Joseph E. Rowe

One-dimensional traveling-wave tube analyses and the effect of radial electric field variations

The equivalence of the differential-equation and integral-equation approaches to the solution of the nonlinear traveling-wave amplifier problem is shown rigorously. The equations can be transformed one into the other without making any additional assumptions. The space-charge expression developed on the basis of considering the electron distribution in phase space is shown to give the same form for the space-charge weighting function as a space-charge expression based on the electron distribution in space. Efficiency calculations are compared for the two methods and the agreement is excellent. Corrections to earlier calculations are included. The effect of radial electric field variations due to the circuit is considered and it is shown that the efficiency for large streams is reduced in direct proportion to the square of the field reduction function.

Theory of the Crestatron: A Forward-Wave Amplifier

In the past a considerable amount of experimental evidence presented by various workers has indicated that gain apparently occurs in a traveling-wave type device even though the voltage may be so high that growing waves cease to exist. This means, in terms of Pierces traveling-wave tube theory, that the growth constant of the growing wave x1 is zero in this regime of operation. A theory explaining this phenomenon has been worked out and both small-signal and large-signal calculations have been carried out to investigate the characteristics of this type of operation. The gain occurs in this region due to a beating effect produced between the three small-signal forward waves described in traveling-wave tube theory as they travel along the RF structure. The maximum achievable gain is determined by the injection velocity and not by the length of the tube as in the normal case. Based on the above theory a device named the Crestatron, which utilizes this new mode of operation, has been built and tested to verify the theory, and it has been found that moderate gain (10-20 db) and high operating efficiency coupled with a very short length (4-6 wave-lengths) characterize this mode of operation.

Electron Dynamics and Energy Conversion in O-Type Linear-Beam Devices*

A general nonlinear interaction theory is used to investigate the effects of transverse fields (i.e., radial circuit fields and radial space-charge fields) in traveling-wave amplifiers for a variety of beam-focusing conditions. Magnetic focusing fields which are periodic or tapered (increased) with distance along the device are considered in addition to uniform magnetic fields. Results are presented for Brillouin flow and near-Brillouin flow, and the minimum magnetic field strength required to effectively constrain the electron beam is determined as a function of the operating parameters for the various focusing systems. Confined flow is also examined for the uniform-field case in order to have a basis of comparison from which the effects of radial motion of the beam electrons can be determined. The results indicate the importance of transverse effects and further yield information on the stability of strongly modulated cylindrical electron beams.-

N-beam nonlinear traveling-wave amplifier analysis

In large-diameter electron stream traveling-wave amplifiers there is a significant variation of the circuit electric field across the stream. Most analyses neglect the effects of these field variations. An approximate method has been used to study the effect of transverse field variations on the gain and effciency of large-signal traveling-wave amplifiers. The annular electron stream is subdivided into a number of annular rings each containing an equal fraction of the total current. It is assumed that the circuit field varies over the stream cross section and that each segment has a different coupling to the circuit. The space-charge field is assumed independent of radius. The effect on gain and efficiency is calculated for a stream diameter of B = 1 and it is found that a subdivision of the stream into two segments with different couplings to the circuit gives a lower saturation efficiency but that further subdivision does not appreciably charge the results.

Analog Representation of Poisson's Equation in Two Dimensions

A new analog device, called a Poisson cell, has been developed which aids in obtaining solutions to either Laplaces equation or Poissons equation. The cell may be used to simulate such potentials as electric potential, magnetic potential, gravitational potential, and the velocity potential of irrotational flow; it has applications in the fields of hydrodynamics, heat conduction, and aerodynamics. The cell is a solid volume-conducting medium made from a homogeneous mixture of hydrostone and graphite. Electrode configurations may be painted on the surface with conducting paint or imbedded directly in the structure. In the case of Poissons equation, where ?2?(x, y) = f(x, y), the function f(x, y) is simulated by injecting currents into the underside of the cell. The application of the Poisson cell to numerous problems and in particular to problems in electron flow is discussed m detail, along with the incorporation of the cell into either an analog computer system or a combined analog-digital computer system.

General design procedure for high-efficiency traveling-wave amplifiers

A general design procedure is developed for the design of both low-power and high-power high-efficiency traveling-wave amplifiers. The process is based on the selection of optimum values (for highest efficiency) of the design parameters C, QC, B and b from the large-signal curves and design of an amplifier with the particular type of RF structure specified by power and bandwidth requirements and operating parameters as near the optimum values as possible. In cases where the optimum design parameters cannot all be realized simultaneously, the design engineer will be able to select the parameter that he wishes to adjust. The procedure is first developed for helix-type tubes and then correction factors are derived that permit the design of amplifiers with any type of RF structure from the same set of curves.

Michigan multioption program in electrical engineering

A multioption (three) program in electrical engineering is proposed to meet the needs of a rapidly advancing technology and a wide range of student interests and objectives. A specific program is described which includes a wide range of technical electives outside of electrical engineering, and also features a novel treatment of advanced mathematics for electrical engineering students in both the systems and science areas. An integrated humanities-social sciences program is additionally described.

Efficiency enhancement by phase focusing and collector depression

Nonlinear calculations [1], [2], [3] of the el ectron-wave interaction process in TWA’ s, klystrons and BWo’ S have permitted the calculation of interaction efficiencies along with information about the energy state of the spent beam. These calculations have been primarily concerned with the r. f. interaction process and have not considered the effects of collector depression on the overall efficiency of the particular device. In this paper the effect of collector depression on device efficiency is studied theoretically and calculations are presented for the TWA and the BWO under a variety of operating conditions.

Classification of the Operating Modes of Hot-Cathode Parallel-Plane Plasma Diodes

Many specialized theoretical and experimental studies have been carried out on noble-gas plasma diodes in order to determine the operating characteristics of a particular mode. Even though the modes of cesium plasma diodes have been characterized rather completely by Bullis, no comparable summary has been developed for noble-gas systems. In this paper, the operation of hotcathode parallel-plane plasma diodes is reviewed and the characteristics of the anode-glow, ball-of-fire, Langmuir, temperature-limited, low-voltage arc, and tufted-anode modes are classified and discussed in terms of the volt-ampere characteristics for different load lines. The operation of noble-gas diodes is compared to that of cesium diodes and the interpretation of the volt-ampere characteristic is related to available experimental data. The visual characteristics of each mode are also displayed to aid in the interpretation of the behavior. The correlation between theory and a variety of experiments substantiates the contention that the limitation imposed on the diode current by the cathode is responsible for the previous confusion about the various modes of operation.

General design procedure for high-efficiency helix-type traveling-wave amplifiers

Heretofore traveling-wave tubes have been designed using Pierces small signal theory, and the design then modified according to previously obtained experimental results in order to achieve high saturation output and a reasonable efficiency. A procedure has been developed that makes use of the large-signal calculations on traveling-wave amplifiers to design tubes to operate at high saturution efficiency. The design procedure is particularly useful in the design of tubes for high power output and may be applied to the design of either cw or pulsed tubes. A procedure has been developed which enables the design of a traveling-wave tube to be completed with the use of a minimum number of curves and requires a minimum of calculation on the part of the designer. The design curves for helix-type tubes were calculated using the sheath helix impedance modified by the appropriate impedance reduction factors.