A general expression for the frequency spectrum of radio waves scattered by the random thermal fluctuations of electron density in a plasma in a magnetic field is derived. The derivation is based on the generalized Nyquist noise theorem used in part I. The exact result is then; simplified by means of an approximation which amounts to assuming the velocity of light to be infinite. It is shown that this approximation is quite adequate for ionospheric applications of the theory. Next it is proved, without appealing to any approximation, that the magnetic held can never alter the total scattered signal power; it can only redistribute this power over the spectrum. Finally, the detailed shape of the frequency spectrum of the scattered signal is examined. Analytic expressions are given for certain limiting cases, but for the cases of most interest, numerical methods must be used. The results of some numerical calculations are shown in figures 1 and 2. From these results, it can be seen that the magnetic field has a significant effect on the shape of the spectrum only if the incident radio beam is very nearly orthogonal to the magnetic lines of force. For example, for an operating frequency of 40 Mc/s, no significant magnetic effect is observed even when the beam is within 5 of orthogonality. As this angle is decreased further, however, the spectrum rapidly begins to develop spikes at Doppler shifts which are approximate multiples of the ion gyro-frequency. These spikes are quite pronounced when the beam is 2° from orthogonality. At higher operating frequencies, the beam must be proportionally closer to orthogonality to achieve the same effect.
Elasticity of connected semiflexible quadrilaterals
