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.     

Variational problems for the canonical profiles

A noncontradictory formulation of the variational problem for a canonical profile is proposed that refines the problem posed by B.B. Kadomtsev for a circular plasma cylinder. The results are generalized to a toroidal plasma with an arbitrary cross section. For the problem in toroidal geometry, boundary conditions are proposed with which to single out the Kadomtsev-like solution (the canonical profile) from the solutions to the Euler equation. Canonical profiles for the L-and H-modes are constructed. For a number of interesting examples, it is numerically shown that the second variation of the magnetic energy functional is positive. The canonical profile transport model is outlined, and the relationship between the canonical, numerical, and experimental profiles in tokamaks is briefly discussed.     

2D calculation method based on composite beam theory for the determination of local homogenised stiffnesses of long bones

A calculation method using the finite element technique is presented. Its main objective was to determine strains, stresses and more particularly stiffnesses in any cross section of a tibia, thus enabling the localisation of tibial torsion in vivo. Each tibial cross section was considered to be a non-uniform cross section of a composite beam with arbitrary orientation of fibres. The determination of stresses, strains and stiffnesses within a composite beam cross section has been defined by solving a variational problem. The validation of this method was performed on a tibial diaphysis of which each cross section was assumed to be the cross section of a composite beam made of orthotropic materials with orthotropic axes of any orientation with respect to the principal axis of the bone. The comparison of the results, from our model and that of a three-dimensional one, was performed on each nodal value (strains, stresses) of the meshed cross section as it was impossible to obtain local stiffnesses by experimentation. The good agreement between the results has validated our finite element program. Actually, this method has enabled to treat directly 2D geometric reconstructions from CT scan images with a good accuracy to determine locally the homogenised mechanical characteristics of human tibia in vivo, and particularly to quantify torsional tibial abnormalities of children without approximation of the shape of the cross section and by calculating the real moment of inertia J. The importance of the fibre orientation with regards to the stiffness values has been emphasised. This 2D method has also allowed to reduce CPU time of the 3D modelling and calculation.     

Effect of the shape of the cross section of a plasma-dielectric interface on the dispersion properties of azimuthal surface modes

A theoretical study is made of the propagation of a packet of surface electromagnetic waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide partially filled with plasma in an axial magnetic field. The cross section of the plasma column is assumed to be noncircular. The effect of the noncircular shape of the plasma cross section on the dispersion properties of azimuthal surface modes is investigated by the method of successive approximations. The fields of the waves and their eigenfrequencies are determined to second order in a small parameter.     

Diagnostics of a magnetized plasma by the field of surface waves guided by a discharge channel

A diagnostic method for determining plasma density from the dispersion of surface waves guided by a discharge channel in an axial magnetic field is discussed. The diagnostic characteristics that are the easiest to record experimentally are determined by analyzing the theoretical dispersion curves, and the ways of exploiting these characteristics for plasma diagnostics are suggested. To determine the slowing-down factor of a probing wave in a plasma channel, it is proposed to use diagnostic-signal resonances that occur when the wavelength of the slowed wave becomes equal to the length of the emitting or receiving antenna. The dependence of the plasma density averaged over the cross section of the plasma column on the strength of the external magnetic field is determined for a discharge channel formed as a result of the ionization self-channeling of plasma (lower hybrid) waves and whistlers.     

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.     

Topology of drift trajectories of charged particles in a tokamak

The topology of drift orbits in a tokamak is analyzed in the entire cross section of the device both near the magnetic axis and at the periphery of the plasma column. The use of invariants of the drift equations (the generalized momentum, magnetic moment, and total energy) as variables for the entire cross section of the plasma column and self-similar variables near the magnetic axis makes it possible to comprehensively classify closed drift orbits in a tokamak. When describing orbits of different types and domains of their existence, discriminant and locus curves obtained by the methods of differential geometry are used to determine the ranges in which the invariants vary. The influence of the nonuniformity of the longitudinal current on the drift trajectories of fast particles is studied. The works in which, together with known types of orbits, trajectories along which particles leave the plasma column and can fall on the chamber wall are analyzed.     

Influence of the shape of the cross section of a plasma-dielectric interface on the dispersion properties of high-frequency azimuthal surface modes

Theoretical study of the propagation of a packet of surface electromagnetic surface waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide within the frequency range that is higher than upper hybrid resonance is carried out. The waveguide is partially filled by plasma and immersed into axial magnetic field. The cross section of the plasma column is assumed to differ from circular shape. The effect of this shape on the dispersion properties of azimuthal surface modes is investigated by the method of successive approximations. The fields of the waves and their eigenfrequencies are determined up to terms of the second order in the deviation of the plasma cross section shape from the ring one. The correction to the eigenfrequency of azimuthal surface modes caused by this feature of the plasma column section is proved to increase with decreasing the external magnetic field and increasing the value of the dielectric constant of the dielectric, that separates the plasma from the metal wall of the waveguide. The spectral composition of the wave packet, in the form of which these modes propagate, is studied. The amplitudes of the satellite harmonics of these modes are found to increase with increasing the plasma density and decreasing the external magnetic field.     

Numerical simulations of a high-current plasma lens

The dynamic processes by which an electrostatic plasma lens with a wide-aperture ion beam and electrons produced from the secondary ion-electron emission relaxes to a steady state is investigated for the first time by the particle-in-cell method. The parameters of a two-dimensional mathematical model were chosen to correspond to those of actual plasma lenses used in experimental studies on the focusing of high-current heavy-ion beams at the Institute of Physics of the National Academy of Sciences of Ukraine (Kiev, Ukraine) and the Lawrence Berkeley National Laboratory (Berkeley, USA). It is revealed that the ion background plays a fundamental role in the formation of a high potential relief in the cross section of a plasma lens. It is established that, in the volume of the plasma lens, a stratified electron structure appears that is governed by the nonuniform distribution of the external potential over the fixing electrodes and the insulating magnetic field. The stratification is very pronounced because of the finite sizes of the cylindrical fixing electrodes of the lens. It is shown that the presence of such a structure limits the maximum compression ratio for an ion beam to values that agree with those observed experimentally.     

Geodesic acoustic modes in noncircular cross section tokamaks

The influence of the shape of the plasma cross section on the continuous spectrum of geodesic acoustic modes (GAMs) in a tokamak is analyzed in the framework of the MHD model. An expression for the frequency of a local GAM for a model noncircular cross section plasma equilibrium is derived. Amendments to the oscillation frequency due to the plasma elongation and triangularity and finite tokamak aspect ratio are calculated. It is shown that the main factor affecting the GAM spectrum is the plasma elongation, resulting in a significant decrease in the mode frequency.     

Analysis of the differential cross section for ionization of a hydrogen atom by fast electrons in a uniform electric field

The differential cross section for ionization of a hydrogen atom by fast electrons in an external uni-form electric field is calculated using the nonrelativistic Born approximation. It is shown that the cross section obtained can differ substantially from a similar ionization cross section of an isolated atom in the angular dis-tribution of secondary electrons in momentum space, oscillation terms, and magnitude.     

Measurements of the plasma radiative loss profile in the M-11M tokamak with the help of a tangential-view AXUV photodiode array

The plasma radiative loss profile in the T-11M tokamak operating with a lithium limiter was measured using a sixteen-channel absolute extreme-ultraviolet photodiode array. The field of view of the detector was set in a vertical plane tangential to the plasma column axis. The radiative loss profile was recovered by solving an inverse problem under the assumption of toroidal and poloidal symmetry of the plasma column. A stable algorithm is developed for solving the problem with this geometry, and the possible errors of the method are evaluated. The radiative loss profiles and their evolution in various tokamak regimes are derived.     

A parameter optimization approach for the optimal control of large-scale musculoskeletal systems.

This paper describes a computational method for solving optimal control problems involving large-scale, nonlinear, dynamical systems. Central to the approach is the idea that any optimal control problem can be converted into a standard nonlinear programming problem by parameterizing each control history using a set of nodal points, which then become the variables in the resulting parameter optimization problem. A key feature of the method is that it dispenses with the need to solve the two-point, boundary-value problem derived from the necessary conditions of optimal control theory. Gradient-based methods for solving such problems do not always converge due to computational errors introduced by the highly nonlinear characteristics of the costate variables. Instead, by converting the optimal control problem into a parameter optimization problem, any number of well-developed and proven nonlinear programming algorithms can be used to compute the near-optimal control trajectories. The utility of the parameter optimization approach for solving general optimal control problems for human movement is demonstrated by applying it to a detailed optimal control model for maximum-height human jumping. The validity of the near-optimal control solution is established by comparing it to a solution of the two-point, boundary-value problem derived on the basis of a bang-bang optimal control algorithm. Quantitative comparisons between model and experiment further show that the parameter optimization solution reproduces the major features of a maximum-height, countermovement jump (i.e., trajectories of body-segmental displacements, vertical and fore-aft ground reaction forces, displacement, velocity, and acceleration of the whole-body center of mass, pattern of lower-extremity muscular activity, jump height, and total ground contact time).     

Numerical simulation of the instability of a nonuniform plasma flow: Nonlinear dynamics of slipping instability

A kinetic model is proposed that describes the nonlinear dynamics of the instabilities of a transversely nonuniform plasma flow. It is shown that, in the linear approximation, the model yields the familiar boundary-value problem for the scalar potential in plasma. The slipping instability in a plane waveguide is considered as an example. The general dispersion relation for a flow with a stepwise uniform density profile and with a tangential discontinuity in its longitudinal velocity is analyzed qualitatively. The dynamics of the slipping instability is investigated numerically for a flow that is detached from the waveguide walls and whose longitudinal velocity obeys a linear, a sinusoidal, or a discontinuous distribution. In the nonlinear stage of the instability, the flow expands in such a way as to come into contact with the walls, the spread in the longitudinal velocities remains smaller than the initial velocity variation, and the longitudinal velocities of different transverse layers in the flow are not completely equalized.     

Modeling of the tearing instability in unreduced two-fluid magnetohydrodynamics

The problem of the tearing instability is solved numerically in cylindrical geometry by using the unreduced two-fluid MHD model. It is shown that the duration of the nonlinear stage of the tearing instability in a hot plasma is rather sensitive to such factors as the initial radial density and temperature profiles, the initial ion-to-electron pressure ratio, and the longitudinal thermal conductivity. Depending on these factors, the two-fluid effects (primarily, the Hall effect) can either greatly hasten the magnetic reconnection process (in comparison to that in the one-fluid MHD model) or greatly slow it. An illustrative explanation of the results obtained is given.     

Resonant effect of the noncircular shape of the plasma surface on the dispersion properties of extraordinary azimuthal surface modes in magnetoactive waveguides

A theoretical study is made of the resonant effect of the shape of the cross section of the plasma column on the propagation of a packet of extraordinary electromagnetic waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide in an axial magnetic field. The waveguide is assumed to be partially filled with a plasma. The effect of the noncircular shape of the plasma cross section on the dispersion properties of surface eigenmodes propagating strictly transverse to the external magnetic field is investigated by the method of successive approximations for the case in which the angular period of the wave perturbations is twice the ripple period of the interface between the plasma and the dielectric. In this resonant case, the fields and eigenfrequencies of the eigenmodes are determined to second order in the small parameter describing the rippling of the plasma-dielectric interface.     

Reconfigurable RCS Reduction from Curved Structures Using Plasma Based FSS

Plasmonics - The radar cross section (RCS) reduction from curved surfaces using plasma based frequency selective surfaces (FSS) is investigated. A frequency reconfigurable plasma based FSS...     

Transverse glow discharges in supersonic air and methane flows

Transverse glow discharges in supersonic air and methane flows are studied both experimentally and theoretically. The experiments show that a diffuse volume discharge filling the whole cross section of the flow can easily be initiated in air, whereas a diffuse discharge in a methane flow shows a tendency to transition into a constricted mode. The electron transport coefficients (mobility and drift velocity) and the kinetic coefficients (such as collisional excitation rates of the vibrational levels of a methane molecule, as well as dissociation and ionization rates) are calculated by numerically solving the Boltzmann equation for the electron energy distribution function. The calculated coefficients are used to estimate the parameters of the plasma and the electric field in the positive column of a discharge in methane.     

Analytical Solution to External Equilibrium Problem for Plasma with Elliptic Cross Section in a Tokamak

Plasma Physics Reports - Expressions are obtained for the magnetic field created by the currents flowing in the tokamak plasma with elliptic cross section. The analytical approach is based on the...     

The Role of Resonance Frequency of the Plasmons in Electromagnetic Wave Scattering Process from a Dielectric Covered Metallic Rod Placed in a Plasma Antenna

The electromagnetic wave scattering due to excitation of surface plasmons from a metallic rod with dielectric layer embedded in the long plasma column is investigated. In the first part, for short-wavelength waves by investigating the variations of surface polarized charge density on the boundaries, the resonance frequencies and the effective factors on it such as the geometrical dimensions, the radius of the metal, the dielectric thickness, and the plasma radius will be analyzed. In the second part, for presenting an exact analysis and categorizing types of resonant frequency to the dominant resonant frequency and subsidiary resonant frequency of the plasmons, the scattering of long-wavelength waves from the mentioned object will be reviewed. In both cases, the backscattering cross section which is a scale of the scattered power in the direction of incident will be presented.