ABSTRACT The Doppler effect is treated for motion of an oscillator along the axis of an anisotropic ferrite. Explicit expressions for the field components are obtained. Those can be used, in particular, to obtain formulas for the Cerenkov radiation of a charge and of a dipole. A number of properties of the radiation that are peculiar to an anisotropic medium are pointed out. Some new effects, occurring themselves in changes of the components of the electromagnetic field and in additional splitting of the original frequency, depend on degree of anisotropy and on the values of the tensor parameters of the ferrite.
ABSTRACT The propagation of coupled, electromagnetic and plasma (acoustical) waves generated by a moving and oscillating dipole in an infinitely long, compressible, plasma cylinder surrounded by vacuum is investigated. The fields of the moving sources can be decomposed into two modes—the electromagnetic mode and the plasma (acoustic) mode. These two modes are coupled on the plasma-vacuum boundary. The electric dipole may excite pure, longitudinal, plasma waves since the plasma mode is associated with charge accumulation, but not with a magnetic field It is shown that if an oscillating dipole of frequency ω0 (when Ω= ω—ω0) moves along the axis of the plasma cylinder, it modifies radial wave-numbers of electromagnetic waves in such a way that both the electromagnetic and the plasma (acoustic) waves may propagate without decaying. The coupled plasma and electromagnetic waves do not form a radiation cone analogous to a Cerenkov cone. Requirements for coupled, non-evanescent waves in optical and acoustical spectra are given, respectively, by the expressions : $ If cos θ0≤1, then the above relationship for θ0 will hold only for radiation Doppler frequencies, and if cos θa≤1 then, similarly, the above expression for θa will (may) hold for both superluminal Doppler frequencies ( Ω= ω+ω0) and radiation Doppler frequencies Ω= ω—ω0) The various aspects of the wave phenomena involving coupled, electro-acoustical waves are determined by examining the disperison relationships corresponding to superluminal Doppler frequencies and radiation Doppler frequencies.
In the past only a few reports of noise-figure for crossed-field amplifiers have appeared in the literature. The reported measurements were spot cheeks and did not reveal the dependence on operating parameters of the amplifier. An extensive set of measurements discussed in this paper yielded continuous and repeatable data giving the dependence on parameters. For a variation of beam voltage from 107 v to 367 v and a corresponding variation in beam current from 15 mA to 49·5 mA, gain improvement from 8·5 dB to 15·5 dB and noise-figure improvement from 27 dB to 22·5 dB have resulted with the beam centred between the sole and circuit electrodes. A novel experimental technique was used to achieve repeatable measurements and is described here. Over the past decade a great deal has been said in the literature about inherent excess noise in crossed-field amplifiers. Furthermore, numerous papers have shown that much more noise exists when the cathode is space-charge-limited rather than temperature-limited—the opposite of the counterpart longitudinally focused amplifiers. The noise-figure measurements reported in this paper have shown that neither of these generally accepted assertions need be true in all crossed-field amplifiers. In particular, for a beam voltage of 367 v a significant reduction in noise-figure of about 5 de has resulted in space-charge-limited operation as compared to the temperature-limited operation. Experimental results showing an improvement of 10 dB in noise-figure as the beam is moved close to the circuit from its midway position between the sole and circuit electrodes are discussed. Finally the variation of noise-figure with pressure is reported. By combining optimum focusing, space-charge smoothing, and beam displacement, a noise figure of 10·5 dB is obtained without using noise transducers.
ABSTRACT For a plant consisting of two integrators with saturable control input, a controller is known which gives a minimum value of integral-error-squared. In the present paper it is shown that this value is the absolute minimum (not merely a local minimum), and that the control input which gives it is unique.
A few of several possible sets of system condition numbers or sensitivity coefficients are defined relating small changes in system parameters to such measures of system performance as state variables, eigensystems and state variable fuiictionals. Sensitivity functionals are defined also for use in cases where anticipated but undesirable system perturbations occur. The linear or approximately linear dynamical system is of special interest and for these systems it is shown that the condition numbers of all eigenvalues with respect to all elements of the n × n system matrix A are expressible by n 1-term dyads of the form v i X i T, the reciprocal vectors and eigenvectors of A respectively. These matrices are particularly useful in design processes based upon eigenvalue configurations, and it is shown also how they may be employed in the evaluation of a particular class of time weighted functional of the form a of free, stationary, linear systems. Finally it is noted how these matrices are modified by scaled models of the actual system and what is the significance of this process.
A fresh attack on the current-voltage response of space charge in thermodynamic equilibrium proves fruitful in wresting new features not discovered in earlier analyses. Those include a simple relationship expressing the thermalization of the electrostatic energy in the drift dominated region. The latter, moreover, provides a vital ingredient in correctly describing the current-voltage behaviour in this very region. Thus the formula applicable to the planar diode in the limit of extreme collisional damping is extended to allow for thermal energy ordinarily ignored in previous theories.
A stream of electrons has been focused solely by the fields of a slow (0pc) electromagnetic wave An analysis was obtained by transforming to the wave frame in which the equations of motion of electrostatic periodic focusing are valid. Using the well-known results for the static case, and retransforming to the laboratory frame, focusing behaviour and design information (circuit size, frequency, power for a given stream) wore obtained. A second but more appropriate analysis was made by transforming to the average electron frame in order to predict both fast and slow-wave results; for the axially symmetric modes considered, the slow-wave focusing requires orders of magnitude less power than for fast waves and has a more favourable field shape Several experiments were performed using a helix as the slow waveguide. The stream was launched into the helix and was collected both on the helix and by a collector at the opposite end. Typically 10 to 50% of the current would be transmitted with no wave, rising linearly with wave power to a best transmission of over 80%. The best results were obtained with the wave velocity in the same direction and greater than the average velocity of the stream; use of oppositely directed wave and stream velocities gave poorest results. At best, a I vv stream (roughly I mA at 1000 v) was focused by about 10 w of r.f. wave power at 1000 Mc. These results are in rough agreement with the theory. For a given injected stream there appears to be a maximum r.f. power beyond which focusing decreases; this effect may be due to either a strong localized lens effect at the point of stream injection or to r.f. voltages largo compared with the average steam voltage.
ABSTRACT In the usual analyses of transistor action various assumptions are frequently made; for example, that space charge neutrality exists in the base region, that pn junctions are depleted of mobile carriers, that minority carrier densities next to reverse biased junctions arc near zero, etc. It is shown that none of these assumptions is strictly valid. A now examination of the problem, in which those assumptions are put in better perspective, leads to: (a) a complete, partially numerical, analysis of abrupt pn junctions in equilibrium showing the spatial distribution of holes, electrons and field; (6) a qualitative discussion of these distributions when current is flowing; (c) a revised expression for the small signal capacitance of abrupt pn junctions; (d) a now space-charge-neutral solution for the complex current gain of transistors (this is compared with Shockley's solution). Finally a preliminary numerical solution of the carrier and field distribution in a collector junction, under conditions of reverse bias and large reverse current, is shown.
The effective damping constant 𝛌eff is measured as a function of frequency by U.H.F. ferromagnetic resonance. The results are compared with those obtained by using a small angle free oscillations technique. In addition, both methods offer a means of determining the gyromagnetic ratio γ. The damping factor 𝛌eff is measured as a function of the anisotropy field Hk, and also of the composition of the nickel—iron film. A possible dispersion of 𝛌eff within the film is discussed. 𝛌eff is also deduced from the exponential decay times of the damped oscillations which occur in experimental hard direction switching waveforms. Such waveforms agree qualitatively with coherent rotational theory. Experimental switching waveforms obtained with large amplitude pulsed reversing fields, applied at 135° to the easy direction, also agree qualitatively with theoretical predictions. Small observed deviations from theory are, perhaps, related to local inhomogeneities of both the anisotropy field and the easy direction. For 135 switching with lower fields, the rotation is incoherent, probably on account of the same inhomogeneities. Switching threshold curves are measured, and these differ markedly from the theoretical astroid stability diagram, because of the disturbing influences of domain switching and incoherent rotation.
The use of double-gap bunching in klystrons is investigated theoretically and it is shown that under suitable conditions the beam coupling coefficient may be 40% higher than for a single gap. Also, the loading of the buncher by the beam under these conditions may be eliminated. It is estimated that the double-gap buncher can improve the overall gain by about 6 dB. The theoretical results have been confirmed in a positive-ion klystron operating at a frequency of 5 Mc/s.
ABSTRACT A positive-ion klystron oscillator is described. It is capable of generating about 1 w of r.f. power at 4·5 Mc/s. The performance agrees well with theoretical predictions.
ABSTRACT A hybrid amplifier made up of two active helix sections separated by a drift tube is utilized to investigate the effect of pre-bunched electron beams on TWA performance. A one-dimensional non-linear theory is used to calculate gain and efficiency results and evaluate the fundamental current amplitude in the beam. Experimental results with the pre-bunched amplifier indicate an increased gain, power output and efficiency. Reasonable agreement with theoretical predictions is obtained.
ABSTRACT Recombination coefficients, in afterglows following pulsed radio-frequency discharges in iodine vapour, are determined by a radio-frequency probing method, which uses the variation of the dielectric constant to measure the ion concentration. A small linear radio-frequency mass spectrometer is used to identify the ions present. The results show that the recombination coefficient, α, for the mutual neutralization process I2 ++I−→I2'+I'' is independent of pressure between 0.23 and 1.0 torr, and is dependent on ion temperature. At ion temperatures of 296±3, 328±5 and 338±5°k, the mean values of α are l.22( ± 0.03) × 10−7, l.04( ± 0.05) × 10−7, and 1.01 (±0.08) × 10−7 cm3sec−2, respectively. Diffusion becomes noticeable at pressures lower than 0.23 torr. From the limited information available the product of diffusion coefficient and pressure, Dap, is estimated to be 10± 3 cm2 sec−1 torr.
ABSTRACT The problem of optimal control is considered for the system ˙x=Ax + Bu; x(0)= c, where A is subject to random change, u is restricted to a closed, bounded region U, and a quadratic performance index is used. A general formulation of the problem is given and results are obtained for a particular, simple behaviour of A The optimal system shows adaptive behaviour of an elementary kind, and uses the whole of the available control effort at each instant. It is not known whether the last property would persist for less simple behaviour of A, or for systems disturbed by noise.
ABSTRACT A scheme which can be used to optimize a continuous complex process by means of the maximum principle is presented. The continuous complex process is a process which is composed of interconnected branches whose performances can be described by a sot of differential equations. An example of optimizing a simple feedback process is given to illustrate the use of the method.
ABSTRACT The amplification (A) and transit time (T) of an electron avalanche whilst crossing a gap have been calculated in terms of the electron ionization coefficient (α) and the electron drift velocity (v) with allowance for both electron diffusion and electrode effects. It has been shown that when both α and v are calculated from experimental values for A and T, that errors greater than the experimental error may occur if diffusion and electrode effects are neglected.
ABSTRACT Propagation of electromagnetic waves through a homogeneous anisotropic column of a medium of infinite length is studied. The anisotropy of the medium is characterized by the dyadic form of the permittivity ε and the permeability μ. This anisotropic column is surrounded coaxially by a homogeneous isotropic medium characterized by the scalars ε2 and μ2, the complete structure being enclosed by a perfectly conducting metallic circular-cylindrical wave-guide. A magnetic current ring source of arbitrary angular variation is introduced symmetrically in the isotropic medium. For this general problem, the complete expressions for fields (due to the source), the average power flow, and the dispersion relation have been obtained. Dispersion relations for various special cases are also derived. To solve the source problem, dyadic Green functions for both point electric current source and point magnetic current source have been constructed in a formal way from the source-free solutions of the appropriate Maxwell equations. These dyadic Green functions can be used for any arbitrary source.
