Consider the electrons in a plasma acted upon by a small, constant, and uniform external electric field E. Under steady-state conditions with no spatial gradients, obtain an expression for the nonequilibrium distribution function f for the electrons, by applying a perturbation technique to the Boltzmann equation (take f = f₀ + f₁ with |f₁|≪ f₀ and neglect all second-order terms), using the relaxation model for the collision term

where ν is a relaxation collision frequency and f₀ is the equilibrium Maxwellian distribution function. Assuming that ν is independent of velocity, obtain an expression for the electric conductivity σ₀ of the plasma, by taking J = σ₀E.

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St / coll =-v(f-fo)