Stiff- One-Dimensional Poisson Equation in Plasma

In summary: Expert]In summary, the conversation discussed the challenge of accurately modeling the development of a collisional plasma in time, particularly at the sheath boundary where the changes in charge densities are rapid. Traditional solvers like Gauss Siedel and Successive Over relaxation may not be suitable for this problem, but using a more advanced solver like a finite element method (FEM) may be helpful. It was also suggested to incorporate more physics into the model, such as collisions and ionization, for better accuracy.
  • #1
aditya.p
5
0
Hey Guys,

So I am trying to model the development of a collisional plasma in time. Now the problem I face is at the sheath boundary the changes in the charge densities is very large.

I use the charge densities to evaluate the electric potential at different points in the plasma. I have the charge densities as a number available at all points.

Now comes the problem. When I use a regular solver like Gauss Siedel or Successive Over relaxation, the changes in charge density in space is still too rapid for these methods to give me a solution within respectable error tolerances. (at least 1e-2).

The in built poisson solver in MATLAB requires a two dimensional case. I was curious if anyone know of a robust poisson solver for a one-d case which can handle stiff cases.

Its is a dirichlet problem. I know the potential at both boundaries (one is the electrode and the other is the wall).

Would be great if I can get some insight.

Thanks

Aditya
 
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  • #2


Hello Aditya,

I am a scientist who specializes in plasma physics and I may be able to provide some insight into your problem. The development of a collisional plasma in time can be a complex process, and it is not uncommon for the charge densities at the sheath boundary to change rapidly. This can make it difficult to accurately model the electric potential using traditional solvers like Gauss Siedel or Successive Over relaxation.

One approach you could try is using a more advanced solver, such as a finite element method (FEM) solver. FEM solvers are better suited for solving complex and stiff problems, and they can handle both one-dimensional and two-dimensional cases. There are several FEM solvers available for MATLAB, such as PDE Toolbox and FEATool Multiphysics, which could be useful for your problem.

Additionally, you may want to consider incorporating more physics into your model, such as taking into account the effects of collisions and ionization. This could help to better capture the behavior of the plasma and potentially improve the accuracy of your results.

I hope this information is helpful to you and good luck with your research!


 

1. What is the Stiff-One-Dimensional Poisson Equation in Plasma?

The Stiff-One-Dimensional Poisson Equation in Plasma is a mathematical equation used to describe the distribution of electric potential in a plasma, which is a state of matter consisting of ions and electrons that are not bound together. It is a one-dimensional version of the more general Poisson Equation, and is characterized by its stiff nature, meaning that it can be difficult to solve numerically.

2. What is the physical significance of the Stiff-One-Dimensional Poisson Equation in Plasma?

The Stiff-One-Dimensional Poisson Equation in Plasma has many important applications in plasma physics and engineering. It is used to study the behavior of charged particles in a plasma, and can be used to predict the effects of electric fields on the plasma. This equation is also important in understanding the behavior of plasma in fusion reactors and other plasma-based technologies.

3. How is the Stiff-One-Dimensional Poisson Equation in Plasma solved?

There are several numerical methods that can be used to solve the Stiff-One-Dimensional Poisson Equation in Plasma. These include finite difference methods, finite element methods, and spectral methods. These methods involve discretizing the equation and using iterative techniques to find a solution that satisfies the equation.

4. What are the assumptions made in the Stiff-One-Dimensional Poisson Equation in Plasma?

The Stiff-One-Dimensional Poisson Equation in Plasma makes several simplifying assumptions about the plasma. It assumes that the plasma is homogeneous and isotropic, meaning that its properties are the same at all points and in all directions. It also assumes that the plasma is in a steady state, meaning that its properties do not change with time.

5. How is the Stiff-One-Dimensional Poisson Equation in Plasma related to other equations in plasma physics?

The Stiff-One-Dimensional Poisson Equation in Plasma is closely related to other equations in plasma physics, such as the continuity equation and the momentum equation. Together, these equations describe the behavior of a plasma and can be solved to understand the dynamics of plasmas in different environments. The Poisson Equation is also related to the Maxwell's equations, which describe the behavior of electromagnetic fields in plasmas.

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