Generation of Waves by a Neutron Beam in a Quantum Plasma of Nonzero Spin. An Influence of the Spin-orbit Interaction

In the present paper we model the electromagnetic process in a plasma placed in an external magnetic field. This plasma is an anisotropic medium with strongly expressed electromagnetic properties. For the modeling of the electromagnetic quantum properties, we use the Schrodinger equation. Based on a Hamiltonian of a charged particle system with an intrinsic magnetic moment in an external electromagnetic field quantum, hydrodynamic equations are derived. The Coulomb, spin-spin, spin-current and spin-orbit in the Hamiltonian are included. The equations for number of particles, momentum and magnetic moment are obtained. The self-consistent field approximations of these equations are considered. Based on the quantum hydrodynamic equations the process of generation of waves by a neutron beam in a dense quantum plasma of nonzero spin is considered. Existence of new wave solutions of the quantum hydrodynamic equations is shown (with respect to our previous works as described in [1,2]). One type of such waves propagates perpendicularly to the direction of the external magnetic field. Another type is the spin waves which propagate at arbitrary angle with respect to the direction of the external magnetic field. Dispersion relations for waves in a medium traversed by a beam of neutrons whose velocity has a nonzero constant component are derived. Extreme cases of waves propagation parallel or transverse to the direction of the external magnetic field are considered. Generation of plasma, electromagnetic and self-consistent spin waves is investigated. The analytic formulas for the increments of instability are obtained. The contributions of spin-orbit interaction in the process of generation waves are investigated. The spin-spin, spin-current and spin-orbit interactions are the physical mechanism of instabilities in two-component quantum plasma traversed by a beam of neutrons. The collective dynamic of the magnetic moment of particles and methods of generation of this process can influence the properties of spintronic devices.