An Analysis of the Effect of an Imposed Magnetic Field on the Spectrum of Incoherent Scattering

Abstract
The results of some recent theoretical work indicate that the assumption of free gyration of electrons probably cannot be made unless both the scale of scattering and the electron gyro radius are smaller than the Debye length. An ionized medium tends to remain neutral over scales larger than the Debye length, and we show that if at such scales of scattering the ions could be assumed to gyrate unperturbed, our electron line spectrum would be replaced by one in which the separation of the lines is equal to the gyromagnetic frequency of the positive ions. At large scales, however, the effects of the internal electric fields on the behavior of the charged particles should be taken into account, and until this is done in the presence of an imposed magnetic field, it will not be clear to what extent the ion line spectrum is smeared by these fields. Even if the charged particles could be assumed to gyrate unperturbed, some smearing of the lines is shown co result if particles drift through the antenna beam, and also if the magnetic lines of force do not lie in the surfaces of constant path length. Curves given in the paper reveal that even if we started out with a line spectrum, it would get smeared out quite rapidly as the angle between the surfaces of constant path length and the magnetic field is increased from zero. The envelope of the line spectrum is derived under the assumption that the spatial distribution of particles is random and that their velocity distribution is Maxweliian. The results show that if the radius of gyration of the particles is large compared to the scale of scattering, the envelope is given simply by the thermal Doppler-spectrum curve that would have existed in the absence of any magnetic field. In that case the presence of a magnetic field causes no change in the total width of the spectrum, although it should in general lead to its narrowing, if the gyro radii were small compared to the scale of scattering.

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