Express method of designing magnetic mass analyzers

An original method for designing magnetic mass analyzers that is represented in the form of a computer program is proposed. The thorough optimization of the method makes it possible to rapidly and accurately simulate the focusing properties of a mass analyzer along its focal line, as well as to select designs appropriate for a given problem.     

Relativistic effects in the calibration of electrostatic electron analyzers. II. Parallel plate and cylindrical mirror analyzers

Relativistic correction terms up to the second order are derived for the kinetic energy of an electron travelling along the central trajectory, which crosses the non-relativistic foci of electrostatic parallel plate and cylindrical mirror analyzers. The effects of fringing fields and source geometry are neglected. In both cases the magnitude of relativistic corrections depends on the geometry of the analyzer, but generally it is smaller than for the toroidal family of analyzers.     

Mirror-type mass analyzer with cylindrical poles

A static mass analyzer of charged particles operating under a nonuniform magnetic field is suggested. An expression for the magnetic potential distribution is obtained in explicit form. From this expression, formulas for the basic parameters in the dispersion plane are derived for first-order angular focusing. Conditions for space focusing are found when a source and a detector are beyond the magnetic field region. Operating conditions where the trajectory exhibits three turns (in other words, charged particles travel a longer distance in the field) are established. The extended trajectory causes a considerable increase in the mass linear dispersion.     

Natural convection mass transfer behavior of serially connected cylindrical electrodes

Natural convection mass transfer rates at both vertical and horizontal serially connected tubes were reported using the electrochemical technique involving the measurement of limiting currents for the deposition of copper on copper cylinders from acidified cupric sulphate solutions. Measurements were carried out with: (a) one tube active; (b) two tube surfaces active; (c) three tube surfaces active.

The electrolyte concentration and a number of serial connections of tubes were varied to provide a range of GrSc extending from 5.3×10⁸ to 9.5×10¹¹. The mass transfer rates at serially connected horizontal cylinders were in good agreement with mass transfer data in the literature. Correlation of results covered both laminar and turbulent conditions separately. The mass transfer rates at serially connected vertical cylinders were controlled by the boundary layer development at the multi-electrodes. The results for vertical electrodes, which are single, serially connected two and three electrodes, were separately correlated in the turbulent region.

The results illustrate the important effect of boundary layer development in determining current distribution in multi-electrode electrochemical cells.     

The mechanics of particles inside a rotating cylindrical mass shell

It is shown that up to the second order in the gravitational constant the effect of a rotating mass shell on a particle moving near its axis is the same as that of a rotating coordinate system. Coriolis force and centrifugal force have, contrary to the case discussed by Thirring[1, 2], the value expected in a rotating reference frame.     

Polaron self-energy and effective mass in a freestanding cylindrical quantum wire

The polaron self-energy and correction to the electron effective mass in a freestanding quantum wire is investigated by the perturbation approach.The polaron effect of the electron-confined longitudinal optical (LO) phonon and surface optical (SO) phonon interactions are separately worked out. Numerical calculation on a GaAs quantum wire shows that the confined LO phonon contribution to the polaron self-energy is relatively small for a narrow wire and gradually approach that of the bulk material when the radius of the wire increases. While the contribution of the SO phonon modes is big for small wire radius and then decreases as the radius increases.     

Relativistic effects in the calibration of electrostatic electron analyzers. I. Toroidal analyzers

Relativistic correction terms up to the second order are derived for the kinetic energy of an electron travelling along the circular central trajectory of a toroidal analyzer. Furthermore, a practical energy calibration equation of the spherical sector plate analyzer is written for the variable-plate-voltage recording mode. Accurate measurements with a spherical analyzer performed using kinetic energies from 600 to 2100 eV are in good agreement with this theory showing our approximation (neglect of fringing fields, and source and detector geometry) is realistic enough for actual calibration purposes.     

Nonlinear stability in magnetic fluids of cylindrical interface with mass and heat transfer

The nonlinear Rayleigh-Taylor stability of the cylindrical interface between the vapor and liquid phases of a magnetic fluid is studied when the phases are enclosed between two cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The method of multiple scale expansion is used for the investigation. The evolution of amplitude is shown be governed by a nonlinear Ginzburg-Landau equation. The various stability criteria is discussed, and the region of stability is displayed graphically. Received 18 January 2002 Published online 13 August 2002     

The stability of Mott polarization analyzers

The stability of Mott conventional spherically symmetric and retarding-potential conical polarimeters are compared for the case when the position of the electron beam at their inputs is changed. The primary electron energies are 500 and 1600 eV. When the electron beam is shifted by 0.6 mm, the count rate of the former polarimeter remains unchanged, while for the latter, it changes by ≈7 and ≈18% for the energies 1600 and 500 eV, respectively. This instability may cause errors in measuring the degree of polarization of the electron beam.     

Combined ESCA/Auger system based on the double pass cylindrical mirror analyzer.

In comparison with other ESCA apparatus, the presently described instrument offers several unique advantages. First, it is possible to accomplish high     

Stability of cylindrical conducting fluids with heat and mass transfer in longitudinal periodic electric field

A novel system to study the effect of an axial periodic electric field on the stability of a system of cylinders of conducting fluids in the presence of heat and mass transfer is investigated. The stability of a cylindrical interface between the vapor and liquid phases of a fluid is studied when the vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface. The linear dispersion relation is found to be of damped Mathieu-type equation with real coefficients. The method of multiple time scales is used to obtain approximate solution and analyze the stability criteria for both the nonresonant and resonant cases. The stability of the system is also discussed analytically and numerically for such cases. It is found that both the heat and mass transfer coefficient and the dimensions of the system have destabilizing influences on the considered system, while azimuthal wavenumber is found to have a stabilizing effect. The dual role of the electric field frequency is also observed on the stability of the system depending on the electrical conductivities values. Finally the behaviour of the resonance points corresponding to the effects of each of the above physical parameters are determined, and a comparison between the obtained results with the corresponding results in the case of a constant applied electric field is achieved.     

Combined mass spectrometer and electron spectrometer for investigation of solids

The possibility to develop the electron-and-ion energy analyzer and mass spectrometer combined in one optical system for the investigation of the properties of solids has been considered. This device allows one to obtain information on the chemical composition and energy spectrum for all the particles emitted by the surface of a solid subjected to various effects in one experiment. The combined spectrometers are based on the source of the particle flux, which transforms the mass spectrum into the energy spectrum due to the effect of electric-field pulses on the ion flux, and the high-resolution electrostatic energy analyzer. The particles appear in the source as a result of the interaction of the exciting radiation from an independent source with the surface of the solid under study. The type of exciting radiation (fluxes of ions, atoms, electrons, and laser radiation) is chosen depending on the goals of the study. Numerical modeling of the device operation, which confirms the possibility of its implementation in the form of a compact informative system for the investigation of characteristics of solids, has been performed.     

Dynamic stability of a base-excited thin orthotropic cylindrical shell with top mass: Simulations and experiments

Considering both an experimental and a numerical approach, the dynamic stability of a harmonically base-excited thin orthotropic cylindrical shell carrying a top mass is examined. To be able to compare the experimentally obtained results with numerical results, a semi-analytical coupled shaker-structure model is derived. Using the semi-analytical model, it is shown that the dynamic stability analysis of the base-excited cylindrical shell with top mass should be concentrated near a low frequency resonance, corresponding to a mode, in which axial vibrations of the (cylindrical shell with) top mass dominate. In this frequency region, the shell may exhibit an aperiodic beating type of response, if some critical value of the amplitude of the harmonic base-excitation is exceeded. This beating response is characterized by severe out-of-plane deformations. The experimental results qualitatively confirm the numerical observations.     

Polarization analyzers operating in a wide spectral range

Different versions of practical realization of customary optical systems for full measurement of the polarization state of quasi-monochromatic partially polarized light are considered. They can be used to overcome measurement difficulties associated with the finite width of the spectral range being studied. The effect of changes in characteristics of optical and polarization elements over a spectral range on the character of polarization measurements is analyzed. Methods for elimination of chromatism or taking into account its effect on measurements are suggested. Relations for taking into account the effect of chromatism of a phase plate with constant thickness on measurement results are given. Operation of a classical four-channel scheme for studing quasi-monochromatic partially polarized light in the visible and near-IR regions is considered. For this system, expressions are derived which make possible determination of Stokes parameters taking into account the effect of a finite spectral range. A system using phase modulation of radiation by an electrooptical cell and measurement of the maximum and minimum intensities of the modulated signal is considered. Measurements are carried out by using a two-channel system. Expressions are derived which make possible determination of Stokes parameters for the system under consideration in the visible and near-IR spectral regions. A system for measuring the polarization state of radiation in the visible and near-IR regions and based on modulation of radiation by an electrooptical phase cell is described. Measurements are carried out for the fundamental modulation frequency and its harmonics using a two-channel scheme. Relations for determining Stokes parameters of the system are presented.     

Advances in crystal analyzers for inelastic X-ray scattering

The realization of spherical crystal analyzers for inelastic X-ray scattering experiments (IXS) is an ongoing project at the ESRF since 1992. We developed reliable techniques to routinely produce silicon spherical analyzers with very high (ΔE=1÷10 meV) and high energy resolution (ΔE=0.2÷1.5 eV), and with very good focal properties and efficiency. In this article we report the state of the art of the analyzer construction and the main improvements made during the last years.     

Objective local theories and the symmetry between analyzers

It is shown that a necessary condition for objective local theories to be equivalent to quantum mechanics in correlation experiments in the existence of a dissymmetry between analyzers or, alternately, a space anisotropy. No supplementary assumption is made about detection probabilities when the variables of the local theory all lie in the plane of the analyzers. The proof extends to three-dimensional variables if one supposes the detection process to be free of instabilities.