In LTE, the average kinetic energies of electrons and ions are equal. Since the electrons are much less massive, their speeds are much higher, and we can make the approximation that the ions are nearly stationary during an interaction. Since only the logarithms of both parameters appear in Equation 4B2, these estimates don't have to be precise. This result is based on our purely classical treatment of the interaction See also Jackson's Classical Electrodynamics , section Because electrostatic forces always dominate gravity on small scales, electrons in the vicinity of a nearly stationary ion are free to rearrange themselves to neutralize, or shield, the ionic charge.
The characteristic scale length of this shielding is called the Debye length. To see which is smaller, we calculate the limits for a typical HII region and a typical radio frequency.
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Modern Physics, 33, very detailed derivation. Unfortunately both sign conventions are found in the literature, and you have to look carefully at each paper to find out which one is being used. For example, ionized winds from stars are quite inhomogeneous. We also suppose that the temperature and density are constant throughout this volume. Then it is very easy to estimate physical parameters of the HII region e.
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The warm ionized gas is largely confined to the disk of our Galaxy, where we reside. We can use this result to estimate the typical electron density in the warm ISM. Eidman, V. Ellis, G. Epstein, R. Fermi, E.
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