No restoring force in atoms of gas of free electrons (as we have in the upper atmosphere) While reading about the dependence of wavelength on refractive index, we assume an atom model where atoms stick to their mean position and they are disturbed by the applied electric field causing a restoring force. My question is when we take the special case of the gas of free electrons (say, as we have in upper atmosphere), we take into account that their is no restoring force. Why ? Is that has to do with the absence of electric field in upper atmosphere ? Is is actually absent?
 A: By upper atmosphere, do you mean the ionosphere?  If so, there are both ions and electrons, which do work upon each other to form a quasi-neutral fluid-like substance called a plasma.  So I am not sure why you argue there is no restoring force, because any displacement of electrons will result in an electric field that will act as restoring force (consequently, in its simplest form, this is the idea behind Langmuir waves).
There are electric fields in the ionosphere and magnetosphere, which often couple to the plasma in the form of electromagnetic waves, e.g., whistler mode waves.
Your special case:
Assume one has a gas composed entirely of free electrons and in the presence of no external forces.  The only force acting on any arbitrary electron will then be the combined Coulomb potentials of all the other electrons.  There will be no force that will act to return the gas to its initial state, thus why one says there are no restoring forces.  
A restoring force acts against any force that tries to displace a system from its equilibrium state.  A gas consisting of only free electrons would simply expand into a more and more tenuous gas without bound, never returning to its original state.
