Admittance of a rectangular slot which is backed by a rectangular cavity

The rectangular cavity backed slot is excited by a current source connected across its center. The longitudinal voltage variation across the slot is obtained from the variational solution of an integral equation. For shallow and narrow cavities the slot appears inductive and the voltage is rapidly attenuated along the slots. The slot may resonate for deeper and/or wider cavities, when the voltage along the slot is approximated by a half-cycle of a sine wave. The resonant cavity depth and the antenna bandwidth are examined for various cavity and Slot parameters. Dielectric cavity loading is shown to decrease both the resonant cavity depth and the antenna bandwidth.     

ELF and VLF fields of a horizontal electric dipole

The waves in the spherical guide between the earth and ionosphere are excited by a horizontal electric dipole. The guide boundaries are characterized by surface impedances and the resulting waves are expressed as a superposition of TM and TE modes. The wavenumbers, excitation factors, height-gain functions, and height-dependent impedances are examined for both types of modes. A thin-shell approximation of the radial wave functions is shown to be adequate for phase velocity estimates; but other propagation parameters are of restricted validity in the VLF range where Airy integral approximations provide more reliable data. A horizontal electric dipole is shown to provide a nearly omnidirectional coverage of horizontal field components in the frequency range of the lower Schumann resonances. For an elevated source the horizontal fields are essentially omnidirectional also in the VLF range. Near fields are expressed as a summation of waveguide modes. The vertical field components vanish at the antipode, but the horizontal components remain of finite magnitude.     

Impedance of a finite insulated antenna in a cold plasma with a perpendicular magnetic field

A variational formulation is developed for the impedance of a finite strip antenna embedded in a planar dielectric slab which is surrounded by a magnetoionic medium (cold electron plasma) with a static magnetic field impressed in a direction perpendicular to the antenna surface. Closed form expressions are obtained in the limit of low frequencies, and for a short antenna in a uniaxial medium. The impedance becomes large at the plasma frequency, near the upper hybrid resonance frequency, and further resonances are observed near the gyro-frequency if the gyro-frequency exceeds the plasma frequency. The reactance of a short antenna is inductive at low frequencies, but becomes capacitive as the thickness of the insulation around the antenna is increased. For very thin insulating layers the wave number of the variationally approximated current distribution exceedssqrt{sqrt{epsilon_{1}} sqrt{epsilon_{3}}} k_{0}(epsilon_{1}andepsilon_{3}are the two diagonal elements of the permittivity matrix), whereepsilon_{1}andepsilon_{3}may have positive or negative real parts. However, this approximation does not apply to current distributions along an insulated antenna. The present calculations are also compared with earlier work on antenna impedances.     

On the excitation of VLF waves

The ratio between the excitation factors of vertically and horizontally polarized sources is equal to the squared ratio between the characteristic impedance of free space and the ground level coupling impedance of TE and TM field components. This relation provides an analytical check of numerically calculated excitation factors. Also, the need of directly calculating the two excitation factors of an anisotropic environment may be obviated if the excitation factor of an isotropic environment is used for estimating the dominant field components of a given quasi-TM or quasi-TE mode.     

Impedance of a finite insulated cylindrical antenna in a cold plasma with a longitudinal magnetic field

A variational formulation is developed for the impedance of a finite cylindrical antenna embedded in a dielectric cylinder, which is surrounded by a magnetoionic medium (cold electron plasma) with the static magnetic field impressed in a direction parallel to the antenna axis. Closed form expressions are obtained in the limit of low frequencies, and for short antennas in a uniaxial medium. The impedance of a short antenna is nearly the same as for an assumed triangular current distribution, except that further resonances are observed in the vicinity of the gyro frequency, where the antenna becomes electrically long. These resonances may be shifted to frequencies exceeding the gyro frequency in the presence of an insulating layer around the antenna. For very thin insulating layers the wave number of the variationally approximated current distribution is to the first order equal tosqrt{epsilon_{1}} k_{0}(epsilon_{1}is the leading diagonal element of the permittivity matrix), where the gyro frequency may be both smaller or larger than the plasma frequency. However, this approximation does not apply to current distributions along the insulated antenna. The present calculations are also compared with earlier work on antenna impedances.     

Slot antenna impedance for plasma layers

The rectangular cavity or waveguide backed slot is covered by a plasma layer of finite thickness. The longitudinal variation of the voltage across the slot is obtained from the variational solution of an integral equation. The solution for plasma layer of finite thickness is obtained from the free space Green's function by the method of images. The fields outside the slot depend on the surface integral of the fields over the slot plane and over the surface of the plasma layer. If the thickness of the plasma layer is large compared with the wavelength, the fields on the surface of the plasma may be related to the voltage distribution along the slot by plane wave reflection coefficients. This leads to an integral equation that is reduced to a form suitable for machine computations. These calculations show the slot admittance to remain almost constant for plasma layers of various thicknessesh. The slot conductance tends to increase forh/ lambda <0.5. The presence of a plasma layer affects the voltage distribution along the slot for a center excited slot. The field distribution along the waveguide excited slot differs only slightly from the principal mode field distribution in the guide.     

VLF propagation across discontinuous daytime-to nighttime transitions in anisotropic terrestrial waveguide

Discontinuity effects are analyzed after referring the ionospheric surface impedance of daytime and nighttime waveguide portions to the same common altitudeh. The properties of the waveguide junction are determined by field matching, and the resulting linear equations are rearranged in a form that permits a sequential determination of transmission and reflection coefficients. Simple dominant mode approximations of the transmission and reflection coefficients are also developed. Field calculations of reciprocal geometries illustrate the consistency of the formulation and reflection coefficients are found to be of negligible magnitudes. The discontinuous surface impedance tends to excite higher order waveguide modes of larger amplitudes than a ground based source in homogeneous waveguide.