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Chapter 1
1.1 What is a Plasma?
1.1.1 An ionized gas
A plasma is a gas in which an important fraction of the atoms is ionized, so that the electrons and ions are separately free.
When does this ionization occur? When the temperature is hot enough.
Balance between collisional ionization and recombination: |
Figure 1.1: Ionization and Recombination
Ionization has a threshold energy. Recombination has not but is much less probable.
Threshold is ionization energy (13.6eV, H). χi |
Figure 1.2: Ionization and radiative recombination rate coefficients for atomic hydrogen
Integral over Maxwellian distribution gives rate coefficients (reaction rates). Because of the tail of the Maxwellian distribution, the ionization rate extends below T = χi. And in equilibrium, when

| nionsnneutrals | = | < σi v >< σr v > | , | | (1.1) | the percentage of ions is large ( ∼ 100%) if electron temperature: Te >~χi/10. e.g. Hydrogen is ionized for Te >~1eV (11,600°k). At room temp r ionization is negligible.
For dissociation and ionization balance figure see e.g. Delcroix Plasma Physics Wiley (1965) figure 1A.5, page 25.
1.1.2 Plasmas are Quasi-Neutral
If a gas of electrons and ions (singly charged) has unequal numbers, there will be a net charge density, ρ.

ρ = ne(−e) + ni(+e) = e (ni − ne) | | (1.2) |
This will give rise to an electric field via

∇ . E= | ρϵ0 | = | eϵ0 | (ni − ne) | | (1.3) |
Example: Slab. |
Figure 1.3: Charged slab

| | dEdx | | | = | | | ρϵ0 | | | | (1.4) | | → E | | = | | ρ | xϵ0 | | | | (1.5) | |
This results in a force on the charges tending to expel whichever species is in excess. That is, if ni > ne, the E field causes ni to decrease, ne to increase tending to reduce the charge.
This restoring force is enormous!
Consider Te = 1eV, ne = 1019m−3 (a modest plasma; c.f. density of atmosphere nmolecules ∼ 3 ×1025m−3). Suppose there is a small difference in ion and electron densities ∆n = (ni − ne)

so ρ = ∆n e | | (1.6) |
Then the force per unit volume at distance x is

Fe = ρE = ρ2 | xϵ0 | = (∆n e)2 | xϵ0 | | | (1.7) |
Take ∆n / ne = 1% , x = 0.10 m.

Fe = (1017 ×1.6 ×10−19)2 0.1 / 8.8 ×10−12 = 3 ×106 N.m−3 | | (1.8) |
Compare with this the pressure force per unit volume ∼ p/x : p ∼ ne Te (+ ni Ti)

Fp ∼ 1019 ×1.6 ×10−19 / 0.1 = 16 Nm−3 | | (1.9) |
Electrostatic force >> Kinetic Pressure Force.
This is one aspect of the fact that, because of being ionized, plasmas exhibit all sorts of collective behavior, different from neutral gases, mediated by the long distance electromagnetic forces E, B.
Another example (related) is that of longitudinal waves. In a normal gas, sound waves are propagated via the intermolecular action of collisions. In a plasma, waves can propagate when collisions are negligible because of the coulomb interaction of the particles.
1.2 Plasma Shielding
1.2.1 Elementary Derivation of the Boltzmann Distribution
Basic principle of Statistical Mechanics:
Thermal Equilibrium ↔ Most Probable State i.e. State with large number of possible arrangements of micro-states. |
Figure 1.4: Statistical Systems in Thermal Contact
Consider two weakly coupled systems S1, S2 with energies E1, E2. Let g1, g2 be the number of microscopic states which give rise to these energies, for each system. Then the total number of micro-states of the combined system is (assuming states are independent)

g = g1 g2 | | (1.10) |
If the total energy of combined system is fixed E1 + E2 = Et then this can be written as a function of E1:

| g | | = | | g1 (E1) g2 (Et − E1) | | | (1.11) | | and | dgdE1 | | | = | | | dg1dE | g2 − g1 | dg2dE | . | | | (1.12) | |
The most probable state is that for which [dg/(dE1)] = 0 i.e.

| 1g1 | | dg1dE | = | 1g2 | | dg2dE | or | ddE | lng1 = | ddE | lng2 | | (1.13) |
Thus, in equilibrium, states in thermal contact have equal values of [d/dE] lng.
One defines σ ≡ lng as the Entropy.
And [ [d/dE] lng ]−1 = T the Temperature.
Now suppose that we want to know the relative probability of 2 micro-states of system 1 in equilibrium. There are, in all, g1 of these states, for each specific E1 but we want to know how many states of the combined system correspond to a single microstate of S1.
Obviously that is just equal to the number of states of system 2. So, denoting the two values of the energies of S1 for the two microstates we are comparing by EA, EB the ratio of the number of combined system states for S1A and S1B is

| g2 (Et − EA)g2 (Et − EB) | = exp[ σ(Et − EA) − σ(Et − EB) ] | | (1.14) |
Now we suppose that system S2 is large compared with S1 so that EA and EB represent very small changes in S2's energy, and we can Taylor expand

| g2 (Et − EA)g2 (Et − EA) | ≅ exp | ⎡
⎣ | − EA | dσdE | + EB | d σdE | ⎤
⎦ | | | (1.15) |
Thus we have shown that the ratio of the probability of a system (S1) being in any two micro-states A, B is simply

exp | ⎡
⎣ | − (EA − EB)T | ⎤
⎦ | , | | (1.16) | when in equilibrium with a (large) thermal "reservoir". This is the well-known "Boltzmann factor".
You may notice that Boltzmann's constant is absent from this formula. That is because of using natural thermodynamic units for entropy (dimensionless) and temperature (energy).
Boltzmann's constant is simply a conversion factor between the natural units of temperature (energy, e.g. Joules) and (e.g.) degrees Kelvin. Kelvins are based on°C which arbitrarily choose melting and boiling points of water and divide into 100.
Plasma physics is done almost always using energy units for temperature. Because Joules are very large, usually electron-volts (eV) are used.

1 eV = 11600 K = 1.6 ×10−19 Joules. | | (1.17) |
One consequence of our Botzmann factor is that a gas of moving particles whose energy is 1/2 mv2 adopts the Maxwell-Boltzmann (Maxwellian) distribution of velocities ∝ exp[ − [(mv2)/2T] ].
1.2.2 Plasma Density in Electrostatic Potential
When there is a varying potential, ϕ, the densities of electrons (and ions) is affected by it.
If electrons are in thermal equilibrium, they will adopt a Boltzmann distribution of density

ne ∝ exp( | eϕTe | ) . | | (1.18) |
This is because each electron, regardless of velocity possesses a potential energy −eϕ.
Consequence is that (fig 1.5) |
Figure 1.5: Self-consistent loop of dependencies a self-consistent loop of dependencies occurs.
This is one elementary example of the general principle of plasmas requiring a self-consistent solution of Maxwell's equations of electrodynamics plus the particle dynamics of the plasma.
1.2.3 Debye Shielding
A slightly different approach to discussing quasi-neutrality leads to the important quantity called the Debye Length. |
Figure 1.6: Shielding of fields from a 1-D grid.
Suppose we put a plane grid into a plasma, held at a certain potential, ϕg.
Then, unlike the vacuum case, the perturbation to the potential falls off rather rapidly into the plasma. We can show this as follows. The important equations are:

| Poisson′s Equation | | | | ∇2 ϕ = | d2ϕdx2 | = − | eϵ0 | (ni − ne) | | | (1.19) | | Electron Density | | | | ne = n∞ exp(e ϕ/Te) . | | | (1.20) | |
[This is a Boltzmann factor; it assumes that electrons are in thermal equilibrium. n∞ is density far from the grid (where we take ϕ = 0).]

Ion Density ni = n∞ . | | (1.21) |
[Applies far from grid by quasineutrality; we just assume, for the sake of this illustrative calculation that ion density is not perturbed by ϕ-perturbation.]

| d2 ϕd x2 | = | e n∞ϵ0 | | ⎡
⎣ | exp | ⎛
⎝ | e ϕTe | ⎞
⎠ | − 1 | ⎤
⎦ | . | | (1.22) |
This is a nasty nonlinear equation, but far from the grid |e ϕ/ Te | << 1 so we can use a Taylor expression: exp[(e ϕ)/(Te)] ≅ 1 + [( e ϕ)/(Te)]. So

| d2 ϕd x2 | = | e n∞ϵ0 | | eTe | ϕ = | e2 n∞ϵ0 Te | ϕ | | (1.23) |
Solutions: ϕ = ϕ0 exp(− |x| / λD ) where

λD ≡ | ⎛
⎝ | ϵ0 Tee2 n∞ | ⎞
⎠ | 1/2

| | | (1.24) |
This is called the Debye Length
Perturbations to the charge density and potential in a plasma tend to fall off with characteristic length λD.
In Fusion plasmas λD is typically small. [e.g. ne = 1020 m−3 Te = 1keV λD = 2 ×10−5m = 20 μm]
Usually we include as part of the definition of a plasma that λD << the size of plasma. This ensures that collective effects, quasi-neutrality etc. are important. Otherwise they probably aren't.
1.2.4 Plasma-Solid Boundaries (Elementary)
When a plasma is in contact with a solid, the solid acts as a "sink" draining away the plasma. Recombination of electrons and ions occur at surface. Then: 1. Plasma is normally charged positively with respect to the solid. | 2. Figure 1.7: Plasma-Solid interface: Sheath 3. There is a relatively thin region called the "sheath", at the boundary of the plasma, where the main potential variation occurs.
Reason for potential drop: Different velocities of electrons and ions.
If there were no potential variation (E= 0) the electrons and ions would hit the surface at the random rate

| 14 | n | -v | per unit area | | (1.25) |
[This equation comes from elementary gas-kinetic theory. See problems if not familiar.]
The mean speed ―v = √{ [8 T/(πm)]} ∼ √{ T/m}.
Because of mass difference electrons move ∼ √{ [(mi)/(me)]} faster and hence would drain out of plasma faster. Hence, plasma charges up enough that an electric field opposes electron escape and reduces total electric current to zero.
Estimate of potential:
Ion escape flux 1/4 n′i―vi
Electron escape flux 1/4 n′e ―vi
Prime denotes values at solid surface.
Boltzmann factor applied to electrons:

n′e = n∞ exp[ e ϕs / Te ] | | (1.26) | where ϕs is solid potential relative to distant (∞) plasma.
Since ions are being dragged out by potential assume n′i ∼ n∞ (Zi = 1). [This is only approximately correct.]
Hence total current density out of plasma is

| j | | = | | qi | 14 | n′i | -v | i | + qe | 14 | n′e | -v | e | | | | (1.27) | | | | = | | | e n∞4 | { | -v | i | − exp | ⎡
⎣ | e ϕsTe | ⎤
⎦ | | -v | e | } | | | (1.28) | |
This must be zero so

| ϕs | | = | | | Tee | ln| | | -v | i | -v | e | | | = | Tee | | 12 | ln | ⎛
⎝ | TiTe | | memi | ⎞
⎠ | | | | (1.29) | | | | = | | | Tee | | 12 | ln | ⎛
⎝ | memi | ⎞
⎠ | [if Te = Ti.] | | | (1.30) | |
For hydrogen [( mi)/(me)] = 1800 so 1/2 ln[(me)/(mi)] = − 3.75.
The potential of the surface relative to plasma is approximately −4 [(Te)/e].
[Note [(Te)/e] is just the electron temp r in electron-volts expressed as a voltage.]
1.2.5 Thickness of the sheath
Crude estimates of sheath thickness can be obtained by assuming that ion density is uniform. Then equation of potential is, as before,

| d2 ϕd x2 | = | e n∞ϵ0 | | ⎡
⎣ | exp | ⎛
⎝ | eϕTe | ⎞
⎠ | − 1 | ⎤
⎦ | | | (1.31) |
We know the rough scale-length of solutions of this equation is

λD = | ⎛
⎝ | ϵ0Tee2 n∞ | ⎞
⎠ | 1/2

| the Debye Length. | | (1.32) |
Actually our previous solution was valid only for |eϕ/Te| << 1 which is no longer valid.
When −eϕ/Te > 1 (as will be the case in the sheath). We can practically ignore the electron density, in which case the solution will continue only quadratically. One might expect, therefore, that the sheath thickness is roughly given by an electric potential gradient

− | Te | | 1λD | | | (1.33) | extending sufficient distance to reach ϕS = − 4 [( Te)/e] i.e. distance x ∼ 4 λD
This is correct for the typical sheath thickness but not at all rigorous.
1.3 The `Plasma Parameter'
Notice that in our development of Debye shielding we used nee as the charge density and supposed that it could be taken as smooth and continuous. However if the density were so low that there were less than approximately one electron in the Debye shielding region this approach would not be valid. Actually we have to address this problem in 3-d by defining the `Plasma Parameter', ND, as
ND = Number of particles in the `Debye Sphere'.

= n . | 43 | πλ3D | ⎛
⎝ | ∝ | T3/2n1/2 | ⎞
⎠ | . | | (1.34) |
If ND <~1 then the individual particles cannot be treated as a smooth continuum. It will be seen later that this means that collisions dominate the behaviour: i.e. short range correlation is just as important as the long range collective effects.
Often, therefore we add a further qualification of plasma:

ND >> 1 (Collective effects dominate over collisions) | | (1.35) |
1.4 Summary
Plasma is an ionized gas in which collective effects dominate over collisions.

[ λD << size , ND >> 1 .] | | (1.36) |
1.5 Occurrence of Plasmas
Gas Discharges: Fluorescent Lights, Spark gaps, arcs, welding, lighting
Controlled Fusion
Ionosphere: Ionized belt surrounding earth
Interplanetary Medium: Magnetospheres of planets and starts. Solar Wind.
Stellar Astrophysics: Stars. Pulsars. Radiation-processes.
Ion Propulsion: Advanced space drives, etc.
& Space Technology Interaction of Spacecraft with environment
Gas Lasers: Plasma discharge pumped lasers: CO2, He, Ne, HCN.
Materials Processing: Surface treatment for hardening. Crystal Growing.
Semiconductor Processing: Ion beam doping, plasma etching & sputtering.
Solid State Plasmas: Behavior of semiconductors.
For a figure locating different types of plasma in the plane of density versus temperature see for example Goldston and Rutherford Introduction to Plasma PhysicsIOP Publishing, 1995, figure 1.3 page 9. Another is at
1.6 Different Descriptions of Plasma 1. Single Particle Approach. (Incomplete in itself). Eq. of Motion. 2. Kinetic Theory. Boltzmann Equation.

| ⎡
⎣ | ∂∂t | + v. | ∂∂x | + a . | ∂∂v | ⎤
⎦ | f = | ∂f∂t | ⎞
⎠ |

col. | | | (1.37) | 3. Fluid Description. Moments, Velocity, Pressure, Currents, etc.
Uses of these. Single Particle Solutions → Orbits → Kinetic Theory Solutions → Transport Coefs. → Fluid Theory → Macroscopic Description
All descriptions should be consistent. Sometimes they are different ways of looking at the same thing.
1.6.1 Equations of Plasma Physics

| ∇. E | | = | | | ρϵ0 | | | ∇. B | | = | | 0 | | | | | | | | | ∇∧E | | = | | − | ∂B∂t | | | ∇∧B | | = | | μ0 j + | 1c2 | | ∂E∂t | | | | | | | | | | | | | | F = q ( E+ v∧B) | | | | | | | | (1.38) |
1.6.2 Self Consistency
In solving plasma problems one usually has a `circular' system:
The problem is solved only when we have a model in which all parts are self consistent. We need a `bootstrap' procedure.
Generally we have to do it in stages: * Calculate Plasma Response (to given E,B) * Get currents & charge densities * Calculate E & B for j, p.
Then put it all together.


Plasma (physics)
From Wikipedia, the free encyclopedia

For other uses, see Plasma.

Plasma globe, illustrating some of the more complex phenomena of a plasma, including filamentation. The colors are a result of relaxation of electrons in excited states to lower energy states after they have recombined with ions. These processes emit light in a spectrum characteristic of the gas being excited.

This film exhibits a number of interesting solar phenomena. The primary feature of interest is the whirling tower of plasma on the lower right limb. Continuum mechanics | | Laws[show] | Solid mechanics[show] | Fluid mechanics[show] | Rheology[show] | Scientists[show] | * v * t * e |
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles is ionized. Heating a gas may ionize its molecules or atoms (reduce or increase the number of electrons in them), thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions.[1] Ionization can be induced by other means, such as strong electromagnetic field applied with a laser or microwave generator, and is accompanied by the dissociation of molecular bonds, if present.[2]
The presence of a non-negligible number of charge carriers makes the plasmaelectrically conductive so that it responds strongly to electromagnetic fields. Plasma, therefore, has properties quite unlike those of solids, liquids, or gasesand is considered a distinct state of matter. Like gas, plasma does not have a definite shape or a definite volume unless enclosed in a container; unlike gas, under the influence of a magnetic field, it may form structures such as filaments, beams and double layers. Some common plasmas are found instars and neon signs. In the universe, plasma is the most common state of matter for ordinary matter, most of which is in the rarefied intergalactic plasma(particularly intracluster medium) and in stars. Much of the understanding of plasmas has come from the pursuit of controlled nuclear fusion and fusion power, for which plasma physics provides the scientific basis. Contents [hide] * 1 Common plasmas * 2 Plasma properties and parameters * 2.1 Definition of a plasma * 2.2 Ranges of plasma parameters * 2.3 Degree of ionization * 2.4 Temperatures * 2.4.1 Thermal vs. non-thermal plasmas * 2.5 Potentials * 2.6 Magnetization * 2.7 Comparison of plasma and gas phases * 3 Complex plasma phenomena * 3.1 Filamentation * 3.2 Shocks or double layers * 3.3 Electric fields and circuits * 3.4 Cellular structure * 3.5 Critical ionization velocity * 3.6 Ultracold plasma * 3.7 Non-neutral plasma * 3.8 Dusty plasma and grain plasma * 4 Mathematical descriptions * 4.1 Fluid model * 4.2 Kinetic model * 5 Artificial plasmas * 5.1 Generation of artificial plasma * 5.1.1 Electric arc * 5.2 Examples of industrial/commercial plasma * 5.2.1 Low-pressure discharges * 5.2.2 Atmospheric pressure * 6 History * 7 Fields of active research * 8 See also * 9 Notes * 10 References * 11 External links |
Common plasmas

Plasma trail from Space Shuttle Atlantisduring re-entry into the atmosphere, as seen from the International Space Station.
Further information: Astrophysical plasma, Interstellar medium, and Intergalactic space
Plasmas are by far the most common phase of matter in the universe, both by mass and by volume.[3] All the stars are made of plasma, and even the interstellar space is filled with a plasma, albeit a very sparse one. In our solar system, the planet Jupiter accounts for most of the non-plasma, only about 0.1% of the mass and 10−15% of the volume within the orbit ofPluto. Very small grains within a gaseous plasma will also pick up a net negative charge, so that they in turn may act like a very heavy negative ion component of the plasma (see dusty plasmas). Common forms of plasma | Artificially produced | Terrestrial plasmas | Space and astrophysicalplasmas | * Those found in plasma displays, including TVs * Inside fluorescent lamps (low energy lighting), neon signs[4] * Rocket exhaust and ion thrusters * The area in front of a spacecraft'sheat shield during re-entry into theatmosphere * Inside a corona discharge ozonegenerator * Fusion energy research * The electric arc in an arc lamp, an arc welder or plasma torch * Plasma ball (sometimes called a plasma sphere or plasma globe) * Arcs produced by Tesla coils(resonant air core transformer or disruptor coil that produces arcs similar to lightning, but withalternating current rather thanstatic electricity) * Plasmas used in semiconductor device fabrication includingreactive-ion etching, sputtering,surface cleaning and plasma-enhanced chemical vapor deposition * Laser-produced plasmas (LPP), found when high power lasers interact with materials. * Inductively coupled plasmas (ICP), formed typically in argon gas for optical emission spectroscopy ormass spectrometry * Magnetically induced plasmas (MIP), typically produced using microwaves as a resonant coupling method | * Lightning * St. Elmo's fire * Upper-atmospheric lightning * The ionosphere * The polar aurorae * Some extremely hotflames[citation needed] | * The Sun and otherstars
(plasmas heated bynuclear fusion) * The solar wind * The interplanetary medium
(space between planets) * The interstellar medium
(space between star systems) * The Intergalactic medium
(space between galaxies) * The Io-Jupiter flux tube * Accretion discs * Interstellar nebulae |
Plasma properties and parameters

Artist's rendition of the Earth'splasma fountain, showing oxygen, helium, and hydrogen ions that gush into space from regions near the Earth's poles. The faint yellow area shown above the north pole represents gas lost from Earth into space; the green area is the aurora borealis, where plasma energy pours back into the atmosphere.[5]
Definition of a plasma
Plasma is loosely described as an electrically neutral medium of positive and negative particles (i.e. the overall charge of a plasma is roughly zero). It is important to note that although they are unbound, these particles are not ‘free’. When the charges move they generate electrical currents with magnetic fields, and as a result, they are affected by each other’s fields. This governs their collective behavior with many degrees of freedom.[2][6] A definition can have three criteria:[7][8] 1. The plasma approximation: Charged particles must be close enough together that each particle influences many nearby charged particles, rather than just interacting with the closest particle (these collective effects are a distinguishing feature of a plasma). The plasma approximation is valid when the number of charge carriers within the sphere of influence (called the Debye sphere whose radius is the Debye screening length) of a particular particle is higher than unity to provide collective behavior of the charged particles. The average number of particles in the Debye sphere is given by the plasma parameter, "Λ" (the Greek letter Lambda). 2. Bulk interactions: The Debye screening length (defined above) is short compared to the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, where boundary effects may take place. When this criterion is satisfied, the plasma is quasineutral. 3. Plasma frequency: The electron plasma frequency (measuring plasma oscillations of the electrons) is large compared to the electron-neutral collision frequency (measuring frequency of collisions between electrons and neutral particles). When this condition is valid, electrostatic interactions dominate over the processes of ordinary gas kinetics.
Ranges of plasma parameters
Plasma parameters can take on values varying by many orders of magnitude, but the properties of plasmas with apparently disparate parameters may be very similar (see plasma scaling). The following chart considers only conventional atomic plasmas and not exotic phenomena like quark gluon plasmas:

Range of plasmas. Density increases upwards, temperature increases towards the right. The free electrons in a metal may be considered an electron plasma.[9] Typical ranges of plasma parameters: orders of magnitude (OOM) | Characteristic | Terrestrial plasmas | Cosmic plasmas | Size in meters | 10−6 m (lab plasmas) to
102 m (lightning) (~8 OOM) | 10−6 m (spacecraft sheath) to
1025 m (intergalactic nebula) (~31 OOM) | Lifetime in seconds | 10−12 s (laser-produced plasma) to
107 s (fluorescent lights) (~19 OOM) | 101 s (solar flares) to
1017 s (intergalactic plasma) (~16 OOM) | Density in particles per cubic meter | 107 m−3 to
1032 m−3 (inertial confinement plasma) | 1 m−3 (intergalactic medium) to
1030 m−3 (stellar core) | Temperature in kelvins | ~0 K (crystalline non-neutral plasma[10]) to
108 K (magnetic fusion plasma) | 102 K (aurora) to
107 K (solar core) | Magnetic fields in teslas | 10−4 T (lab plasma) to
103 T (pulsed-power plasma) | 10−12 T (intergalactic medium) to
1011 T (near neutron stars) |
Degree of ionization
For plasma to exist, ionization is necessary. The term "plasma density" by itself usually refers to the "electron density", that is, the number of free electrons per unit volume. The degree of ionization of a plasma is the proportion of atoms that have lost or gained electrons, and is controlled mostly by the temperature. Even a partially ionized gas in which as little as 1% of the particles are ionized can have the characteristics of a plasma (i.e., response to magnetic fields and high electrical conductivity). The degree of ionization, αis defined as α = ni/(ni + na) where ni is the number density of ions and na is the number density of neutral atoms. The electron densityis related to this by the average charge state <Z> of the ions through ne = <Z> ni where ne is the number density of electrons.
See also: Nonthermal plasma
Plasma temperature is commonly measured in kelvins or electronvolts and is, informally, a measure of the thermal kinetic energy per particle. Very high temperatures are usually needed to sustain ionization, which is a defining feature of a plasma. The degree of plasma ionization is determined by the "electron temperature" relative to the ionization energy, (and more weakly by the density), in a relationship called the Saha equation. At low temperatures, ions and electrons tend to recombine into bound states—atoms,[11] and the plasma will eventually become a gas.
In most cases the electrons are close enough to thermal equilibrium that their temperature is relatively well-defined, even when there is a significant deviation from a Maxwellian energy distribution function, for example, due to UV radiation, energetic particles, or strongelectric fields. Because of the large difference in mass, the electrons come to thermodynamic equilibrium amongst themselves much faster than they come into equilibrium with the ions or neutral atoms. For this reason, the "ion temperature" may be very different from (usually lower than) the "electron temperature". This is especially common in weakly ionized technological plasmas, where the ions are often near the ambient temperature.
Thermal vs. non-thermal plasmas
Based on the relative temperatures of the electrons, ions and neutrals, plasmas are classified as "thermal" or "non-thermal". Thermal plasmas have electrons and the heavy particles at the same temperature, i.e., they are in thermal equilibrium with each other. Non-thermal plasmas on the other hand have the ions and neutrals at a much lower temperature (normally room temperature), whereas electrons are much "hotter".
A plasma is sometimes referred to as being "hot" if it is nearly fully ionized, or "cold" if only a small fraction (for example 1%) of the gas molecules are ionized, but other definitions of the terms "hot plasma" and "cold plasma" are common. Even in a "cold" plasma, the electron temperature is still typically several thousand degrees Celsius. Plasmas utilized in "plasma technology" ("technological plasmas") are usually cold in this sense.

Lightning is an example of plasma present at Earth's surface. Typically, lightning discharges 30,000 amperes at up to 100 million volts, and emits light, radio waves, X-rays and even gamma rays.[12] Plasma temperatures in lightning can approach ~28,000 kelvin and electron densities may exceed 1024 m−3.
Since plasmas are very good conductors, electric potentials play an important role. The potential as it exists on average in the space between charged particles, independent of the question of how it can be measured, is called the "plasma potential", or the "space potential". If an electrode is inserted into a plasma, its potential will generally lie considerably below the plasma potential due to what is termed a Debye sheath. The good electrical conductivity of plasmas makes their electric fields very small. This results in the important concept of "quasineutrality", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma (ne = <Z>ni), but on the scale of the Debye length there can be charge imbalance. In the special case that double layers are formed, the charge separation can extend some tens of Debye lengths.
The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the "Boltzmann relation":
Differentiating this relation provides a means to calculate the electric field from the density:
It is possible to produce a plasma that is not quasineutral. An electron beam, for example, has only negative charges. The density of a non-neutral plasma must generally be very low, or it must be very small, otherwise it will be dissipated by the repulsive electrostatic force.
In astrophysical plasmas, Debye screening prevents electric fields from directly affecting the plasma over large distances, i.e., greater than the Debye length. However, the existence of charged particles causes the plasma to generate and can be affected by magnetic fields. This can and does cause extremely complex behavior, such as the generation of plasma double layers, an object that separates charge over a few tens of Debye lengths. The dynamics of plasmas interacting with external and self-generated magnetic fields are studied in the academic discipline of magnetohydrodynamics.
Plasma with a magnetic field strong enough to influence the motion of the charged particles is said to be magnetized. A common quantitative criterion is that a particle on average completes at least one gyration around the magnetic field before making a collision, i.e., ωce/νcoll > 1, where ωce is the "electron gyrofrequency" and νcoll is the "electron collision rate". It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are anisotropic, meaning that their properties in the direction parallel to the magnetic field are different from those perpendicular to it. While electric fields in plasmas are usually small due to the high conductivity, the electric field associated with a plasma moving in a magnetic field is given by E = −v × B (where E is the electric field, v is the velocity, and B is the magnetic field), and is not affected by Debye shielding.[13]
Comparison of plasma and gas phases
Plasma is often called the fourth state of matter. It is distinct from other lower-energy states of matter; most commonly solid, liquid, andgas. Although it is closely related to the gas phase in that it also has no definite form or volume, it differs in a number of ways, including the following: Property | Gas | Plasma | Electrical conductivity | Very low: Air is an excellent insulator until it breaks down into plasma at electric field strengths above 30 kilovolts per centimeter.[14] | Usually very high: For many purposes, the conductivity of a plasma may be treated as infinite. | Independently acting species | One: All gas particles behave in a similar way, influenced by gravityand by collisions with one another. | Two or three: Electrons, ions, protons and neutrons can be distinguished by the sign and value of their charge so that they behave independently in many circumstances, with different bulk velocities and temperatures, allowing phenomena such as new types of waves and instabilities. | Velocity distribution | Maxwellian: Collisions usually lead to a Maxwellian velocity distribution of all gas particles, with very few relatively fast particles. | Often non-Maxwellian: Collisional interactions are often weak in hot plasmas and external forcing can drive the plasma far from local equilibrium and lead to a significant population of unusually fast particles. | Interactions | Binary: Two-particle collisions are the rule, three-body collisions extremely rare. | Collective: Waves, or organized motion of plasma, are very important because the particles can interact at long ranges through the electric and magnetic forces. |
Complex plasma phenomena

The remnant of "Tycho's Supernova", a huge ball of expanding plasma. The outer shell shown in blue is X-ray emission by high-speed electrons.
Although the underlying equations governing plasmas are relatively simple, plasma behavior is extraordinarily varied and subtle: the emergence of unexpected behavior from a simple model is a typical feature of a complex system. Such systems lie in some sense on the boundary between ordered and disordered behavior and cannot typically be described either by simple, smooth, mathematical functions, or by pure randomness. The spontaneous formation of interesting spatial features on a wide range of length scales is one manifestation of plasma complexity. The features are interesting, for example, because they are very sharp, spatially intermittent (the distance between features is much larger than the features themselves), or have a fractal form. Many of these features were first studied in the laboratory, and have subsequently been recognized throughout the universe. Examples of complexity and complex structures in plasmas include:
Striations or string-like structures[15], also known as birkeland currents, are seen in many plasmas, like the plasma ball, the aurora,[16] lightning,[17]electric arcs, solar flares,[18] and supernova remnants.[19] They are sometimes associated with larger current densities, and the interaction with the magnetic field can form a magnetic rope structure.[20] High power microwave breakdown at atmospheric pressure also leads to the formation of filamentary structures.[21] (See also Plasma pinch)
Filamentation also refers to the self-focusing of a high power laser pulse. At high powers, the nonlinear part of the index of refraction becomes important and causes a higher index of refraction in the center of the laser beam, where the laser is brighter than at the edges, causing a feedback that focuses the laser even more. The tighter focused laser has a higher peak brightness (irradiance) that forms a plasma. The plasma has an index of refraction lower than one, and causes a defocusing of the laser beam. The interplay of the focusing index of refraction, and the defocusing plasma makes the formation of a long filament of plasma that can be micrometers to kilometers in length.[22] (See also Filament propagation)
Shocks or double layers
Plasma properties change rapidly (within a few Debye lengths) across a two-dimensional sheet in the presence of a (moving) shock or (stationary) double layer. Double layers involve localized charge separation, which causes a large potential difference across the layer, but does not generate an electric field outside the layer. Double layers separate adjacent plasma regions with different physical characteristics, and are often found in current carrying plasmas. They accelerate both ions and electrons.
Electric fields and circuits
Quasineutrality of a plasma requires that plasma currents close on themselves in electric circuits. Such circuits follow Kirchhoff's circuit laws and possess a resistance and inductance. These circuits must generally be treated as a strongly coupled system, with the behavior in each plasma region dependent on the entire circuit. It is this strong coupling between system elements, together with nonlinearity, which may lead to complex behavior. Electrical circuits in plasmas store inductive (magnetic) energy, and should the circuit be disrupted, for example, by a plasma instability, the inductive energy will be released as plasma heating and acceleration. This is a common explanation for the heating that takes place in the solar corona. Electric currents, and in particular, magnetic-field-aligned electric currents (which are sometimes generically referred to as "Birkeland currents"), are also observed in the Earth's aurora, and in plasma filaments.
Cellular structure
Narrow sheets with sharp gradients may separate regions with different properties such as magnetization, density and temperature, resulting in cell-like regions. Examples include the magnetosphere, heliosphere, and heliospheric current sheet. Hannes Alfvén wrote: "From the cosmological point of view, the most important new space research discovery is probably the cellular structure of space. As has been seen in every region of space accessible to in situ measurements, there are a number of 'cell walls', sheets of electric currents, which divide space into compartments with different magnetization, temperature, density, etc."[23]
Critical ionization velocity
The critical ionization velocity is the relative velocity between an ionized plasma and a neutral gas, above which a runaway ionization process takes place. The critical ionization process is a quite general mechanism for the conversion of the kinetic energy of a rapidly streaming gas into ionization and plasma thermal energy. Critical phenomena in general are typical of complex systems, and may lead to sharp spatial or temporal features.
Ultracold plasma
Ultracold plasmas are created in a magneto-optical trap (MOT) by trapping and cooling neutral atoms, to temperatures of 1 mK or lower, and then using another laser to ionize the atoms by giving each of the outermost electrons just enough energy to escape the electrical attraction of its parent ion.
One advantage of ultracold plasmas are their well characterized and tunable initial conditions, including their size and electron temperature. By adjusting the wavelength of the ionizing laser, the kinetic energy of the liberated electrons can be tuned as low as 0.1 K, a limit set by the frequency bandwidth of the laser pulse. The ions inherit the millikelvin temperatures of the neutral atoms, but are quickly heated through a process known as disorder induced heating (DIH). This type of non-equilibrium ultracold plasma evolves rapidly, and displays many other interesting phenomena.[24]
One of the metastable states of a strongly nonideal plasma is Rydberg matter, which forms upon condensation of excited atoms.
Non-neutral plasma
The strength and range of the electric force and the good conductivity of plasmas usually ensure that the densities of positive and negative charges in any sizeable region are equal ("quasineutrality"). A plasma with a significant excess of charge density, or, in the extreme case, is composed of a single species, is called a non-neutral plasma. In such a plasma, electric fields play a dominant role. Examples are charged particle beams, an electron cloud in a Penning trap and positron plasmas.[25]
Dusty plasma and grain plasma
A dusty plasma contains tiny charged particles of dust (typically found in space). The dust particles acquire high charges and interact with each other. A plasma that contains larger particles is called grain plasma. Under laboratory conditions, dusty plasmas are also called complex plasmas. [26]
Mathematical descriptions

The complex self-constricting magnetic field lines and current paths in a field-aligned Birkeland currentthat can develop in a plasma.[27]
Main article: Plasma modeling
To completely describe the state of a plasma, we would need to write down all the particle locations and velocities and describe the electromagnetic field in the plasma region. However, it is generally not practical or necessary to keep track of all the particles in a plasma. Therefore, plasma physicists commonly use less detailed descriptions, of which there are two main types:
Fluid model
Fluid models describe plasmas in terms of smoothed quantities, like density and averaged velocity around each position (see Plasma parameters). One simple fluid model, magnetohydrodynamics, treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier–Stokes equations. A more general description is the two-fluid plasma picture, where the ions and electrons are described separately. Fluid models are often accurate when collisionality is sufficiently high to keep the plasma velocity distribution close to a Maxwell–Boltzmann distribution. Because fluid models usually describe the plasma in terms of a single flow at a certain temperature at each spatial location, they can neither capture velocity space structures like beams or double layers, nor resolve wave-particle effects.
Kinetic model
Kinetic models describe the particle velocity distribution function at each point in the plasma and therefore do not need to assume a Maxwell–Boltzmann distribution. A kinetic description is often necessary for collisionless plasmas. There are two common approaches to kinetic description of a plasma. One is based on representing the smoothed distribution function on a grid in velocity and position. The other, known as the particle-in-cell (PIC) technique, includes kinetic information by following the trajectories of a large number of individual particles. Kinetic models are generally more computationally intensive than fluid models. The Vlasov equation may be used to describe the dynamics of a system of charged particles interacting with an electromagnetic field. In magnetized plasmas, a gyrokinetic approach can substantially reduce the computational expense of a fully kinetic simulation.
Artificial plasmas
Most artificial plasmas are generated by the application of electric and/or magnetic fields. Plasma generated in a laboratory setting and for industrial use can be generally categorized by: * The type of power source used to generate the plasma—DC, RF and microwave * The pressure they operate at—vacuum pressure (< 10 mTorr or 1 Pa), moderate pressure (~ 1 Torr or 100 Pa), atmospheric pressure (760 Torr or 100 kPa) * The degree of ionization within the plasma—fully, partially, or weakly ionized * The temperature relationships within the plasma—thermal plasma (Te = Tion = Tgas), non-thermal or "cold" plasma (Te >> Tion =Tgas) * The electrode configuration used to generate the plasma * The magnetization of the particles within the plasma—magnetized (both ion and electrons are trapped in Larmor orbits by the magnetic field), partially magnetized (the electrons but not the ions are trapped by the magnetic field), non-magnetized (the magnetic field is too weak to trap the particles in orbits but may generate Lorentz forces) * The application
Generation of artificial plasma

Artificial plasma produced in air by aJacob's Ladder
Just like the many uses of plasma, there are several means for its generation, however, one principle is common to all of them: there must be energy input to produce and sustain it.[28]For this case, plasma is generated when an electrical current is applied across a dielectric gas or fluid (an electrically non-conducting material) as can be seen in the image below, which shows a discharge tube as a simple example (DC used for simplicity).

Cascade process of ionization. Electrons are ‘e−’, neutral atoms ‘o’, and cations ‘+’.
The potential difference and subsequent electric field pull the bound electrons (negative) toward the anode (positive electrode) while the cathode (negative electrode) pulls the nucleus.[29] As the voltage increases, the current stresses the material (by electric polarization) beyond its dielectric limit (termed strength) into a stage of electrical breakdown, marked by an electric spark, where the material transforms from being an insulator into aconductor (as it becomes increasingly ionized). This is a stage of avalanching ionization, where collisions between electrons and neutral gas atoms create more ions and electrons (as can be seen in the figure on the right). The first impact of an electron on an atom results in one ion and two electrons. Therefore, the number of charged particles increases rapidly (in the millions) only “after about 20 successive sets of collisions”,[30] mainly due to a small mean free path (average distance travelled between collisions).
Electric arc
With ample current density and ionization, this forms a luminous electric arc (essentiallylightning) between the electrodes.[Note 1] Electrical resistance along the continuous electric arc creates heat, which ionizes more gas molecules (where degree of ionization is determined by temperature), and as per the sequence: solid-liquid-gas-plasma, the gas is gradually turned into a thermal plasma.[Note 2] A thermal plasma is in thermal equilibrium, which is to say that the temperature is relatively homogeneous throughout the heavy particles (i.e. atoms, molecules and ions) and electrons. This is so because when thermal plasmas are generated, electrical energy is given to electrons, which, due to their great mobility and large numbers, are able to disperse it rapidly and by elastic collision (without energy loss) to the heavy particles.[31][Note 3]
Examples of industrial/commercial plasma
Because of their sizable temperature and density ranges, plasmas find applications in many fields of research, technology and industry. For example, in: industrial and extractive metallurgy,[31] surface treatments such as thermal spraying (coating), etching in microelectronics,[32] metal cutting[33] and welding; as well as in everyday vehicle exhaust cleanup and fluorescent/luminescentlamps,[28] while even playing a part in supersonic combustion engines for aerospace engineering.[34]
Low-pressure discharges * Glow discharge plasmas: non-thermal plasmas generated by the application of DC or low frequency RF (<100 kHz) electric field to the gap between two metal electrodes. Probably the most common plasma; this is the type of plasma generated within fluorescent light tubes.[35] * Capacitively coupled plasma (CCP): similar to glow discharge plasmas, but generated with high frequency RF electric fields, typically 13.56 MHz. These differ from glow discharges in that the sheaths are much less intense. These are widely used in the microfabrication and integrated circuit manufacturing industries for plasma etching and plasma enhanced chemical vapor deposition.[36] * Cascaded Arc Plasma Source: a device to produce low temperature (~1eV) high density plasmas. * Inductively coupled plasma (ICP): similar to a CCP and with similar applications but the electrode consists of a coil wrapped around the discharge volume that inductively excites the plasma.[citation needed] * Wave heated plasma: similar to CCP and ICP in that it is typically RF (or microwave), but is heated by both electrostatic and electromagnetic means. Examples are helicon discharge, electron cyclotron resonance (ECR), and ion cyclotron resonance (ICR). These typically require a coaxial magnetic field for wave propagation.[citation needed]
Atmospheric pressure * Arc discharge: this is a high power thermal discharge of very high temperature (~10,000 K). It can be generated using various power supplies. It is commonly used in metallurgical processes. For example, it is used to melt rocks containing Al2O3 to producealuminium. * Corona discharge: this is a non-thermal discharge generated by the application of high voltage to sharp electrode tips. It is commonly used in ozone generators and particle precipitators. * Dielectric barrier discharge (DBD): this is a non-thermal discharge generated by the application of high voltages across small gaps wherein a non-conducting coating prevents the transition of the plasma discharge into an arc. It is often mislabeled 'Corona' discharge in industry and has similar application to corona discharges. It is also widely used in the web treatment of fabrics.[37] The application of the discharge to synthetic fabrics and plastics functionalizes the surface and allows for paints, glues and similar materials to adhere.[38] * Capacitive discharge: this is a nonthermal plasma generated by the application of RF power (e.g., 13.56 MHz) to one powered electrode, with a grounded electrode held at a small separation distance on the order of 1 cm. Such discharges are commonly stabilized using a noble gas such as helium or argon.[39]
Plasma was first identified in a Crookes tube, and so described by Sir William Crookes in 1879 (he called it "radiant matter").[40] The nature of the Crookes tube "cathode ray" matter was subsequently identified by British physicist Sir J.J. Thomson in 1897.[41] The term "plasma" was coined by Irving Langmuir in 1928,[42] perhaps because the glowing discharge molds itself to the shape of the Crooks tube (Gr. πλάσμα – a thing moulded or formed).[43] Langmuir described his observations as:
Except near the electrodes, where there are sheaths containing very few electrons, the ionized gas contains ions and electrons in about equal numbers so that the resultant space charge is very small. We shall use the name plasma to describe this region containing balanced charges of ions and electrons.[42]
Fields of active research

Hall effect thruster. The electric field in a plasma double layer is so effective at accelerating ions that electric fields are used in ion drives.
This is just a partial list of topics. See list of plasma (physics) articles. A more complete and organized list can be found on the web site Plasma science and technology.[44] * Plasma theory * Plasma equilibria and stability * Plasma interactions with waves and beams * Guiding center * Adiabatic invariant * Debye sheath * Coulomb collision * Plasmas in nature * The Earth's ionosphere * Northern and southern (polar) lights * Space plasmas, e.g. Earth'splasmasphere (an inner portion of the magnetosphere dense with plasma) * Astrophysical plasma * Interplanetary medium * Industrial plasmas * Plasma chemistry * Plasma processing * Plasma spray * Plasma display * Plasma sources * Dusty plasmas | * Plasma diagnostics * Thomson scattering * Langmuir probe * Spectroscopy * Interferometry * Ionospheric heating * Incoherent scatter radar * Plasma applications * Fusion power * Magnetic fusion energy (MFE) —tokamak, stellarator, reversed field pinch, magnetic mirror, dense plasma focus * Inertial fusion energy (IFE) (also Inertial confinement fusion — ICF) * Plasma-based weaponry * Ion implantation * Ion thruster * MAGPIE (short for Mega Ampere Generator for Plasma Implosion Experiments) * Plasma ashing * Food processing (nonthermal plasma, aka "cold plasma") * Plasma arc waste disposal, convert waste into reusable material with plasma. * Plasma acceleration * Plasma medicine (e. g. Dentistry [45]) * Plasma window |
Definition: A superfluid is a special phase of matter in which, when cooled to temperatures near absolute zero, the molecules exhibit strange quantum effects.
Some superfluids, such as helium-4 (helium with 4 nucleons - 2 protons & 2 neutrons), are bosons and therefore form a Bose-Einstein condensate when cooled into liquid form.
One effect of this is that the viscosity of superfluid helium-4 becomes zero, meaning that normal rules of surface tension, such as capillarity, are no longer obeyed. A superfluid in a glass tube will literally "crawl" up the side of the tube in a thin film because of this property.
Other superfluids, such as helium-3, are fermions, but they can also exhibit superfluid properties due to other quantum effects that are part of the BCS theory of superconducitivity.
Superfluid - key concepts
As most people know (or don't know, whichever is the case) the component of an electrical circuit that causes energy loss is called "resistance," which can be defined as a materials opposition to current being passed through it. Usually, this resistance results in the production of heat, sound, or another form of energy. In many cases, this transformation of energy is useful in such applications as toasters, heaters, and light bulbs. Even though it is a useful property, resistance often gets in the way of performance in such cases as high voltage transmission wires, electric motor output, and other cases where internal system energy losses are unwanted. This is where the phenomenon of superconducting materials comes into play and may present the solution to this energy loss problem.
Superconductors are materials that display zero resistance under certain conditions. These conditions are called the "critical temperature" and "critical field," denoted Tc and Hc respectively. The Tc is the highest temperature state the material can attain and remain superconductive. The Hc is the highest magnetic field the material can be exposed to before reverting to its normal magnetic state. Within the substances currently known to superconduct, there is a divide between what has come to be called type I and type II superconductors. Type I are composed of pure substances, usually metals, and type II are composite compounds, usually some sort of ceramic.
Additional differences between type I and type II exist, mainly that type II display superconducting qualities at much higher temperatures and can remain superconductive in the presence of much higher magnetic fields. While type I have Tc's that hover just a few degrees from absolute zero, type II can have Tc's of over 130 K. The graph below shows how type I and type II superconductors compare as related to Tc and Hc:
The difference in magnetic fields is also quite large. Type I superconductors can stand fields up to approximately 2000 Gauss, which translates to about .2 Tesla, while type II can with stand fields of up to several hundred thousand Gauss, which translates to more than 10 Tesla. The magnetic field for any temperature below the Tc is given by the follwoing eqution:
Bc ≈ Bc(0) * [1 - (T/Tc)^2] efinition: A superconductor is an element or metallic alloy which, when cooled to nearabsolute zero, dramatically lose all electrical resistance. In principle, superconductors can allow electrical current to flow without any energy loss (although, in practice, an ideal superconductor is very hard to produce). This type of current is called a supercurrent.
In addition, superconductors exhibit the Meissner effect in which they cancel all magnetic flux inside, becoming perfectly diamagnetic (discovered in 1933). In this case, the magnetic field lines actually travel around the cooled superconductor. It is this property of superconductors which is frequently used in magnetic levitation experiments.
Superconductivity was first discovered in 1911, when mercury was cooled to 4 degrees Kelvin by Dutch physicist Heike Kamerlingh Onnes, which earned him the 1913 Nobel Prize in physics. In the years since, this field has greatly expanded and many other forms of superconductors have been discovered. The basic theory of superconductivity, BCS Theory, earned the scientists - John Bardeen, Leon Cooper, and John Schrieffer - the 1972 Nobel Prize in physics. A portion of the 1973 Nobel Prize in physics went to Brian Josephson, also for work with superconductivity.
Bose–Einstein correlations
From Wikipedia, the free encyclopedia
In physics, Bose–Einstein correlations[1][2] are correlations between identical bosons. They have important applications in astronomy, optics, particle and nuclear physics. Contents [hide] * 1 From intensity interferometry to Bose–Einstein correlations * 2 Bose–Einstein correlations and quantum coherence * 3 Quantum coherence in strong interactions * 4 Bose-Einstein correlations and the principle of identical particles in particle physics * 5 References |
[edit]From intensity interferometry to Bose–Einstein correlations
The interference between two (or more) waves establishes a correlation between these waves. In particle physics, in particular, where to each particle there is associated a wave, we encounter thus interference and correlations between two (or more) particles, described mathematically by second or higher order correlation functions[3]. These correlations have quite specific properties for identical particles. We then distinguish Bose–Einstein correlations for bosons and Fermi–Dirac correlations for fermions. While in Fermi–Dirac second order correlations the particles are antibunched, in Bose–Einstein correlations (BEC)[4] they are bunched. Another distinction between Bose–Einstein and Fermi–Dirac correlation is that only BEC can present quantum coherence (cf. below).
In optics two beams of light are said to interfere coherently, when the phase difference between their waves is constant; if this phase difference is random or changing the beams are incoherent.
The coherent superposition of wave amplitudes is called first order interference. In analogy to that we have intensity or second orderHanbury Brown and Twiss (HBT) interference, which generalizes the interference between amplitudes to that between squares of amplitudes, i.e. between intensities.
In optics amplitude interferometry is used for the determination of lengths, surface irregularities and indexes of refraction; intensity interferometry, besides presenting in certain cases technical advantages (like stability) as compared with amplitude interferometry, allows also the determination of quantum coherence of sources.
[edit]Bose–Einstein correlations and quantum coherence
The concept of higher order or quantum coherence of sources was introduced in quantum optics by Glauber[5]. While initially it was used mainly to explain the functioning of masers and lasers, it was soon realized that it had important applications in other fields of physics, as well: under appropriate conditions quantum coherence leads to Bose–Einstein condensation. As the names suggest Bose–Einstein correlations and Bose–Einstein condensation are both consequences of Bose–Einstein statistics and thus applicable not only to photons but to any kind of bosons. Thus Bose–Einstein condensation is at the origin of such important condensed matter phenomena as superconductivity and superfluidity, and Bose–Einstein correlations manifest themselves also in hadron interferometry.
Almost in parallel to the invention by Hanbury-Brown and Twiss of intensity interferometry in optics Gerson Goldhaber, Sulamith Goldhaber, Wonyong Lee, and Abraham Pais (GGLP) discovered[6] that identically charged pions produced in antiproton-proton annihilation processes were bunched, while pions of opposite charges were not. They interpreted this effect as due to Bose–Einstein statistics. Subsequently[7] it was realized that the HBT effect is also a Bose–Einstein correlation effect, that of identical photons[8].
The most general theoretical formalism for Bose–Einstein correlations in subnuclear physics is the quantum statistical approach[9],[10][ based on the classical current[11] and coherent state[12],[13] formalism: it includes quantum coherence, correlation lengths and correlation times.
Starting with the 1980s BEC has become a subject of current interest in high-energy physics and at present meetings entirely dedicated to this subject take place[14]. One reason for this interest is the fact that BEC are up to now the only method for the determination of sizes and lifetimes of sources of elementary particles. This is of particular interest for the ongoing search of quark matter in the laboratory: To reach this phase of matter a critical energy density is necessary. To measure this energy density one must determine the volume of the fireball in which this matter is supposed to have been generated and this means the determination of the size of the source; that can be achieved by the method of intensity interferometry. Furthermore a phase of matter means a quasi-stable state, i.e. a state which lives longer than the duration of the collision that gave rise to this state. This means that we have to measure the lifetime of the new system, which can again be obtained by BEC only.
[edit]Quantum coherence in strong interactions
Bose–Einstein correlations of hadrons can also be used for the determination of quantum coherence in strong interactions[15],[16],.To detect and measure coherence in Bose–Einstein correlations in nuclear and particle physics has been quite a difficult task, because these correlations are rather insensitive to even large admixtures of coherence, because of other competing processes which could simulate this effect and also because often experimentalists did not use the appropriate formalism in the interpretation of their data[17].
The most clear evidence[18] for coherence in BEC comes from the measurement of higher order correlations in antiproton-proton reactions at the CERN SPS collider by the UA1-Minium Bias collaboration[19]. This experiment has also a particular significance because it tests in quite an unusual way the predictions of quantum statistics as applied to BEC: it represents an unsuccessful attempt of falsification of the theory [1]. Besides these practical applications of BEC in interferometry, the quantum statistical approach [10] has led to quite an unexpected heuristic application, related to the principle of identical particles, the fundamental starting point of BEC.
[edit]Bose-Einstein correlations and the principle of identical particles in particle physics
As long as the number of particles of a quantum system is fixed the system can be described by a wave function, which contains all the information about the state of that system. This is the first quantisation approach and historically Bose–Einstein and Fermi–Dirac correlations were derived through this wave function formalism. In high-energy physics, however, one is faced with processes where particles are produced and absorbed and this demands a more general field theoretical approach called second quantisation. This is the approach on which quantum optics is based and it is only through this more general approach that quantum statistical coherence, lasers and condensates could be interpreted or discovered. Another more recent phenomenon discovered via this approach is the Bose–Einstein correlation between particles and anti-particles.
The wave function of two identical particles is symmetric or antisymmetric with respect to the permutation of the two particles, depending whether one considers identical bosons or identical fermions. For non-identical particles there is no permutation symmetry and according to the wave function formalism there should be no Bose–Einstein or Fermi–Dirac correlation between these particles. This applies in particular for a pair of particles made of a positive and a negative pion. However this is true only in a first approximation: If one considers the possibility that a positive and a negative pion are virtually related in the sense that they can annihilate and transform into a pair of two neutral pions (or two photons), i.e. a pair of identical particles, we are faced with a more complex situation, which has to be handled within the second quantisation approach. This leads[20],[21] to a new kind of Bose–Einstein correlations, namely between positive and negative pions, albeit much weaker than that between two positive or two negative pions. On the other hand there is no such correlation between a charged and a neutral pion. Loosely speaking a positive and a negative pion are less unequal than a positive and a neutral pion. Similarly the BEC between two neutral pions are somewhat stronger than those between two identically charged ones: in other words two neutral pions are “more identical” than two negative (positive) pions.
The surprising nature of these special BEC effects made headlines in the literature[22]. These effects illustrate the superiority of the field theoretical second quantisation approach as compared with the wave function formalism. They also illustrate the limitations of the analogy between optical and particle physics interferometry: They prove that Bose–Einstein correlations between two photons are different from those between two identically charged pions, an issue which had led to misunderstandings in the theoretical literature and which was elucidated in [23] (see also Ref. [1]).

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...CORPUS CHRISTI SCHOOL END OF THIRD TERM EXAMINATION SECTION A (50 MARKS) 1) How loud or soft a music is termed ………………………….. a. Dynamic b. Rhythm c. pitch 2. Using alphabet to create patterns by arranging and pasting is called …………………………….. a. letter colle b. frottage c. drawing 3. The combination of long and short sounds in music is called…………………….. a. dynamics b. rhythm c. pitch 4. In music how high or low the music is termed ………………………………. a. dynamics b. rhythm c. pitch 5. In dancing when someone lift the arm high and wave in the air it can be referred to as ….............. a. instruments b. ensemble c. gesture 6. A design or a pattern used as a decoration is called ………………………………… a. appliqué b. pattern c. motif 7. A type of needle work in which small pieces of fabric are sewn or stuck in a pattern onto a larger piece is ……………………………….. a. appliqué b. pattern c. motif 8. ………………………………… is the expression of feelings and ideas using tools like pencil, crayon, and charcoal on a flat surface. a. Drawing b. Frottage c. Letter colle 9. A way in which something such as lines, shapes, colours are arranged to form a design is called ……………………………………….. a. colouring b. drawing c. pattern making 10. Rubbing the surface of paper against a rough surface using pencil, crayon or charcoal is called ………………………………………… a. letter colle b. frottage c. copying 11. Which of these is used for measuring? a.......

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...parliament.[157] The executive branch of the Indian government consists of the president, the vice-president, and the Council of Ministers—the cabinet being its executive committee—headed by the prime minister. Any minister holding a portfolio must be a member of one of the houses of parliament.[154] In the Indian parliamentary system, the executive is subordinate to the legislature; the prime minister and his council directly responsible to the lower house of the parliament.[159] Legislative: The legislature of India is the bicameral parliament. It operates under a Westminster-style parliamentary system and comprises the upper house called the Rajya Sabha ("Council of States") and the lower called the Lok Sabha ("House of the People").[160] The Rajya Sabha is a permanent body that has 245 members who serve in staggered six-year terms.[161] Most are elected indirectly by the state and territorial legislatures in numbers proportional to their state's share of the national population.[158] All but two of the Lok Sabha's 545 members are directly elected by popular vote; they represent individual constituencies via five-year terms.[162] The remaining two members are nominated by the president from among the Anglo-Indian community, in case the president decides that they are not adequately represented.[163] Judicial: India has a unitary three-tier independent judiciary[164] that comprises the Supreme Court, headed by the Chief Justice of India, 21 High Courts, and a large......

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...Associate Level Material Appendix B Sexual Response Cycles Use your own words to complete the table below with the experiences and changes in anatomy of males and females during the various sexual response phases. |Stage of Masters |Male Experience |Female Experience | |and Johnson |and Anatomy |and Anatomy | |Sexual Response Cycle | | | |Excitement Phase |During the experiment phase, the male will become |During the experimental phase, the female is | | |sexually aroused by mental or physical |sexually aroused by physical or mental | | |stimulation. This will result in a penile |stimulation. Increased blood flow to the | | |erection, which is due to the increase in blood |vagina will lubricate the vaginal walls, | | |flow to the corpora cavernosa. |which causes swelling of the female’s | | | |external genitals. The vaginal lips spread ...

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...1. I chose a story about domesticating wild animals and its history that starts 30 to 40 thousand years ago. Link: 2. The Onion`s argument is that people are domesticating wild animals, like wolves, in order to “comfort” children whose parents had separated. According to The Onion, our ancient ancestors first tamed and bred gray wolves 30 to 40 thousand years as a means of providing their children with a companion to keep them occupied and feeling less alone as they dealt with the emotional trauma of their mother and father splitting up. The funnies part of this article is in its arguments about taming wild animals. Nowadays, we can rarely see a tamed wolf, all because they are wild and dangerous. I can`t possibly imagine a wolf instead of a cat for example, as a friend for children. In my opinion, The Onion`s article is parodying a story about Mowgli from “The Jungle Book” series, where a boy whose name is Mowgli was found as a baby and raised by the wolves. 3. I chose this story because I found it unrealistic and funny. It also reminded me about a story of Mowgli that I read in my childhood. 4. I know that people always tried to tame different animals, including wild ones. Taming a wild horse is difficult; taming a wild elephant is even more difficult. However it`s almost impossible to tame a wild hunter, like wolf or lion, unless you do it since their first days of......

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...English Grammar in Use A self-study reference and practice book for intermediate learners of English Fourth Edition with answers Raymond Murphy CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Information on this title: Fourth Edition © Cambridge University Press 2012 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. English Grammar in Use first published 1985 Fourth edition 2012 4th printing 2013 Printed in Italy by L.E.G.O. S.p.A. A catalogue record for this publication is available from the British Library ISBN 978-0-521-18906-4 ISBN 978-0-521-18908-8 ISBN 978-0-521-18939-2 ISBN 978-0-511-96173-1 ISBN 978-1-107-64138-9 Edition with answers Edition without answers Edition with answers and CD-ROM Online access code pack Online access code pack and book with answers Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Information regarding prices, travel timetables and other......

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...STANLEY S. NYAMAWI, P.O. BOX 67 080200, MALINDI, KENYA. 21TH: OCTOBER: 2013. Dear Mr. Habeni, RE: MAKAO YA KUISHI Salam nyingi mwanzo, za heri, fanaka, maendeleo na siku nyingi hapa Duniani za kuishi ili mzidi kutuongoza kama watoto wenu maishani. Natoa shukruni zangu zadhati nazisizo na kifani, kwanza kwa kunikubali mimi kama mwanao, sawa na Yule aliye ni zaa, sijaona tofauti. Nami na kukubali kama Baba wa dhati, daima siku zote na milele na milele, uniongoze, uniombee ufanisi maishani, tuajaliwe sote kupata au kukosa ni MOLA mwenyewe. Tuwakuze au tuwaleye Familia hizi kwa dhati, heri...

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...Supervisors Celeste Blanco Nadiya Sedasey Leticia Arzu Sharony Chen Shari Allen Lliana Cho Yulisa Bernadives Alisha Waight Lulu Chang Sulema Ewens Edith Charlesworth Imani Ramos Ysenia Cho Olivia Garcia Sasha Gallego Marissa Cain Julia Gonzalez Tamarah Phillips Ellen Glenn Jennel Carey Adelaine King Rodesha Rodriguez G’ Anne Humes Nicolette Davis Courtney Lightfoot April Samos Joanna Joseph Lavonda Lambey Charnell Martin Kenysha Stanford Liliani Mai Chelsie Lorenzo Gabriela Munoz Khalilah Marin Sulmi Murillo Kiara Mejia Reniece Tillett Judith Mai Brittany Robateau Catherine Rios Whitney Usher Chelsea Johnston Ashley Seguro KeelyShae Anthony Bernadine Wewe Rochelle Shaw Daneesha Staine Chelsie Goodger Chelsea Thompson Aim The researcher of this SBA aims to record the transactions correctly into different books of original entry and ledgers such as the purchases day book, sales day book and the journal. The researcher will also learn how to draw up proper financial statement such a s balance sheet and trading and profit and loss account. Description of the business 4 BAS Sweet Paradise was the combination of different selective names from the fourth formers. This simulated business is located at Sr. Benedicts Hall, in front of the library. This business started 7th of October, 2013 and closed on 1st of November, 2013. The opening hours of the business were......

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...114 ways to say... I LOVE YOU Neal Justine English - I love you Neal Justine Afrikaans - Ek het jou lief Neal Justine Albanian - Te dua Neal Justine Arabic - Ana behibak Neal Justine Armenian - Yes kez sirumen Neal Justine Bambara - M'bi fe Neal Justine Bangla - Aamee tuma ke bhalo aashi Neal Justine Belarusian - Ya tabe kahayu Neal Justine Bisaya - Nahigugma ako kanimo Neal Justine Bulgarian - Obicham te Neal Justine Cambodian – Oun Srorlagn Bung Neal Justine Cantonese Chinese - Ngo oiy ney Neal Justine Catalan - T'estimo Neal Justine Cheyenne - Ne mohotatse Neal Justine Chichewa - Ndimakukonda Neal Justine Corsican – Ti tengu caru Neal Justine Creol - Mi aime jou Neal Justine Croatian - Volim te Neal Justine Czech - Miluji te Neal Justine Danish - Jeg Elsker Dig Neal Justine Dutch - Ik hou van jou Neal Justine Esperanto - Mi amas vin Neal Justine Estonian - Ma armastan sind Neal Justine Ethiopian - Ewedihalehu' Neal Justine Faroese - Eg elski teg Neal Justine Farsi - Doset daram Neal Justine Filipino - Mahal kita Neal Justine Finnish - Mina rakastan sinua Neal Justine French - Je t'aime, Je t'adore Neal Justine Frisian - Ik hâld fan dy Neal Justine Gaelic - Ta gra agam ort Neal Justine Georgian - Mikvarhar Neal Justine German - Ich liebe dich Neal Justine Greek - S'agapo Neal Justine Gujarati - Hoo thunay prem karoo choo Neal Justine Hiligaynon - Palangga ko ikaw Neal Justine Hawaiian - Aloha Au Ia`oe Neal Justine Hebrew - Ani ohev......

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...Campbell Brogdon June 22 2016 |Core Content: Wants a better mother in law | | |Core Affect: Anger and frustration | | |Time code 00:04-10:21 | | |Identify skills used. Paraphasing, clarification summerizing | | |Circle or Highlight the feeling words. | | |Client (Sarah) |School Counselor’s Response (Campbell) |Alternate Response |Self-Awareness | | |Hi Sarah, so What brings you in today? | | | | Well um I recently got married about a year and a | | | | |half ago and um I have a really hard time um | | | | |appreciating...

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...FF FF F or Peor Pe or Peor Pe or Pe ople, Naople, Na ople, Naople, Na ople, Na tt tt t ure, and ure, and ure, and ure, and ure, and tt tt t he Ehe E he Ehe E he E cc cc c oo oo o nn nn n oo oo o mm mm m yy yy y 1. AGRICULTURE TAKES A BIG BITE: THE ECOLOGICAL FOOTPRINT OF THE GLOBAL FOOD SYSTEM After air and water, food is the most essential resource people require to sustain themselves. These resources are provided by the layer of interconnected life that covers our planet: the biosphere. Yet the way the food system provides food often severely damages the health of the biosphere through soil and aquifer depletion, deforestation, aggressive use of agrochemicals, fishery collapses, and the loss of biodiversity in crops, livestock, and wild species. The global food system has become such a dominant force shaping the surface of this planet and its ecosystems that we can no longer achieve sustainability without revamping the food system. At the same time sustainable food systems provide great hope for building a sustainable future—a future in which all can lead satisfying lives within the means of the biosphere. In this brief, we use Ecological Footprint analysis to document the current food system’s demand on the biosphere. Ecological Footprint accounts track the area of biologically productive land and water needed to produce the resources consumed by a given population and to absorb its waste. The Ecological......

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