|Dec4-12, 11:16 PM||#1|
What is a Self Consistent Electric Field?
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?
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.
|Dec5-12, 01:22 AM||#2|
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.
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