Small pitch-angle magnetobremsstrahlung in inhomogeneous curved magnetic fields

TL;DR

This paper investigates the radiation of relativistic particles near curved magnetic fields, revealing a smooth trajectory regime responsible for curvature radiation, with implications for interpreting pulsar gamma-ray spectra.

Contribution

It introduces a Hamiltonian formalism to identify smooth particle trajectories near curved magnetic lines, accounting for stochastic curvature variations at small pitch angles.

Findings

Existence of smooth trajectories without rapid curvature oscillations.

Trajectory curvature varies stochastically over time.

Implications for gamma-ray spectral measurements of pulsars.

Abstract

The character of radiation of relativistic charged particles in strong magnetic fields largely depends on the disposition of particle trajectories relative to the field lines. The motion of particles with trajectories close to the curved magnetic lines is usually referred to the so-called curvature radiation. The latter is treated within the formalism of synchrotron radiation by replacing the particle Larmor radius with the curvature radius of the field lines. However, even at small pitch angles, the curvatures of the particle trajectory and the field line may differ significantly. Moreover, as we show in this paper the trajectory curvature varies with time, i.e. the process has a stochastic character. Therefore for calculations of observable characteristics of radiation by an ensemble of particles, the radiation intensities should be averaged over time. In this paper, for determination of particle trajectories we use the Hamiltonian formalism, and show that that close to curved magnetic lines, for the given configuration of the magnetic field, the initial point and particle energy, always exist a smooth trajectory without fast oscillations of the curvature radius. This is the trajectory which is responsible for the curvature radiation. The realization of this regime requires the initial particle velocity to be directed strictly along the smooth trajectory. This result might have direct relation to the recent spectral measurements of gamma-radiation of pulsars by the Fermi Gamma-ray Space Telescope.