Brillouin Diagram Research Articles

Smith-Purcell radiation from a narrow tape helix

A theoretical investigation of a narrow tape helix excited by a modulated electron beam gives quantitative results which can be used to estimate the strengths of interactions obtainable in experimental configurations. Extensive results are presented for the radiation emitted by a single fast space harmonic when a slow beam is in synchronism with the azimuthally symmetric space harmonic. The effects of beam velocity, frequency, beam diameter, tape width, and pitch angle are illustrated. The analysis also demonstrates the influence of the synchronism or electromagnetic resenance condition on the interaction and, further, points out the usefulness of the complex Brillouin (k - β) diagram in predicting some of the quantitative as well as most of the qualitative properties of this influence.

Power Flow in Plasma-Filled Waveguides

The power flow of two types of cyclotron modes propagating in a waveguide filled with a cold collisionless axially magnetized plasma is studied as a function of the location of the point of operation on the Brillouin (ω-β) diagram. Dynamic analysis is used throughout. Partition of the total power flow corresponding to E, H, and EH power is examined and compared with results obtained by the quasistatic approximation in the domain of its presumed validity. The inadequacy of the quasistatic approximation for the analysis of the power flow, and hence the field patterns, is shown. New properties of cyclotron and plasmaguide modes obtained from the analysis are presented. A possible explanation is offered for the lack of published experimental observation of cyclotron modes in the superluminous phase velocity region.

Wave Propagation along Warm Plasma Columns

Dispersion relations for waves propagating along homogeneous, isotropic, warm plasma columns surrounded by a dielectric medium are obtained. A steady-state linearized model with temperature introduced through a scalar pressure is analyzed both quasistatically and more rigorously from Maxwell's equations. The results show effects of temperature on the cold plasma surface wave and predict a new series of propagating modes above the plasma frequency related to the Tonks-Dattner scattering resonances near cutoff and to the Bohm-Gross longitudinal plasma waves for large wave numbers. Warm and cold plasmas, large and small columns, and quasistatic and rigorous predictions are contrasted. Regions of the Brillouin diagram corresponding to different bound and radiating wave types are delineated and related to their physical properties.

Behavior of separation constants for finite gyromagnetic plasmas

The type of the functions appearing in the expressions for electromagnetic fields in finite magnetoplasmas depends only on the properties of the medium manifested in separation constants. The \omega-\beta plane of the Brillouin diagram is partitioned into a definite number of zones characterized by the type of possible field solutions. The general behavior of the separation constants in the \omega-\beta plane including the complex region based on calculations covering a wide variation of the determining parameter is described. Effects of ion motions are discussed, and the generality of the presented approach is pointed out.

Theoretical Brillouin (κ-β) diagrams for monopole and dipole arrays and their application to log-periodic antennas

In this paper, we derive the characteristic equation for the complex propagation constant in a transmission line periodically loaded with dipole elements. This equation is solved for real and imaginary parts of the mode propagation constants. The effect of mutual impedance between antenna elements is included in the formulation and calculation. Theoretical calculations are compared with experimental results reported by Mayes and Ingerson [9]. The usefulness and limitation of the Brillouin ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k-\beta</tex> ) diagram for analyzing log-periodic (LP) structures are discussed briefly.

Theoretical brillouin (k-&amp;#946;) diagrams for monopole and dipole arrays and their applications to log-periodic antennas

In this paper we derive the characteristic equation for the complex propagation constant in a transmission line periodically loaded with dipole elements. This equation is solved for real and imaginary parts of the mode propagation constants. The effect of mutual impedance between antenna elements is included in the formulation and calculation. Theoretical calculations are compared with experimental results reported by Mayes and Ingerson. The usefulness and limitation of the Brillouin ( k-\beta ) diagram for analyzing LP structures is discussed briefly.

Propagation characteristics of magneto-ionic plasma columns

The propagation characteristics of uniform, cylindrical plasma columns of circular cross section, in constant axial magnetic fields are determined. The ratios (plasma wave-length)/(free-space wavelength) and (power flowing in the plasma)/(power flowing outside) are evaluated and discussed as functions of the diameter/wavelength ratio and of the plasma permittivity, for propagation of circularly syrnmetracl modes. Brillouin diagrams are also derived and compared with the results predicted by the quasi-static approximation. The analysis is carried out for a nonattenuating plasma, but formulas giving the attenuation caused by electron-molecule collisions are also included. (auth)

Fast-wave Propagation in Plasma-filled Waveguides†

ABSTRACT In the analysis of the waves which propagate in a waveguide completely or partially filled with a stationary plasma column or an electron beam drifting with a uniform velocity and collimated with a magnetic field of finite magnitude, it is necessary to include the effects of the rotation of the electric field in order to treat the waves which have phase velocities comparable to or greater than the velocity of light. Certain interesting features of perturbed waveguide modes and cyclotron modes become apparent only when the dynamic nature of the electric field is recognized in the analysis. These features are the influence of cyclotron frequency and the polarization of waves on the propagation characteristics. The cyclotron modes are found to be purely transverse electric at cut-off, gradually changing in character along their propagation curves through hybrid to purely transverse magnetic modes at cyclotron resonance. A classification of modes of propagation is proposed, and formulae for cut-off frequencies as functions of the cyclotron frequency as well as some representative Brillouin diagrams are given. Equations for neutralized electron beams are obtained when the Lorentz transformation is applied to the equations for stationary plasmas. The solutions for stationary plasmas can be transformed directly into the solutions for neutralized electron beams.

Iterative Traveling-Wave Parametric Amplifiers

It is well known that the parametric principle can give low noise amplification at microwave frequencies. The conventional parametric amplifier involves a single variable-element and one or more resonant cavities. Such an amplifier is extremely narrow band, it suffers from large changes in gain due to small changes in pump level, and it must be used with a circulator if unilateral gain is desired. These difficulties can be overcome by using a number of variable elements in a traveling-wave circuit. This paper presents the circuit considerations appropriate to wideband operation in a traveling-wave parametric amplifier. The model which is analyzed is a transmission line periodically loaded with parametric diodes. The diodes constitute the variable elements. Across each diode is fed a large pumping voltage which produces a time-varying capacitance. A Brillouin diagram for the structure (i.e., a plot of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega</tex> vs <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\beta</tex> ) can be computed from the analysis. The conditions for high gain, wide band, and other desirable characteristics are conveniently determined from this diagram.