
#1
Dec412, 11:16 PM

P: 40

Hi,
Ive been doing some reading into 1 dimensional plasma numerical simulations and they keep referring to solving for a "selfconsistent" 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
Dec512, 01:22 AM

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PF Gold
P: 10,919

The electric field depends on a distribution of charges  but the distribution of charges depends on the electric field. This creates a chickenandegg 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 ρ_{0}, 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 ρ_{1}=(1λ)ρ_{0}+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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