Degenerate plasma in a half-space under an external electric field

An analytic solution is found for the problem on the behavior of a collisional plasma in a variable external electric field. We elucidate the structure of the screened electric field and investigate the case where the frequency of the external field is close to the plasma oscillation frequency (resonance). We show that there are two near-surface layers where the behavior of the screened field differs essentially. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 3, pp. 487–502, June, 2006.     

Behavior of a plasma with the collision rate proportional to the electron velocity in an external electric field

We solve the problem of the behavior of a gas plasma in a half-space analytically using the kinetic equation with the collision rate proportional to the modulus of the electron velocity. The plasma is in a variable external electric field. The specular reflection of electrons from the plasma boundary is used as a boundary condition. We use the solution to find the screened electric field. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 409–421, December, 2007.     

Longitudinal electric current generated by a transverse electromagnetic field in a collisional plasma

We consider a collisional plasma with an arbitrary degree of degeneration of the electron gas. The plasma is located in an external electromagnetic field. We calculate the electric current generated in the plasma by the electromagnetic field. We show that the electric current has two nonzero components. One component is a transverse current, obtained by a linear analysis. The second component is a longitudinal current directed along the wave vector and orthogonal to the transverse current. We consider the case of small wave numbers. As the collision rate tends to zero, all the derived formulas pass into formulas for a collisionless plasma. We perform a graphical investigation of the dimensionless current density depending on the wave number, the oscillation frequency of the electromagnetic field, and the rate of electron collisions with plasma particles.     

Reflection and transmission of plasma waves at the interface of crystallites

A linearized problem of the reflection and transmission of a plasma wave at the boundary of a half-space (namely, the plane separating two crystallites) is formulated and analytically solved. The electron distribution function and the electric field inside the half-space of a degenerate plasma are found. The reflection and transmission coefficients are determined as functions of the input parameters of the problem. The longwave limit (i.e., the resonance case when the oscillation frequency of the self-consistent electric field is close to the natural (Langmuir) oscillation frequency) is analyzed.     

Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space

We consider the first mixed problem for the Vlasov–Poisson equations with an external magnetic field in a half-space. This problem describes the evolution of the density distributions of ions and electrons in a high temperature plasma with a fixed potential of electric field on a boundary. For arbitrary potential of electric field and sufficiently large induction of external magnetic field, it is shown that the characteristics of the Vlasov equations do not reach the boundary of the halfspace. It is proved the existence and uniqueness of classical solution with the supports of charged-particle density distributions at some distance from the boundary, if initial density distributions are sufficiently small.     

Ion acoustic solitary wave solutions of two‐dimensional nonlinear Kadomtsev–Petviashvili–Burgers equation in quantum plasma

Propagation of two‐dimensional nonlinear ion‐acoustic solitary waves and shocks in a dissipative quantum plasma is analyzed. By applying the reductive perturbation theory, the two‐dimensional ion acoustic solitary waves in a dissipative quantum plasma lead to a nonlinear Kadomtsev–Petviashvili–Burgers (KPB) equation. By implementing extended direct algebraic mapping, extended sech‐tanh, and extended direct algebraic sech methods, the ion solitary traveling wave solutions of the two‐dimensional nonlinear KPB equation are investigated. An analytical as well as numerical solution of the two‐dimensional nonlinear KPB equation is obtained and analyzed with the effects of external electric field and ion pressure. Copyright © 2016 John Wiley & Sons, Ltd.     

Charge density fluctuation of low frequency in a dusty plasma

The charge density fluctuation of low frequency in a dusty plasma, which is derived from the longitudinal dielectric permittivity of the dusty plasma, has been studied by kinetic theory. The results show that theP value, which describes the relative charge density on the dust in the plasma, and the charging frequency of a dust particle Ω _c , which describes the ratio of charge changing of the dust particles, determine the character of the charge density fluctuation of low frequency. For a dusty plasma ofP≪1, when the charging frequency Ω _c , is much smaller than the dusty plasma frequency ω_d, there is a strong charge density fluctuation which is of character of dust acoustic eigenwave. For a dusty plasma ofP≫1, when the frequency Ω _c , is much larger than ω _d there are weaker fluctuations with a wide spectrum. The results have been applied to the ionosphere and the range of radius and density of dust particles is found, where a strong charge density fluctuation of low frequency should exist.     

Analytic solution to the problem of the behavior of a collisional plasma in a half-space in an external alternating electric field

An exact solution to the linearized problem of the behavior of a collisional plasma in a half-space in an external alternating electric field is obtained. Mirror boundary conditions are used. The eigenvectors of the corresponding characteristic system are found in the space of generalized functions, and the eigenvalue spectrum is investigated. A theorem on the expansion of the solution of the investigated boundary-value problem with respect to eigenvectors is proved. An expression for calculating a discrete mode is found explicitly.Pedagogical University, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 2, pp. 299–311, May, 1995.     

Vlasov–Poisson equations for a two-component plasma in a half-space

The Vlasov–Poisson equations for a two-component high-temperature plasma with an external magnetic field in a half-space are considered. The electric field potential satisfies the Dirichlet condition on the boundary, and the initial density distributions of charged particles satisfy the Cauchy conditions. Sufficient conditions for the induction of the external magnetic field and the initial charged-particle density distributions are obtained that guarantee the existence of a classical solution for which the supports of the charged-particle density distributions are located at some distance from the boundary.     

Generation of a longitudinal current by a transverse electromagnetic field in collisional degenerate plasma

From the Vlasov–Boltzmann kinetic equation for a collisional degenerate plasma, the electron distribution function is constructed in the quadratic approximation in the electric field strength. A formula for calculating the electric current is derived. It is shown that nonlinearity leads to the rise of a longitudinal electric current directed along the wave vector. The longitudinal current is orthogonal to the known transverse classical current obtained in the linear analysis. When the collision frequency tends to zero, all results obtained for a collisional plasma pass into the corresponding results for a collisionless plasma. The case of small wavenumbers is considered. It is shown that, when the collision frequency tends to zero, the expression for the current passes into the corresponding expression for the current in a collisionless plasma. Graphic analysis of the real and imaginary parts of the current density is performed. The dependence of the electromagnetic field oscillation frequency and electron–plasma-particle collision frequency on the wavenumber is studied.     

Spectral properties of a linearized magnetohydrodynamics model

One considers the linear oscillations of a perfectly conducting nonviscous plasma in an external rectilinear magnetic field. One studies the frequency spectrum corresponding to a fixed harmonic mode. One has investigated the asymptotic behavior of the discrete spectrum at infinity and around the boundary of the essential spectrum.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 120–123, 1985.The author expresses his deep gratitude to his scientific adviser Professor M. Sh. Birman for his help and for numerous discussions and to A. E. Lifshits for consultations and for his interest in this paper.     

Study of small perturbations of a stationary state in a model of upper hybrid plasma oscillations

Theoretical and Mathematical Physics - We show that a constant external magnetic field, generally speaking, is not able to prevent breaking (loss of smoothness) of relativistic plasma oscillations,...     

Effect of cold plasma permittivity on the radiation of the dominant TEM‐wave by an impedance loaded parallel‐plate waveguide radiator

The effects of wall impedances on the radiation of the dominant transverse electromagnetic wave by an impedance loaded parallel‐plate waveguide radiator immersed in a cold plasma have been analyzed. The solution to the governing mathematical model in cold plasma is determined while using the Wiener–Hopf technique. It is observed that the amplitude of the radiated field increases with increasing permittivity of the plasma. The work presented may be of great interest to quantify the effects of ionosphere plasma on the communicating signals between Earth station and an artificial satellite in the Earth's atmosphere. Copyright © 2015 John Wiley & Sons, Ltd.     

Plasma waves reflection from a boundary with specular accommodative boundary conditions

In the present work the linearized problem of plasma wave reflection from a boundary of a half-space is solved analytically. Specular accommodative conditions of plasma wave reflection from plasma boundary are taken into consideration. Wave reflectance is found as function of the given parameters of the problem, and its dependence on the normal electron momentum accommodation coefficient is shown by the authors. The case of resonance when the frequency of self-consistent electric field oscillations is close to the electron (Langmuir) plasma oscillations frequency, namely, the case of long-wave limit is analyzed in the present paper.     

Magnetohydrodynamics with regard to electron inertia: Some exact solutions

Magnetohydrodynamic (MHD) equations are derived with the finite electron mass taken into account. The low-frequency spectrum of a cold two-component plasma can be described using these equations. In the linear approximation, the MHD equations lead to results coinciding with those of multifluid hydrodynamics. An exact solution to the generalized MHD equations is obtained as a stationary nonlinear wave. A soliton-like solution is found for a wide range of Mach numbers and external magnetic field intensities. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 3, pp. 349–361, September, 1998.     

Explicit piecewise smooth solutions of Landau-Lifshitz equation with discontinuous external field

In this paper, we shall construct some explicit piecewise smooth （global continuous） solutions as well as blow up solutions to the multidimensional Landau-Lifshitz equation, subject to the external magnetic fields being both discontinuous and unbounded. When the external magnetic field is continuous, some explicit exact smooth solutions and blow up solution are also constructed. We also establish some necessary and sufficient conditions to ensure that the solution of multidimensional Landau-Lifshitz equation with external magnetic field converges to the solution of equation without external magnetic field when the external magnetic field tends to zero.     

Time Evolution of a Vlasov-Poisson Plasma with Infinite Charge in ℝ3

We study existence and uniqueness of the solution to the Vlasov-Poisson system describing a one-species plasma evolving in ?³, whose particles interact via the Coulomb potential. It is assumed that initially the particles have bounded velocities and are distributed according to a non integrable density.     

Transversal line defects induced by an electric field in a period-2 oscillatory medium

The dynamical behavior of spiral waves in a period-2 oscillatory medium is investigated under the influence of an external applied alternating current field. Open and closed transversal line defects which wiggle along the direction parallel to the wave fronts, are generated in the spiral-wave patterns when the stimulus frequency of the electric field is equal to one, three or five times of the local oscillatory frequency in the period-2 state. Their generations are directly related with the change in the spatial wavelength induced by the electric field. These wigglings proliferate along the transverse direction parallel to the wave fronts as the stimulus strength increases, and become denser when the stimulus frequency increases by multiples of the period-2 oscillatory frequency.     

Long-time asymptotics for a classical particle interacting with a scalar wave field

We consider the Harniltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to a confining external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. We prove that solutions of finite energy converge, in suitable local energy seminorms, to the set of stationary solutions in the long time limit t f oo. The rate of relaxation to a stable stationary solution is determined by spatial decay of initial data. 'Supported partly by French-Russian A.M.Liapunov Center of Moscow State University, by research grants of RFBR (9601-00527) and of Volkswagen-Stiftung.     

Ellipsoid flowed around by a harmonic vector field

We consider the screening of an external magnetic field in which a superconducting ellipsoid is inserted and a change in the velocity distribution in an ideal liquid flowing around an ellipsoid inserted in it. In both cases, the solution is given by a harmonic vector field parallel to the surface near the ellipsoid.