Debye sheath

To define a unique solution, we must specify the corresponding boundary and initial conditions. Normally electrolyte solutions are in contact with or bounded by electrodes. An electrode in its simplest form is a metal immersed in an electrolyte solution so that it makes contact with it. For example, copper in a solution of cupric sulfate is an example of an electrode. A system consisting of two electrodes forms an electrochemical cell. If the cell generates an emf by chemical reactions at the electrodes, it is termed a galvanic cell, whereas if an emf is imposed across the electrodes it is an electrolytic cell (Fig. 6.1.1). If a current is generated by the imposed emf, the electrochemical or electrolytic process that occurs is known as electrolysis. Now whether or not a current flows, the electrolyte can be considered to be neutral except at the solution-electrode interface. There a thin layer, termed a Debye sheath or electric double layer, forms that is composed predominately of ions of charge opposite to that of the metal electrode. We shall examine this double layer in Section 6.4, but for our purposes here it may be neglected. 

Equation (17) is not valid a few mean free paths from the wall, where ambipolar diffusion ceases. This region is the Debye sheath and contains... 

Fig. 2. A graph of the radial electric field and potential versus the distance from the plasma column axis in centimeters. The shaded region is the Debye sheath. The electron temperature is 5 eV, m+ is 20 amu, and the radius of the discharge tube is 2.4 cm. The electron temperature is approximately that for neon at 0.2 Torr. ...

Stronger electric fields than the center of the plasma. The Debye sheath extends into the plasma roughly a Debye length Ad or less (the units for ( ) is eV and for... 

General Aspects Radiofrequency or microwave electric fields of sufficient strength can break down a gas under appropriate conditions and produce an electrically conducting medium, denoted as plasma. By definition, a plasma is a partially ionized gas, confined to a certain volume with equal numbers of positive and negative charges. The charged particles are free and exhibit a collective behavior. Similar to soap bubbles, plasmas possess at their boundaries a skin called the plasma sheath or Debye sheath. The main hody of a plasma always has a positive... 

In addn, for an ionized gas to be called a plasma, it must have an equal number of pos and neg charges for, by definition, a plasma has no net charge. Regions termed "sheaths , having large (net charges) do develop at the plasma boundaries. Such sheaths are to the plasma what the surface is to a solid or liquid, and their thickness is of the order of the "Debye length ... 

The motive diagram for the potential energy of electrons in an ignited mode thermionic converter has a more complicated shape, as shown at the top of Figure 4. The presence of positive ions in the plasma creates a minimum in the electron motive inside the interelectrode gap. There are narrow collisionless sheaths (the order of a Debye length in thickness) at both the emitter and collector edges of the plasma. 

The simplest model assumes that the N water molecules in each hydration sheath have a different relaxation time tji = pT from that of the pure water in the remaining volume of the solution, t . The water in the hydration sheath contributes a certain fraction q of the entire static permittivity of the solution. The frequency variation of the complex permittivity is taken to be a sum of two Debye terms (subsoripts w and h respectively for pure water and hydration sheath water) as shown in equation (47) where... 

This is an excellent assumption for the plasmas of interest since the Debye length is exceedingly small (10s of pm) compared to the reactor dimensions. Of course, the electroneutrality constraint can t be applied in the sheath, where the Poisson equation... 

When an+ 1 ions traverse the sheath in a short time compared to the field oscillations. Under this condition, an ion traversing the sheath experiences the sheath voltage prevailing at the time the ion entered the sheath. In the absence of collisions, the lED function will reflect precisely the variation of the sheath voltage with time. This quasi steady-state condition of cut+ 1 is satisfied for low RF frequencies or short ion transit times, i.e., thin sheaths (low sheath voltage or small Debye length). 

Condition (3-235) of a sheath existence is usually referred to as the Bohm sheath criterion. To provide ions with the energy required to satisfy the Bohm criterion, there must be a qrrasi-neutral region (wider than sheath, several Debye radii) with some electric field. This regiort, illustrated in Fig. 3-18, is called the presheath. The minimtrm presheath potential (between btrlk plasma and sheath) shottld be eqtral to... 

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