1629373397-425d4de58b7aea127ffc7c337418ea8d (846389), страница 5
Текст из файла (страница 5)
Furthermore, λD increases withincreasing KTe. Without thermal agitation, the charge cloud would collapse to aninfinitely thin layer. Finally, it is the electron temperature which is used in thedefinition of λD because the electrons, being more mobile than the ions, generallydo the shielding by moving so as to create a surplus or deficit of negative charge.Only in special situations is this not true (see Problem 1.5).The following are useful forms of Eq.
(1.16):λD ¼ 69ðT e =nÞ1=2 m,λD ¼ 7430ðKT e =nÞ1=2 m,T e in Kð1:18ÞKT e in eVWe are now in a position to define “quasineutrality.” If the dimensions L of a systemare much larger than λD, then whenever local concentrations of charge arise orexternal potentials are introduced into the system, these are shielded out in adistance short compared with L, leaving the bulk of the plasma free of large electricpotentials or fields. Outside of the sheath on the wall or on an obstacle, ∇2ϕ is verysmall, and ni is equal to ne, typically to better than one part in 106. It takes only asmall charge imbalance to give rise to potentials of the order of KT/e.
The plasma is“quasineutral”; that is, neutral enough so that one can take ni ’ ne ’ n, where n is acommon density called the plasma density, but not so neutral that all the interestingelectromagnetic forces vanish.A criterion for an ionized gas to be a plasma is that it be dense enough that λD ismuch smaller than L.The phenomenon of Debye shielding also occurs—in modified form—in singlespecies systems, such as the electron streams in klystrons and magnetrons or theproton beam in a cyclotron. In such cases, any local bunching of particles causes alarge unshielded electric field unless the density is extremely low (which it often is).An externally imposed potential—from a wire probe, for instance—would beshielded out by an adjustment of the density near the electrode.
Single-speciessystems, or unneutralized plasmas, are not strictly plasmas; but the mathematicaltools of plasma physics can be used to study such systems.Debye shielding can be foiled if electrons are so fast that they do not collide withone another enough to maintain a thermal distribution. We shall see later thatelectron collisions are infrequent if the electrons are very hot. In that case, someelectrons, attracted by the positive charge of the ion, come in at an angle so fast thatthey orbit the ion like a satellite around a planet.
How this works will be clear in thediscussion of Langmuir probes in a later chapter. Some like to call this effect antishielding.1.6 Criteria for Plasmas1.511The Plasma ParameterThe picture of Debye shielding that we have given above is valid only if there areenough particles in the charge cloud. Clearly, if there are only one or two particlesin the sheath region, Debye shielding would not be a statistically valid concept.Using Eq. (1.17), we can compute the number ND of particles in a “Debye sphere”:N D ¼ n 43 πλ3D ¼ 1:38 106 T 3=2 =n1=2 ðT in KÞð1:19ÞIn addition to λD L, “collective behavior” requiresND ⋙ 11.6ð1:20ÞCriteria for PlasmasWe have given two conditions that an ionized gas must satisfy to be called a plasma.A third condition has to do with collisions.
The weakly ionized gas in an airplane’sjet exhaust, for example, does not qualify as a plasma because the charged particlescollide so frequently with neutral atoms that their motion is controlled by ordinaryhydrodynamic forces rather than by electromagnetic forces. If ω is the frequency oftypical plasma oscillations and τ is the mean time between collisions with neutralatoms, we require ωτ > 1 for the gas to behave like a plasma rather than aneutral gas.The three conditions a plasma must satisfy are therefore:1.
λD L:2. N D ⋙1:3. ωτ > 1:Problems1.3. Calculate n vs. KTe curves for five values of λD from 108 to 1, and threevalues of ND from 103 to 109. On a log-log plot of ne vs. KTe with ne from 106to 1028 m3 and KTe from 102 to 105 eV, draw lines of constant λD (solid) andND (dashed). On this graph, place the following points (n in m3, KT in eV):1.
Typical fusion reactor: n ¼ 1020, KT ¼ 30,000.2. Typical fusion experiments: n ¼ 1019, KT ¼ 100 (torus); n ¼ 1023,KT ¼ 1000 (pinch).3. Typical ionosphere: n ¼ 1011, KT ¼ 0.05.4. Typical radiofrequency plasma: n ¼ 1017, KT ¼ 1.55. Typical flame: n ¼ 1014, KT ¼ 0.1.6. Typical laser plasma; n ¼ 1025, KT ¼ 100.7. Interplanetary space: n ¼ 106, KT ¼ 0.01.121 IntroductionConvince yourself that these are plasmas.1.4.
Compute the pressure, in atmospheres and in tons/ft2, exerted by a thermonuclear plasma on its container. Assume KTe ¼ KTi ¼ 20 keV, n ¼ 1021 m3, andp ¼ nKT, where T ¼ Ti + Te.1.5. In a strictly steady state situation, both the ions and the electrons will followthe Boltzmann relationn j ¼ n0 exp qi ϕ=KT jFor the case of an infinite, transparent grid charged to a potential ϕ, show thatthe shielding distance is then given approximately byλ2D ¼ne211þ20 KT e KT iShow that λD is determined by the temperature of the colder species.1.6. An alternative derivation of λD will give further insight to its meaning.Consider two infinite parallel plates at x ¼ d, set at potential ϕ ¼ 0.
Thespace between them is uniformly filled by a gas of density n of particles ofcharge q.(a) Using Poisson’s equation, show that the potential distribution betweenthe plates isϕ¼nq 2d x22ε0(b) Show that for d > λD, the energy needed to transport a particle from aplate to the midplane is greater than the average kinetic energy of theparticles.1.7. Compute λD and ND for the following cases:(a) A glow discharge, with n ¼ 1016 m3, KTe ¼ 2 eV.(b) The earth’s ionosphere, with n ¼ 1012 m3, KTe ¼ 0.1 eV.(c) A θ-pinch, with n ¼ 1023 m3, KTe ¼ 800 eV.1.7Applications of Plasma PhysicsPlasmas can be characterized by the two parameters n and KTe. Plasma applications cover an extremely wide range of n and KTe: n varies over 28 orders ofmagnitude from 106 to 1034 m3, and KT can vary over seven orders from 0.1 to106 eV. Some of these applications are discussed very briefly below.
The tremendous range of density can be appreciated when one realizes that air and water1.7 Applications of Plasma Physics13differ in density by only 103, while water and white dwarf stars are separated byonly a factor of 105. Even neutron stars are only 1015 times denser than water. Yetgaseous plasmas in the entire density range of 1028 can be described by the sameset of equations, since only the classical (non-quantum mechanical) laws ofphysics are needed.1.7.1Gas Discharges (Gaseous Electronics)The earliest work with plasmas was that of Langmuir, Tonks, and their collaborators in the 1920s. This research was inspired by the need to develop vacuumtubes that could carry large currents, and therefore had to be filled with ionizedgases. The research was done with weakly ionized glow discharges and positivecolumns typically with KTe ’ 2 eV and 1014 < n < 1018 m3.
It was here that theshielding phenomenon was discovered; the sheath surrounding an electrode couldbe seen visually as a dark layer. Before semiconductors, gas discharges wereencountered only in mercury rectifiers, hydrogen thyratrons, ignitrons, sparkgaps, welding arcs, neon and fluorescent lights, and lightning discharges.The semiconductor industry’s rapid growth in the last two decades has broughtgas discharges from a small academic discipline to an economic giant. Chipsfor computers and the ubiquitous handheld devices cannot be made withoutplasmas.
Usually driven by radiofrequency power, partially ionized plasmas(gas discharges) are used for etching and deposition in the manufacture ofsemiconductors.1.7.2Controlled Thermonuclear FusionModern plasma physics had its beginnings around 1952, when it was proposed thatthe hydrogen bomb fusion reaction be controlled to make a reactor. A seminalconference was held in Geneva in 1958 at which each nation revealed its classifiedcontrolled fusion program for the first time. Fusion power requires holding a30-keV plasma with a magnetic field for as long as one second.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
