## Abstract

This paper describes a theory of the resonant effects observed by sounding equipment on the ionospheric satellite 'Alouette'. The model consists of an oscillating dipole immersed in a uniform hot plasma with uniform magnetic field. A formal expression for the electric field throughout space is readily constructed. In simple cases (zero temperature and either no magnetic field or infinite light velocity) this reduces to an integral which can be evaluated analytically and the resonance shown explicitly. In general we try to locate the frequencies at which resonance will occur without evaluating the field. This can be done by the 'pinching-poles' technique used in quantum field theory. The results show that resonances would occur at the following frequencies: the plasma frequency, $\omega_p$; the gyrofrequency of the electrons, $\Omega_e$ and its harmonics n$\Omega_e$, the 'hybrid' frequency, ($\omega^2_p$ + $\Omega^2_e$)$^\frac{1}{2}$, and the 'zero range' frequencies, which satisfy $\omega^2 \pm \Omega\omega - \omega^2_p = 0.$ Some idea of the relative importance of these resonances can also be gained for the theory. The fundamental of the gyrofrequency series, and the zero-range frequencies, would give only weak resonances. The series $\omega$ = n$\Omega_e$ has a complicated structure, and is really the superposition of four series, some of which are slightly shifted from the exact harmonics.