  Twisted photons can be emitted by free electrons in circular or spiral
motion, which carry orbital angular momentum (OAM) and possess a helical phase
structure. However, classical radiation reaction (RR) effects has not been
investigated as an accelerated electron emits vortex radiation during the
interaction with a electromagnetic field. This work focuses on investigating
the effects of radiation reaction on the production of twisted photons in the
Nonlinear Inverse Thomson Scattering (NITS) process. Using the precise electron
trajectory obtained by Landau-Lifshitz (LL) equation with a circularly
polarized (CP) plane-wave field, we find that the radiation reaction effects
can be significant for a sufficiently long pulse of a plane wave. They observe
modifications in the frequency, phase structure, rotational asymmetry of OAM
density, and energy distribution of the vortex field due to radiation reaction.
This finding could provide an unique signature for the detection of radiation
reaction.
