Radial Focusing Research Articles

Theorie erster ordnung eines spektrometers hoher dispersion MIT Wendelförmigem magnetfeld

A winding magnetic field is proposed for a high-dispersion β-ray spectrometer. The focusing properties have been investigated with a first-order perturbation theory. It is shown that winding fields at focusing angles of more than 2 π lead to a high dispersion. With a first field coefficient of a 1 = −0.929728 and a slope of k = 0.1 at the radius of the normal orbit the radial focusing angle is found to be I = 913.32° , and the dispersion D = 49.30.

Measurement of the radial focusing aberrations in the chalk river iron free π√2 β spectrometer

Abstract This paper reports detailed measurements of the manner in which this double focusing spectrometer focuses electrons from a point source. An electron gun mounted on a universal joint pivot at the spectrometer source position could direct 6 keV electrons emerging from its 0.3 mm diameter exit hole at any desired angle relative to the optic circle. The radial focusing aberrations as functions of the electron departure angles at the source, φ r and φ z , were deduced from the values of the spectrometer current necessary to keep the electron beam focused on a 0.25 mm wide slit fixed in the image plane of the spectrometer. The electrons passing through this slit were detected in a Faraday cage connected to an electrometer. The radial focusing aberrations determined experimentally are compared with theoretical values computed by Lee-Whiting for this spectrometer. He determined the dependence of the radial aberrations on the source departure angles of the electrons by computing the electron orbits for some 90 sets of departure angles φ r and φ z . The present measurements confirm his theoretical predictions to within the accuracy of the relative electron momentum measurements,± 0.004%. The results indicate that the spectrometer should operate without a serious loss in transmission at resolution settings of≲ 0.005% provided that sufficiently narrow and thin radioactive sources can be prepared. As a by-product, the aberration patterns corresponding to the apertures defined by the existing baffle system have also been studied. These show that the baffles are quite adequate for experimental work at the highest resolutions although minor modifications would permit a small increase in transmission.

A three-magnet extraction system for the 1 GeV Orsay linear accelerator

The three-magnet extraction system consists of three identical magnets with normal entrance and exit, bending alternately right and left. The distances between the magnets are such that the center of each magnet is at the radial focus of the preceding one. A set of quadrupole lenses focuses the beam onto the target. Measurements to date indicate that the system behaves as predicted, notably with non-observable aberrations.

Development of the magnetic cone for the center of the Berkeley 88-inch cyclotron

General requirements for a vertically focusing negative magnetic gradient region near the cyclotron center are stated. Cone shapes were studied with computer program CENREG (IBM 704) and with magnetic measurements in a fifth-scale model magnet. Principal parameters studied were Vertical and radial focusing, particle phase slip, and magnetic first harmonic. Shaping of iron to achieve the desired conical field profile in conjunction with circular trim coils is described. A pattern of holes with magnetically saturated iron caps in the 8-in.-diam center plug was needed to get the desired cone shape at all field levels from 8 to 16 kG. Proper placement of holes and modification of the movable ion-source hole in the upper pole tip were necessary to reduce first harmonic at 5 in. radius to less than 2 G at all field levels and at all ion-source positions. Small adjustments of center-region iron were made during full-scale magnet testing. Cyclotron operations to date have shown the choice of center cone to be very satisfactory.

Radial Focusing in the Linear Accelerator

The focusing mechanism described in the previous paper is applied to the linear accelerator. The defocusing forces in the linear accelerator are derived, and the particular example of a 4-million-volt accelerator 10 meters long is discussed. It is shown that the defocusing forces can be compensated by magnetic or electric lenses of the alternating gradient type using easily attainable field gradients. For example, a defocusing field gradient of 1000 volts per centimeter on a 100-kv proton beam can be compensated by a lens 20 cm long with field gradients of the order of 1000 gauss per centimeter.

A sector-type doublefocusing magnetic spectrometer.

An analysis is made of the focusing characteristics of a magnetic spectrometer having an annular magnetic field which varies approximately with 1/r½, thus permitting axial as well as radial focusing of particles of a given energy. By considering the field angle and source location as independently variable, the analysis provides for an instrument more flexible in use than similar existing types. An optical analogy is developed from which a first approximation to the field shape is made, and from which the source and image location, magnification, dispersion and resolution can be readily obtained. Information thus obtained, combined with the results of an investigation into the image shape based on a series expansion, through second order, of expressions for the field strength and particle coordinates, yields more detailed information on the field shape which gives optimum focusing conditions and resolution for any chosen set of initial conditions. Comparisons are made with the homogeneous field spectrometer and with the spectrometer of Svartholm and Siegbahn.