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A high efficiency, high power magnicon amplifier at 34.272 GHz has been designed as a radiation source to drive a multi-TeV electron-positron linear collider. Simulations predict a peak output power of 45 MW in a 1.5 microsecond pulse with an efficiency of 45% and a gain of 55 dB. The amplifier is a frequency tripler, or third harmonic amplifier, in that the output frequency of 34.272 GHz is three times the input drive frequency of 11.424 GHz. Thus the rotating TM110 modes in the drive cavity, 3 gain cavities and 2 penultimate cavities are resonant near 11.424 GHz; and the rotating TM310 mode in the output cavity is resonant at 34.272 GHz. A 500 kV, 215 A high area compression electron gun will provide an electron beam with a diameter less then 1 mm. A superconducting solenoid magnet will provide a magnetic field of 13 kG in the deflection system and 23 kG in the output cavity. Simulation results for the operation of the entire magnicon amplifier (gun, magnetic system, RF system and collector) will be giv...

The report presents experimental results obtained on 7 GHz pulsed magnicon amplifier with a new version of the output cavity, as well as plans of the next investigations. This magnicon was developed at INP as a prototype of a microwave power source for the next generation of linear colliders. The tube operates in frequency-doubling mode of the drive signal. At present time the following parameters were achieved: maximum output power of 55 MW, efficiency of 56%, gain of 72 dB, pulse length of 1.1 μs.

In this paper there are presented (1) a quite general method of antenna analysis; (2) a physical picture of transmission phenomena in antennas, based on this method; and (3) an expression for the input impedance of antennas of any shape, whose transverse dimensions are small compared with the wavelength. In a brief historical sketch of the antenna problem the factors which must be taken into consideration in solving the problem are discussed. While in ordinary transmission lines the voltage is proportional to the charge, this is not the case in antennas. The explanation lies in the fact that antennas are multiple transmission lines (like wave guides) and not simple, that is, single-mode transmission lines. Our present theory is based on the voltage-current equations since these appear to be considerably simpler than charge-current equations. The latter are considered only briefly. In the absence of dissipation and in so far as the total voltage wave and the "principal" current wave are concerned, radiation is strictly an end effect. In so far as the total current and the total charge waves are concerned, radiation effects are distributed (nonuniformly) along the entire antenna. In the first approximation, regardless of the shape of the wire the charge is proportional to the voltage and waves are sinusoidal, the current wave having nodes while the voltage wave and the charge wave antinodes at the ends of the antenna. The second approximation depends on the shape of the longitudinal cross section of the antenna as well as on the size of the transverse cross section. Our analysis is based on Maxwell's equations but the final results are quite simple and the physical picture growing out of this mathematics is attractive to an engineer. It is permissible to think that a wave emerging from a generator in the center of an antenna is guided by an antenna until it reaches its "boundary sphere" passing through the ends of the antenna and separating the antenna region from the external space; at the boundary sphere some energy passes into the external space and some is reflected back--a situation existing at the juncture between two transmission lines with different characteristic impedances. We may also think of the antenna as the wall of an electric horn with an aperture so wide that one can hardly see the horn itself--just like a Cheshire Cat: only the grin can be seen. In fact, the mathematics that we use is that appropriate to wave guides and electric horns. The antenna problem is stated in Section I and its history is briefly discussed in Section II; Section III contains a summary and a discussion of the results for antennas with uniformly distributed capacitance (conical antennas); Section IV is devoted to antennas with non-uniformly distributed capacitance; Section V presents a derivation of the formulas contained in Section III; Section VI reviews the induced-electromotive-force method of computing radiation and its use in the present problem; Section VII is devoted to the current-charge equations; Section VIII is devoted to wave propagation along parallel wires; in Section IX an expression is given for the impedance of an infinitely long cylindrical wire, and Section X deals with an approximation needed in our discussion of the problem.

The general theory of coaxial pairs was dealt with in an article on “The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields” by S. A. Schelkunoff (B. S. T. J., Oct., 1934). The present paper considers a specific aspect of the general theory, namely, crosstalk. Formulae for the crosstalk are developed in terms of the distributed mutual impedance, the constants of the transmission lines and the terminal impedances. Some limiting cases are given special consideration. The theory is then applied to a few special types of coaxial structures studied experimentally and a close agreement is shown between the results of calculations and of laboratory measurements. If the outer members of coaxial pairs are complicated structures rather than solid cylindrical shells, the crosstalk formulae still apply but the mutual impedances and the transmission constants which are involved in these formulae must be determined experimentally since these quantities cannot always be calculated with sufficient accuracy. The crosstalk between coaxial pairs with solid outer conductors rapidly decreases with increasing frequency while the crosstalk between unshielded balanced pairs increases. In the low frequency range there is less crosstalk between such balanced pairs than between coaxial pairs but at high frequencies the reverse is true. The diminution of crosstalk between coaxial pairs with increasing frequency is caused by an ever increasing shielding action furnished by the outer conductors of the pairs. Finally, crosstalk in long lines using coaxial conductors is discussed and the conclusion is reached that, unlike the case of the balanced structure, the far-end crosstalk imposes a more severe condition than the near-end crosstalk in two-way systems which involve more than two coaxial conductors.

In response to an increased interest in mathematical aspects of antenna theory, this paper presents details of analysis of cylindrical and other nonconical antennas as a supplement to a previous paper containing the outline of the method and the main results. In the course of the present discussion the theory of principal waves on cylindrical conductors is extended to include the case in which the diameter is not small compared with the wavelength.

This paper presents a discussion of ideas involved in various mathematical methods of electromagnetic field analysis and of the inter-relations between these ideas. It stresses the points of contact between circuit and field theories and their mutually complementary character. While the field theory focuses our attention on the electromagnetic state as a function of position in space, the generalized circuit theory is preoccupied with the electromagnetic state as a function of time. The points of contact between the field and circuit theories are many. Thus, Maxwell's equations are identical with Kirchhoff's equations (really Lagrange-Maxwell equations) of certain three-dimensional networks in which only the adjacent meshes are coupled. The integral equations for the electrical current in conductors embedded in dielectric media are also Kirchhoff equations of certain networks containing infinitely many meshes with a coupling between every two meshes. From the point of view of electrical performance the difference between a physical network of lumped elements and a continuous network, such as a resonator, is due to a certain difference in the distribution of the zeros and poles of associated impedance functions in the complex impedance plane. Similarly, the difference between ordinary transmission lines and wave guides is due to a difference in the distribution o(natural propagation constants. The paper ends with a general discussion of the discontinuities in wave guides, idealized boundary conditions for simplification of electromagnetic problems, and the analytical character of field vectors regarded as functions of the complex oscillation constant.

In this paper it is explained how Maxwell's field equations together with the appropriate boundary conditions may be converted into equations analogous to those for coupled transmission lines. This makes it possible to use the well-known techniques of dealing with transmission lines to solve certain field problems in those cases in which either the method of separating the variables fails or the boundary conditions are too complicated for the conventional method. For example, this method may be applied to studying waveguide to horn junctions, bending of waveguides, propagation of waves over an imperfect earth in the vicinity of the source, etc. Other applications are suggested in the course of the paper. On the theoretical side, this conversion of field equations into transmission line equations brings together two heretofore independent theories of wave propagation on wires, namely, Lord Kelvin's theory based on circuit concepts and Kirchhoff's laws and Mie's theory based on field concepts and Maxwell's equations. The “Generalized Telegraphist's Equations” derived in this paper differ from Kelvin's classical Telegraphist's Equations in two respects. Firstly, for a pair of conductors Kelvin obtained one pair of differential equations implying the existence of only one mode of propagation. For the same pair of conductors we obtain an infinite set of equations implying an infinite number of modes, from which Kelvin's equations are obtained by neglecting the

A form of circuit which is of considerable interest for the transmission of high frequency currents is one consisting of a cylindrical conducting tube within which a smaller conductor is coaxially placed. Such tubes have found application in radio stations to connect transmitting and receiving apparatus to antennae. As a part of the development work on such coaxial systems, it has been necessary to formulate the theory of transmission over a coaxial circuit and of the shielding against inductive effects which is afforded by the outer conductor. This paper deals generally with the transmission theory of coaxial circuits and extends the theory beyond the range of present application both as regards structure and frequency.

A MATHEMATICAL theory, suitable for appraising and controlling directive properties of linear antenna arrays, can be based upon a simple modification of the usual expression for the radiation intensity of a system of radiating sources. The first step in this modification is closely analogous to the passage from the representation of instantaneous values of harmonically varying quantities by real numbers to a symbolic representation of these quantities by complex numbers. The second step consists in a substitution which identifies the radiation intensity with the norm1 of a polynomial in a complex variable. The complex variable itself represents a typical direction in space. This mathematical device permits tapping the resources of algebra and leads to a pictorial representation of the radiation intensity.

Linear differential equations with variable coefficients occur in many fields of applied mathematics: in the theories of acoustics, elastic waves, electromagnetic waves in stratified media, nonuniform transmission lines, wave guides, antennas, wave mechanics. The “Wave Perturbation” method described in greater detail elsewhere1 is particularly useful in those ranges of the independent variable in which the “WKB Approximation” is not sufficiently accurate. The present paper endeavors to illustrate the remarkable accuracy of this method, particularly when compared with Picard's method.

This paper presents: (1) a comparison between several approximate theoretical formulas for the input impedance of cylindrical antennas in the light of available experimental evidence; and (2) a discussion of the local capacitance in the vicinity of the input terminals, mathematical difficulties created by its presence, and methods of overcoming these difficulties. No exact solution of the antenna problem is available at present and so far it is impossible to set definite limits for errors which may be involved in various approximations. For this reason in appraising these approximations one is forced to rely on one's judgment and on experimental evidence. It is hoped that this paper will aid in correlating theory and experiment to the advantage of both.

In this paper we illustrate by a simple example that when we wish to express the admittance of a cavity excited through a hole in terms of natural frequencies of oscillations which can exist when the cavity is short‐circuited, it is important to remember that the short‐circuit must conform to the impressed field. When this is done, one need not fear that the ``obvious'' set of natural modes may be incomplete.

After a review of the general aspects of the classical electromagnetic theory several “equivalence” theorems are established and illustrated with a number of examples from the diffraction theory. Then follows a discussion of possible applications of these theorems to radiation problems. The latter part of the paper is devoted to the calculation of the power radiated from an open end of a coaxial pair.

When Doctor S. A. Schelkunoff presented the material contained in this article as a lecture before the basic science group of the New York Section, he remarked that it was “nonmathematical.” Certainly the electrical engineer will welcome any concept which allows an easier approach to the solution of certain problems involved in wave guides than the more complete equivalent field-theory method. In this fourth article in a series of six on ultrashort electromagnetic waves, Doctor Schelkunoff combines transmission-line theory with optical analogy and derives useful relations for both wave guides and cavity resonators. The three preceding articles appeared in the March, April, and May issues of “Electrical Engineering.”

This paper presents some theoretical remarks and experimental data relating to applications of the transmission-line theory to antennas. It is emphasized that the voltage, the current, and the charge are affected by radiation in different ways, a fact which should be considered in any adaptation of line equations to antennas. It is shown experimentally and theoretically that in an antenna of length equal to an integral number of half wavelengths, which is energized at a current antinode, the effect of radiation on the current and the charge (but not on the voltage) can roughly be represented by adding to the resistance of the wires another fairly simple term.

Inasmuch as it is rarely possible to treat diffraction of electromagnetic waves exactly, the Kirchhoff formulation of Huygens' Principle has been frequently used in approximate calculations. If the Kirchhoff formula is applied directly to the field intensities of the incident wave over the aperture, the diffracted field is found to be inconsistent with Maxwell's equations. If, on the other hand, this formula is applied to some auxiliary vector potential from which the diffracted field is subsequently deduced by differentiation, the result (although consistent with Maxwell's equations) depends on the particular choice of the auxiliary vector and in some instances, at least, is obviously unreasonable (Appendix III). The calculations of diffracted fields and radiation fields, based either on the Equivalence Principle or on the more general Induction Theorem, depend upon a priori verifiable approximations to the actual fields in the neighborhoods of the sources of the diffracted and radiated waves. For this reason we feel that these methods are preferable to those based on the Kirchhoff formula.

This paper formulates the essential properties of spherical waves in terms of familiar engineering concepts. The physical picture resulting from this point of view facilitates the solution of certain physical problems, notably those having to do with reflection, refraction, shielding and power absorption.

Amongst electric waves that can be propagated inside metal tubes of circular cross section there are some with attenuation constants diminishing indefinitely with increasing frequency. The purpose of this note is to discuss what happens to these waves as the tubes are slightly deformed from perfect circularity. The conclusion is that in a deformed tube the attenuation constants of the above‐mentioned waves diminish with increasing frequency until a certain frequency is reached, depending upon the degree of departure from perfect circularity, and then they begin to increase indefinitely with further increase in frequency.

This paper calls attention to the practical value of a more extended use of the impedance concept. It brings out a certain underlying unity in what otherwise appear diverse physical phenomena. Although an attempt has been made to trace the history of the concept of “impedance” and many interesting early suggestions have been found, reference to these lies beyond the scope of this paper. Apparently, Sir Oliver Lodge was the first to use the word “impedance,” but the concept has been developed gradually as circumstances demanded through the efforts of countless workers. The main body of the paper is divided into three parts: Part I, dealing with the exposition of the impedance idea as applied to different types of physical phenomena; Part II, in which the general formulae are deduced for reflection and transmission coefficients; Part III, presenting some special applications illustrating the practical utility of the foregoing manner of thought.

Following a brief historical sketch, this paper deals with the mathematical theory of wave transmission in two novel kinds of cylindrical wave guides of circular cross section; namely, the hollow conductor and the dielectric wire. These transmission systems behave as high pass filters with exceedingly high critical frequencies. The attenuation and impedance characteristics of the hollow conductor, heretofore ignored as far as the writers are aware, are given especial attention. This investigation discloses the remarkable fact that there exists in this system one and only one type of wave, the attenuation of which decreases with increasing frequency, a characteristic which attaches to no other type of guided wave known to the writers.

In this paper Maxwell's partial differential equations and the boundary conditions for waveguides filled with a heterogeneous and non-isotropic medium are converted into an infinite system of ordinary differential equations. This system represents a generalization of “telegraphist's equations” for a single mode transmission to the case of multiple mode transmission. A similar set of equations is obtained for spherical waves. Although such generalized telegraphist's equations are very complicated, it is very likely that useful results can be obtained, by an appropriate modal analysis.

This paper presents the input admittance of a symmetric biconical antenna of an arbitrary angle as the limit of a certain sequence of functions. The first term of this sequence approaches the exact expressions for the input admittance as the cone angle approaches either zero or 90°. For this reason our conjecture is that this term represents a good first approximation for all angles.

A nonmathematical discussion of the mechanism whereby energy may be transmitted over long distances at high frequencies by the use of ``coaxial conductors'' is presented in this paper. A coaxial system consists of a cylindrical conducting tube within which a smaller conductor is coaxially placed. Such conductors, which reduce interference and cross-talk are applicable for the transmission of telephone, telegraph, and television signals over a very wide range of frequencies.