The electromagnetic interaction of an intense relativistic coasting beam with itself, including the effect of a confining nonperfect vacuum tank, or a quiescent rf cavity, is investigated theoretically. It is shown that the resonances that may occur between harmonics of the particle circulation frequencies and the electromagnetic modes of the cavities can lead to a longitudinal instability of the beam. A criterion for stability of the beam against such longitudinal bunching is obtained as a restriction on the shunt impedance of the rf cavity, or the Q of the vacuum tank. This criterion contains the energy spread and intensity of the coasting beam, as well as the parameters of the accelerator. Numerical examples are given which indicate that in general the resonances with the vacuum tank will not cause instabilities, while those with an rf cavity can be prevented from causing instabilities by choosing the shunt impedance at a sufficiently low but still convenient value.

Modern {beta}-ray spectrometers are based upon the concept, first introduced by Svartholm and Siegbahn in 1946, of focusing in both the radial and vertical directions. The theory of axially symmetric devices has been carefully studied by a large number of workers, culminating in the analysis, in 1956, of Lee-Whiting and Taylor. These last authors calculate aberrations through the sixth order and show that by appropriate choice of the magnetic field a spectrometer can be designed with a relatively large transmission and a high resolution. The acceptable transmission is remarkable because the second-order 'spherical' aberration in the median plane of the image cannot be made to vanish identically, and consequently the design is forced to a tall thin aperture (or a slightly less advantageous short wide aperture) which a priori would seem to imply a low transmission. It is the purpose of this communication to show that if the arbitrary restriction to axially symmetric fields is removed, then both the radial and the vertical contributions to the 'spherical' aberration can be made to vanish in second order. That azimuthally varying field (AVF) afford the freedom to accomplish this end may well be suspected in view of the technological revolution that the …

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Diverse methods proposed for the acceleration of particles by means of collective fields are reviewed. A survey is made of the various currently active experimental programs devoted to investigating collective acceleration, and the present status of the research is briefly noted.

The purpose of this paper is twofold: to introduce the reader to the subject of instabilities exhibited by relativistic particle beams, and to summarize the present state of our knowledge concerning these phenomena. Most of the material in the first part of the paper is not new. It has been known to some specialists for a good many years; what is new is that the problems that can be solved are now of much more interest to the general community of accelerator physicists. Consequently, many accelerator physicists who have not paid much attention to these matters may now want to become informed; it is my hope that this paper will provide an introduction to the field. The second part of the article consists of two sections. The first summarizes the experimental information presently available, with emphasis upon the degree to which it confirms or disagrees with theory. Our current level of understanding is delineated: considering the generality and reliability of the theoretical analysis as well as the degree of experimental confirmation, the author expresses his opinion as to what can be considered relatively well established. The final section contains a discussion of subjects needing further investigation and, consequently, supplements the …

In this letter the author describes a measurement of the absolute decay rate {Gamma}{sub 2}({+-}0) {approx_equal} {Gamma}(K{sub 2}{sup 0} {yields} {pi}{sup +}{pi}{sup -}{pi}{sup 0}). The result is based on 16 events of the type {pi}{sup -} p {yields} {Lambda}K{sup 0} followed by {Lambda} {yields} p{pi}{sup -} and K{sub 2}{sup 0} {yields} {pi}{sup +}{pi}{sup -}{pi}{sup 0}, and 2608 double-vec events {pi}{sup -} p {yields} {Lambda}K{sup 0} with {Lambda} {yields} p{pi}{sup -} and K{sub 1}{sup 0} {yields} {pi}{sup +}{pi}{sup -}.