A method to analyze the scattering characteristics of a Laguerre–Gaussian (LG) vortex beam by a low-velocity charge in a steady applied magnetic field is investigated in this paper. Based on the plane wave angular spectrum representation and the electromagnetic radiation theory of a moving charge, the expressions of the scattered field and scattered power per unit solid angle are presented. Considering a low-velocity electron, the distribution of the scattered power per unit solid angle is numerically simulated. The effects of electron motion parameters, beam parameters, and applied magnetic field are discussed in detail. The results show that the longitudinal motion of the electron, which is parallel to the direction of the applied magnetic field, makes the distribution of the scattered power no longer maintain radial consistency but has a concave–convex distribution. Due to the periodicity of the circular motion of the electron in the applied magnetic field, the scattering power distribution pattern consists of many annular lobes. The spectral characteristics of the backscattered field are analyzed by fast Fourier transform. It is confirmed that the scattered field satisfies the rotational and the linear Doppler effects, and the accuracy of the formula provided in this paper is verified. This work lays a foundation for further study of the scattering characteristics of plasma on vortex electromagnetic waves and helps to promote the in-depth development of vortex beams in the field of plasma diagnosis.

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Thomson scattering of a vector Bessel vortex beam (VBVB) by a non-relativistic electron is studied in this paper in order to explore the prospects of vortex beams in Thomson scattering diagnostic in ionospheric or laboratory plasmas. Combining with the plane wave angular spectrum representation of a VBVB, the expressions of scattered electric and magnetic fields are derived with the aid of Thomson scattering theory. The scattered power per unit solid angle and the frequency spectrum of the scattered field in the backscatter direction are simulated numerically, and the effects of polarization, topological charge, half-cone angle, and the electron's motion are analyzed in detail. The results show that the polarization affects the spatial distribution of scattered power. The distance between the electron and the observer's location, where maximum power is received, is affected by the topological charge, and the gaps between sub-maxima are related to the half-cone angle. These characteristics are the manifestation of the retarded effect in radiation. The amplitude spectrum of scattered field is analyzed in which a feature of double peaks is observed. The frequency shifts of peaks are the sum of the shifts brought by the electron's velocity components parallel and perpendicular to the beam's axis. The work provides a significant theoretical foundation for deeply investigating the Thomson scattering of vortex beams by plasmas and is meaningful for the development of plasma diagnostic.

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