Generation of Magnetic Fields and Jitter Radiation in GRBs. I. Kinetic Theory

Abstract

We present a theory of generation of strong (sub-equipartition) magnetic fields in relativistic collisionless GRB shocks. These fields produced by the kinetic two-stream instability are tangled on very small spatial scales. This has a clear signature in the otherwise synchrotron(-self-Compton) $γ$-ray spectrum. Second, we present an analytical theory of jitter radiation, which is emitted when the correlation length of the magnetic field is smaller then the gyration (Larmor) radius of the accelerated electrons. We demonstrate that the spectral power $P(ν)$ for pure jitter radiation is well-described by a sharply broken power-law: $P(ν)\proptoν^1$ for $ν<ν_j$ and $P(ν)\proptoν^{-(p-1)/2}$ for $ν>ν_j$, where $p$ is the electron power-law index and $ν_j$ is the jitter break, which is independent of the magnetic field strength and depends on the shock energetics and kinematics. Here we mostly focus on the first problem. The radiation theory and comparison with observations will be discussed in the forthcoming publications.