# Ambipolar diffusion and sheaths in a bounded plasma

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In summary, the conversation discusses two concepts in plasma physics: the congruence assumption, which states that in a quasi neutral plasma in steady state, the ion and electron flux must be equal, and the formation of a positive sheath due to the higher mobility of electrons. These two concepts may seem contradictory, but they actually refer to different states of the plasma - steady state and a transient phenomenon. In steady state, the equilibrium between the sheath region and the ambipolar diffusion region ensures flux equality across the entire plasma, except inside the sheath.
Decimal
Hello,

I am currently working through an introductory textbook on plasma physics, and I have encountered two topics that I separately understand but seem to be at odds with one another. In a quasi neutral plasma in steady state, the following relation must hold, $$\Gamma_i = \Gamma_e.$$ In other words, the ion and electron flux must be equal. My textbook refers to this as the congruence assumption, which can be derived from the continuity equations for both ions and electrons. By using this assumption one can derive the equation for ambipolar diffusion, which ensures that this condition is always fulfilled.

In the next chapter however, it is explained that due to higher mobility of electrons they will tend to diffuse out of the plasma much more quickly than ions. Thus in this case $$\Gamma_i << \Gamma_e.$$This will cause any boundary of the plasma to become negatively charged, which leads to the formation of a positive sheath. This in isolation seems logical to me. However how does it not conflict with the statement made before about ambipolar diffusion?

If ambipolar diffusion in a plasma ensures that the two fluxes are always equal, then how can a sheath ever form. I realize that the quasi neutrality condition is violated inside the sheath, so here the congruence assumption no longer holds. This however still doesn't explain to me how the sheath could ever form in the first place.

It would be really helpful if someone could explain how these two concepts relate.

Thanks!

The first case is "a quasi neutral plasma in steady state".
The second case is a transient phenomenon. Note the words "due to higher mobility of electrons they will tend to diffuse out of the plasma much more quickly than ions". This is clearly not a system in steady state.

Decimal
tnich said:
The first case is "a quasi neutral plasma in steady state".
The second case is a transient phenomenon. Note the words "due to higher mobility of electrons they will tend to diffuse out of the plasma much more quickly than ions". This is clearly not a system in steady state.

Thanks for the response, that makes a lot of sense! Would it then be correct to say that in steady state an equilibrium builds up between the sheath region and the ambipolar diffusion region, where both phenomena ensure flux equality across the entire plasma? (Except for inside the sheath of course).

## 1. What is ambipolar diffusion?

Ambipolar diffusion is a process in which ions and electrons in a plasma move at different speeds, causing a net flow of charge. This occurs due to collisions between particles and is important for understanding plasma dynamics in various applications.

## 2. How does ambipolar diffusion affect plasma sheaths?

Ambipolar diffusion can significantly impact the formation and structure of plasma sheaths, which are regions of electric fields that exist at the boundaries of plasmas. This is because the different velocities of ions and electrons can lead to charge accumulation and changes in the electric potential.

## 3. What is the role of ambipolar diffusion in bounded plasmas?

In bounded plasmas, ambipolar diffusion plays a crucial role in maintaining a balance between the flux of particles entering and exiting the plasma. This is important for controlling the density and temperature of the plasma, which can affect its behavior and stability.

## 4. How is ambipolar diffusion related to plasma instabilities?

Ambipolar diffusion can contribute to the development of plasma instabilities, which are disruptions in the equilibrium of the plasma. This is because the process can lead to changes in the electric fields and particle velocities, which can trigger instabilities and affect the overall behavior of the plasma.

## 5. What are some applications of studying ambipolar diffusion and sheaths in bounded plasmas?

Understanding ambipolar diffusion and plasma sheaths is crucial for various applications, such as in plasma processing for materials synthesis, plasma propulsion for space travel, and fusion energy research. It can also help improve the efficiency and control of plasma-based technologies, such as plasma TVs and semiconductor manufacturing processes.

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