Plasma conductivity

The efficiency of open cycle MHD generator systems depends directly on the plasma conductivity in the generator channel. 

However, other parameters can also play a significant role in setting core plasma conductivity levels and limits on generator efficiency. In coal-fired systems, one phenomenon which has received considerable study is the effect of electron attachment by gas-phase molecules formed from ash components on plasma conductivities. 

Wormhoudt, J., Freedman, A., and Kolb, C.E., "Phosphorus Thermochemistry and MHD Plasma Conductivity," 19th Conference on Engineering Aspects of MHD, University of Tennessee, Space Institute, Tullahoma, June 1981. 

Isotropic and Anisotropic Parts of the Electron Distribution Functions EEDF and Plasma Conductivity... 

The previonsly considered EEDFs are related to the isotropic part of the electron velocity distribution /(v). This distribntion /(v), in general, is anisotropic in an electric field, which determines electric crment and plasma conductivity. Electrons receive additional velocity u (3-40) dtrring the free motion between collisions. If the anisotropy is not very strong ( v), we can asstrme that the fraction of electrons in the point v of real anisotropic... 

Electron Mobility, Plasma Conductivity, and Joule Heating... 

Plasma conductivity (3-67) is determined by electron density (the contribution of ions will be discussed next) and the frequency of electron-neutral collisions, Ven. The electron density can be found using the Saha equation (3-14) for quasi-equilibrium thermal discharges and from the balance of charged particles in non-equilibrium non-thermal discharges. The frequency of electron-neutral collisions, Ven, is proportional to pressure and can be found numerically for some specific gases from Table 3-1. Relations (3-67) and (3-68) determine the power transferred from the electric field to plasma electrons. This power, calculated per unit volume, is referred to as Joule heating ... 

Plasma Conductivity in Crossed Electric and Magnetic Fields... 

Assuming also that the frequency of the field is low with respect to plasma conductivity and, hence, the displacement current (second current term in (3-245) can be neglected), we can conclude... 

If this space scale 5 is smaller than the plasma sizes, then the external fields and currents are located only on the plasma surface layer with a penetration depth 5. This effect is known as the skin effect. The boundary layer, where the external fields penetrate and where plasma currents are located, is called the skin layer. The depth of the skin layer depends on the electromagnetic field frequency (/ = co/ln) and plasma conductivity. For calculation of the skin layer depth it is convenient to use the following numeric formula ... 

If the plasma conductivity is high (a oo), the diffusion coefficient of the magnetic field is small (Dm 0) and the magnetic field is unable to move with respect to plasma. One can say that the magnetic field sticks to the plasma or, in other words, the magnetic field is jrozen in plasma. 

High-Frequency Plasma Conductivity and Dielectric Permittivity... 

High-frequency plasma conductivity and dielectric permittivity are important concepts to analyze the propagation of electromagnetic waves in plasma. One-dimensional electron motion in the electric field E = Eq cos cot = Re Eoe ) can be described by the equation ... 

The imaginary component of (3-283) corresponds to the high-frequency plasma conductivity ... 

Attenuation of the electromagnetic wave is determined by the plasma conductivity if BraSoco, the electromagnetic field damping can be neglected. The explicit expression for the refractive index is... 

The Steenbeck-Raizer charmel model (Fig. 4-38) is based on the strong dependence of plasma electric conductivity on temperature (Saha equation, Section 3.1.3). At temperatures below 3000 K, plasma conductivity is low it grows signiflcantly only when the temperature exceeds 4000 K. The temperature decrease T (r) from the axis to the walls is gradual, whereas the conductivity change with radius a[T r)] is sharp. Thus, according to the model, arc current is located mostly in a charmel of radius ro. Temperature and electric conductivity are considered constant inside of the arc charmel and equal to their maximum value on the discharge axis Tm and a(7A). The total arc current can be then expressed as... 

Figure 4-38. Gas temperature and thermal plasma conductivity distributions in arc discharges illustrating the Steenbeck channel model.

Plasma resistance at the critical point becomes equal to the external one, and maximum value of the discharge power equals half of the maximum generator power. When the arc length exceeds the critical value (/ > hnt), the heat losses wl continue to grow. But the power from the power supply cannot be increased anymore, and the gas temperatme rapidly decreases. Plasma conductivity can still be maintained by electron temperatures ( 1 eV) and stepwise ionization (Fridman et al., 1999). The fast equilibrium-to-non-equilibrium transition is due to the increase of electric field E = w/1 and electron temperature T ... 

Thermal ICP Temperature as a Funetion of Solenoid Current. Combining equation (4-89) with the formula for plasma conductivity and the Saha equation, derive relation (4-90) for the ICP temperature with explicit expression for constants. Analyze this relation and show that ICP temperature in the case of a strong skin effect does not depend on the frequency of the electromagnetic field. 

Figure 3 Etching-deposition experiment in a microwave plasma conducted in the system shown in Fig. 1.

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