboratory plasma by using quasi-monoenergetic electron beams to generate and then probe a region of current filamentation, and show that the jitter radiation may be used as a radiative diagnostic to determine features of the magnetic field distribution within this region. For gamma-ray bursts, this instability may play a significant role in generating magnetic field strength from relativistic collisionless shocks or other particle acceleration mechanisms. We show that the viewing angle dependence of the jitter radiation spectrum can result in a rapidly time-evolving spectrum whose hard-to-soft evolution, synchrotron-violating low-energy spectral indices, and correlation between low-energy spectral hardness and the flux at peak energy may explain trends noticed in time-resolved GRB spectral evolution. We generate the jitter radiation spectra as would be produced in the co-moving frame by a single, instantantaneously-illuminated shock front, which may then be relativistically transformed with appropriate geometry into a time-evolving spectrum and multiple such signals assembled to produce "synthetic" GRB for comparison with observations