Hamiltonian for complex plasmas

The Hamiltonian for a complex plasma involving dust spinning motion in a magnetic field is proposed. The formulation is in a classical limit of a quantum mechanical approach based on the Dirac equation, a relativistic wave equation in which the spin of particles is considered. The quantum mechanical spin term -cs B [c = gq/2m, g = 2ðLande g - factorÞ; q is a charge, m is a mass of a particle, and s = spin operator] is replaced by -cs B [c with g = 1, s = I(x þ cB), I is the moment of inertia of a dust particle, and x is the spinning angular velocity of a dust particle] in a classical limit. The wave-particle interaction involving spin motion is described as an interaction between particles and quasiparticles by the second quantization. The equation of motion with a damping term shows the relaxation of spinning dust particles aligning with the magnetic field. © 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC) license (https://creativecommons.org/licenses/by-nc/4.0/)