Magnetic Prism Research Articles

SIMPLIFIED EXPRESSIONS FOR THE MAGNETIC ANOMALIES DUE TO VERTICAL RECTANGULAR PRISMS*

AbstractThe magnetic anomaly due to a uniformly magnetized vertical rectangular prism and that due to an arbitrary structure which can be divided into a number of such prisms are expressed in forms suitable for rapid computation. Both two‐dimensional and three‐dimensional cases are considered. The simplified expressions will find use in interpretation techniques where repeated computations have to be made of the anomaly due to prisms as in automated fitting of prism anomalies to observed magnetic anomalies using non‐linear optimization techniques or related methods.

Interpretation of three‐component borehole magnetometer data

We have made a theoretical study of the problem of locating and defining a magnetized prism in the vicinity of a drillhole. The study shows that a three‐component borehole magnetometer can be very useful in exploration for deep magnetic targets, which are difficult to intersect by drilling. There are nine parameters to be estimated from the data: the x, y, and z positions of the center of the prism; length, width and depth extent; and the three parameters defining the magnetization vector. The parameters are estimated by minimizing the sum of squared differences between the predicted and observed data. Since the problem is nonlinear, it must be solved iteratively. At each iteration a singular value analysis of the sensitivity matrix is performed, and a particular solution is chosen from a set of minimal length solutions; each solution corresponds to a different rank of the sensitivity matrix. The main difficulty is an ambiguity involving the position parameters and the parameters defining the magnetization vector. In order to minimize this obstacle, a parameter scaling matrix is introduced. The effects of noise, wrong model, probe orientation errors, borehole length, and data density are analyzed. We have found that the position and depth extent of the body can be estimated with reasonable accuracy.

Definition of a corrected magnetic prism spectrometer for electron microscopy

Abstract Suggestions resulting from the use of a magnetic prism are presented in order to optimize the adaptation of a spectrometer to an electron microscope. The parameters of a prism, corrected for the three predominant second order aberrations, are given.

A magnetic prism beta spectrometer for low energies

A prism beta spectrometer intended for studying electron spectra in the low-energy range is described. Because the radii of curvature of electron trajectories in the pole gap of the magnetic prism are small, the required magnetic field strength is comparatively large, even for low-energy electrons. Thus the spectrum is less distorted by changes in the field distribution associated with hysteresis than it would be with an iron-cored instrument requiring a smaller field strength. The beta-spectrometer design presented has two pole gaps. The radius of curvature of the trajectory in the middle of the pole gap is σ m = 216 mm the (momentum) dispersion is D = 4780 mm. The transmission is 0.018% (of 4π). The spectrum of the KLL Auger electrons of samarium in the energy interval 30.6 – 33.8 keV obtained with a radioactive source 1 mm wide by 60 mm long is presented. The (momentum) half-width of the spectral lines is 0.08%. Since their natural half-width is 0.044%, the instrumental half-width is about 0.04%.

A perfect-crystal neutron polarizer as an application of magnetic prism refraction

It is demonstrated experimentally that the well known spin-selective deflection of neutrons transmitted through a static magnetic field region with triangular geometric boundaries combined with the high angular resolution of a non-dispersive double-crystal arrangement can be used to polarize a thermal neutron beam to a degree close to unity at reasonably low laboratory fields of 1.0 to 1.5 T.

Multichannel Neutral Atom Energy Spectrometers for Plasma Diagnostics

Multichannel neutral atom energy spectrometers for energies of 0.3-10 keV for use on fast pulsed plasma experiments are described. The spectrometers consist of a gas stripping cell, a fixed or variable magnetic prism, and a row of scintillator-photomultiplier detectors. Calibration, data analysis, and some operating experience are described.

Extended range field emission spectroscopy

We have measured the energy distribution of field emitted electrons by first accelerating them to about 20 keV and then directly energy analyzing these high energy electrons with a high-performance magnetic prism spectrometer. Our preliminary results indicate that it may be possible to extend the energy range of field emission spectroscopy to more than 5 eV below the Fermi level.

Magnetic spectrometers with corrected second-order aberrations

Recent years have seen tremendous advances in analytical electron microscopy and increased interest in electron energy loss spectroscopy has been especially prominent. Due to these developments there have been many discussions in the literature of the use of magnetic spectrometers in energy analysis. The aberrations of magnetic prisms have also received numerous treatments [1-4] although not specifically emphasizing energy analysis in the electron microscope. The importance of the objective and post-specimen lenses on the effective spectrometer resolution, however, has been discussed in recent papers by Crewe [5,6]. To our knowledge, the correction of those aberrations of importance in an electron microscope spectrometer have not been adequately delineated. Recent work of H. Shuman, et al. [7] has demonstrated whole sets of uniform field magnetic prisms with curved pole faces which simultaneously eliminate the main second-order aberrations affecting the energy resolution in addition to making the focal plane perpendicular to the central ray (useful for parallel recording of spectra).

An improved magnetic prism design for a transmission electron microscope energy filter

Energy selecting electron microscopes of the Castaing-Henry prism-mirror-prism design suffer from a loss of image and energy resolution with increasing field of view. These effects can be qualitatively understood by examining the focusing properties of the prism shown in Fig. 1. A cone of electrons emerges from the entrance lens crossover A and impinges on the planar face of the prism. The task of the prism is to focus these electrons to a point B at a focal distance f2 from the side of the prism. Electrons traveling in the plane of the diagram (i.e., the symmetry plane of the prism) are focused toward point B due to the different path lengths of different electron trajectories in the triangularly shaped magnetic field. This is referred to as horizontal focusing; the better this focusing effect the better the energy resolution of the spectrometer. Electrons in a plane perpendicular to the diagram and containing the central ray of the incident cone are focused toward B by the curved fringe field of the prism.

Electron optical experiments with a magnetic imaging filter

In the CTEM, imaging filter systems consisting of several magnetic prisms permit the removal of inelastically scattered electrons. Such systems transfer the diffraction plane and the intermediate image stigmatically. A prerequisite for a singly achromatic imaging is that the filter produces a radial intermediate image in its plane of symmetry.The symmetry relations of the magnetic fields and the electron paths permit correction of the second-order distortion and of the second-order aperture aberration [1]. The aperture-dependent magnifications, however, remain uncompensated. These aberrations must be tolerated for filter systems which have stigmatic intermediate images [2], If, however, line foci exist between the prisms, hexapoles can be applied for correction (Fig. 1 [3,4]). Such corrections seem imperative in filters which are used for high resolution electron microscopy.The adjustment of a symmetric optical path in our filter system by means of quadrupoles can be controlled by inserting an edge into the symmetry plane and simultaneously observing the image produced by the filter.

Data Acquisition and Handling Unit for a Quantitative Use of Electron Energy Loss Spectroscopy

An effective use of electron energy loss spectroscopy for chemical characterization of selected areas in the electron microscope can only be achieved with the development of quantitative measurements capabilities.The experimental assembly, which is sketched in Fig.l, has therefore been carried out. It comprises four main elements.The analytical transmission electron microscope is a conventional microscope fitted with a Castaing and Henry dispersive unit (magnetic prism and electrostatic mirror). Recent modifications include the improvement of the vacuum in the specimen chamber (below 10-6 torr) and the adaptation of a new electrostatic mirror.The detection system, similar to the one described by Hermann et al (1), is located in a separate chamber below the fluorescent screen which visualizes the energy loss spectrum. Variable apertures select the electrons, which have lost an energy AE within an energy window smaller than 1 eV, in front of a surface barrier solid state detector RTC BPY 52 100 S.Q. The saw tooth signal delivered by a charge sensitive preamplifier (decay time of 5.10-5 S) is amplified, shaped into a gaussian profile through an active filter and counted by a single channel analyser.

A compact helium monitor

A miniature mass spectrometer is described. The analyser structure has dimensions 44 mm × 28 mm × 12 mm and, with the vacuum chamber and magnet, weighs 2.2 kg. The sensitivity to helium is 1 · 10 −4 A torr −1 and it is maintained up to an operating pressure of 5 · 10 −4. A combination of a short ion path length and an electrostatic energy selector reduces the background current to a negligible level. The compact arrangement is achieved by the use of an ion source in which the ions traverse trochoidal paths, and an ion-energy-sensitive collector at the faces of a 90° magnetic prism.

The optimal arrangement of the energy selecting electron microscope with the double magnetic prism

On the basis of a theoretical and experimental study of the properties of a filter, the optimal arrangement of an energy selecting electron microscope with a double magnetic prismelectrostatic mirror filtering system is designed.

Transfer matrices of real r−1 prisms with a spiral main path

The second order radial and first order axial transfer matrices of r −1 magnetic prisms with a spiral main path are derived. Arbitrary incidence and emergence angles and boundary curvature radii are assumed. Extended fringing field effects are taken into account.

SOME COMMENTS ON THE CALCULATION OF THE GRAVITATIONAL AND MAGNETIC ATTRACTION OF A HOMOGENEOUS RECTANGULAR PRISM *

AbstractThe use of arctangents rather than arcsines in the expression for the gravitational attraction of a homogeneous rectangular prism reduces computational difficulties. Once a subroutine is available to compute one component of attraction in a Cartesian coordinate system, the other components may be obtained by cyclic permutation of the field point and body coordinate parameters. This technique also readily provides derivatives of the gravitational attraction and hence forms a compact method for the calculation of a magnetic anomaly due to a homogeneous rectangular magnetic prism.

A Michelson interferometer using electron waves

An electron interferometer of the Michelson type is realized. Monoenergetic 25 keV electrons emitted from a line source 1000 A in width are deflected by 90 ° in a magnetic Castaing prism and reflected on two mirrorsM 1 andM 2 held at a potential ΔU m negative with respect to the cathode. In the experiment the mirrors are represented by height differences on the surface of an silvered glass plate. The reflected electrons are once more deflected by the magnetic prism behind which the coherent partial beams 1 and 2 reflected on the mirrorsM 1 andM 2, respectively, are superimposed using an electrostatic biprism to form two-beam interferences. The observed fringe shift indicates a phase shift due to differences in height between the equipotentials reflecting the partial beams 1 and 2. It is estimated that path differences less than the electron wavelength of 0.08 A can be observed.

Identification of short polarity events by transforming marine magnetic profiles to the pole

A method is presented that permits marine magnetic anomaly profiles from all parts of the world to be stacked for the purpose of enhancing coherent small anomalies due to short geomagnetic polarity events. In general, the shape of a profile depends not only on the sequence of normally and reversely magnetized magnetic prisms that constitute the source, but also on the following five angles: the declination and inclination of the regional field; the declination and inclination of the magnetization; and the azimuth of the magnetic stripes. Our method transforms a measured anomaly to a second anomaly which would have been produced by an identical source with vertical magnetization and vertical regional field. The method uses Fourier transform and linear systems theory and employs filters with a flat spectral response, so that no information is lost at short wavelengths. No assumptions are made about the true depth or shape of the source: this may be any two-dimensional body or bodies in which the direction of magnetization is constant and the intensity varies arbitrarily. A preliminary application of the method to marine profiles from the East Pacific rise has yielded encouraging results.

The Multipassage Magnetic Mass Spectrometer

A new kind of magnetic mass spectrometer is described. It consists of (n) magnetic prisms integrated into a single pole piece and (n−1) mirrors which return the beam from one prism to the other. It is shown that by an appropriate choice of the parameters of the apparatus the resolving power increases linearly with the number of passages in the prism. Experimental results verify the theory. Other properties of this system are also discussed.

Modification of the High Voltage Supply of an Electron Microscope for Improved Stability

The high voltage power supplies of older transmission electron microscopes lack the feedback regulation that provides the exceptional voltage stability found in modern instruments, A method has been devised to apply feedback control to an existing high voltage supply. The modification requires few changes in the original power supply circuitry and uses relatively inexpensive, commercially available components.A stable accelerating voltage is required to achieve high resolution in transmission electron microscopy; an analysis of the chromatic aberration for a resolution of 2 Å leads to a required voltage stability of about one part in 105 over the period of exposure A stable accelerating voltage is also required when the microscope is used with a magnetic prism electron spectrometer for “selected area“ electron spectrometry. The stability of the accelerating voltage should be significantly better than the thermal energy spread of the electrons if the full resolution of the spectrometer is to be realized.

An electron beam spectrometer for the measurement of the angular distribution of plasma losses in thin films

Details are given of an electron beam spectrometer using a magnetic deflection prism as a momentum analyser. The spectrometer is designed for the measurement, as a function of scattering angle, of the discrete energy losses of 10 keV electrons transmitted through thin solid films. The energy resolution is 0·7 eV and the angular resolution before unfolding is 0·8 mrad. The spectrometer has been used to verify the intensity dependence on scattering angle of the volume and surface plasma loss lines of aluminium to a high accuracy and also to obtain an accurate value for the volume loss, namely 15·19±0·03 eV. A folding technique used to analyse the intensity against angular scattering results is described together with a least-squares method for fitting the experimental data to the folded intensity-angle distribution.