Debye sheath

As a surface layer or Debyeschicht the transition region of a plasma is referred to a limiting wall. The electrons in a plasma usually have a similar or higher temperature than the ions, and are easier to multiples. This means that they are faster by at least a factor and therefore go faster lost on the wall:

In order not to violate the principle of quasi- neutrality within the plasma, in the boundary layer, a negative potential is built up, which reflects the electrons and the ions are accelerated towards the wall. Thus, only a small fraction of the electrons pass through the potential barrier of the surface layer. This is known as the ambipolar diffusion.

Boundary layers have typical thicknesses on the order of a few Debye lengths. They themselves are characterized by a clear violation of the principle of quasi- neutrality, that is, they have an excess of positive space charge on. In ( quasi-) stationary plasmas (eg, capacitively coupled RF plasmas ) is the potential difference across the boundary layer so that the average number of electrons and ions through the same boundary layer.

History

Boundary layers were first described in 1923 by American physicist Irving Langmuir:

Mathematical treatment

The one-dimensional equation

The physics of the boundary layer is determined by four phenomena:

• Conservation of energy of the ions: due to the conservation of energy, if we assume for simplicity cold ions of mass, which occur at the speed in the boundary layer, then:

• Ion number conservation: In a stationary plasma ions are not formed or destroyed, so the river is the same everywhere:

• Boltzmann equation for the electrons: Since most of the electrons reflected, its particle density is given by:

• Poisson's equation: The curvature of the electrostatic potential is related to the net charge density, as follows:

Combining these equations and replaced potential, position and ion velocity through the dimensionless quantities

We obtain the equation for the boundary layer:

The boundary layer equation can be integrated if it is multiplied by:

On the border of the edge layer to the plasma (), the potential is set ( ) equal to zero and the electric field is also assumed to be zero (). With these boundary conditions results in the integration:

This integral can be easily written in closed form, although it can only be solved numerically. Nevertheless, it can provide important analytical conclusions are drawn: since the left side is a quadratic expression, the right side must also assume for each value of a positive value, especially for small values. With a Taylor expansion to be found that the first term, which does not disappear, which is square. We can assume, therefore, that

This inequality is known as the Bohm sheath criterion, named after its discoverer David Bohm. When the ions to slowly penetrate into the boundary layer, the boundary layer potential expands into the plasma to accelerate this. Ultimately, a so-called Vorrandschicht (pre- sheath ) formed with a voltage drop on the order of, and an extension which is determined by the ion source ( often as large as the plasma itself).

• Plasma Physics