Slot Admittance for Compressible Plasma Layers

Abstract

The admittance of a waveguide is calculated for radiation into a general two‐layer compressible plasma which is further specialized to represent a plasma sheath and also an ion sheath in the presence of a plasma half space. The antenna admittance is related by integrals to the electric fields in the waveguide aperture, which are assumed to be a sum of the principal waveguide mode and of surface wave fields which are supported in this plasma geometry. The compressibility of plasma has the largest effect on the slot admittance when the slot width is equal to an odd number of half wavelengths of surface waves, but significant changes occur only if the relative dielectric constant of the plasma is less than 0.2, and the ratio of the free‐space velocity of electromagnetic waves to the acoustic velocity is less than 300. Plasma losses and the presence of an ion sheath tend to lessen the compressibility effects.

Impedance of an Insulated Linear Antenna Between Layers of Compressible Plasma

“…The surface-wave effects on the admittance of a slot antenna immersed in a two-layer compressible plasma was recently reported by Galejs [1966a], and this paper also contains a detailed discussion of past work in this problem area. The dispersion relations of surface waves on cylindrical antennas have been examined by Seshadri [1965b] and Galejs [1965a], and besides the usual electroacoustic surface waves, there are also electromagnetic surface waves for a lossy plasma.…”

“…This behavior of a linear antenna is quite different from that of a wide-slot antenna, where the compressibility of the plasma affects the antenna impedance only when considering the surface waves in a direction transverse to the antenna aperture [Galejs, 1966a]. The waveguide aperture is wide in terms of the plasma wavelengths, and the presence of a compressible plasma would have negligible effects on the impedance of a linear antenna of comparable dimensions.…”

“…The TE and TM parts of the magnetic field H are derived for region n from scalar functions 'I'n and 4>" which are expressed as double Fourier integrals. In the compressible plasma (region n = 2) the electric field E depends also on the pressure Pn, which is also given by a double integral [eq (1) to (16) of Galejs, 1966a]. The fields near the antenna are specified with the amplitudes A1 and B1 of 'l't and cl>t, which are computed after relating tliem to the amplitudes A2, B2, C2, Aa, and Ca, and to the reflection coefficients Rat, Rb1, Raz, and Rcz from a total of 10 boundary conditions (E:r, Ey, H:r, Hu continuous and Vz=O at z=zt and z2)-These equations can be solved for the reflection coefficients Rai and Rbi· A lenithly algebraic manipulation shows that the reflection coefficients of the TE modes Rat and Ra2 are the same as for cold plasma [eq (4), Galejs,196~b].…”

“…For thick insulating layers, k8 z1 ;» 1, (9) is changed to (55) of Galejs [1966a], which represents surface waves guided along the boundary of a semi-infinite plasma. For thin insulating layers, kBz1 ~ I, {9) becomes (10) and the wave number of the surface wave k8 approaches the wave number kp2 of plasma waves in a homogeneous plasma.…”

“…With the exception of very thin pla:;ma layers, the antenna impedance can be derermined by neglecting the presence of surface waves. The impedance of a finite antenna was shown to approach the impedance in the presence of cold plasma as the acoustic velocity is decreased [Balmain, 1965;Galejs, 1966a]. The presence of an insulating layer (or of an ion sheath) around the antenna tends to decrease the compressibility effects, as has been also observed by Seshadri [1965c], Wait and Spies [1966], or Galejs [1966a].…”