Plasma outflow from a corrugated trap in the kinetic regime

The problem of stationary plasma outflow from an open corrugated trap in the kinetic regime is considered with allowance for pair collisions in the framework of a kinetic equation with the Landau collision integral. The distribution function is studied in the limit of small-scale corrugation and a large mirror ratio. In considering a single corrugation cell, a correction for the distribution function is calculated analytically. An equation describing variations of the distribution function along the system is derived and used to study the problem of plasma outflow into vacuum.     

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.     

Skin Effects in a Dusty Plasma

A multifluid MHD model is applied to study the magnetic field dynamics in a dusty plasma. The motion of plasma electrons and ions is treated against the background of arbitrarily charged, immobile dust grains. When the dust density gradient is nonzero and when the inertia of the ions and electrons and the dissipation from their collisions with dust grains are neglected, we are dealing with a nonlinear convective penetration of the magnetic field into the plasma. When the dust density is uniform, the magnetic field dynamics is described by the nonlinear diffusion equations. The limiting cases of diffusion equations are analyzed for different parameter values of the problem (i.e., different rates of the collisions of ions and electrons with the dust grains and different ratios between the concentrations of the plasma components), and some of their solutions (including self-similar ones) are found. The results obtained can also be useful for research in solid-state physics, in which case the electrons and holes in a semiconductor may be analogues of plasma electrons and ions and the role of dust grains may be played by the crystal lattice and impurity atoms.     

Edge Wave Propagating along a Thin Plasma Layer

A wave propagating along the edge of a thin semi-infinite plasma layer is investigated. The edge wave is described by a set of integral equations that are solved explicitly, yielding the wave dispersion and field distribution.     

The Electrical Conductance of Semipermeable Membranes: I. A Formal Analysis

A kinetic analysis of membrane conductance under conditions of stationary flow is presented. The semipermeable membrane is idealized as a homogeneous laminar phase separating ionic solutions on either side. It is assumed, without consideration of the mechanisms involved, that some ion species permeate the membrane while others do not. The flux of a given species is taken to be linearly related to the gradient of its concentration and to the electric field. The resulting flow equations, when combined with Poisson's equation, permit the formulation of the conductance problem in terms of a set of non-linear differential equations. They describe the spatial variation of the electric displacement and contain the ion current densities as parameters. Their integration, subject to appropriate boundary conditions, fixes the values of these parameters and of the corresponding transmembrane potential. The solution of the conductance problem cannot, however, be carried through in analytic form. The numerical analysis of a number of special cases will be presented in subsequent publications.     

Full-scale model of glycolysis in Saccharomyces cerevisiae.

We present a powerful, general method of fitting a model of a biochemical pathway to experimental substrate concentrations and dynamical properties measured at a stationary state, when the mechanism is largely known but kinetic parameters are lacking. Rate constants and maximum velocities are calculated from the experimental data by simple algebra without integration of kinetic equations. Using this direct approach, we fit a comprehensive model of glycolysis and glycolytic oscillations in intact yeast cells to data measured on a suspension of living cells of Saccharomyces cerevisiae near a Hopf bifurcation, and to a large set of stationary concentrations and other data estimated from comparable batch experiments. The resulting model agrees with almost all experimentally known stationary concentrations and metabolic fluxes, with the frequency of oscillation and with the majority of other experimentally known kinetic and dynamical variables. The functional forms of the rate equations have not been optimized.     

Parameter estimation for a mathematical model of the cell cycle in frog eggs.

Parameter values for a kinetic model of the nuclear replication-division cycle in frog eggs are estimated by fitting solutions of the kinetic equations (nonlinear ordinary differential equations) to a suite of experimental observations. A set of optimal parameter values is found by minimizing an objective function defined as the orthogonal distance between the data and the model. The differential equations are solved by LSODAR and the objective function is minimized by ODRPACK. The optimal parameter values are close to the "guesstimates" of the modelers who first studied this problem. These tools are sufficiently general to attack more complicated problems, where guesstimation is impractical or unreliable.     

System of Kinetic Equations for Collisionless Space Plasma in the Approximation of Field-Aligned Force Equilibrium for Electrons

A system of kinetic equations describing relatively slow large-scale processes in collisionless magnetoplasma structures with a spatial resolution on the order of the proton thermal gyroradius is derived. The system correctly takes into account the electrostatic effects in the approximation of field-aligned force equilibrium for electrons. The plasma is considered quasineutral, and the magnetic field is described by the Ampère equation. The longitudinal component of the electric field is found explicitly from the equality of the field-aligned component of the electric force acting on plasma electrons and the divergence of the electron pressure tensor. The electric field component orthogonal to the magnetic field is determined by the distributions of the number densities, current densities, and stress tensors of all plasma species in the instantaneous long-range approximation described by a system of time-independent elliptic equations. Versions of the system of equations adapted to the case of magnetized electrons described by the Vlasov equation in the drift approximation, as well as to the case in which all plasma species are magnetized, are derived. The resulting systems of equations allow creating numerical models capable of describing large-scale processes in nonuniform collisionless space plasma.     

Stability of Ion Flow and Role of Boundary Conditions in a Simplified Model of the E × B Plasma Accelerator with a Uniform Electron Mobility

Plasma Physics Reports - Resistive oscillations of axial plasma with ionization effects are analyzed in configuration similar to the Hall effect thrusters. From analysis of stationary equations we...     

Propagation of excitation in a model of neural system

The study of the characteristic statistical properties of neural systems, which was started in a previous paper, is continued here. The initial value problem for the kinetic equations describing the systems is solved in the one-dimensional case under particular conditions. To handle this problem use is made of certain techniques previously introduced by Landau and later improved by Backus and Turski in the context of the study of oscillations in a linearized plasma. The result is used for the discussion of a very simple neural system.     

One-dimensional hydrodynamic model of the atom and ion dynamics in a stationary plasma thruster

A one-dimensional hydrodynamic model of the atom, ion, and electron dynamics in the channel of a stationary plasma thruster is developed. The relevant set of integrodifferential equations is derived and investigated both analytically (steady-state solutions) and numerically (dynamic regimes). It is shown that adjusting only one parameter (the channel resistivity) makes it possible to achieve a good agreement between the calculated global parameters and experimental data. The general features of oscillations revealed with the help of the model are also found to agree fairly well with the experiment.     

Plasma equilibrium in axisymmetric poloidal magnetic field configurations in flux coordinates

A simple derivation is given of equilibrium equations in flux coordinates in the general case of an anisotropic-pressure plasma. The issue of how to formulate the boundary conditions for these equations is discussed for two types of configurations—a straight system and a system with an internal conductor. Examples of numerical solutions to the equilibrium problem for these configurations are presented.     

Development of an Exactly Solvable Model of Resonance Tunneling of Electromagnetic Waves through Gradient Barriers in a Nonuniform Magnetoactive Plasma

An exactly solvable one-dimensional model describing resonance tunneling (reflectionless transmission) of a transverse electromagnetic wave through wide layers of magnetoactive plasma is developed on the basis of the Helmholtz equation. The plasma layers include a set of spatially localized density structures the amplitudes and thicknesses of which are such that approximate methods are inapplicable for their analysis. The profiles of the plasma density structures strongly depend on the choice of the free parameters of the problem that determine the amplitudes of plasma density modulation, characteristic scale lengths of the density structures, their number, and the total thickness of the nonuniform plasma layer. The plasma layers can also include a set of random inhomogeneities. The propagation of electromagnetic waves through such complicated plasma inhomogeneities is analyzed numerically within the proposed exactly solvable model. According to calculations, there are a wide set of inhomogeneous structures for which an electromagnetic wave incident from vacuum can propagate through the plasma layer without reflection, i.e., the complete tunneling of thick plasma barriers takes place. The model also allows one to exactly solve a one-dimensional problem on the nonlinear transillumination of a nonuniform plasma layer in the presence of cubic nonlinearity. It is important that, due to nonlinearity, the thicknesses of the evanescent plasma regions can decrease substantially and, at a sufficiently strong nonlinearity, such regions will disappear completely. The problem of resonance tunneling of electromagnetic radiation through gradient wave barriers is of interest for various applications, such as efficient heating of dense plasma by electromagnetic radiation and transmission of electromagnetic signals from a source located in the near-Earth plasma or deep in the plasma of an astrophysical object through the surrounding evanescent regions.     

Plasma convection near the threshold for MHD instability in nonparaxial magnetic confinement systems

Using a highly nonparaxial magnetic confinement system with an internal levitated ring as an example, it is shown that, in a plasma near the threshold for ideal MHD instability, the external heating and the original local dissipative processes may give rise to and maintain self-consistent nonlinear MHD convection, which leads to an essentially nonlocal, enhanced heat transport. A closed set of equations is derived that makes it possible to describe such convective processes in a weakly dissipative plasma with β～1. Numerical simulations carried out with a specially devised computer code demonstrate that the quasisteady regime of nonlinear convection actually exists and that the marginally stable profile of the plasma pressure is maintained. A large amount of data on the structure of the nascent convective flows is obtained and analyzed.     

Plasma membrane fluidity measurements on whole living cells by fluorescence anisotropy of trimethylammoniumdiphenylhexatriene

Trimethylammoniumdiphenylhexatriene (TMA-DPH) is a hydrophobic fluorescent probe with a high quantum yield, which was shown earlier to have specific localization properties in the plasma membranes of whole living cells. This probe was used in aqueous suspensions of L929 mouse fibroblasts, rat mast cells and ReH6 leukemic lymphocytes for determining plasma membrane fluidity from fluorescence stationary anisotropy measurements. TMA-DPH was only partially incorporated into the membranes, most of it remained as a stable form in the buffer solution; the distribution was governed by an equilibrium. The measurements were influenced by unavoidable parasitic scattered light and an appropriate correction is described. A set of precautions for the proper use of the probe is proposed. The results indicated that the fluidity was considerably lower in whole cells than in isolated membranes from the same system.     

Nonlinear relativistic plasma resonance: Renormalization group approach

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.     

Nonuniformity of the chemical composition of a capillary discharge plasma

A steady-state distribution of the concentration of two ion species in a capillary discharge plasma is studied using MHD equations for a plasma with a spatially nonuniform, time-dependent chemical composition. In our case, the set of equations is significantly simplified because of the steady-state character and symmetry of the problem. Even with such simplification, however, some results could be obtained only by numerical integration. The factors affecting the distribution of heavy ions are studied. It is shown that the distribution of the heavy impurity over the discharge cross section can be much more nonuniform than the distribution of the main component (hydrogen). A simple criterion for such a nonuniformity is obtained.     

One-Dimensional hybrid model of a stationary plasma thruster

A one-dimensional hybrid model of the dynamics of atoms, ions, and electrons in the channel of a stationary plasma thruster is developed. The relevant set of integrodifferential equations is studied numerically. The results obtained are compared with the results of previous calculations based on a hydrodynamic model. It is shown that, with the use of one fitting parameter (the channel resistance), the calculated integral characteris-tics agree well with the experimental ones. The current-voltage characteristic is obtained. The general features of low-frequency oscillations that have been revealed in numerical simulations using the model proposed are also in fairly good agreement with experimental results. The value of the electron thermal conductivity is estimated.