Linear acceleration emission in pulsar magnetospheres

Abstract: (abbrev.) Linear acceleration emission occurs when a charged particle is accelerated parallel to its velocity. We evaluate the spectral and angular distribution of this radiation for several special cases, including constant acceleration (hyperbolic motion) of finite duration. Based on these results, we find the following general properties of the emission from an electron in a linear accelerator that can be characterized by an electric field E acting over a distance L: (i) the spectrum extends to a cut-off photon energy ~ LE^2 MeV, where E is in units of the Schwinger critical field and L in units of the Compton wavelength of the electron. (ii) the total energy emitted by a particle traversing the accelerator is in agreement with the standard Larmor formula (iii) the low frequency spectrum is flat for hyperbolic trajectories, but in general depends on the details of the accelerator. We also show that linear acceleration emission complements curvature radiation in the strongly magnetized pair formation regions in pulsar magnetospheres. It dominates when the length L of the accelerator is less than the formation length of curvature photons, which is given by the ratio of the radius of curvature of the magnetic field lines to the Lorentz factor of the particle. In standard static models of pair creating regions linear acceleration emission is negligible, but it is important in more realistic dynamical models in which the accelerating field fluctuates on a short length-scale.