In problem 11.12, include the presence of an external magnetostatic field B in the z direction and deduce the following expression for the nonequilibrium distribution function:

Show that the heat flux vector q can be expressed as

where K is the dyadic thermal conductivity, which in matrix form can be written as

with

The solution of the differential equation

is given by

Data from Problem 12.

Consider problem 11.10, but taking E = 0 and, instead of the adiabatic case, consider a constant kinetic pressure

Show that the electron distribution function is given by

Evaluate the heat flux vector q and show that it can be written as

where the thermal conductivity K is equal to 5kp/(2mv).

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.

Transcribed Image Text:

1= {1}(-5 = 2x7)[{f(x-1) + fo{ + mv2. 2kT) + Ωe) vΩce 24mg)*(x+j_5)+v]. Τ T} Ωe)