Longitudinal electric conductivity in a quantum plasma with a variable collision frequency in the framework of the Mermin approach

In the framework of the Mermin approach, we obtain formulas for the longitudinal electric conductivity in a quantum collisional plasma with a collision frequency depending on the momentum. We use a kinetic equation in the momentum space in the relaxation approximation. We show that as the Planck constant tends to zero, the derived formula transforms into the corresponding formula for a classical plasma. We also show that as the frequency of collisions between plasma particles tends to zero (the plasma transforms into a collisionless plasma), the derived formula transforms into the well-known Klimontovich-Silin formula for the collisionless plasma. We show that if the collision frequency is constant, then the derived formula for the permittivity transforms into the well-known Mermin formula.     

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.     

Study of the dust acoustic waves in a magnetized dusty plasma with many different dust grains

The nonlinear dust waves in a magnetized dusty plasma with many different dust grains are analytically investigated. New analytical solutions for the governing equation of this system have been obtained for the dust acoustic waves in a dusty plasma for the first time. We derive exact mathematical expressions for the general case of the nonlinear dust waves in magnetized dusty plasma which contains different dust grains.     

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.     

Analytical study of nonlinear dust acoustic waves in two-dimensional dust plasma with vortex-like ion distribution

The nonlinear dust acoustic waves in two-dimensional dust plasma with vortex-like ion distribution are analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with vortex-like ion distribution.     

Theoretic study of dust acoustic waves in a dusty plasma with dust charge variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is investigated by using the formally variable separation approach. New solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma firsthand. We derive exact mathematical expressions and numerical simulation studies for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.     

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.     

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.     

Analytic continuation for the generalized Bohm criterion in a two-ion-species plasma

The generalized Bohm criterion in a two-ion-species plasma is analytically investigated. The universal iterative formulas of the approximative solutions have been affirmed for the ion acoustic wave (IAW) dispersion relation and the generalized Bohm criterion in the two-ion-species plasma for the first time. For a weakly collisional two-ion-species plasma, it is indicated that the choice of the initial solution and the repetitious iterative operation for the ion drift velocities is the linchpin of the optimized solution for the ion acoustic wave dispersion relation and the generalized Bohm criterion, considering the more general case and extensive physical characteristics.     

Nonlinear evolution of screw modes in finite-conductivity plasma

The paper examines numerical modeling of nonlinear stabilization of screw instability in a plasma with a free surface. The analysis is based on a cylindrical model allowing for finite conductivity of the plasma.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 113–122, 1985.     

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.     

On the existence of the free-boundary for some problems arising in plasma physics

We study some conditions for the existence of a free-boundary for two different bidimensional models arising in the magnetic confinement of a plasma. We derive estimates on the size and location of the region surrounded by the free-boundary (known as plasma region) for both models. We also derive sufficient conditions for the non-existence of the free-boundary.     

Oscillations in quasineutral plasmas

Abstract The purpose of this article is to describe the limit, as the vacuum electric permittivity goes to zero, of a plasma physics system, deduced from the Vlasov—Poisson system for special initial data (distribution functions which are analytic in the space variable, with compact support in velocity), a limit also called "quasineutral regime'' of the plasma, and the related oscillations of the electric field, with high frequency in time.     

On Plane Waves in Diluted Relativistic Cold Plasmas

We briefly report on some exact results (Fiore in J. Phys. A, Math. Theor. 47:225501, 2014) regarding plane waves in a relativistic cold plasma. If the plasma, initially at rest, is reached by a transverse plane electromagnetic travelling-wave, then its motion has a very simple dependence on this wave in the limit of zero density, otherwise can be determined by an iterative procedure whose accuracy decreases with time or the plasma density. Thus one can describe in particular the impact of a very intense and short laser pulse onto a plasma and determine conditions for the slingshot effect (Fiore et al. in arXiv:1309.1400, 2014) to occur. The motion in vacuum of a charged test particle subject to a wave of the same kind is also determined, for any initial velocity.     

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.     

On the Attractive Plasma-Charge System in 2-d

We study a positively charged Vlasov-Poisson plasma in which N negative point charges are immersed. The attractiveness of the system forces us to consider a possibly unbounded plasma density near the charges. We prove the existence of a global in time solution, assuming a suitable initial distribution of the velocities of the plasma particles. Uniqueness remains unsolved.     

等离子体反应器流场的数值模拟

本文采用颗粒轨道模型对等离子体反应器进行数值模拟.数值格式用SIMPLER法.湍流模型用简单的次网格模型.计算结果给出速度场、温度场及颗粒轨道,对工程设计和工艺过程参数控制有参考价值.     

Stimulated Raman scattering in the presence of trapped particle instability

The behaviour of electron gas in a laser plasma corona is studied in the presence of stimulated Raman scattering (SRS). The 1D Vlasov–Maxwell model describing plasma relevant to the experiment PALS (Prague Asterix Laser System), where the nanosecond iodine laser with the wavelength of first harmonic λ_vac = 1.3152 and with the power density in the focal spot I = 10²⁰ W/m² is in operation. For the solution of Vlasov equation for the electron distribution function a Fourier–Hermite transform method is used. For the numerical stabilization a small collision term is added to the Vlasov equation keeping its value realistic for the condition relevant to the PALS experiment. The dominant wave modes in our model are both the backward (SRS-B) and the forward (SRS-F) Raman scattering, each of them accompanied by the forward going electron plasma wave. Several mechanisms were identified such as the SRS-B plasma wave spectral broadening due to a trapped particle instability (TPI) or the formation of an electrostatic quasi-mode by non-resonant interaction of SRS-B and SRS-F plasma waves.