Search

To discuss the small amplitude disturbances propagating through a hot plasma in a uniform magnetic field, or to find the macroscopic quantities of a plasma, it is necessary to solve the Vlasov equation. In this paper a general vector method is presented and it will give a solution of the linearized Vlasov equation with a collision term. The explicit expressions of the perturbed distribution functions for both anisotropic and isotropic equilibrium distributions are derived. The results can be easily applied to find the dispersion equation and the polarization properties of the waves.
In recent years numerous studies have appeared in the literature concerning the high frequency properties of a plasma immersed in a static magnetic field. Such studies are significant in providing the basis for predicting the electromagnetic wave propagation and absorption in the ionosphere, and for explaining the origin of solar radiation, as well as the microwave diagnostic of plasma in thermonuclear reaction, etc. (Gross 1951, Sitenko and Stepanov 1957, Bernstein 1958). When the thermal velocities of the particles are negligible, or when the zero wavelength approximation is valid, the magneto-ionic theory gives a satisfactory treatment of waves in a plasma. However, if the effects of random thermal motions of the particles have to be considered, the kinetic theory will then become a necessity in our discussion. It not only offers a more complete and rigorous description of the plasma but also allows one to see which part the individual particle plays in sustaining the oscillation. The fundamental problem in the kinetic theory is to solve the Vlasov equation for a distribution function which can then be used to determine either the conductivity tensor and the dispersion equation or other macroscopic quantities of the plasma. Our objective in this paper is to present a vector method and to derive an explicit general solution of Vlasov equation. [ABSTRACT FROM AUTHOR]

In this paper the dispersion relation for rectangular waveguides filled with homogeneous lossy drifting plasma under the influence of infinite longitudinal magnetic field is derived and discussed. The properties of TE modes are found to be the same as those of air-filled guides. However, uniaxial anisotropic drifting lossy plasma has a significant effect on the propagation characteristics of TM modes. A comparison of the effects and physical significance of the changes duo to isotropic and anisotropic plasma models is discussed.
1. Introduction
In recent years plasma-filled waveguides have received considerable attention owing to their applications in microwaves. A general solution for the propagating modes in waveguides completely or partially filled with plasma, taking into account an applied static magnetic field, non-uniform density over the guide cross section and non-vanishing temperature, has not yet been found. It is customary to incorporate the effect of plasma by assuming either an equivalent dielectric constant in the absence of an external magnetic field or an equivalent dielectric tensor with an external applied magnetic field. The nature of electromagnetic wave propagation in waveguides filled with cold stationary plasma under the influence of an external magnetic field was the subject of extensive investigation (Allis et al. 1963). Recently Tuan (1969) and Kalluri (1970) have given some idea of the propagation of electromagnetic waves in waveguides filled with warm and drifting plasma. It is the purpose of the present paper to study the dispersion relation in rectangular waveguides filled with homogeneous drifting lossy uniaxial anisotropic plasma. The strong static magnetic field is assumed to be in the direction of the guide axis. [ABSTRACT FROM AUTHOR]

This paper concerns wave phenomena in electron beams and plasmas with internal motions, in the presence of a static magnetic field. It is known that, axially-rotating beams show wave propagation when the Doppler-shifted frequency seen by the beam electrons is approximately a harmonic of the electron cyclotron frequency. Similar propagation in an infinite series of coupled modes can occur for beams and plasmas in which the electrons gyrate about the magnetic field lines, rather than the axis. Associated with each Doppler-shifted cyclotron harmonic, a slow and a fast space-charge wave are propagated along an electron beam. These sets of waves can interact with each other, with slow or fast wave circuits, or with a plasma, to yield growing waves. The nature of these interactions is discussed in the paper. It is suggested that this mechanism of wave amplification along an unneutralized electron beam may provide an explanation of the noise growth observed in electron beams from shielded guns, and in crossed-field devices. [ABSTRACT FROM AUTHOR]

This article is the first part of a series of papers devoted to the computer solutions on the trajectories of the outermost electron in a beam focused by means of different magnet systems. The electron beam is produced by a low -noise gun which is immersed in a constant magnetic field. The beam voltage and beam current have the values usually found in X-band, medium-power, low-noise travelling-wave tubes.
In the present paper, the boundary of an initially 'ideal' beam which is confined by a uniform magnetic field throughout the drift space is determined (1) by linearizing and solving the paraxial-ray differential equation, and (2) by solving the exact equation with use of a computer. Emphasis is laid upon the determination of the size of beam ripples, the wavelength of rippling or the scalloping wavelength, and the lowest constraining magnetic flux density below which the linearization process does not hold valid.
Part II of this series deals with the trajectories traced, by the outer-edge electron in an initially perturbed beam which is focused by a constant magnetic field. Part III treats the profile of the beam when it is focused by a long -period reversed-field magnet system. The conventional short-period periodic permanent magnet can produce a well-behaved beam or a running -away beam, depending on the amplitude and period of the alternating magnetic flux density and on the type of flux compensation between the gun and drift regions. Such beam contours are discussed in Part IV.
The beam boundaries in the electron-gun region are solved for four sots of electrode potentials and spacings, and also for several values of magnetic field; the beam profiles, and the beam radii and boundary slopes at the end of the gun region are to be discussed in Part V.
The mathematical analysis will be relegated for treatment in a subsequent article. [ABSTRACT FROM AUTHOR]

The Corbino effect is calculated for concentric cylindrical semiconductor devices which operate under double- and single-injection. For the two carrier structures, the I-V characteristics are represented by an Proportional toV relationship where = (1+pn B)/[1+(B)][1+(B)] and n=2 for the semiconductor regime and n=3 for the insulator regime.
Similar results are obtained for single-injection space-charge-limited current where n=2 and =[1+(B)].
The present paper describes the effects of a transverse magnetic field on the I-V relationships of double- and single-injection structures which have a concentric cylindrical geometry. The device configuration is a hollow-core coaxial semiconductor with carrier injecting contacts at the inner and outer surfaces of the annulus. At low-injection levels, the I-V relationships are linear and a magnetic field applied perpendicular to the radial direction causes the charge carriers to follow spiral path-lengths between the inner and peripheral contacts (Corbino 1911).
As the injection levels are increased, the I-V relationships are no longer linear because the excess carriers injected into the concentric cylindrical semiconductor lead to various double- and single-injection phenomena. The main purpose is to obtain an estimate of the influence of a magnetic field on the I-V characteristics of annular structures which operate under these high-level injection conditions. [ABSTRACT FROM AUTHOR]

The oscillatory behaviour of the magneto-current with forward bias and its variation with temperature and magnetic field have been studied in various semiconductor diodes. The oscillatory magneto-current has been explained in terms of the oscillations in the probability of transition of carriers through the junction due to the formation of magnetic sub-bands in the semiconductor.
The experimental results of increasing amplitude and period of oscillations with magnetic field and the decrease of the same with temperature also have been explained satisfactorily.
The purpose of the present paper is to explain the oscillatory magnetocurrent. With this in view, the effect of intense magnetic field on the forward current characteristics has been studied in various semiconductor diodes at room temperature and liquid nitrogen temperature. The observations have been explained on the basis of the oscillatory probability of transition of charge carriers through the junction caused by the magnetic sub-bands in semiconductors. [ABSTRACT FROM AUTHOR]

In order to explore the various factors that make the effect of an intense magnetic field on semiconductor diodes temperature dependent, the variations with temperature of physical parameters like lifetime and mobility and the semiconductor diode characteristics have been studied experimentally. It is found that the combined effect of the temperature dependence of these parameters can explain satisfactorily the influence of temperature on the effect of an intense magnetic field on semiconductor diode characteristics. The knowledge of this linear variation of the effect with temperature can be exploited for the automatic compensation of the effect of temperature in solid state diode magnetic fluxmeters.
The present paper gives the study of experimental observations of the effect of an intense magnetic field on the forward characteristic of a semiconductor diode, the lifetime and the variation of this effect with temperature. A suitable theoretical explanation is given in terms of the experimentally determined variation with temperature of physical parameters and diode characteristics. [ABSTRACT FROM AUTHOR]

The paper describes the development of arc discharge rectifiers, employing hydrogen and mercury as working gases, to test the effects of a magnetic field on their deionization characteristics. The discharges were pulsed in the presence of (a) an established magnetic field, and (b) a pulse field switched on near the end of the discharge pulse. The arc back characteristics were studied as a function of the conditions, in which currents were varied to over 1000 amperes and magnetic fields up to 0.11 W/M peak. Deionization was studied by measurement of current drawn to the walls of the tube, together with some radial observations of light output from the discharge. The results indicated that while significant deflections of the discharge were recorded, the magnetic fields did not appreciably improve the arc-back qualities of the rectifiers. [ABSTRACT FROM AUTHOR]

This paper reports the results of an analog computer study of electron beam focusing by a periodically varying magnetic field. A normalized version of the paraxial ray equation was studied with the computer and plots of beam radius as a function of distance are presented. The items investigated include the effects of the entrance magnetic field, harmonics in the periodic field and amplitude variations in the magnetic field.
The results of this investigation present solutions to some problems which might confront those concerned with the design or use of periodic magnetic fields for electron beam focusing. Of primary importance is the fact that the uncertainty concerning the matching of the converging beam to the entrance field has been removed.
It was shown that a PPM field with a harmonic component has a smaller r.m.s. value and is hence less effective in focusing than a pure cosine field with the same peak amplitude. For this reason, it is necessary to design for a higher peak value when harmonies are present. The design curves presented by Sterrett and Heffner (1958) include the contribution of harmonics to the peak field, but there is no correction for the reduction in effective value.
Concerning the problem of amplitude variations in the periodic field, there appears to be little that can be done from the standpoint of design to alleviate it. The phenomenon is probably due to the magnets operating at different points on the B-H or characteristic curve after assembly. It has been observed in stacks made up of magnets which all had the same strength when measured individually prior to assembly. The analog computer results showed that the effect of the amplitude ripple is not too severe unless the period of the ripple approaches the plasma wavelength. It can probably be overlooked in most practical cases. [ABSTRACT FROM AUTHOR]

The problem considers the effect of an angular d.c. magnetic field on the radiation of a uniform magnetic ring source (slot antenna) situated on the surface of an infinitely long metal cylinder covered by a plasma sheath.
It is observed that, in a relatively high density plasma (/ > 1), the application of a static magnetic field improves the transmission of electromagnetic waves. However, it, is shown in this paper that, in a low density plasma for which / < 1, the application of a static magnetic field may deteriorate the transmission of radio waves through the plasma. To substantiate those, statements, both theoretical explanations and numerical results are provided. The numerical results present the comparison of the intensity of the radiated fields for various situations. In absence of a static magnetic field, an increase of collision frequency increases the transmission of radio signals through the plasma, particularly when / > 1. When a static magnetic field is present, the increase of the transmitted signal strength with the increase of v/ through the plasma becomes noticeable particularly for v/ > 1. [ABSTRACT FROM AUTHOR]

This paper extends previous work on the impedance of a parallel plate capacitor, filled with warm plasma, to take account of a static magnetic field. Computations are presented for parallel plate and co-axial cylinder geometries and indicate series of resonances occurring at, and between, the electron cyclotron frequency harmonics. It is suggested that if the theoretical results were confirmed experimentally, plasma admittance measurements would form the basis of a simple and powerful diagnostic technique for measuring plasma parameters such as electron density and temperature in the laboratory and in the ionosphere. [ABSTRACT FROM AUTHOR]

This paper discusses the computer solutions for the profiles of an electron beam which is launched into a constant magnetic field with either positive or negative boundary slope and with initial radius greater or less than the cathode radius. It has been found that the outermost electron traces sine waves and executes limited excursions when the initial boundary slope corresponds to angles up to 1 degree, no matter whether the initial radius is 090 or 110 times the radius of the cathode. For initial inclination angles close to 2 degrees, the beam boundary does not preserve a sinusoidal shape; this statement holds true for focusing magnetic flux densities varying from 200 10 to 700 10 weber per square metre.
The variations of the beam radius and rippling wavelength along the axis of the electron flow as obtained by the computer are compared with the results calculated from formulas that are derived on the basis of linearization of the paraxial-ray differential equation. With an initially perturbed electron beam, the linearization process is applicable only to cases where the initial boundary slope is small, corresponding to angles within the limits 1 degree, and the focusing magnetic field exceeds 300 lO weber per square metre. [ABSTRACT FROM AUTHOR]

The unexpected contraction of the positive columns of the electrophoresis discharge is discussed. The positive column of the Ne-Hg and A-Hg electrophoresis discharges are separately contracted by the uniform magnetic field. The bold clear blue Hg positive column and slender orange Ne, or violet A, positive columns are connected in the same gas luminous tube and their appearance is changed by a magnetic field.
THIS paper reports the effect of a magnetic field on the electrophoresis discharge. It is well known that the electrophoresis discharge (which is also called 'dark end effect' by illumination engineers) appears when the gas discharge lamp is filled with rare gas and a small amount of metal vapor and the metal vapor is drawn by a d.c. field to the front of the cathode and produces various colors along the tube axis. However, the color or the metal vapor distribution along the tube axis is mainly due to the physical characteristics of the metal vapor and the rare gas (Iwata 1960a; b, 1961). [ABSTRACT FROM AUTHOR]

The motion of electrons in a combined electric and magnetic field was investigated theoretically. The purpose of this investigation was to find out whether this special combined field can be used as an electron energy analyser of the kind necessary for inelastic cross-section measurements.
Very interesting cases of the electron motion can arise when various magnitudes of the magnetic field in the investigated structure are used. Some of them are discussed in the paper. [ABSTRACT FROM AUTHOR]