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 –γs·B [γ=gq/2m, g=2(Lande´ g−factor),q is a charge, m is a mass of a particle, and s = spin operator] is replaced by –γs·B [γ with g=1, s = I(ω+γB), I is the moment of inertia of a dust particle, and ω 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.