The ohmic heating given by Equation (B-4) is higher by a factor of two than the result given by Perkins and Valeo. The ohmic heating term given by Equation (B-4) must now be substituted into the hydrodynamic equations for the plasma. This is generally a complicated problem but it is simplified by several assumptions. In particular, it is assumed that not only the electrons but also the ions move parallel to the field. This requires that or, using values appropriate to the F-region, 0 must be less than 87 degrees. With these assumptions we find that the wave is spatially amplified in traveling through the ionosphere by the amount where n is the actual plasma density, k is the thermal conductivity, and n^ the critical plasma density. Again this has an additional factor of two compared with Equation (18) of reference 1. The threshold field is found by setting and y = 0 while the growth rate y is found by setting . On the basis of Equation (B-6), it is stated in reference 1 that, with
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