Plasma is a gaseous, electrically neutral mixture of electrons, ions and atoms (molecules). The electrons of plasma dispose themselves presumably at vicinities of heavy positively charged ions. As a result, the electric fields exist in small domains of space. The dimension of the domain is known as the Debye radius

where ε_{0} is the permittivity of the vacuum, k is the Boltzmann constant, T is the temperature, e is the charge of electron, n_{e} is the electron concentration. The Debye radius is always very small compared with the characteristic dimension of the plasma L, r_{d} << L.

In nature, plasma is ubiguitous (the sun, other stars, upper layers of planetary atmospheres and so on). Electrons and ions in metals and semiconductors also represent plasma-like media.

In laboratory conditions, plasma can be obtained by electric discharges in gases. A low pressure is usually a necessary condition for glow discharge in gases and high pressure results in arc discharges. The latter are characterized by large electric current (up to 10^{5} Ampere), low voltage between electrodes and high brightness.

Plasma may arise in high temperature gases, for example, in the fronts of strong shock waves.

Plasma is classified as ideal and nonideal. In *ideal plasma* the ratio of potential energy to the kinetic energy of the particles is very small. This ratio may be written as

where e^{2}n_{e}^{1/3} is the potential energy of charged particle interaction at the average distance between them. The transition between ideal and nonideal plasma occurs in the range γ = 0.1 to 1 (see Figure 1 which also indicates the position of various examples of plasmas).

Plasma may also be classified as high temperature plasma and low temperature plasma. The assumed upper boundary of the low temperature plasma is T = 10^{5} K. The wide variety of the applications of low temperature plasma include: light sources, arc discharge welding, plasma cutting of metals, hardening of surfaces and so on. The new and very promising direction of plasma technology is synthesizing new chemical composites in plasma media. *Plasma rocket engines* find some special applications; propulsion is a result of outflow of plasma jets.

Hot plasma is being considered in various projects of controlled nuclear fusion (see Fusion, Nuclear Fusion Reactors).

The equilibrium state of plasma is completely defined by their thermodynamic parameters. For ideal equilibrium plasma the pressure is equal to the sum of the partial pressures of plasma components.

In the simplest case plasma consists of the atoms, electrons and single charged ions, the densities of which are related by the Saha equation

where Σ_{i} and Σ_{a} are ion and atomic statistical sums, me is the electron mass, ħ is the Plank constant, I is the atomic energy of ionization.

Thermodynamic equilibrium is realized in closed systems. If plasma is affected by external perturbations—inhomogeneous heating (cooling), emitting charged particles to the environment or receiving them—that means that such a plasma is not a closed system and thermodynamic equilibrium does not exist.

The concept of local thermodynamic equilibrium is very important when the plasma state as a whole is nonequilibrium, but plasma properties in every spatial point are determined by the local values of temperature. Plasma nonequilibrium states are analyzed by methods of physical kinetics.

Plasma properties are determined by plasma composition and are very sensitive to temperature variations. It is very important to note that the physical and chemical processes in plasma (such as dissociation and ionization) require a great deal of energy. Therefore, the contribution of the processes in plasma heat capacity, internal energy and enthalpy may be more closely compared to the contribution of particle motion.

Diffusion of plasma charged particles largely depends on the strong interaction between them and is defined by condition of quasi-neutrality. This diffusion is known as ambipolar diffusion. The ambipolar diffusion coefficient D_{a} is largely depends on the slow motion of the heavy ions (if T_{e} = T_{i}, then D_{a} = 2D_{i}).

For *plasma thermal conductivity*, two processes are very important. The first process is the plasma particle motion; the role of every plasma component largely depends on its density and mobility. The second process is governed by the ambipolar diffusion and by transfer of energy of ionization. Electrons and ions diffuse to the low temperature region and recombine, releasing ionization energy. With the growth of temperature and degree of ionization the role of this mechanism becomes very important, but then decreases as conditions of full ionization are realized (Figure 2).

Plasma energy transfer is also realized by the emission and absorption of electromagnetic radiation. Each radiation process is efficient only in its own spectral interval and largely depends on the thermodynamic parameters of the plasma. As a result, the total emission and absorption coefficients vary sharply and irregularly with frequency (Figure 3). These characteristics lead to the failure of many simple approaches to the theory of these processes (for example, the approximation of a "gray" gas).

The free path length of a photon l_{v} is closely connected with the spectral absorption coefficient K_{v}, l_{v} = 1/K_{v}. This value largely depends on frequency and may be large or small, l_{v} >> or << L. As a result, the value of radiation flux cannot be considered as proportional to the temperature gradient. In consistent theory, the flow of radiation flux should be written as the integral over the whole plasma volume, accounting for the real temperature distribution in plasma volume. Such a characteristic as average emissivity of the plasma layer may be used only for very rough estimates (see Radiation Heat Transfer).

**Figure 3. Total absorption (1) and emission (2) coefficients of electromagnetic radiation from a plasma as a function of frequency v.**

An external electric field creates an electric current in the plasma. *Plasma conductivity* is defined by electron concentration, average length of the mean free path be and average thermal velocity v_{e} = (8kT/πm_{e})^{1/2}. The contribution of ions to the electric conductivity may be neglected because m_{i} << m_{e}. The electrical conductivity may be defined by relation

The conductivity of an ideal plasma at T = *const* decreases with increasing density. However, the plasma conductivity increases again with density when plasma nonideality becomes significant. At large densities, plasma conductivity can reach values close to metallic ones. This growth with increasing density may be explained by the lowering of the energy of atomic ionization in plasma, the emergence of clusters and another consequences of strong interaction between plasma particles.

The motion of charged particles is strongly influenced by external magnetic fields. In the absence of interparticle collisions, plasma charges move along screwed trajectories whose axes are directed along the magnetic field. Plasma charge motion perpendicular to the magnetic field is inhibited. Therefore, the rate of transfer across the magnetic field is greatly suppressed (affecting diffusion, viscosity and thermal conductivity). Plasma may be isolated into specific regions if large enough magnetic fields are used. Magnetic confinement of hot plasma has been used in fusion projects.

If the Knudsen Number is small and local thermodynamic equilibrium is well realized, then the plasma motion is described by the equations of hydrodynamics and magneto-hydrodynamics.

It is difficult to formulate similarity criteria for plasma dynamics, if it is necessary to account for radiation transfer. The uncertainty of the radiation Knudsen number Kn_{R} = l_{n} / L is the first reason of this difficulty arising from the sharp and irregular dependence of l_{v} versus v.

#### REFERENCES

Krall, N. (1973) *Principles of Plasma Physics*, McGraw-Hill Book Co.

Fortov, V., Iakubov, I. (1989) *Physics of Nonideal Plasma*, Hemisphere Publ. Co., New York.

Biberman, L., Vorob'ev, V., Iakubov, I. (1987) *Kinetics of Non-Equilibrium Low-Temperature Plasma*, Plenum Publ. Co., New York.

#### References

- Krall, N. (1973)
*Principles of Plasma Physics*, McGraw-Hill Book Co. - Fortov, V., Iakubov, I. (1989)
*Physics of Nonideal Plasma*, Hemisphere Publ. Co., New York. - Biberman, L., Vorob'ev, V., Iakubov, I. (1987)
*Kinetics of Non-Equilibrium Low-Temperature Plasma*, Plenum Publ. Co., New York.