Radiation reaction and the pitch angle changes for a charge undergoing synchrotron losses

TL;DR

This paper challenges the common assumption that a charge's pitch angle remains constant during synchrotron radiation, deriving a new formula that accounts for pitch angle changes due to radiation reaction effects.

Contribution

It introduces an exact formula for the energy change of radiating electrons considering pitch angle variation caused by radiative losses.

Findings

Pitch angle decreases during synchrotron radiation due to radiation reaction.

Derived decay time for electrons transitioning from relativistic to mildly relativistic.

Quantified the impact of pitch angle change on electron energy loss.

Abstract

In the derivation of synchrotron radiation formulas it has been assumed that the pitch angle of a charge remains constant during the radiation process. However from the radiation reaction formula, while the component of the velocity vector perpendicular to the magnetic field reduces in magnitude due to radiative losses, the parallel component does not undergo any change during radiation. Therefore there is a change in the ratio of the two components, implying a change in the pitch angle. We derive the exact formula for the change in energy of radiating electrons by taking into account the change of the pitch angle due to radiative losses. From this we derive the characteristic decay time of synchrotron electrons over which they turn from highly relativistic into mildly relativistic ones.