An electron gas (Lorentz gas), in a background of stationary ions, is acted upon by a weak,
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An electron gas (Lorentz gas), in a background of stationary ions, is acted upon by a weak, externally applied electric field E, under steady state conditions. Using the Boltzmann equation for the electrons, with the relaxation model for the collision term (considering a constant collision frequency ν),
and considering the adiabatic case for which
show that the electron distribution function is given by
Assume that f = f0 + f1, where |f1| ≪ f0 and where f0 is the following modified Maxwellian distribution
and neglect all second-order terms in the Boltzmann equation. Consider the term involving ∇f1 as a second-order quantity.
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