PROPAGATION OF ELECTROMAGNETIC WAVES ALONG A THIN PLASMA SHEET

1960 ◽  
Vol 38 (12) ◽  
pp. 1586-1594 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Magnetic Field ◽  
Surface Wave ◽  
Plasma Sheet ◽  
Electromagnetic Waves ◽  
Uniform Magnetic Field ◽  
Collision Frequency ◽  
Conducting Plane ◽  
Waveguide Type ◽  
Trapped Surface ◽  
Thin Plasma

It is shown that a thin ionized sheet will support a trapped surface wave. The effect of a constant and uniform magnetic field is to modify the phase velocity and polarization of the surface wave. The essential features are illustrated by numerical results for selected values of the electron density, collision frequency, and gyro frequency. The effect of locating the plasma sheet near and parallel to a conducting plane is also considered. In this situation other modes of a waveguide type are possible in addition to the surface wave.

The oblique reflexion of long wireless waves from the ionosphere at the places where the Earth's magnetic field is regarded as vertical

1952 ◽  
Vol 244 (887) ◽  
pp. 469-503 ◽  
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Electromagnetic Waves ◽  
Hypergeometric Functions ◽  
Collision Frequency ◽  
Path Difference ◽  
Stratified Medium ◽  
Graphical Form ◽  
Confluent Hypergeometric Functions ◽  
Ionization Density

The calculation of reflexion coefficients for long wireless waves incident obliquely on the ionosphere requires an exact solution of the differential equations governing the propagation of electromagnetic waves in the ionosphere. Equations are developed for the electromagnetic field in a horizontally stratified medium of varying electron density, the presence of a vertical external magnetic field and also the collision frequency of the electrons with neutral molecules being taken into account. Provided certain inequalities hold amongst these ionospheric characteristics, the ionosphere splits up effectively into two regions, in each of which the differential equations of wave propagation approximate to simpler forms. If a model ionosphere is chosen in which the ionization density increases exponentially with height/and the collision frequency is assumed constant over the range of height responsible for reflexion, the equations for the two regions can be solved exactly. The solution for the lower region is expressed in terms of hypergeometric functions, and that for the upper region in terms of generalized confluent hypergeometric functions. Exact expressions in terms of factorial functions can then be deduced for the reflexion coefficients of both regions separately. Moreover, these coefficients can be combined, with due allowance for the path difference between the two regions, to give the overall reflexion coefficients for the effect of the ionosphere as a whole on an incident wave. A suitable definition is given for the apparent height of reflexion in terms of the phase of the reflected wave. The results of the theory are illustrated in graphical form for a particular model ionosphere approximating to the 'tail’ of a Chapman region, and a brief comparison with experimental observations concludes the paper.

Propagation of electromagnetic waves normal to a magnetic field in a uniform anisotropic Maxwellian plasma

1968 ◽  
Vol 2 (4) ◽  
pp. 591-595
Author(s):  
P. Stewart
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Uniform Magnetic Field ◽  
Hypergeometric Functions ◽  
Dispersion Relations ◽  
Second Order ◽  
Anisotropic Plasma ◽  
Maxwellian Plasma

Closed forms are found for the dispersion relations describing the propagation through a uniform anisotropic plasma of the three modes of electromagnetic waves whose wave vectors are perpendicular to a steady and uniform magnetic field. Such relations are found to be conveniently expressed in terms of hypergeometric functions of the second order.

scholarly journals Physics of Absorption and generation of Electromagnetic Radiation

2021 ◽  
Author(s):  
Sukhmander Singh ◽  
Ashish Tyagi ◽  
Bhavna Vidhani
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Penetration Depth ◽  
High Frequency ◽  
Electromagnetic Waves ◽  
Collision Frequency ◽  
Numerical Examples ◽  
Beam Density ◽  
The Real ◽  
Real Frequency

The chapter is divided into two parts. In the first part, the chapter discusses the theory of propagation of electromagnetic waves in different media with the help of Maxwell’s equations of electromagnetic fields. The electromagnetic waves with low frequency are suitable for the communication in sea water and are illustrated with numerical examples. The underwater communication have been used for the oil (gas) field monitoring, underwater vehicles, coastline protection, oceanographic data collection, etc. The mathematical expression of penetration depth of electromagnetic waves is derived. The significance of penetration depth (skin depth) and loss angle are clarified with numerical examples. The interaction of electromagnetic waves with human tissue is also discussed. When an electric field is applied to a dielectric, the material takes a finite amount of time to polarize. The imaginary part of the permittivity is corresponds to the absorption length of radiation inside biological tissue. In the second part of the chapter, it has been shown that a high frequency wave can be generated through plasma under the presence of electron beam. The electron beam affects the oscillations of plasma and triggers the instability called as electron beam instability. In this section, we use magnetohydrodynamics theory to obtain the modified dispersion relation under the presence of electron beam with the help of the Poisson’s equation. The high frequency instability in plasma grow with the magnetic field, wave length, collision frequency and the beam density. The growth rate linearly increases with collision frequency of electrons but it is decreases with the drift velocity of electrons. The real frequency of the instability increases with magnetic field, azimuthal wave number and beam density. The real frequency is almost independent with the collision frequency of the electrons.

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