Quantum mechanical approach to plasma waves with helical wavefront

Abstract

Plasma waves with helical wavefront are studied theoretically from the quantum mechanical viewpoint and are shown to produce a spinning motion of a charged macroparticle in a complex plasma. The electrostatic helical perturbations are described by the wave function for a Laguerre–Gaussian beam mode with the radial/angular mode numbers n/l. The interaction and the transfer of angular momentum from the wave to a particle are analyzed by the method of second quantization with the help of the Feynman diagram. Laguerre function, instead of the Born approximation, is introduced to describe plasma waves with helical wavefront. A pair of dust particles in a complex plasma exchange a quasiparticle (virtual plasmon) resulting in the acquisition of angular momentum, which makes a dust particle spin in motion with rotational frequency Ωϕ. The resonance condition ω−kvz−lΩϕ=0 and the conservation of angular momentum IdΩϕ=lℏ determine the rotational frequency, where ω and k are frequency and axial wave number of the helical wave, and vz and Id are axial velocity and the moment of inertia of a dust particle.