APPENDIX B SELF-FOCUSING PLASMA INSTABILITIES Many instabilities are known to be excited in the ionospheric plasma by HF waves with intensities on the order of . Although the threshold for these instabilities increases rapidly with frequency, the much larger intensities planned for the MPTS require careful examination of the possible effects of such instabilities. In this appendix we will consider the possibility of self-focusing instabilities. The theory of this instability has been given by Perkins and Valeo and the self- focusing instability has been observed at HF frequencies as discussed by Thome and Perkins . The basis of the instability can be understood from the diagram in Figure B-l which shows an rf wave propagating in the x-direction and moving across a density perturbation wave in the ionosphere. At the points of greatest plasma density (denoted by the signs), the index of refraction has a minimum, and therefore the rf wave is focused so it has its greatest intensity in the troughs of the plasma wave. These troughs are therefore heated more intensely than the wave crests so that the plasma tends to be pushed towards the crest of the perturbation and the instability grows. Our description up to this point has been overly simplified because it neglects the effect of the magnetic field. The magnetic field causes charged particles to travel mainly along the electric field. We can neglect the motion of electrons 2 across the field unless the plasma gradient (in the Y-direction) satisfies ( ) which means that the Y-direction must make an angle larger than 1/3 degree with the to the field. Here we take k to be the wave vector in the Y-direction and and are its components which are parallel and perpendicular to the magnetic field. Also m is the electron mass, M is the ion mass, . and are the ion and electron collision frequencies and is the ion cyclotron frequency. The instability is driven by the ohmic heating but this would be smoothed out if the thermal conductivity, which is carried by the electrons, has a large component in the Y-direction. The electrons are such efficient carriers of heat that the instability tends to be eliminated unless 9, the angle between the Y-direction and
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