Consider a stationary plasma (electrons and one type of ions) under steady-state conditions at a uniform temperature T₀ , when perturbed by a point charge +Q placed at the origin of a coordinate system. Using the collisionless hydrodynamic equation for the electrons and ions (α = e, i)

with the ideal gas law Pα = n_αkT₀, and the Poisson equation

obtain the following differential equation

for the Debye potential ϕ(r). Assume that the number density of each species can be expressed as n_α = n₀ + n′_α, where n₀ is constant and |n′α | ≪ n₀. What are the approximations necessary to obtain this result?

Transcribed Image Text:

Dua Pma Dt = naga E - Vpa