Physics Forums (http://www.physicsforums.com/index.php)
-   Classical Physics (http://www.physicsforums.com/forumdisplay.php?f=61)
-   -   What is a Self Consistent Electric Field? (http://www.physicsforums.com/showthread.php?t=656890)

 fys iks! Dec4-12 11:16 PM

What is a Self Consistent Electric Field?

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"

 Simon Bridge Dec5-12 01:22 AM

Re: What is a Self Consistent Electric Field?

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.

 All times are GMT -5. The time now is 11:42 PM.