Consider problem 11.10, but taking E = 0 and, instead of the adiabatic case, consider a constant
Question:
Consider problem 11.10, but taking E = 0 and, instead of the adiabatic case, consider a constant kinetic pressure
(a) Show that the electron distribution function is given by
(b) Evaluate the heat flux vector q and show that it can be written as
where the thermal conductivity K is equal to 5kp/(2mv).
(c) What is the value of the electric current density J in this case?
Data from Problem 11.10.
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.
Step by Step Answer:
