Axial Flux Density Distribution Research Articles

Core physics calculation study of miniature lead-bismuth cooled nuclear reactor

Aiming at the application environment of small marine nuclear power platform, a 1MW Lead-Bismuth cooled nuclear reactor design scheme was proposed. The Monte Carlo method was used to calculate the reactor core physical parameters. 469 core fuel rods were arranged in 13 turns and 90% enriched UO2 fuel loading meet the power operation of nearly 10 years, and the core size meets the environmental requirements. The calculation results of fuel consumption show that after each loading, the reactor can run continuously for 1 year at 1 MW power. The radial density and axial flux density distribution and power distribution gradient trend of the core are reasonable, indicating that the design scheme can meet the requirements of small ships. Nuclear power platform use requirements.

Accurate computation of magnetic lenses with FOFEM

Abstract First-order finite element method (FOFEM) is used for computations of rotationally symmetric magnetic electron lenses with saturated materials. An overview of local and global errors in the axial flux density distribution in the first-order finite element method is given, and the coefficient computation in FOFEM providing the best axial fields are shown. The quality of computed results is illustrated on several typical problems. It is shown that with graded dense mesh accurate results can be obtained fast and with small memory requirements.

Focal properties of unsaturated asymmetrical magnetic electron lenses

From axial flux density distributions measured experimentally at a constant excitation, the focal properties of asymmetrical magnetic electron lenses were computed over a wide range of asymmetry under non-saturation conditions. The effect of magnetic field asymmetry on the objective and projector electron-optical properties was investigated systematically up to the extreme case where the lens is considered to be of the single pole-piece type. The results should be useful in the design and operation of unsaturated asymmetrical and single pole-piece objective and projector lenses for various types of electron microscopes.

Design parameters of an unconventional probe-forming lens

The design parameters of an electron probe-forming lens with a zero-bore flat-face single pole piece have been considered under nonsaturation conditions. From the measured axial flux density distribution of an experimental single-pole-piece lens, the maximum flux density, the spherical and chromatic aberration coefficients, the focal length and the object position have been investigated in terms of the diameter of the pole's flat face, which is the effective geometrical parameter. Empirical equations relating the geometrical electron-optical parameters have been put forward and compared with those of a different experimental lens reported in the literature. The focal properties of the probe-forming lens have also been investigated in the telescopic mode of operation. The results should be useful for preliminary design considerations of an unconventional electron probe-forming lens with zero-bore flat-face single pole piece for various types of electron-optical instruments according to the operational requirements.

Characteristics of the axial magnetic field of asymmetrical electron lenses

Using the experimentally measured axial flux density distributions of asymmetrical electron lenses, some of their electron-optical properties were studied in detail over a wide range of asymmetry under nonsaturation conditions. The limitations of some relationships concerning the maximum flux density and the halfwidth of the axial magnetic field of asymmetrical lenses were discussed. Empirical equations describing the chief properties of the flux density distribution were put forward. The effect on the electron-optical properties due to the transfer from the double pole piece asymmetrical lens to the more simple design of the single pole piece lens was investigated. The results should provide a better understanding of some of the electron-optical properties of asymmetrical double pole piece and single pole piece electron lenses which at the present time are widely used in various types of electron microscopes.

Pole design in single pole piece projector electron lenses

Two single pole piece electron lenses of equal dimensions, one with a cylindrical pole and the other with a spherical pole, are described. The projector focal properties of both lenses were calculated from the experimentally measured axial flux density distributions at different diameters of the axial bore in the pole piece. A comparison is made between the electron optical properties of the two experimental lenses including their projector focal length, radial and spiral distortion. The effect of the pole piece shape and the size of the axial bore on the projector focal properties are discussed in detail. Empirical equations concerning some electron optical properties of single pole piece lenses are put forward. The results should be useful in the design of single pole piece projector lenses for the transmission electron microscope.

Properties of the axial flux density distribution of magnetic electron lenses with a single cylindrical pole-piece

The axial flux density distribution of single pole-piece magnetic electron lenses differ from those of conventional design. An experimental investigation has been carried out concerning the effect of the bore size on the shape of the field distribution of single pole-piece lenses. The size of the axial bore in the cylindrical pole-piece of an experimental lens was varied over a wide range and the axial flux density distribution was measured for each bore size. The characteristic features of the field distribution such as its peak value, its penetration inside the lens structure and its mathematical representation by an analytical function were studied in detail. The effect of the bore size on the magnetic asymmetry was also considered. Empirical equations concerning the properties of the field distribution are put forward. The results should be useful in the optimisation of lens design and in field distribution modelling.

Scherzer's formula and the correction of spiral distortion in the electron microscope

Scherzer's general expression of 1937 for the spiral distortion coefficient of electron lenses is used to calculate the spiral distortion of the rectangular-field model for the axial flux density distribution in magnetic projector lenses. The results show why it is difficult to correct the spiral distortion produced by conventional lenses. On the other hand, corresponding calculations for single-polepiece projector lenses indicate that the employment of such lenses could lead to a significant improvement of the projector stage of the electron microscope, especially that of the high voltage electron microscope.