Transverse electric conductivity in collisional quantum plasma

Expressions for the transverse electric conductivity and transverse permittivity of collisional quantum plasma for an arbitrary value of the degeneracy factor of the electron gas are derived using the Wigner-Vlasov-Boltzmann kinetic equation with the Bhatnagar-Gross-Krook collision integral. Different particular cases are analyzed. Special attention is paid to the case of completely degenerate quantum plasma. The results obtained are compared with Lindhard??s formula.     

Transverse and longitudinal permittivities of a gaseous plasma with an electron collision frequency proportional to the electron velocity

The transverse and longitudinal plasma permittivities, ?^tr and ? ^l , are analyzed for the case where the electron collision frequency in the Bhatnagar-Gross-Krook collision integral is proportional to the absolute value of the electron velocity. It is found that, in both the low-and high-frequency limits, the expressions for ?^tr and ? ^l derived for the case of a variable electron collision frequency coincide with the classical formulas obtained under the assumption of a constant collision frequency, whereas for frequencies close to the electron collision frequency, these expressions differ significantly from the classical ones.     

Electromagnetic van Kampen waves

The theory of van Kampen waves in plasma with an arbitrary anisotropic distribution function is developed. The obtained solutions are explicitly expressed in terms of the permittivity tensor. There are three types of perturbations, one of which is characterized by the frequency dependence on the wave vector, while for the other two, the dispersion relation is lacking. Solutions to the conjugate equations allowing one to solve the initial value problem are analyzed.     

Nonstationary kinetic theory of ion transport in plasma with small perturbations

A theory of charged particle transport for small potential perturbations in a fully ionized plasma is developed on the basis of solving a linearized kinetic equation with the Landau collision integral. This theory is free of any constraints on the characteristic time and spatial scales of perturbations. Ion fluxes appropriate for an arbitrary ion-ion collision frequency that can ensure nonlocal space-time transport in the plasma are calculated. The obtained ion transport coefficients are used to calculate the partial contribution of ions to the longitudinal permittivity of collisional plasma. The resulting expression for the plasma permittivity is applicable in the entire range of frequencies and wavenumbers.     

Nonlocal weakly relativistic permittivity tensor of magnetized plasma near electron cyclotron resonances

Compact expressions are derived for the nonlocal permittivity tensor of weakly relativistic plasma in a 2D nonuniform magnetic field near the resonances at the second harmonic of the electron cyclotron frequency for an extraordinary wave and at the first harmonic for an ordinary wave. It is shown that the wave equation with allowance for the obtained thermal correction to the permittivity tensor in the form of a differential operator in transverse (with respect to the external magnetic field) coordinates possesses an integral in the form of the energy conservation law.     

Ponderomotive force of the low-frequency field and modulational instability of drift waves

A study is made of the processes that occur in an inhomogeneous nonisothermal plasma in a strong external magnetic field and whose characteristic frequencies are lower than the ion Langmuir frequency but higher than the collision frequency. An expression for the ponderomotive force of the low-frequency field is derived. The excitation of a long-wavelength low-frequency drift wave during the development of the modulational instability of a drift pump wave is investigated. The growth rates of the instability are obtained, and the conditions for its onset are determined. The possible relation of the modulational instability to the formation of structures in the plasma is discussed.     

Kinetic Theory Model for Ion Movement through Biological Membranes: I. Field-Dependent Conductances in the Presence of Solution Symmetry

A model for ion movement through specialized sites in the plasma membrane is presented and analyzed using techniques from nonequilibrium kinetic theory. It is assumed that ions traversing these specialized regions interact with membrane molecules through central conservative forces. The membrane molecules are approximated as massive spherical scattering centers so that ionic fractional energy losses per collision are much less than one. Equations for steady-state membrane ionic currents and conductances as functions of externally applied electric field strength are derived and numerically analyzed, under the restriction of identical solutions on each size of the membrane and constant electric fields within the membrane. The analysis is carried through for a number of idealized ion-membrane molecule central force interactions. For any interaction leading to a velocity-dependent ion-membrane molecule collision frequency, the membrane chord conductance is a function of the externally applied electric field. Interactions leading to a collision frequency that is an increasing (decreasing) function of ionic velocity are characterized by chord conductances that are decreasing (increasing) functions of field strength. For ion-neutral molecule interactions, the conductance is such a rapidly decreasing function of field strength that the slope conductance becomes negative for all field strengths above a certain value.     

Nonlinear oscillations of a semiconductor plasma with a nonrelativistic electron beam

Nonlinear oscillations of a semiconductor plasma with a low-density electron beam in the absence of an external magnetic field are studied in the hydrodynamic approximation. The beam is assumed to be nonrelativistic and monoenergetic. Cases are studied in which the Langmuir frequency of the electron oscillations in a semiconductor is much higher or much lower than the electron momentum relaxation rate. The self-similar solution obtained for the first case describes the damping of the nonlinear oscillations of the wave potential. Numerical analysis of the second case shows that the electric field distribution in the beam may correspond to that in a shock wave.     

Effect of the longitudinal momentum of electrons on their surfatron acceleration by an electromagnetic wave in space plasma

By numerically calculating the second-order nonlinear time-dependent equation for the wave phase on a particle trajectory, the effect of the longitudinal (with respect to the external magnetic field) momentum of electrons on the dynamics of their surfatron acceleration by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed. It is shown that, for strongly relativistic initial values of the longitudinal component of the electron momentum (the other parameters of the problem being fixed), the electrons are trapped into the ultrarelativistic regime of surfatron acceleration within a definite interval of the initial wave phase Ψ(0) on the particle trajectory. It was assumed in the calculations that Ψ(0) ≤ π. For the initial wave phases lying within the interval of 0 < Ψ(0) ≤ π, the electrons are immediately trapped by the wave, whereas at π ≤ Ψ(0) ≤ 0, no electron trapping is observed even at long computation times. This result substantially simplifies estimates of the wave damping caused by particle acceleration. The dynamics of the velocity components, momentum, and relativistic factor of electrons in the course of their ultrarelativistic acceleration are considered. The obtained results present interest for the development of modern concepts of the mechanisms for the generation of ultrarelativistic particles in space plasma, correct interpretation of experimental data on the flows of such particles, explanation of possible reasons for the deviation of the fast particle spectra observed in the heliosphere from the standard power-law scaling, and analysis of the relation between such deviations and the space weather.     

Propagation of MHD waves in a plasma in a sheared magnetic field with straight field lines

The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is solved using a simplified model: a cold plasma is inhomogeneous in one direction, and the magnetic field lines are straight. The waves are assumed to travel in the plane perpendicular to the radial coordinate (i.e., the coordinate along which the plasma and magnetic field are inhomogeneous). It is shown that the character of the singularity at the resonance surface is the same as that in a homogeneous magnetic field. It is found that the shear gives rise to the transverse dispersion of Alfvén waves, i.e., the dependence of the radial component of the wave vector on the wave frequency. In the presence of shear, Alfvén waves are found to propagate across magnetic surfaces. In this case, the transparent region is bounded by two turning points, at one of which, the radial component of the wave vector approaches infinity and, at the other one, it vanishes. At the turning point for magnetosonic waves, the electric and magnetic fields are finite; however, the radial component of the wave vector approaches infinity, rather than vanishes as in the case with a homogeneous field.     

Magnetic Field Effect on Fresnel Coefficients of the Thin Slab of Graphite Nanocomposite

In this theoretical study, optical properties of a thin slab including graphite nanoparticles doped in a host medium such as silica and silicon have been investigated. A constant magnetic field is used for controlling Fresnel coefficients of the slab. Depending on the direction of the normal vector of the basal plane of the graphite structure with respect to the electric field of the incident electromagnetic wave (perpendicular or parallel), optical behavior of graphite is different. Electric permittivity of an individual magnetized graphite nanoparticle is calculated by a semi-empirical Drude-like model for both kinds of the normal vector of the basal plane orientation. By means of well-known Maxwell-Garnett theory, effective permittivity of the magnetized nanocomposite slab is obtained. It is shown that at the mid-IR frequency range, exerting a magnetic field of few hundred Tesla can lead to the substantial variations of Fresnel coefficients. Effect of the magnetic field on the optical properties of the slab is more evident when the population of the graphite nanoparticles with the parallel orientation of the basal plane is increased.

     

Incoherent Scattering of Electromagnetic Waves by Langmuir Fluctuations Trapped in a Plasma Density Well

Incoherent scattering of a probing wave by Langmuir fluctuations trapped and enhanced near a local minimum of the electron density (plasma density well) in plasma with a parabolic density profile is considered. Steady-state amplitudes of fluctuations are calculated for arbitrary velocity distribution functions of plasma particles with allowance for electron collisions. It is shown that quasi-periodic oscillations with two characteristic scales can be present in the spectrum of the plasma line. The smaller scale is due to the wellknown effect of discretization of the spectrum of Langmuir fluctuations in a plasma density well. The larger scale is associated with the generation of scattered waves in two spatial regions and subsequent interference of these waves at the exit from the density well. Oscillations with this scale are more stable under unsteady plasma conditions and can be more often observed in experiments. The results of this work can be used to experimentally determine the plasma parameters, such as the electron collision frequency and the size and lifetime of the plasma density well.     

Theory of transverse surface electromagnetic waves propagating along a plasma-metal boundary with a finite radius of curvature in a magnetic field

The spectra of electromagnetic waves propagating perpendicular to the axis of a plasma-filled metal waveguide in a magnetic field are studied with allowance for the effects exerted upon the wave frequency by the radial plasma density variation and by the emission of waves through a narrow axial slit in a waveguide wall. The case of wave propagation along the boundary between a plasma and a cylindrical metal waveguide wall with a periodically varying radius of curvature is also considered. The electromagnetic properties of the plasma are described by a dielectric tensor in the hydrodynamic approximation. The spatial distribution of the wave field is determined by the method of successive approximations. Results are presented from both analytical and numerical investigations. Analytical expressions for the corrections to the wave frequency due to the emission of the wave energy from the waveguide and due to the slight corrugation of the waveguide wall are obtained. The rates of wave damping due to the emission of the wave energy through a narrow axial slit and due to collisions between the plasma particles are found. The correction to the frequency that comes from the periodic variation of the radius of curvature of the plasma surface is calculated to within terms proportional to the square of the small parameter describing the azimuthal corrugation of the waveguide wall. The effect of the radial plasma density variation on the dispersion of the surface modes is examined both analytically and numerically.     

Dissipation of Energy of an AC Electric Field in a Semi-Infinite Electron Plasma with Mirror Boundary Conditions

Absorption of the electromagnetic energy in a semi-infinite electron plasma is calculated for an arbitrary degree of the electron gas degeneracy. Absorption is determined by solving the boundary-value problem on the oscillations of electron plasma in a half-space with mirror boundary conditions for electrons. The Vlasov?Boltzmann kinetic equation with the Bhatnagar–Gross–Krook collision integral for the electron distribution function and Maxwell’s equation for the electric field are employed. The electron distribution function and the electric field inside plasma are searched for in the form of expansions in the eigenfunctions of the initial set of equations. The expansion coefficients are found for the case of mirror boundary conditions. The contribution of the plasma surface to absorption is analyzed. Cases with different degrees of electron gas degeneracy are considered. It is shown that absorption of the electromagnetic energy near the surface depends substantially on the ratio between the electric field frequency and the volumetric electron collision frequency.     

Influence of Electron Collisions on the Breaking of Plasma Oscillations

The influence of electron collisions on the breaking of plane nonlinear plasma oscillations is analyzed. Numerical calculations by the particle method and analytical consideration in the weakly nonlinear regime show that the breaking time of plasma oscillations increases with increasing electron collision frequency. The threshold value of the electron collision frequency above which no singularity in the electron density arises is found. In this case, the density maximum formed outside the symmetry plane of oscillations, the growth of which in the weakly collisional regime leads to the breaking effect, begins to decrease after some growth because of oscillation damping.     

Generation of fast charged particles in plasma by a wave with a stochastically jumping phase

The interaction between charged plasma particles and an electromagnetic wave with a stochastic jumping phase is analyzed by numerical simulations. It is demonstrated that, in the course of interaction, the particle energy can increase by more than one order of magnitude. Optimal conditions for efficient interaction of charged plasma particles with a wave having a stochastically jumping phase are determined. According to the simulation results, substantial acceleration of charged plasma particles by a wave with a stochastically jumping phase takes place both at fixed time intervals between phase jumps and when these intervals are random. The influence of the wave parameters, such as the wave amplitude, the characteristic time interval between phase jumps, and the characteristic magnitude of these jumps, on the acceleration dynamics is analyzed.     

Analysis of the dependence of surfatron acceleration of electrons by an electromagnetic wave in space plasma on the particle momentum along the wave front

Based on the numerical solution of the nonlinear nonstationary second-order equation for the wave phase on the particle trajectory, the dynamics of surfatron acceleration of electrons by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed as a function of the electron momentum along the wave front. Numerical calculations show that, for strongly relativistic initial values of the electron momentum component along the wave front g _y (0) (the other parameters of the problem being the same), electrons are trapped into the regime of ultrarelativistic surfatron acceleration within a certain interval of the initial wave phase Ψ(0) on the particle trajectory. It is assumed in the calculations that |Ψ(0)| ≤ π. For strongly relativistic values of g _y (0), electrons are immediately trapped by the wave for 19% of the initial values of the phase Ψ(0) (favorable phases). For the rest of the values of Ψ(0), trapping does not occur even at long times. This circumstance substantially simplifies estimations of the wave damping due to particle acceleration in subsequent calculations. The dynamics of the relativistic factor and the components of the electron velocity and momentum under surfatron acceleration is also analyzed. The obtained results are of interest for the development of modern concepts of possible mechanisms of generation of ultrarelativistic particle fluxes in relatively calm space plasma, as well as for correct interpretation of observational data on the fluxes of such particles and explanation of possible reasons for the deviation of ultrarelativistic particle spectra detected in the heliosphere from the standard power-law scalings and the relation of these variations to space weather and large-scale atmospheric processes similar to tropical cyclones.     

Reflection and penetration depth of millimeter waves in murine skin

Millimeter (mm) wave reflectivity was used to determine murine skin permittivity. Reflection was measured in anesthetized Swiss Webster and SKH1-hairless mice in the 37-74 GHz frequency range. Two skin models were tested. Model 1 was a single homogeneous skin layer. Model 2 included four skin layers: (1) the stratum corneum, (2) the viable epidermis plus dermis, (3) fat layer, and (4) muscle which had infinite thickness. We accepted that the permittivity of skin in the mm wave frequency range results from the permittivity of cutaneous free water which is described by the Debye equation. Using Fresnel equations for reflection we determined the skin parameters best fitting to the reflection data and derived the permittivity of skin layers. The permittivity data were further used to calculate the power density and specific absorption rate profiles, and the penetration depth of mm waves in the skin. In both murine models, mm waves penetrate deep enough into tissue to reach muscle. In human skin, mm waves are mostly absorbed within the skin. Therefore, when extrapolating the effects of mm waves found in animals to humans, it is important to take into account the possible involvement of muscle in animal effects.     

Nonlinear ion flux caused by a periodic ion-acoustic wave in plasma with two-temperature electrons

The propagation of periodic ion-acoustic waves in plasma with two-temperature electrons and cold ions is analyzed. The equations for the wave potential are derived in the first- and second-orders of the perturbation theory, and their nonsecular periodic solutions are obtained. The average nonlinear ion flux is determined, and its properties are studied as functions of the ratios between the densities and temperatures of the cold and hot electron components. The conditions are analyzed under which the ion flux is co- or counter-directed to the wave propagation direction. For the case in which, depending on the plasma parameters, the ion flux at a given wave amplitude can be either positive or negative, the domains of existence of positive and negative ion fluxes in the “temperature ratio-density ratio” plane are determined.