What is a Self Consistent Electric Field?

fys iks!

Hi,

Ive been doing some reading into 1 dimensional plasma numerical simulations and they keep referring to solving for a "self-consistent" field. If the simulation is in one dimension with periodic boundary conditions, how would I go about solving this electric field?

Example:

dE/dx = n - ρ(x)

where: n = const = 1
ρ(x) is the charge density and I want to solve for E numerically where E is "self consistent"


Thanks for your input.

Simon Bridge

The electric field depends on a distribution of charges - but the distribution of charges depends on the electric field. This creates a chicken-and-egg situation.

A "self consistent" field is one which makes the charges distributed so that they generate the field. We can compute them using an iterative procedure.

You start with a guess for a charge distribution ρ₀, compute the field that distribution gives rise to. That field will push the charges into a new configuration ρ' - so work out that new distribution as if the field were fixed at what you calculated.

Now repeat the procedure for ρ₁=(1-λ)ρ₀+λρ' where 0<λ<1.
You have to guess lambda.

Keep going until you keep getting the same result to the desired level of accuracy.

The exact method will depend on the context.