Potential sheath

Fig. 10.36 Variation of cable sheath potential due to stray d.c. traction currents...

Figure 2. Schematic diagram of a solid surface exposed to a plasma. Typical values for important parameters are indicated. The symbols AK, and vi represent the sheath thickness, sheath potential, ion concentration, and ion velocity, respectively.

The most essential plasma device characteristics that are needed in order to obtain impurity release rates are the fluxes of photons and of charged and neutral particles to the wall. It will be necessary to have detailed information on the energy spectra and fluxes to walls, limiters and beam dumps of thermal electrons and ions, photons, a-particles, runaway electrons, charge exchange neutrals, neutral beam and impurity neutrals and ions. The effects of sheath potentials, secondary electron emission and unipolar arcing need to be included in these calculations. 

The principal method of introducing metal impurities into early pinch discharges was considered to be arcing. The externally applied voltages, although low, still permit the occurrence of unipolar arcing between the plasma and the wall when driven by the sheath potential. Local electron emission from a cathode spot is balanced by a uniform flow back to the surface of energetic electrons in the tail of the Maxwellian distribution. 

The sheath potential is minimized, when the electrode area ratio equals 1. The design of Fig. 3 fulfills this requirement. The lowest possible pressure, for which a stable plasma can be established, is 30 Pa. 

There are two potential explanations of why the ion bombardment is more intense at low frequencies. First, the sheath potential drop, on average, will be higher at the lower frequencies. The electrons are lighter than ions, so they... 

Secondly, the plasma potential will vary with time, depending on the cycle of the applied potential.22 If the ion can transit the sheath before the applied electric field reverses, it can experience the maximum sheath potential. As the frequency is raised, the ion cannot cross the sheath before the field reverses, so it experiences the average sheath potential which is approximately one-third the maximum. Therefore, ion bombardment will be less intense at the highest frequencies. 

Additionally, the incident impurity ions in a fusion device will be multiply charged, e.g., a charge state of 4 can be assumed for Be, C, O, and even higher values for W ions. This will result in increased acceleration of the ions in the sheath potential such that the most probable energies for multiply charged ions in a divertor plasma with Te = 10 eV will be around 200 eV, i.e., well above the threshold energy. 

The high energy efficiency (high plasma density and low sheath potentials)... 

Typical spatiotemporal profiles of potential are shown in Fig. 8 [26]. The left electrode is driven by a sinusoidal radio frequency voltage Frf = Fosin(a)t). The case shown is for an argon discharge with Fq = 100 V and u>/2n — 13.56 MHz. The potential distribution is such that the electrodes are bombarded by positive ions during the whole period of the RF cycle, while most electrons are trapped in the plasma. Only electrons with kinetic energy greater than the sheath potential can reach the walls. Electrons leak to the walls during a short time in the cycle when... 

The sheath potential (voltage) is the difference between the plasma potential and the electrode (or wall) potential. The potential of the sheath over the grounded electrode (right electrode in Fig. 8) is equal to the plasma potential. The potential of the sheath over the powered electrode (left electrode in Fig. 8) is the difference between the plasma potential and the electrode potential. The time-average potential of the powered electrode (with respect to ground) is called the DC self-bias or DC bias. Actually, the DC-bias is the difference of the time-average potential of the sheath... 

Application to capacitively-coupled reactors Figure 24a shows the electron temperature distribution in an argon discharge sustained in a one-dimensional parallel plate reactor of the kind shown in Fig. 7. The temperature peaks near the plasma-sheath interface, where the product of the current and electric field (Eq. 31) is highest, and steep gradients develop in that region. Electrons which diffuse towards the electrode during the sheath potential minimum (around r = 0.25 at left electrode, see also Fig. 

The is the sheath potential and represents the potential drop from the sheath edge to the wall that is necessary to produce an equal flux at the wall of positive and negative species. The steady-state flux of ions and electrons to the wall is given by... 

The above equation assumes a Maxwellian velocity distribution. The sheath potential for ( ) = 5 eV, = 0.1 eV, and = 20 amu is 34 V. This potential, of course, must be added to that from Eq. (17) to obtain the total plasma-wall potential. A probe in the wall would be at a potential of about 50 V in this case (Fig. 2). 

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