Ion density in sheath of Langmuir probe in plasma

In summary, the conversation is about the principles of Langmuir probe and the questions that arise during studying it. The first question is about the expression for the ion density within the sheath, which is derived using the conservation of energy and particle conservation. The second question is about the equilibrium of electrons and ions within the sheath and the use of Maxwell distribution and Boltzmann factor for their distribution and density. The expert suggests that the ion density distribution is obtained using current and energy conservation, and that electrons are treated as in equilibrium due to their light mass and fast thermalization time.
  • #1
goodphy
216
8
Hello.

I'm studying principle of Langmuir probe and got several questions.

1st, the textbook suddenly tells that ion density within sheath is

ni(x) = nis(Vs/V(x))1/2

where nis, Vs are ion density and plasma potential at sheath edge.

I found some document which shows that it is obtained by using

(1/2)miV2 = -eV (Conservation of energy)
niv = const (Particle conservation) where v is velocity of the particle.

but I still don't get how to combine them to get desired result.

1. Could you please tell me how to get the expression above?And I have impression during studying that in derivation of I-V characteristic curve of probe in plasma, electrons are all in thermal equilibrium thus Maxwell distribution and Boltzmann factor are used for their distribution and density while ions are not.

2. Why are ions not in equilibrium and why electrons are treated as equilibrium even within sheath where they're repelling or attracting depending on probe voltage?

Please help me to get deeper understanding.
 
  • #3
I've found personal conclusion.

First, ion density distribution is obtained by using
1. Current conservation; vi(x)ni(x) = nisvis.
2. Energy conservation; vis = (2eVs/mi)1/2, vi(x) = (2eV(x)/mi)1/2.
Combining these two gives ion density in my question.

Second, electron has light mass, which leads
1. Electron heat flux (nevth where vth = (kBTe/me)1/2) is large so fast thermalization time.
2. Thermal velocity vth is normally exceeding drift velocity by E-field within sheath. If this doesn't holds, for example, high bias voltage of probe than plasma potential Vp, Electron can follow similar density distribution of ions above.
 

FAQ: Ion density in sheath of Langmuir probe in plasma

1. What is ion density in the sheath of a Langmuir probe in plasma?

The ion density in the sheath of a Langmuir probe in plasma refers to the number of ions present in the region surrounding the probe. This region, known as the sheath, is created by the electric field between the probe and the plasma and plays a crucial role in the accurate measurement of plasma parameters.

2. How does the ion density in the sheath affect Langmuir probe measurements?

The ion density in the sheath affects Langmuir probe measurements by influencing the electric potential and current between the probe and the plasma. This, in turn, affects the interpretation of the probe's current-voltage characteristics and the accuracy of the measured plasma parameters.

3. What factors can affect the ion density in the sheath?

Several factors can affect the ion density in the sheath, including the plasma density, electron temperature, and the potential of the Langmuir probe. The geometry and size of the probe can also have an impact on the ion density in the sheath.

4. How do scientists measure the ion density in the sheath of a Langmuir probe?

Scientists typically use Langmuir probes to measure the ion density in the sheath. These probes consist of a small metal electrode that is inserted into the plasma and connected to a circuit that measures the current and voltage. By analyzing the probe's current-voltage characteristics, the ion density in the sheath can be determined.

5. Why is the ion density in the sheath important in plasma research?

The ion density in the sheath is important in plasma research because it provides valuable information about the plasma's properties and behavior. By accurately measuring the ion density, scientists can better understand the plasma's composition, temperature, and other important parameters, which are crucial for various industrial and scientific applications of plasma technology.

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