Vol 40, No 5 (2019)

We dedicate this paper to the memory of Victor Pavlovich Silin. The paper contains a modern formulation of the principles and main results of the quantum theory of spin waves in a conduction electron system in a crystal that does not have spontaneous spin ordering. Based on the quantum Fermi-liquid kinetic equation, we describe the propagation of electron spin oscillations in an isotropic system along the direction of a quantizing magnetic field while analyzing the dispersion equation, including the classical and quantum contributions. We present the fundamental results on quantum physics of Silin’s spin waves consisting in the existence of quantum magnetic field oscillations of wave frequencies in the region, where the classical collisionless absorption is absent and new quantum spin waves appear in the transparency windows formed due to quantum suppression of classical absorption.

Similarly to electromagnetic waves, plasma waves can also carry an orbital angular momentum. A key distinction from electromagnetic waves is that plasma waves are intrinsically coupled to electrons and may deposit their momentum with electrons, resulting in their secular motion and generation of quasistatic magnetic fields. In this paper, we present an analysis of kinetic plasma waves carrying an orbital angular momentum in the paraxial approximation by considering the energy and momentum exchange between the wave and electrons and the average electron motion induced by plasma wave damping.

We study the effect of the distance of plasma–beam interaction on the parameters of the output radiation of a plasma relativistic microwave generator (PRMO). In the experimental PRMO based on the Sinus 550-80 accelerator, the characteristics of the output microwave radiation (spectral width, spectral density of the amplitude of the radiation) vary during a single pulse of the relativistic electron beam (REB). We analyze and numerically simulate the experimental data; the geometric and physical parameters of the device used in the simulation are close to those in the experiments. We show that increase in the distance of the plasma–beam interaction (the length of the system) causes the duration of the effective microwave pulse generation to approach that of the REB despite the presence of ion background and the plasma density profile modification, i.e., no disruption or change in the generation regime occurs during the REB pulse, while the microwave radiation spectrum broadens.

A “transparent point” is a particular value of a governing parameter in a nontranslationally invariant system that makes the system “almost” translationally invariant. This concept was introduced recently in the context of the discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity — it was discovered that a tuning of the lattice spacing parameter h in this model affects the soliton mobility. In this paper, we study the DNLS equation with competing cubic–quintic nonlinearity that also admits the transparent points with respect to the lattice spacing parameter h. We give a geometrical interpretation of the transparent points in terms of dynamical system theory and present a simple asymptotical formula for them at h → 0. Although the derivation of this formula is heuristic and nonrigorous, it gives the values of transparent points with remarkable accuracy even for quite large values of h.

We investigate the interaction between a test monochromatic wave and semibounded plasma formed by multiphoton ionization of gas atoms. Under conditions where photoelectron distribution is isotropic and has a narrow peak in energy, the field in the plasma is represented by two contributions. The first of them arises from a pole in the complex plane of wave numbers and decays exponentially deeper into plasma. The second contribution comes from banks of the cut in the same plane and leads to a power-law decrease of the field under conditions of the anomalous skin effect. We obtain analytical expressions for the field under conditions of high-frequency and anomalous skin effects and find the surface impedance and absorption coefficient.

We discuss the possibility to formulate the dynamics of spin states described by the Schr¨odinger equation for pure states and the von Neumann equation (as well as the GKSL equation) for mixed states in the form of quantum kinetic equations for probability distributions. We review an approach to the spin-state description by means of the probability distributions of dichotomic random variables.