Electron density and temperature measurements in the lower ionosphere as deduced from the warm plasma theory of the h.f. quadrupole probe

Abstract

The frequency response of the h.f. quadrupole probe is calculated to be used as a diagnostic tool for measurements of electron density and temperature. In §2 the magnetic field is assumed to be zero, and ion motions are neglected. For a Maxwellian plasma, the so-called ‘Landau wave approximation’ is compared with various more sophisticated treatments, such as numerical integration or super-Cauchy and multiple water-bag models. The range of validity of this approximation is shown to be large, and the results can be applied to the most interesting parts of the experimental observations. All results previously established are recovered with greater speed. Having studied various disturbances (collisions, inhomogeneity and relative motion of the probe with respect to the plasma), it is deduced that the best way to determine the electron temperature is to use the anti-resonances due to beating between the Landau wave and the cold plasma field. In § 3 we describe the quadrupole probe, launched in December 1971 as part of the CISASPE rocket experiment. To deduce the electron density and temperature from these measurements, it is necessary to consider the influence of a static magnetic field, such as the earth's magnetic field. The general case could be treated by numerical integration, though with great difficulty, but it is shown that in most ionospheric conditions, in the vicinity of the upper hybrid frequency ωT the above treatment is again possible, the plasma frequency simply being replaced by ωT, and the thermal velocity slightly modified. These assumptions are used to deduce the electron density and temperature profiles.

Impulsive and transient excitation of Bohm–Gross waves in a dissipative plasma

“…28,29 The amplitude limit of the numerically calculated wave potential difference referenced above is consistent with that deduced from our analytical formula ͑45͒. Now, we are in position to definitely state the condition of validity for the steady state periodic approach.…”

“…Indeed, their asymptotic forms are consistent, for example, with Crawford and Vidmar approximate expressions 21 for impulsive and harmonic Green's functions. Moreover, in the case of nonresonant excitation, the results of the familiar time periodic or modal description 6,10,25,26,[28][29][30] of the wave in a macroscopic plasma were recovered, and the exact analytical expression for the corresponding correction term was deduced. The validity range of this description ͓see Eq.…”

“…͑C6a͒ of Ref. 22.͔ The first term in ͑41͒ represents the steady state or modal solution, [25][26][27][28][29][30] and the exact correction term takes the analytical form ⌼͑r,t ͒ϭ p ͓U 1 ͑ s p 2 w p Ϫ1 e Ϫ ,s p ͒ϪU 1 ͑ w p e Ϫ ,s p ͔͒. ͑42͒…”

Integral equation for electrostatic waves generated by a point source in a spatially homogeneous magnetized plasma

“…It can be verified by direct calculation that this is the solution of the partial differential equation (14). Thus, from (13), the solution of the Vlasov equation (6) is…”

“…Because t = 0 is equivalent to ξ = η, the integration is performed from the lower limit ξ ′ = η to ξ ′ = ξ, where ξ ′ is the variable of integration. To express the right-hand side of (14) in terms of η and ξ, substitute ϕ = η + ξ and t = (η − ξ)/Ω e so, for example,…”