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.     

Turbulent shock waves in a collisionfree plasma

The paper deals with the structure of collisionless shocks arising from turbulent wave-particle interactions. The conditions under which wave-particle interaction effects could become significant leading to growing waves and a shock are discussed. Using the Mott-Smith expression for the zero-order distribution functions for the ions within the shock, the dielectric constant as well as the integral representing the wave-particle interaction term in the Lenard-Balescu equation are evaluated for a collisionless plasma. An expression is given for the ion distribution function within the shock. It is shown that the component of the pressure tensor perpendicular to the direction of flow of the plasma leads to a new kind of viscosity term arising from the interaction of the particles with the growing waves and this provides a dissipative mechanism to account for the conversion of the kinetic energy of the incoming plasma into the thermal energy of the hot ionised gas behind the shock.     

Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics

The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions.     

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.     

Distribution Functions in Quantum Mechanics and Wigner Functions

We formulate and solve the problem of finding a distribution function F(r,p,t) such that calculating statistical averages leads to the same local values of the number of particles, the momentum, and the energy as those in quantum mechanics. The method is based on the quantum mechanical definition of the probability density not limited by the number of particles in the system. The obtained distribution function coincides with the Wigner function only for spatially homogeneous systems. We obtain the chain of Bogoliubov equations, the Liouville equation for quantum distribution functions with an arbitrary number of particles in the system, the quantum kinetic equation with a self-consistent electromagnetic field, and the general expression for the dielectric permittivity tensor of the electron component of the plasma. In addition to the known physical effects that determine the dispersion of longitudinal and transverse waves in plasma, the latter tensor contains a contribution from the exchange Coulomb correlations significant for dense systems.     

Finding the coefficients in the new representation of the solution of the Riemann–Hilbert problem using the Lauricella function

The solution of the Riemann–Hilbert problem for an analytic function in a canonical domain for the case in which the data of the problem is piecewise constant can be expressed as a Christoffel–Schwartz integral. In this paper, we present an explicit expression for the parameters of this integral obtained by using a Jacobi-type formula for the Lauricella generalized hypergeometric function F _D ^(N). The results can be applied to a number of problems, including those in plasma physics and the mechanics of deformed solids.     

On the fluctuation spectrum of plasma

The spectrum of electron phase space density fluctuations of a plasma is calculated by a novel method that parallels conventional calculations of the partition function in statistical physics. Expressions for the electric field fluctuations and the closely related form factor agree with existing results. The method clears up ambiguities about equipartition and provides a new expression for the spectrum of electrostatic phase space density fluctuations about stable non-Maxwellian equilibria.     

Balance equation and the quasitemperature of channeled particles in equilibrium

Using the methods of nonequilibrium statistical thermodynamics, we obtain the equation for the transverse energy and momentum balance for fast atomic particles moving in the planar channeling regime. Based on the solution of this equation, we obtain an expression for the transverse quasitemperature in the quasiequilibrium in terms of the basic parameters of the theory. We show that the equilibrium quasitemperature of channeled particles is established because of particle diffusion in the space of transverse energies (subsystem “heating”), the dissipative process (“cooling”), and the anharmonic effects of particle oscillations between the channel walls (the redistribution of energies over the oscillatory degrees of freedom is the internal thermalization of the subsystem). According to the estimates for particles with an energy of the order of 1 MeV, the quasitemperature values are in the characteristic temperature range for a low-temperature plasma.     

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.     

Nondegenerate plasma with a diffusive boundary condition in a high-frequency electric field near resonance

An analytical solution of the linearized problem concerning the behavior of collisional non-degenerate plasma in an external electric field is obtained. It is assumed that the electrons are diffusively scattered from the plasma boundary. The resulting solution is used to determine the screening field. The case of a high-frequency external field with a frequency close to the plasma resonance frequency is examined.     

Computation of axisymmetric MHD flows in a channel with an external longitudinal magnetic field

A numerical study of two-dimensional plasma flows in coaxial channels of plasma accelerators is presented. Two new results are obtained. First, for the computation of MHD problems belonging to the class under consideration, Zalesak’s method is used. It is based on an explicit finite difference scheme with flux correction. This method is free of space splitting, and, therefore, is well suited for parallel computations on multiprocessors. Second, the statement of the problem is extended so that the acceleration of the plasma by the azimuth magnetic self-field goes on in the presence of an external longitudinal field. The results of test computations demonstrate the efficiency of the method and made it possible to investigate the influence of the longitudinal field on the properties of the plasma flows.     

Condensation of charged bosons in plasma physics and cosmology

We consider the screening of impurities in plasma with a Bose-Einstein condensate of electrically charged bosons and show that the screened potential is drastically different from the usual Debye potential. The polarization operator of photons in plasma acquires infrared singular terms at small photon momentum, and the screened potential drops down as a power of distance and even has an oscillating behavior, similar to the Friedel oscillations in plasma with degenerate fermions. We also discuss the magnetic properties of the cosmological plasma with condensed W bosons and show that W bosons condense in the ferromagnetic state. This could lead to spontaneous magnetization of the primeval plasma. The created magnetic fields may seed galactic and intergalactic magnetic fields observed in the present-day Universe.     

Numerical simulation of anomalous plasma transport in the presence of magnetic turbulence

The structure of plasma in the interplanetary space is briefly presented, and the problems related to the variability of solar activity are discussed. The features of magnetic turbulence in the solar wind are also described. Magnetic field fluctuations are one of the causes of enhanced transport both in laboratory and astrophysical plasmas. To a first approximation, the plasma particles follow the magnetic field lines, whose equations form a non-linear one and a half degrees of freedom system. Unless the fluctuation level is very low, numerical simulations are needed to study such a system. We review three-dimensional numerical simulations of field line transport in anisotropic magnetic turbulence. Several transport regimes are found: for low Kubo number, anomalous transport is obtained, featuring both subdiffusion, corresponding to trapping in cantori structures, and superdiffusion, corresponding to Levy flights in the stochastic layer. Increasing the Kubo number, and hence stochasticity, quasilinear, intermediate, and percolative regimes are found, in the order. An expression of the diffusion coefficient valid for generalized anisotropy is presented.     

Prediction of the disposition of a P-gp substrate in wild-type and knockout mice tissues: Development of a physiologically based pharmacokinetic (PBPK) model and its global sensitivity analysis

In order to improve understanding and prediction of drug disposition prior to in vivo experiments, we aimed to develop a PBPK model that accounts for the involvement of P-glycoprotein activity and expression in mouse brain, liver, kidney and heart tissues. Model parameters of P-gp activity and drug diffusion were mainly extrapolated from in vitro data. Model simulations, compared with tissue concentration of 3H-domperidone intravenously administered toWT and KO mice, suggest the involvement of additional membrane transporters in heart and brain tissues. The global sensitivity analysis showed that the variability of model predictions is related to the variability of the unbound fraction to plasma protein, whereas the uncertainty of the model predictions is associated with the uncertainty of the parameters related to P-gp genetic expression, and to the activity of additional transporters in heart and brain tissues. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the convexity of equilibrium plasma configurations

We investigate the problem of plasma confinement by a magnetic field in an infinite cylinder. We show that if the cylinder has convex cross-section, then there exists an equilibrium plasma configuration with convex cross-section.     

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.     

Hydrodynamic action functional and absorption of electromagnetic waves in plasma

The path integration method is used to study the absorption of waves in plasma. The absorption is considered of longitudinal electromagnetic waves as a consequence of scattering on the transverse waves, which requires the introduction of an integration with respect to a supplementary field of the vector potential. The scattering on the transverse waves becomes the determining one for a one-component plasma in the long wavelength limit. The hydrodynamic action functional is constructed for a magnetized electron-ion plasma by the method of successive integration, first with respect to “fast” fields and, next, with respect to “slow” fields. The absorption of the longitudinal waves is computed with the aid of this functional. The domains of frequencies of the order of the plasma frequency and of the order of the cyclotron frequency are considered. In comparison with the case of a free plasma, here the Coulomb logarithm is varied.     

Instabilities and pattern formation in low temperature plasmas

This paper is concerned with a dynamical systems analysis of an instability occurring in a cylindrical high frequency plasma discharge. Stationary, spatially periodic modulations of the plasma density and temperature have been observed in experiments and reproduced in kinetic simulations. A macroscopic model is proposed in order to determine parameter ranges for which these plasma “striations” may form. The model consists of two nonlinear, coupled partial differential equations which describe ambipolar diffusion of electrons and ions and electron energy transport. We emphasize the importance of a particular thermoelectric transport coefficient, usually neglected in fluid models of plasma discharges, which proves essential in describing the pattern formation mechanism.     

Modeling and simulation of plasma jet by lattice Boltzmann method

In order to find a simple and efficient simulation for plasma spray process, an attempt of modeling was made to calculate velocity and temperature field of the plasma jet by hexagonal 7-bit lattice Boltzmann method (LBM) in this paper. Utilizing the methods of Chapman–Enskog expansion and multi-scale expansion, the authors derived the macro equations of the plasma jet from the lattice Boltzmann evolution equations on the basis of selecting two opportune equilibrium distribution functions. The present model proved to be valid when the predictions of the current model were compared with both experimental and previous model results. It is found that the LBM is simpler and more efficient than the finite difference method (FDM). There is no big variation of the flow characteristics, and the isotherm distribution of the turbulent plasma jet is compared with the changed quantity of the inlet velocity. Compared with the velocity at the inlet, the temperature at the inlet has a less influence on the characteristics of plasma jet.