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plasma,in physics, fully ionized gas of low density, containing approximately equal numbers of positive and negative ions (see electronelectron,
elementary particle carrying a unit charge of negative electricity. Ordinary electric current is the flow of electrons through a wire conductor (see electricity). The electron is one of the basic constituents of matter.
..... Click the link for more information. and ionion,
atom or group of atoms having a net electric charge. Positive and Negative Electric Charges
A neutral atom or group of atoms becomes an ion by gaining or losing one or more electrons or protons.
..... Click the link for more information. ). It is electrically conductive and is affected by magnetic fields. The study of plasma, called plasma physics, is especially important in research efforts to produce a controlled thermonuclear reaction (see nuclear energynuclear energy,
the energy stored in the nucleus of an atom and released through fission, fusion, or radioactivity. In these processes a small amount of mass is converted to energy according to the relationship E = mc2, where E is energy, m
..... Click the link for more information. ). Such a reaction requires extremely high temperatures; it has been computed that a temperature of about 10 million degrees Celsius would be needed to initiate the reaction between deuterium and tritium. By passing a very high electric current through plasma great heat is produced and, simultaneously, an electromagnetic field is created, causing the plasma to withdraw from the walls of its container. The contraction of the plasma, called the pinch effect, prevents the container from being destroyed, but the effect may become unstable too quickly for the fusion reaction. The properties of plasma are distinct from those of the ordinary states of matterstates of matter,
forms of matter differing in several properties because of differences in the motions and forces of the molecules (or atoms, ions, or elementary particles) of which they are composed.
..... Click the link for more information. , and for this reason many scientists consider plasma a fourth state of matter. Interstellar gases, as well as the matter inside stars, are thought to be in the form of plasma, thus making plasma a common form of matter in the universe. See also condensatecondensate,
matter in the form of a gas of atoms, molecules, or elementary particles that have been so chilled that their motion is virtually halted and as a consequence they lose their separate identities and merge into a single entity.
..... Click the link for more information. .
The field of physics that studies highly ionized gases. Plasma is a gas of charged and neutral particles which exhibits collective behavior. All gases become ionized at sufficiently high temperatures, creating what has been called a fourth state of matter, together with solids, liquids, and gases. It has been estimated that more than 99% of the universe is in the plasma state. On the Earth, plasmas are much less common. Lightning is a familiar natural manifestation, and fluorescent lights are a practical application. Plasma applications and studies make use of an enormous range of plasma temperatures, densities, and neutral pressures. They extend from plasma processing applications at relatively low temperatures (such as plasma etching of semiconductor chips at low pressure, or plasma cutting torches at atmospheric pressure) to studies of controlled fusion at very high temperatures.
Plasma physics is a many-body problem that can be described by a combination of Newton's laws and Maxwell's equations. The charged particles in plasmas are usually ions, both positive and negative, and electrons. Plasmas are normally quasineutral; that is, the net positive ion charge density approximately equals the net negative charge density everywhere in the bulk of the plasma. Quasineutrality refers to charge density and does not imply equal densities of electrons and ions since ions can be multiply charged and can also have negative charge. In space and fusion plasmas, plasmas are normally magnetized, while in application plasmas on Earth, such as plasma processing, both magnetized and unmagnetized plasmas are employed. See Maxwell's equations, Newton's laws of motion
It is convenient to keep track of plasma properties in terms of characteristic lengths, frequencies, and velocities. Among these are the Debye length, the electron and ion plasma frequencies, the electron and ion gyrofrequencies and gyroradii, the electron and ion thermal velocities, the ion sound velocity, the Alfvén velocity, and various collision lengths. The definition of a plasma depends on several of these characteristic parameters, and the magnitude of ratios of these parameters to system size or applied frequencies determines most plasma behavior.
The simplest plasma is a collisionless, unmagnetized collection of ions and electrons with no significant currents. Such plasmas have quasineutral regions and nonneutral regions. The nonneutral regions are highly localized. They are usually located near boundaries (where they are known as sheaths), but are sometimes located within the plasma (where they are known as double layers).
Collective behavior refers to the plasma properties not present in single-particle motion. Collective behavior is a distinguishing characteristic of a plasma. It consists of flows, waves, instabilities, and so forth. Common examples are fluctuations in the aurora, generation of microwaves in devices such as magnetrons and klystrons, and reflection of electromagnetic waves from the ionosphere.
Curiously, very high density collections of equal numbers of ions and electrons are not plasmas. Such systems are referred to as strongly coupled plasmas (even though, strictly speaking, they are not plasmas at all).
A collection of either electrons or ions can exhibit properties similar to those of an electrically neutral plasma if the charged-particle density is sufficiently large. For such so-called plasmas, the Debye length and the characteristic frequency of electrons or ions can still be defined, and collective behavior is still exhibited when the Debye length is less than the system's characteristic dimension. So-called pure electron plasmas or pure ion plasmas are unconfined in an unmagnetized system. However, particle traps consisting of a combination of electric and magnetic fields can be used to confine the charges. See Particle trap
The visual appearance of a plasma depends on the kind of ion present, the electron temperature, and the plasma density. Some plasmas are invisible. Curiously, if a plasma is present and not glowing, it is either very hot or very cold. For example, an H+ plasma, or any other relatively hot plasma with fully stripped ions, contains atomic nuclei with no electrons, so there is no atomic physics and no optical emission or absorption. If plasma electrons and ions are very cold, there is insufficient energy to excite optical transitions. The glow often associated with plasmas indicates only where visible energy transitions are excited by energetic electrons or perhaps absorption of ultraviolet radiation, and may have little to do with the presence of bulk plasma. In fusion plasmas, the edges are often copious sources of emission associated with the dissociation and ionization of hydrogen and edge-generated impurities, while much of the hotter core plasma is fully ionized and invisible.
Direct-current glow-discharge plasmas originate from electrons created by secondary electron emission due to ion bombardment of a negatively biased cathode. The secondary electrons are accelerated through the cathode sheath potential (called the cathode fall) to energies the order of 1 keV, and partially ionize the neutral gas, releasing additional energetic electrons in a multiplicative process. The energetic electrons also undergo inelastic collisions with neutrals which result in optical emission that contributes to the so-called glow. See Secondary emission
The understanding of plasma physics begins with an understanding of the motion of single charged particles in a combination of electric and magnetic fields (E and B), produced by a combination of external fields and the motion of the charged particles themselves. The motion of a single particle, with mass m, charge q, and velocity v , is governed by the Lorentz force, as given in Eq. (1).
In addition to the motion parallel to the magnetic field and the gyromotion about the magnetic field, there are drifts perpendicular to the magnetic field. For a general force, F , in the presence of a magnetic field, the perpendicular drift velocity is given by Eq. (2). (2)
Given a perpendicular electric field, particles can walk across a magnetic field. Forces associated with magnetic-field curvature give rise to a curvature drift in the direction orthogonal to the magnetic field, and to the radius of curvature of the magnetic field lines.
For gyro motion in a slowly changing magnetic field, which is approximately periodic, it can be shown that the ratio of the perpendicular energy to the magnetic field is approximately constant. This means that a charged particle moving parallel to a magnetic field and gyrating about the field will gyrate faster as the magnetic field increases. If the magnetic field changes in space and is constant in time, the total energy is conserved. For a sufficiently large magnetic field, a point is reached where the total energy equals the perpendicular energy, so that the parallel energy goes to zero and the particle reflects. This is known as magnetic mirroring.
Magnetic mirroring is the chief natural mechanism of charged-particle confinement. For example, this process confines charged particles in the ionosphere and magnetosphere. The magnetic field lines that connect the north and south magnetic poles of the Earth provide a mirror magnetic field which increases as either pole is approached. In the absence of collisions, a particle moving along and gyrating about such a magnetic field is magnetically confined, if it has a sufficiently large velocity perpendicular to the magnetic field. The Van Allen belts are composed of such mirror-trapped charged particles. The source of these particles is the solar wind, a stream of charged particles continuously emitted by the Sun.
For fully ionized plasmas, it is convenient to describe the plasma as a single fluid together with Maxwell's equations. This gives the magnetohydrodynamic (MHD) equations, which are used to describe plasma equilibria and plasma waves and instabilities. Their relative simplicity has made them ideal for solutions of fusion problems in complicated geometries, and they have been widely used to describe astrophysical plasmas and magnetohydrodynamic energy conversion. See Magnetohydrodynamics
Plasmas can support an impressive variety of electrostatic and electromagnetic waves not present in the absence of plasma. The waves are distinguished by their frequency, the presence or absence of dc magnetic fields, and the plasma temperature and density.
Ionization is the key to plasma production and can be accomplished in many different ways. The most common approach is to employ energetic electrons with energies greater than the ionization potential of the gas being ionized. In dc glow discharges, electrons produced by ion secondary electron emission are accelerated by the cathode sheath potential, as are electrons created by thermionic emission in hot-cathode plasmas. Electrons can also pick up energy by reflecting from oscillating radio-frequency sheath electric fields, or by cyclotron resonance in magnetic fields, or from collisions with other energetic electrons. See Electrical conduction in gases, Gas discharge, Ionization potential, Thermionic emission
Several other approaches involving collisions, which do not require energetic electrons, also exist. These techniques include photoionization, ion-neutral charge exchange, surface ionization, and Penning ionization. Ions can also be produced in the dissociation of molecules. Yet another mechanism, called critical ionization velocity, is instability driven, and occurs when the kinetic energy of the neutral gas atoms streaming perpendicular to a magnetic field exceeds their ionization potential. See Ion sources, Ionization, Photoionization
A vacuum chamber provides the simplest approach to confinement. In an unmagnetized plasma, electrons are lost more rapidly than ions, and the plasma acquires a net positive charge. The excess positive charge appears in a sheath at the plasma boundary with the bulk plasma potential more positive than the boundary potential. The decrease in potential at the boundary provides plasma electron confinement, reducing their loss rate to balance the ion loss rate.
Addition of a uniform magnetic field reduces the loss rate of ions and electrons transverse to the magnetic field, but has no effect on losses parallel to the magnetic field because the Lorentz force has no components along this field. Effective confinement by magnetic fields requires that the ion and electron gyroradii be small compared to device dimensions. Plasma transport across the magnetic field can still occur as a result of collisions or of perpendicular drifts.
In the absence of magnetic fields (both inside and outside the plasma), an equilibrium can be achieved by establishing a pressure balance between plasma and edge walls or edge gas. The existence of an equilibrium does not guarantee that a particular configuration is stable.
Plasma processing can be defined as the collection of techniques which make use of plasmas to create new materials or to modify properties of existing materials. It is used in a large variety of applications including semiconductor etching, preparing plastic surfaces to accept ink, depositing polymers, depositing diamond films, and hardening artificial hip joints. The technique has its foundations in plasma physics, chemistry, electrical and chemical engineering, and materials science.
Controlled fusion aims at taking advantage of nuclear fusion reactions to generate net power. Advances in fusion studies have been tied to the techniques developed for plasma confinement and heating. Fusion experiments employ either magnetic confinement or inertial confinement, in which fusion reactions take place before the plasma has a chance to expand to chamber boundaries. Magnetic mirrors are an example of open systems, while tokamaks, stellarators, and reversed-field pinches are examples of closed toroidal systems. Most magnetic confinement research experiments are done on tokamaks. See Nuclear fusion
Naturally occurring plasmas exist throughout the solar system and beyond. Above the atmosphere, most matter is ionized. The lower-density ionized materials are considered to be plasmas, and they behave in manners very different from the behavior of nonplasmas. Some dense materials, such as stellar matter or electrolytic solutions, are often not considered to be plasmas even though they are ionized; they behave, for the most part, as do ordinary fluids.
Some of the major plasma-physics issues that are under study with naturally occurring plasmas are the energization of charged particles, the reconnection of magnetic fields (temporal changes in magnetic-field topology), the production of magnetic fields by dynamos, the production of electromagnetic waves, the interaction between waves and particles, and the transport of mass, momentum, and energy across magnetic fields.
Naturally occurring plasmas are in general difficult to measure. The solar-wind, ionospheric, and magnetospheric plasmas are diagnosed by single-point measurements by rockets and satellites; the solar atmosphere and all astrophysical plasmas are unreachable and must be diagnosed by the light and radio waves that they emit; and lightning is unpredictable and inhospitable to instruments and must be diagnosed primarily by the light that it emits. As a consequence of limited diagnostics, theoretical analysis and laboratory-plasma experiments play supporting roles in the investigations of naturally occurring plasmas.
plasma(plaz -mă) A state of matter consisting of ions and electrons moving freely. A plasma is thus a fully ionized gas that can be formed at high temperatures (as in stars) or by photoionization (as in interstellar gas). There is plasma in the interstellar medium, in the interplanetary medium in the form of the solar wind, and within planetary magnetospheres. The properties of plasmas differ from those of neutral gases primarily because of the effects of magnetic and electric fields on and arising from the moving charged particles. For example, in a plasma spread over a large area, plasma and magnetic field move together; the magnetic field is said to be ‘frozen in’ to the plasma. See also magnetohydrodynamics.
a partially or completely ionized gas in which the densities of the positive and negative charges are practically the same. Upon sufficiently strong heating, any substance vaporizes and becomes a gas. If the temperature is further increased, the process of thermal ionization is sharply intensified—that is, the molecules of the gas begin to break down into their constituent atoms, which then are converted to ions. The ionization of a gas can also be brought about by the interaction of the gas with electromagnetic radiation (photoionization) or by bombarding the gas with charged particles.
Free charged particles, especially electrons, are easily displaced by an electric field. In a state of equilibrium the space charges of the negative electrons and positive ions making up the plasma must therefore counterbalance each other in order that the total field within the plasma be equal to zero. Hence arises the necessity of the “quasi-neutrality” of a plasma, that is, the approximate equality of the electron and ion densities. If the quasi-neutrality is violated in the region occupied by a plasma, strong electric fields of space charges at once appear and immediately restore the quasi-neutrality. The ratio of the number of ionized atoms to the total number of atoms per unit volume of the plasma is called the plasma’s degree of ionization a. Depending on the magnitude of a, we speak of weakly, strongly, and completely ionized plasmas.
The average energies of the different types of particles constituting a plasma may differ. In this case, the plasma cannot be characterized by a single value of the temperature T, and a distinction is made between the electron temperature Te, the ion temperature T1 (or ion temperatures, if the plasma contains ions of several kinds), and the temperature of the neutral atoms Ta (the neutral component). Such a plasma is said to be nonisothermal; a plasma for which the temperatures of all components are equal is said to be isothermal.
When applied to plasmas, the terms “low-temperature” and “high-temperature” take on a meaning somewhat different from that found in other branches of physics. A plasma with Ti< 105 °K is considered low-temperature, and a plasma with Ti, ~ 106–108 °K or higher is regarded as high-temperature. This conventional division is connected both with the possibility for a plasma to attain extremely high temperatures and with the particular importance of high-temperature plasmas for the achievement of controlled thermonuclear fusion.
By far most of the matter in the universe—stars, stellar atmospheres, galactic nebulas, and the interstellar medium—is in the plasma state. In the region of the earth, a plasma exists in space in the form of the solar wind, a plasma fills the earth’s magneto-sphere forming the earth’s radiation belts, and a plasma forms the ionosphere. Magnetic storms and the auroras are due to processes in the plasma in the vicinity of the earth. The reflection of radio waves from the ionospheric plasma makes possible long-range radio communication on the earth.
Under laboratory conditions and in industrial applications plasmas are formed in electric discharges in gases—such as arc discharges, spark discharges, and glow discharges—and in combustion and explosion processes. Plasmas are made use of in plasma accelerators, magnetohydrodynamic generators, and many other devices.
High-temperature plasmas are produced in devices for the investigation of possible ways of accomplishing controlled fusion. Many properties characteristic of a plasma are possessed by ensembles of conduction electrons and holes in semiconductors and ensembles of conduction electrons (neutralized by stationary positive ions) in metals. Such ensembles are thus referred to as solid-state plasmas. A distinctive feature of solid-state plasmas is that they can exist at temperatures that are extremely low for “gaseous” plasmas—from room temperature down to absolute zero.
The possible values of the plasma density n—the number of electrons or ions per cubic centimeter—lie in a very broad range: from n ~ 10–6 in intergalactic space and n ~ 10 in the solar wind to n ~ 1022 for solids and even greater values in the central regions of stars.
The term “plasma” was introduced into physics in 1929 by the American scientists I. Langmuir and L. Tonks, who made probe measurements of the parameters of a low-temperature gas-discharge plasma. Plasma kinetics were considered in studies by L. D. Landau in 1936 and 1946 and by A. A. Vlasov in 1938. In 1942, H. Alfvén set forth the equations of magnetohydrody-namics to explain a number of phenomena in cosmic plasmas. In 1950, 1. E. Tamm, A. D. Sakharov, and the American physicist L. Spitzer proposed the magnetic thermal isolation of a plasma to achieve controlled fusion. From the 1950’s to the 1970’s research on plasmas was stimulated by various practical applications and by the development of astrophysics, space physics (the observation of cosmic plasmas and the explanation of the processes in such plasmas), and the physics of the earth’s upper atmosphere—particularly in connection with spacecraft flights. An additional important stimulus to plasma study was the intensification of research on the problem of controlled fusion.
Basic properties. Two factors play a decisive role in the sharp difference of the properties of a plasma from the properties of neutral gases. First, the interaction of plasma particles with each other is characterized by Coulomb forces of attraction and repulsion that decrease much more slowly with distance—that is, are much “longer-range”—than the forces of interaction of neutral particles. For this reason the interaction of particles in a plasma is strictly speaking not a pair effect but a collective effect—a large number of particles interact with each other simultaneously. Second, electric and magnetic fields exert a very strong effect on a plasma, whereas they have an extremely weak effect on neutral gases. As a result, space charges and space currents appear in plasmas. This second factor also accounts for a number of the specific properties of plasmas. Because of these differences, a plasma can be considered a separate, fourth state of matter.
The quasi-neutrality referred to above is among the most important properties of plasmas. It obtains if the linear dimensions of the region occupied by a plasma are much greater than the Debye shielding distance where ee and ei are the charges of the electrons and ions, ne and n, are the electron and ion densities, and k is the Boltz-mann constant (the Gaussian system of units is used here and below). Consequently, only when this condition is satisfied may we speak of a plasma as such. The electric field of an individual particle in a plasma is “shielded” by particles of the opposite sign —that is, it practically vanishes—at distances of the order of D from the particle. The value of D determines also the penetration depth of an external electrostatic field into the plasma; shielding of this field is also caused by the appearance in the plasma of compensating fields of space charges. Quasi-neutrality may be violated near the plasma surface, where the faster electrons can fly out to a distance of ~ D because of momentum stemming from their thermal motion (Figure 1).
A plasma is called ideal if the potential energy of interaction of the particles is small in comparison with the particles’ thermal energy. This condition is satisfied when the number of particles in a sphere of radius D is large: No = (4/3)πD3n ≫ 1. In lightning, T ~ 2 × 104oK, n ~ 2.5 × 1019 (the density of air), and consequently D ~ 10–7 cm, but ND~ 1/10. Such a plasma is said to be slightly nonideal.
In addition to random thermal motion, plasma particles can participate in ordered collective processes, the most characteristic of which are longitudinal oscillations of the space charge called Langmuir waves. Their angular frequency where m = 9 × 10–28 g is the mass of an electron, is called the plasma frequency. The large number and the diversity of collective processes in a plasma—a feature that distinguishes a plasma from a neutral gas—are due to the long-range property of the Coulomb interaction of the plasma particles. Because of this long-range property, a plasma may be considered an elastic medium in which various noises, oscillations, and waves are easily excited and propagated.
A Lorentz force acts on plasma particles in a magnetic field with induction B. As a result, the charged particles of the plasma revolve with cyclotron frequencies ωB= eB/mc in Larmor spirals (circles) of radius pB = V1/WB, where c is the speed of light, e and m are the charge and mass of the electron or ion, and vi is the component of the particle’s velocity perpendicular to B. The diamagnetism of a plasma is manifested in such an interaction: the circular currents generated by the electrons and ions reduce the external magnetic field; here, the electrons revolve clockwise, and the ions counterclockwise (Figure 2). The magnetic moments of the circular currents are equal to μ, = mv /2B. In an inhomogeneous field a diamagnetic force that tends to drive a plasma particle from the region of a strong field to the region of a weaker field acts on the currents; this fact is the most important cause of plasma instability in inhomogeneous fields.
Mutual collisions of particles in a plasma are described by the effective cross sections, which characterize the “target area” that must be “struck” for a collision to occur. For example, an electron flying past an ion at the distance of the impact parameter p (Figure 3) is deflected by the Coulomb force of attraction through an angle 0, which is approximately equal to the ratio of the potential energy to the kinetic energy: θ ≈ 2p1/p, where p1 = e2/mv2 ≈ e2/kT—p1 being the impact distance at which the angle of deflection is θ = 90°. All electrons striking within a circle with area σclose ≈ 4πp21, which may be called the “close” collision cross section, are scattered at large angles θ ~ 1 radian. If, however, distant encounters with p ≫ p1 are also taken into account, then the effective cross section increases by the factor Λ = ln(D/p1), which is called the Coulomb cutoff parameter. In a completely ionized plasma A usually is about 10–15, and the contribution of close collisions may be totally ignored in view of the long-range nature of interactions in a plasma. Since for distant encounters the particle velocities change by only small amounts, the motion of the particles can be regarded as a diffusion process in a distinctive velocity space. Although, as noted above, every plasma particle interacts simultaneously with a large number of other particles, the processes in a plasma can be described by using the concept of pair collisions. The average effect of a collective interaction is equivalent to the effect of a sequence of binary collisions.
If intense oscillations and instabilities are not excited in the plasma, then particle collisions determine its dissipative properties—electrical conductivity, viscosity, thermal conductivity, and diffusion. In a completely ionized plasma the electrical conductivity cr is independent of the plasma density and is proportional to T3/2. For T ~ 15 × 106 °K, σexceeds the electrical conductivity of silver, and a plasma therefore may often be considered, especially for fast, large-scale motions, approximately an ideal conductor with σ —. ∞. If such a plasma moves in a magnetic field, then the electromotive force induced in any closed circuit moving together with the plasma is equal to zero; this fact, in view of Faraday’s law of electromagnetic induction, implies the constancy of the magnetic flux threading the circuit (Figure 4). This freezing in of the magnetic field is also among
the most important properties of a plasma. It accounts in particular for the possibility of self-excitation (generation) of a magnetic field as a result of an increase in the length of the magnetic lines of force during random turbulent motion of the medium. For example, a filamentary structure that indicates the presence of a magnetic field excited in this manner can often be seen in cosmic nebulas.
Methods of theoretical description. The principal methods of theoretical description of a plasma are (1) investigation of the motion of the individual particles of the plasma, (2) magnetohy-drodynamic description of the plasma, and (3) kinetic analysis of the particles and waves in the plasma.
The velocity v of an individual plasma particle in a magnetic field can be represented as the sum of the components v∥ (parallel to the field) and vL (perpendicular to the field). In a rarefied plasma, where collisions may be ignored, a charged particle moves with a velocity V∥ along a magnetic line of force while rapidly revolving in a Larmor spiral (see Figure 2). When a perturbing force F is present, the particle also drifts slowly in a direction perpendicular to both the magnetic field and the direction of F. For example, in an electric field E directed at an angle to the magnetic field, electrical drift occurs with a velocity Vdr-ei = cEi/B, where Ei is the electric field strength component perpendicular to the magnetic field B. If, however, E = 0 but the magnetic field is inhomogeneous, centrifugal drift occurs in the direction of the binormal to the line of force, and in the longitudinal direction the diamagnetic force brakes a particle approaching the region of the stronger magnetic field. Here, the total energy of the particle (m/2)(v2 + vi2) and the particle’s magnetic moment μ = mv2/2B remain invariant. Such, for example, is the motion of cosmic-ray particles in the earth’s magnetic field (Figure 5). These particles are reflected from the polar regions, where the field is stronger, and at the same time drift around the earth—ions to the west, electrons to the east. The earth’s field is a magnetic trap: it confines in radiation belts the particles captured by it. The magnetic mirror traps used in research on controlled fusion have similar properties of plasma confinement.
When a plasma is described by the equations of magnetohy-drodynamics, it is considered a continuous medium in which currents can flow. The interaction of these currents with a magnetic field creates electrodynamic space forces that must balance the gas-dynamic pressure of the plasma, which is analogous to the pressure in a neutral gas. In the equilibrium state the magnetic lines of force and the lines of flux must run along constant-pressure surfaces. If a field does not penetrate the plasma (the ideal conductor model), then the plasma boundary itself is such a surface and the gas-dynamic plasma pressure on it, pgas, must be equal to the external magnetic pressure pmag = B2/8π. A very simple example of such equilibrium—the Z pinch, which arises during a discharge between two electrodes—is illustrated in Figure 6. The hatching indicates the flow lines on the plasma surface. The equilibrium of a Z pinch is unstable—flutes running along the magnetic field are readily formed on a Z pinch. As the flutes develop, they turn into thin sausage-type instabilities and can result in a current break. In powerful discharges with currents of approximately 106 amperes in a deuterium plasma, such a process is accompanied by a certain number of nuclear reactions and by the emission of neutrons and hard X rays. This was first observed by L. A. Artsimovich, M. A. Leontovich, and co-workers in 1952.
If a longitudinal magnetic field B\\ is created within a pinch, it will move with the plasma because it is frozen in and will hinder the development of sausage-type instabilities by virtue of
its pressure. Flutes may arise even in this case along the helical lines of force of the total magnetic field, which consists of the longitudinal field and the transverse field B1 created by the plasma current Iǀǀ. This occurs, for example, in an equilibrium toroidal pinch. When, however, B‖\/B > R/a, where R and a are the larger and smaller radii of the torus (Figure 7), the pitch of the helical lines of force of the total field is greater than the length of the closed plasma column 2πR and, as experiments show, a flute instability does not develop. Such systems, called Tokamaks, are used for research on controlled fusion.
The most detailed method of describing a plasma is the kinetic method, which is based on the use of the particle distribution function in the coordinates and momenta f = f (t, r, p). The momentum p of a particle is equal to my. In a state of thermodynamic equilibrium this function has the form of the universal Maxwellian distribution, and in the general case is found from the Boltzmann kinetic equation
Here, F = eE + (e/c) [vB] is the external force acting on the charged plasma particle, and the term C(f) takes into account mutual collisions of particles. In considering fast plasma motions the collisions may frequently be ignored, so that C(f) ~ 0. The kinetic equation is then called the Vlasov collisionless equation with self-consistent fields E and B, which are themselves determined by the motion of charged particles. If the plasma is completely ionized—that is, if only charged particles are present in it—then, because of the predominant role of distant encounters, the particle collisions are equivalent to a diffusion process in the momentum (velocity) space. The expression for C(f) for such a plasma was derived by L. D. Landau and may be written as
C (f) = ∇(D̂ ‧ ∇ – Fcf)
where ∇ = ∂/∂P is the gradient in momentum space, D̂ is the tensor coefficient of diffusion in the same space, and F, is the force of the mutual, or dynamical, friction of the particles.
At high temperatures and a low density, particle-particle collisions may be ignored in a plasma. When, however, waves of some type are excited in a plasma, the “collisions” of particles with waves must be taken into account. When the oscillations in a plasma have amplitudes that are not too large, such collisions, as for distant encounters, are accompanied by small changes in particle momentum and the term c(f) retains its diffusion form with the difference that the coefficient D̂ is determined by the wave intensity. The most important result of the kinetic description of a plasma is the allowance for the interaction of a wave with the group of resonance particles, whose velocities coincide with the rate of wave propagation. It is these particles that can most efficiently exchange energy and momentum with the wave. In 1946, L. D. Landau predicted the possibility of the collision-less damping of Langmuir waves on the basis of such exchange. This effect was subsequently detected in plasma experiments. If an additional particle beam is directed into a plasma, then such exchange may result not in damping but in amplification of the waves. This effect is to some extent analogous to Cherenkov-Vavilov radiation.
Plasma oscillations and instabilities. The waves in a plasma are distinguished by their spatial character and diverse properties. By expansion in a Fourier series, any small perturbation in a plasma can be represented as a set of simple sine waves (Figure 8). Each of these monochromatic waves is characterized by a certain frequency <a, wavelength λ, and a phase velocity of propagation vPhase- Moreover, the waves may differ in polarization, that is, in the direction of the electric field vector in the wave. If this field is directed parallel to the velocity of propagation, the wave is said to be longitudinal; if the field is directed perpendicular to the velocity, the wave is called transverse. Waves of three types are possible in a plasma without a magnetic field: longitudinal Langmuir waves with a frequency ωo, longitudinal sound waves (or more accurately, ion-sound waves), and transverse electromagnetic waves (light or radio waves). The transverse waves may have two polarizations and can be propagated in a plasma without a magnetic field as long as their frequency w exceeds the plasma frequency ω0 Otherwise (ω < ωo), the refractive index of the plasma is imaginary and transverse waves cannot propagate within the plasma but are reflected by its surface just as light rays are reflected by a mirror. It is for this reason that radio waves with X > ~ 20 m are reflected by the ionosphere—thus making possible long-range radio communication on the earth.
If, however, a magnetic field is present, transverse waves, on resonating with ions and electrons at the ion and electron cyclotron frequencies, can propagate within a plasma even when w < tuo- This fact signifies the appearance of two more types of waves in the plasma, called Alfvén and fast magnetosonic waves. An Alfvén wave is a transverse disturbance propagated along the magnetic field with a velocity where M1 is the mass of the ions. The nature of the wave is due to the freezing in and elasticity of the lines of force, which tend to shorten their length and are “loaded” with plasma particles, particularly massive ions, and thus oscillate like taut strings. A fast magnetosonic wave in the low-frequency region essentially differs only in polarization from an Alfvén wave. The velocities of the waves are similar and are determined by the magnetic field and the inertia of the heavy ions. In the high-frequency region, where the ions may be considered stationary, the magnetosonic wave is determined by the inertia of the electrons and has a specific helical polarization. For this reason a fast magnetosonic wave in this region is called a “helicon branch” of the oscillations, or a “whistler branch,” since in the magnetospheric plasma it appears as the characteristic whistling in radio communications. In addition, a slow magnetosonic wave, which is an ordinary sound wave with characteristics somewhat altered by the magnetic field, can propagate in a plasma.
Thus, when a magnetic field is present in a homogeneous plasma, waves of six types are possible: three high-frequency and three low-frequency. If the plasma temperature or density in the magnetic field is nonuniform, then drift waves are also possible. For large amplitudes collisionless shock waves (observed at the boundary of the magnetosphere), solitary waves (solitons), a number of other nonlinear waves, and, finally, strongly developed turbulence of the plasma motion are possible.
In a nonequilibrium plasma “instability build-up,” that is, an increase in some of these types of waves to some saturation level, is possible under certain conditions. More complex cases of induced excitation of waves of one type through the energy of waves of another type are possible as well.
Plasma radiation. The radiation spectrum of a low-temperature plasma, such as a gas-discharge plasma, consists of individual spectral lines. Not only ionization but the inverse process of ion and electron recombination, which produces recombination radiation with a broadband spectrum, occurs in the fluorescent tubes used, in particular, for advertising and lighting (“daylight” lamps).
Bremsstrahlung radiation, which arises in collisions of electrons with ions, has a continuous spectrum and is characteristic of high-temperature plasma with a significant degree of ionization. In a magnetic field the Larmor rotation of plasma electrons leads to the appearance of magnetobraking radiation at the harmonics of the cyclotron frequency; this radiation is particularly important for high, or relativistic, electron energies. Induced radiation of the inverse Compton effect type plays an important role in cosmic plasmas. It and the magnetobraking mechanism are responsible for the radiation of certain cosmic nebulas, such as the Crab nebula.
Fast particles emitted from a nonequilibrium plasma as a result of the development of various types of instabilities are called corpuscular plasma radiation. Characteristic oscillations whose energy is then imparted to a small group of resonant particles are preferentially built up in the plasma. This mechanism apparently explains the acceleration of relatively low-energy cosmic-ray particles in the solar atmosphere and in the nebulas formed during explosions of supernovas of the pulsar type in the Crab nebula.
Plasma diagnostics. By placing an electric probe, that is, a small electrode, in a plasma and recording the dependence of the current on the voltage supplied, it is possible to determine the temperature and density of a plasma. The variation of the magnetic field with time can be measured by means of a magnetic probe, which consists of a miniature induction coil. These methods, however, involve active intervention in the plasma and can introduce undesirable contaminations. “Trans-illumination” of a plasma with beams of neutral particles and beams of radio waves are cleaner methods. The various forms of laser transillumination of a plasma, including the use of holography, constitute the most delicate and at the same time the most localized method of laboratory plasma diagnostics.
Passive diagnostic techniques are also frequently used. These include the observation of the plasma radiation spectrum (the only method in astronomy), the extraction of fast neutral atoms formed as a result of ion charge exchange in a plasma, and the measurement of the radio noise level. Dense plasmas are studied by means of superspeed photography (several million frames per second) and optical scanning. The X-ray bremsstrahlung spectrum and the neutron radiation of a deuterium plasma also are recorded in controlled fusion research.
Applications. A high-temperature plasma (T ~ 108 °K) consisting of deuterium and tritium is the primary object of controlled fusion research. Such a plasma is created by heating and rapidly compressing a plasma with a current (high-frequency heating is also used); by injecting high-energy neutral particles into a magnetic field, where they are ionized; or by exposing a target to powerful lasers or to relativistic electron beams.
Low-temperature plasmas (T ~ 103 °K) are used in gas-discharge light sources, gas lasers, thermionic converters, and magnetohydrodynamic
generators. In magnetohydrodynamic generators a plasma jet is braked in a channel with a transverse magnetic field B. This results in the appearance of an electric field E with strength of the order of Bv/c, where v is the velocity of the plasma flow, between the upper and lower electrodes (Figure 9); the voltage from the electrodes is fed to an external circuit.
If a magnetohydrodynamic generator is “inverted” by passing a current from an external source through a plasma in a magnetic field, a plasma engine, which is extremely promising for long space flights, is formed.
Plasmatrons, which create jets of dense low-temperature plasma, have found broad application in various fields of technology. In particular, they are used to cut and weld metals and to apply coatings. In plasma chemistry low-temperature plasmas are used to produce certain chemical compounds, for example, halides of inert gases such as KrF, that cannot be produced by other means. In addition, high plasma temperatures bring about a high rate of chemical reactions—both direct reactions of synthesis and the reverse reactions of decomposition. If synthesis is carried out while a plasma jet is “in transit,” the reverse reactions of decomposition can be impeded—and the yield of the required product thereby substantially increased—by expanding the jet and thus rapidly cooling it in the next leg of the trajectory, an operation called quenching.
REFERENCESArtsimovich, L. A. Elementarnaia fizika plazmy, 3rd ed. Moscow, 1969.
Artsimovich, L. A. Upravliaemye termoiadernye reaktsii, 2nd ed. Moscow, 1963.
Frank-Kamenetskii, D. A. Lektsii po fizike plazmy. Moscow, 1963.
Alfvén, H. and C.-G. Fälthammer. Kosmicheskaia elektrodinamika, 2nd ed. Moscow, 1967. (Translated from English.)
Spitzer, L. Fizika polnost’iu ionizovannogo gaza. Moscow, 1957. (Translated from English.)
Ginzburg, V. L. Rasprostranenie elektromagnitnykh voln v plazme, 2nd ed. Moscow, 1967.
Trubnikov, B. A. Vvedenie v teoriiu plazmy. Moscow, 1969.
Voprosy teoriiplazmy. Collection edited by M. A. Leontovich. Fascicles 1–7. Moscow, 1963–73.
B. A. TRUBNIKOV
["A PLASMA Primer", B. Smith et al, AI Lab Working Paper 92, MIT Oct 1975].
["Viewing Control Structures as Patterns of Passing Messages", C. Hewitt, AI Lab Memo 410, MIT 1976].