What is a Self Consistent Electric Field?

  1. 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.
     
  2. jcsd
  3. Simon Bridge

    Simon Bridge 14,920
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?